Deck 8: Linear Systems and Matrices

ملء الشاشة (f)
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سؤال
If possible, find AB. <strong>If possible, find AB.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>

A) <strong>If possible, find AB.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
B) <strong>If possible, find AB.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
C)not possible
D) <strong>If possible, find AB.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
E) <strong>If possible, find AB.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
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سؤال
Write the augmented matrix for the system of linear equations. <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
If possible, find 3A - 2B. <strong>If possible, find 3A - 2B.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>

A) <strong>If possible, find 3A - 2B.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
B) <strong>If possible, find 3A - 2B.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
C)not possible
D) <strong>If possible, find 3A - 2B.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
E) <strong>If possible, find 3A - 2B.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
سؤال
Solve the system by the method of elimination. <strong>Solve the system by the method of elimination.  </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the system by the method of elimination.  </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
B)inconsistent
C) <strong>Solve the system by the method of elimination.  </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the system by the method of elimination.  </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the system by the method of elimination.  </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
سؤال
During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 239 tickets and collected $1389. If adult tickets sold for $10 and children's tickets sold for $3, how many of each type of ticket were sold?

A)adult tickets sold = 92; children's tickets sold = 156
B)adult tickets sold = 143; children's tickets sold = 96
C)adult tickets sold = 139; children's tickets sold = 92
D)adult tickets sold = 92; children's tickets sold = 139
E)adult tickets sold = 96; children's tickets sold = 143
سؤال
The currents in an electrical network are given by the solutions of the system <strong>The currents in an electrical network are given by the solutions of the system   where I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are measured in amperes. Solve the system of equations using matrices.</strong> A)I<sub>1</sub> = 3, I<sub>2</sub> = 3, I<sub>3</sub> = 6 B)I<sub>1</sub> = 4, I<sub>2</sub> = 2, I<sub>3</sub> = 6 C)I<sub>1</sub> = 4, I<sub>2</sub> = 6, I<sub>3</sub> = 2 D)I<sub>1</sub> = 3, I<sub>2</sub> = 3, I<sub>3</sub> = 7 E)no solution <div style=padding-top: 35px> where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

A)I1 = 3, I2 = 3, I3 = 6
B)I1 = 4, I2 = 2, I3 = 6
C)I1 = 4, I2 = 6, I3 = 2
D)I1 = 3, I2 = 3, I3 = 7
E)no solution
سؤال
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)   C)   D)not possible E)   <div style=padding-top: 35px>

A) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)not possible E)   <div style=padding-top: 35px>
B) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)not possible E)   <div style=padding-top: 35px>
C) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)not possible E)   <div style=padding-top: 35px>
D)not possible
E) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)not possible E)   <div style=padding-top: 35px>
سؤال
Solve the system by the method of substitution. <strong>Solve the system by the method of substitution.  </strong> A)(3, 2) B)(2, 3) C)(2, -3) D)(-3, 2) E)(-2, 3) <div style=padding-top: 35px>

A)(3, 2)
B)(2, 3)
C)(2, -3)
D)(-3, 2)
E)(-2, 3)
سؤال
Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form. <strong>Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.  </strong> A)row-echelon form B)row-echelon form and reduced row-echelon form C)neither <div style=padding-top: 35px>

A)row-echelon form
B)row-echelon form and reduced row-echelon form
C)neither
سؤال
Applying Kirchhoff's Laws to the electrical network in the figure, the currents I1, I2, and I3 are the solution of the system <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> Find the currents. <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>

A) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
B) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
C) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
D) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
E) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
سؤال
Solve using any method. <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>

A) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
B) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
C) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
D) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
E)inconsistent
سؤال
Determine which one of the ordered triples below is a solution of the given system of equations. <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
An object moving vertically is at the given heights at the specified times. Find the position equation <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> for the object. At t = 1 second, s = 421 feet
At t = 2 seconds, s = 358 feet
At t = 3 seconds, s = 263 feet

A) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)not possible C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Evaluate the expression.  </strong> A)   B)not possible C)   D)   E)   <div style=padding-top: 35px>
B)not possible
C) <strong>Evaluate the expression.  </strong> A)   B)not possible C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Evaluate the expression.  </strong> A)   B)not possible C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Evaluate the expression.  </strong> A)   B)not possible C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand
Supply <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px> <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px>

A) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px>
B) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px>
C) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px>
D)inconsistent
E) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px>
سؤال
Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.) <strong>Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)  </strong> A)254 units B)254 units or 281 units C)272 units D)281 units E)no real solution <div style=padding-top: 35px>

A)254 units
B)254 units or 281 units
C)272 units
D)281 units
E)no real solution
سؤال
Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. <strong>Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.  </strong> A)x = -4, y = -2, z = 5 B)x = -2, y = 4, z = -5 C)no solution D)x = -4, y = 2, z = 5 E)x = 4, y = 2, z = 5 <div style=padding-top: 35px>

A)x = -4, y = -2, z = 5
B)x = -2, y = 4, z = -5
C)no solution
D)x = -4, y = 2, z = 5
E)x = 4, y = 2, z = 5
سؤال
An airplane flying into a headwind travels 690 miles in 3 hours and 50 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

A)plane speed = 220 mph; wind speed = 25 mph
B)plane speed = 182 mph; wind speed = 194 mph
C)plane speed = 205 mph; wind speed = 25 mph
D)plane speed = 220 mph; wind speed = 212 mph
E)plane speed = 182 mph; wind speed = 25 mph
سؤال
Find the equation of the circle <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> that passes through the points <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve using any method. <strong>Solve using any method.  </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve using any method.  </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
B)inconsistent
C) <strong>Solve using any method.  </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve using any method.  </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve using any method.  </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve using any method. <strong>Solve using any method.  </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px>

A) <strong>Solve using any method.  </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px>
B) <strong>Solve using any method.  </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px>
C) <strong>Solve using any method.  </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px>
D)inconsistent
E) <strong>Solve using any method.  </strong> A)   B)   C)   D)inconsistent E)   <div style=padding-top: 35px>
سؤال
Determine which one of the ordered triples below is a solution of the given system of equations. <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the inverse of the matrix <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   <div style=padding-top: 35px> (if it exists).

A) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   <div style=padding-top: 35px>
B) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   <div style=padding-top: 35px>
C)does not exist
D) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   <div style=padding-top: 35px>
E) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   <div style=padding-top: 35px>
سؤال
Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.) <strong>Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)  </strong> A)904 units B)837 units C)837 units or 904 units D)no real solution E)882 units <div style=padding-top: 35px>

A)904 units
B)837 units
C)837 units or 904 units
D)no real solution
E)882 units
سؤال
Solve the system by the method of substitution. <strong>Solve the system by the method of substitution.  </strong> A)(-4, 2) B)(2, -4) C)(-2, -4) D)(-4, -2) E)(4, 2) <div style=padding-top: 35px>

A)(-4, 2)
B)(2, -4)
C)(-2, -4)
D)(-4, -2)
E)(4, 2)
سؤال
Find the determinant of <strong>Find the determinant of   .</strong> A)14 B)7 C)-8 D)6 E)12 <div style=padding-top: 35px> .

A)14
B)7
C)-8
D)6
E)12
سؤال
Solve using any method. <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>

A) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
B) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
C) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
D) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
E)inconsistent
سؤال
Applying Kirchhoff's Laws to the electrical network in the figure, the currents I1, I2, and I3 are the solution of the system <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> Find the currents. <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>

A) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
B) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
C) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
D) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
E) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
سؤال
Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand
Supply <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px> <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
B)inconsistent
C) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve for x given the following equation involving a determinant. <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the equation of the circle <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> that passes through the points <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form. <strong>Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.  </strong> A)row-echelon form and reduced row-echelon form B)row-echelon form C)neither <div style=padding-top: 35px>

A)row-echelon form and reduced row-echelon form
B)row-echelon form
C)neither
سؤال
An airplane flying into a headwind travels 432 miles in 3 hours and 36 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

A)plane speed = 147 mph; wind speed = 12 mph
B)plane speed = 109 mph; wind speed = 12 mph
C)plane speed = 109 mph; wind speed = 121 mph
D)plane speed = 147 mph; wind speed = 139 mph
E)plane speed = 132 mph; wind speed = 12 mph
سؤال
During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 218 tickets and collected $1410. If adult tickets sold for $7 and children's tickets sold for $6, how many of each type of ticket were sold?

A)adult tickets sold = 80; children's tickets sold = 141
B)adult tickets sold = 94; children's tickets sold = 80
C)adult tickets sold = 102; children's tickets sold = 116
D)adult tickets sold = 116; children's tickets sold = 102
E)adult tickets sold = 80; children's tickets sold = 94
سؤال
Use Cramer's Rule to solve the following system of linear equations: <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. <strong>Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.  </strong> A)x = 5, y = -2, z = -6 B)x = 2, y = -5, z = 6 C)x = -2, y = -5, z = 6 D)no solution E)x = 2, y = 5, z = 6 <div style=padding-top: 35px>

A)x = 5, y = -2, z = -6
B)x = 2, y = -5, z = 6
C)x = -2, y = -5, z = 6
D)no solution
E)x = 2, y = 5, z = 6
سؤال
Solve the system by the method of elimination. <strong>Solve the system by the method of elimination.  </strong> A)inconsistent B)   C)   D)   E)   <div style=padding-top: 35px>

A)inconsistent
B) <strong>Solve the system by the method of elimination.  </strong> A)inconsistent B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the system by the method of elimination.  </strong> A)inconsistent B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the system by the method of elimination.  </strong> A)inconsistent B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the system by the method of elimination.  </strong> A)inconsistent B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
An object moving vertically is at the given heights at the specified times. Find the position equation <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> for the object. At t = 1 second, s = 284 feet
At t = 2 seconds, s = 221 feet
At t = 3 seconds, s = 126 feet

A) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the determinant of the matrix <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Write the augmented matrix for the system of linear equations. <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
An airplane flying into a headwind travels 216 miles in 2 hours and 42 minutes. On the return flight, the distance is traveled in 2 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

A)plane speed = 109 mph; wind speed = 101 mph
B)plane speed = 109 mph; wind speed = 14 mph
C)plane speed = 71 mph; wind speed = 83 mph
D)plane speed = 71 mph; wind speed = 14 mph
E)plane speed = 94 mph; wind speed = 14 mph
سؤال
If possible, find AB. <strong>If possible, find AB.  </strong> A)not possible B)   C)   D)   E)   <div style=padding-top: 35px>

A)not possible
B) <strong>If possible, find AB.  </strong> A)not possible B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>If possible, find AB.  </strong> A)not possible B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>If possible, find AB.  </strong> A)not possible B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>If possible, find AB.  </strong> A)not possible B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.) <strong>Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)  </strong> A)782 units B)782 units or 852 units C)852 units D)831 units E)no real solution <div style=padding-top: 35px>

A)782 units
B)782 units or 852 units
C)852 units
D)831 units
E)no real solution
سؤال
Solve the system by the method of substitution. <strong>Solve the system by the method of substitution.  </strong> A)(4, 3) B)(-3, 4) C)(3, 4) D)(4, -3) E)(-4, 3) <div style=padding-top: 35px>

A)(4, 3)
B)(-3, 4)
C)(3, 4)
D)(4, -3)
E)(-4, 3)
سؤال
Determine which one of the ordered triples below is a solution of the given system of equations. <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
If possible, find 5A - 4B. <strong>If possible, find 5A - 4B.  </strong> A)   B)not possible C)   D)   E)   <div style=padding-top: 35px>

A) <strong>If possible, find 5A - 4B.  </strong> A)   B)not possible C)   D)   E)   <div style=padding-top: 35px>
B)not possible
C) <strong>If possible, find 5A - 4B.  </strong> A)   B)not possible C)   D)   E)   <div style=padding-top: 35px>
D) <strong>If possible, find 5A - 4B.  </strong> A)   B)not possible C)   D)   E)   <div style=padding-top: 35px>
E) <strong>If possible, find 5A - 4B.  </strong> A)   B)not possible C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve using any method. <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>

A) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
B) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
C) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
D) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
E)inconsistent
سؤال
An object moving vertically is at the given heights at the specified times. Find the position equation <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> for the object. At t = 1 second, s = 161 feet
At t = 2 seconds, s = 98 feet
At t = 3 seconds, s = 3 feet

A) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>

A) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
B) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
C) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
D) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
E)not possible
سؤال
Find the inverse of the matrix <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   <div style=padding-top: 35px> (if it exists).

A) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   <div style=padding-top: 35px>
B) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   <div style=padding-top: 35px>
C)does not exist
D) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   <div style=padding-top: 35px>
E) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   <div style=padding-top: 35px>
سؤال
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>

A) <strong>Evaluate the expression.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
B) <strong>Evaluate the expression.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
C)not possible
D) <strong>Evaluate the expression.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
E) <strong>Evaluate the expression.  </strong> A)   B)   C)not possible D)   E)   <div style=padding-top: 35px>
سؤال
Use Cramer's Rule to solve the following system of linear equations: <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 200 tickets and collected $1372. If adult tickets sold for $8 and children's tickets sold for $6, how many of each type of ticket were sold?

A)adult tickets sold = 97; children's tickets sold = 125
B)adult tickets sold = 86; children's tickets sold = 114
C)adult tickets sold = 114; children's tickets sold = 86
D)adult tickets sold = 125; children's tickets sold = 97
E)adult tickets sold = 97; children's tickets sold = 99
سؤال
Solve using any method. <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>

A) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
B) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
C) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
D) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
E)inconsistent
سؤال
Solve the system by the method of elimination. <strong>Solve the system by the method of elimination.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>

A) <strong>Solve the system by the method of elimination.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
B) <strong>Solve the system by the method of elimination.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
C) <strong>Solve the system by the method of elimination.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
D) <strong>Solve the system by the method of elimination.  </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
E)inconsistent
سؤال
Find the determinant of the matrix <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve for x given the following equation involving a determinant. <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
The currents in an electrical network are given by the solutions of the system <strong>The currents in an electrical network are given by the solutions of the system   where I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are measured in amperes. Solve the system of equations using matrices.</strong> A)I<sub>1</sub> = 4, I<sub>2</sub> = 5, I<sub>3</sub> = 9 B)I<sub>1</sub> = 2, I<sub>2</sub> = 3, I<sub>3</sub> = 6 C)I<sub>1</sub> = 2, I<sub>2</sub> = 3, I<sub>3</sub> = 5 D)I<sub>1</sub> = 4, I<sub>2</sub> = 9, I<sub>3</sub> = 5 E)no solution <div style=padding-top: 35px> where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

A)I1 = 4, I2 = 5, I3 = 9
B)I1 = 2, I2 = 3, I3 = 6
C)I1 = 2, I2 = 3, I3 = 5
D)I1 = 4, I2 = 9, I3 = 5
E)no solution
سؤال
Find the determinant of <strong>Find the determinant of   .</strong> A)-828 B)512 C)-768 D)-736 E)-64 <div style=padding-top: 35px> .

A)-828
B)512
C)-768
D)-736
E)-64
سؤال
Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand
Supply <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px> <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>

A) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
B) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
C) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
D) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent <div style=padding-top: 35px>
E)inconsistent
سؤال
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>

A) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
B) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
C) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
D) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
E)not possible
سؤال
If possible, find AB. <strong>If possible, find AB.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>

A) <strong>If possible, find AB.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
B) <strong>If possible, find AB.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
C) <strong>If possible, find AB.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
D) <strong>If possible, find AB.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
E)not possible
سؤال
Determine which ordered pair is a solution of the system. <strong>Determine which ordered pair is a solution of the system.  </strong> A)(8, 1) B)(-9, 3) C)(-9,8) D)(8, -1) E)(1, -8) <div style=padding-top: 35px>

A)(8, 1)
B)(-9, 3)
C)(-9,8)
D)(8, -1)
E)(1, -8)
سؤال
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>

A) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
B) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
C) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
D) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
E)not possible
سؤال
Solve for x given the following equation involving a determinant. <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Determine which ordered pair is a solution of the system. <strong>Determine which ordered pair is a solution of the system.  </strong> A)(-3, 6) B)(-1, -2) C)(-2, -1) D)(1, -2) E)(6, 3) <div style=padding-top: 35px>

A)(-3, 6)
B)(-1, -2)
C)(-2, -1)
D)(1, -2)
E)(6, 3)
سؤال
Use Cramer's Rule to solve the following system of linear equations: <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the determinant of <strong>Find the determinant of   .</strong> A)14 B)7 C)12 D)-8 E)6 <div style=padding-top: 35px> .

A)14
B)7
C)12
D)-8
E)6
سؤال
Write the augmented matrix for the system of linear equations. <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
The currents in an electrical network are given by the solutions of the system <strong>The currents in an electrical network are given by the solutions of the system   where I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are measured in amperes. Solve the system of equations using matrices.</strong> A)I<sub>1</sub> = 5, I<sub>2</sub> = 8, I<sub>3</sub> = 3 B)I<sub>1</sub> = 5, I<sub>2</sub> = 3, I<sub>3</sub> = 8 C)I<sub>1</sub> = 3, I<sub>2</sub> = 5, I<sub>3</sub> = 9 D)I<sub>1</sub> = 3, I<sub>2</sub> = 5, I<sub>3</sub> = 8 E)no solution <div style=padding-top: 35px> where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

A)I1 = 5, I2 = 8, I3 = 3
B)I1 = 5, I2 = 3, I3 = 8
C)I1 = 3, I2 = 5, I3 = 9
D)I1 = 3, I2 = 5, I3 = 8
E)no solution
سؤال
Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form. <strong>Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.  </strong> A)row-echelon form B)row-echelon form and reduced row-echelon form C)neither <div style=padding-top: 35px>

A)row-echelon form
B)row-echelon form and reduced row-echelon form
C)neither
سؤال
Solve the system. <strong>Solve the system.  </strong> A)   B)   C)   D)   E)no solution <div style=padding-top: 35px>

A) <strong>Solve the system.  </strong> A)   B)   C)   D)   E)no solution <div style=padding-top: 35px>
B) <strong>Solve the system.  </strong> A)   B)   C)   D)   E)no solution <div style=padding-top: 35px>
C) <strong>Solve the system.  </strong> A)   B)   C)   D)   E)no solution <div style=padding-top: 35px>
D) <strong>Solve the system.  </strong> A)   B)   C)   D)   E)no solution <div style=padding-top: 35px>
E)no solution
سؤال
Find the inverse of the matrix <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)   D)   E)does not exist <div style=padding-top: 35px> (if it exists).

A) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)   D)   E)does not exist <div style=padding-top: 35px>
B) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)   D)   E)does not exist <div style=padding-top: 35px>
C) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)   D)   E)does not exist <div style=padding-top: 35px>
D) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)   D)   E)does not exist <div style=padding-top: 35px>
E)does not exist
سؤال
Applying Kirchhoff's Laws to the electrical network in the figure, the currents I1, I2, and I3 are the solution of the system <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> Find the currents. <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>

A) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
B) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
C) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
D) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
E) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px> <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <div style=padding-top: 35px>
سؤال
Solve the system by substitution, if possible. <strong>Solve the system by substitution, if possible.  </strong> A)(4, 8) B)(8, 4) C)(-4, 13) D)(12, -3) E)no solutions <div style=padding-top: 35px>

A)(4, 8)
B)(8, 4)
C)(-4, 13)
D)(12, -3)
E)no solutions
سؤال
Find the equation of the circle <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> that passes through the points <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the determinant of the matrix <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the system of equations by graphing. <strong>Solve the system of equations by graphing.  </strong> A)(-4, 6) B)(-5, 5) C)(6, 1) D)(5, -5) E)(3, 13) <div style=padding-top: 35px>

A)(-4, 6)
B)(-5, 5)
C)(6, 1)
D)(5, -5)
E)(3, 13)
سؤال
If possible, find 2A - 5B. <strong>If possible, find 2A - 5B.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>

A) <strong>If possible, find 2A - 5B.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
B) <strong>If possible, find 2A - 5B.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
C) <strong>If possible, find 2A - 5B.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
D) <strong>If possible, find 2A - 5B.  </strong> A)   B)   C)   D)   E)not possible <div style=padding-top: 35px>
E)not possible
سؤال
Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. <strong>Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.  </strong> A)x = -5, y = -3, z = 2 B)x = 5, y = -3, z = 2 C)x = 5, y = 3, z = 2 D)x = 3, y = -5, z = -2 E)no solution <div style=padding-top: 35px>

A)x = -5, y = -3, z = 2
B)x = 5, y = -3, z = 2
C)x = 5, y = 3, z = 2
D)x = 3, y = -5, z = -2
E)no solution
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Deck 8: Linear Systems and Matrices
1
If possible, find AB. <strong>If possible, find AB.  </strong> A)   B)   C)not possible D)   E)

A) <strong>If possible, find AB.  </strong> A)   B)   C)not possible D)   E)
B) <strong>If possible, find AB.  </strong> A)   B)   C)not possible D)   E)
C)not possible
D) <strong>If possible, find AB.  </strong> A)   B)   C)not possible D)   E)
E) <strong>If possible, find AB.  </strong> A)   B)   C)not possible D)   E)
not possible
2
Write the augmented matrix for the system of linear equations. <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)

A) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
B) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
C) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
D) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
E) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
3
If possible, find 3A - 2B. <strong>If possible, find 3A - 2B.  </strong> A)   B)   C)not possible D)   E)

A) <strong>If possible, find 3A - 2B.  </strong> A)   B)   C)not possible D)   E)
B) <strong>If possible, find 3A - 2B.  </strong> A)   B)   C)not possible D)   E)
C)not possible
D) <strong>If possible, find 3A - 2B.  </strong> A)   B)   C)not possible D)   E)
E) <strong>If possible, find 3A - 2B.  </strong> A)   B)   C)not possible D)   E)
4
Solve the system by the method of elimination. <strong>Solve the system by the method of elimination.  </strong> A)   B)inconsistent C)   D)   E)

A) <strong>Solve the system by the method of elimination.  </strong> A)   B)inconsistent C)   D)   E)
B)inconsistent
C) <strong>Solve the system by the method of elimination.  </strong> A)   B)inconsistent C)   D)   E)
D) <strong>Solve the system by the method of elimination.  </strong> A)   B)inconsistent C)   D)   E)
E) <strong>Solve the system by the method of elimination.  </strong> A)   B)inconsistent C)   D)   E)
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5
During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 239 tickets and collected $1389. If adult tickets sold for $10 and children's tickets sold for $3, how many of each type of ticket were sold?

A)adult tickets sold = 92; children's tickets sold = 156
B)adult tickets sold = 143; children's tickets sold = 96
C)adult tickets sold = 139; children's tickets sold = 92
D)adult tickets sold = 92; children's tickets sold = 139
E)adult tickets sold = 96; children's tickets sold = 143
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6
The currents in an electrical network are given by the solutions of the system <strong>The currents in an electrical network are given by the solutions of the system   where I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are measured in amperes. Solve the system of equations using matrices.</strong> A)I<sub>1</sub> = 3, I<sub>2</sub> = 3, I<sub>3</sub> = 6 B)I<sub>1</sub> = 4, I<sub>2</sub> = 2, I<sub>3</sub> = 6 C)I<sub>1</sub> = 4, I<sub>2</sub> = 6, I<sub>3</sub> = 2 D)I<sub>1</sub> = 3, I<sub>2</sub> = 3, I<sub>3</sub> = 7 E)no solution where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

A)I1 = 3, I2 = 3, I3 = 6
B)I1 = 4, I2 = 2, I3 = 6
C)I1 = 4, I2 = 6, I3 = 2
D)I1 = 3, I2 = 3, I3 = 7
E)no solution
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7
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)   C)   D)not possible E)

A) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)not possible E)
B) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)not possible E)
C) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)not possible E)
D)not possible
E) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)not possible E)
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8
Solve the system by the method of substitution. <strong>Solve the system by the method of substitution.  </strong> A)(3, 2) B)(2, 3) C)(2, -3) D)(-3, 2) E)(-2, 3)

A)(3, 2)
B)(2, 3)
C)(2, -3)
D)(-3, 2)
E)(-2, 3)
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9
Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form. <strong>Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.  </strong> A)row-echelon form B)row-echelon form and reduced row-echelon form C)neither

A)row-echelon form
B)row-echelon form and reduced row-echelon form
C)neither
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10
Applying Kirchhoff's Laws to the electrical network in the figure, the currents I1, I2, and I3 are the solution of the system <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       Find the currents. <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)

A) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
B) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
C) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
D) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
E) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
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11
Solve using any method. <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent

A) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
B) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
C) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
D) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
E)inconsistent
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12
Determine which one of the ordered triples below is a solution of the given system of equations. <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)

A) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
B) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
C) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
D) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
E) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
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13
An object moving vertically is at the given heights at the specified times. Find the position equation <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)   for the object. At t = 1 second, s = 421 feet
At t = 2 seconds, s = 358 feet
At t = 3 seconds, s = 263 feet

A) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)
B) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)
C) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)
D) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)
E) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet</strong> A)   B)   C)   D)   E)
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14
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)not possible C)   D)   E)

A) <strong>Evaluate the expression.  </strong> A)   B)not possible C)   D)   E)
B)not possible
C) <strong>Evaluate the expression.  </strong> A)   B)not possible C)   D)   E)
D) <strong>Evaluate the expression.  </strong> A)   B)not possible C)   D)   E)
E) <strong>Evaluate the expression.  </strong> A)   B)not possible C)   D)   E)
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15
Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand
Supply <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)   <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)

A) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)
B) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)
C) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)
D)inconsistent
E) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)inconsistent E)
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16
Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.) <strong>Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)  </strong> A)254 units B)254 units or 281 units C)272 units D)281 units E)no real solution

A)254 units
B)254 units or 281 units
C)272 units
D)281 units
E)no real solution
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17
Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. <strong>Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.  </strong> A)x = -4, y = -2, z = 5 B)x = -2, y = 4, z = -5 C)no solution D)x = -4, y = 2, z = 5 E)x = 4, y = 2, z = 5

A)x = -4, y = -2, z = 5
B)x = -2, y = 4, z = -5
C)no solution
D)x = -4, y = 2, z = 5
E)x = 4, y = 2, z = 5
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18
An airplane flying into a headwind travels 690 miles in 3 hours and 50 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

A)plane speed = 220 mph; wind speed = 25 mph
B)plane speed = 182 mph; wind speed = 194 mph
C)plane speed = 205 mph; wind speed = 25 mph
D)plane speed = 220 mph; wind speed = 212 mph
E)plane speed = 182 mph; wind speed = 25 mph
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19
Find the equation of the circle <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   that passes through the points <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
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20
Solve using any method. <strong>Solve using any method.  </strong> A)   B)inconsistent C)   D)   E)

A) <strong>Solve using any method.  </strong> A)   B)inconsistent C)   D)   E)
B)inconsistent
C) <strong>Solve using any method.  </strong> A)   B)inconsistent C)   D)   E)
D) <strong>Solve using any method.  </strong> A)   B)inconsistent C)   D)   E)
E) <strong>Solve using any method.  </strong> A)   B)inconsistent C)   D)   E)
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21
Solve using any method. <strong>Solve using any method.  </strong> A)   B)   C)   D)inconsistent E)

A) <strong>Solve using any method.  </strong> A)   B)   C)   D)inconsistent E)
B) <strong>Solve using any method.  </strong> A)   B)   C)   D)inconsistent E)
C) <strong>Solve using any method.  </strong> A)   B)   C)   D)inconsistent E)
D)inconsistent
E) <strong>Solve using any method.  </strong> A)   B)   C)   D)inconsistent E)
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22
Determine which one of the ordered triples below is a solution of the given system of equations. <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)

A) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
B) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
C) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
D) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
E) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
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23
Find the inverse of the matrix <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   (if it exists).

A) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)
B) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)
C)does not exist
D) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)
E) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)
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24
Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.) <strong>Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)  </strong> A)904 units B)837 units C)837 units or 904 units D)no real solution E)882 units

A)904 units
B)837 units
C)837 units or 904 units
D)no real solution
E)882 units
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25
Solve the system by the method of substitution. <strong>Solve the system by the method of substitution.  </strong> A)(-4, 2) B)(2, -4) C)(-2, -4) D)(-4, -2) E)(4, 2)

A)(-4, 2)
B)(2, -4)
C)(-2, -4)
D)(-4, -2)
E)(4, 2)
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26
Find the determinant of <strong>Find the determinant of   .</strong> A)14 B)7 C)-8 D)6 E)12 .

A)14
B)7
C)-8
D)6
E)12
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27
Solve using any method. <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent

A) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
B) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
C) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
D) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
E)inconsistent
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28
Applying Kirchhoff's Laws to the electrical network in the figure, the currents I1, I2, and I3 are the solution of the system <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       Find the currents. <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)

A) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
B) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
C) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
D) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
E) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
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29
Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand
Supply <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)   <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)

A) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)
B)inconsistent
C) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)
D) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)
E) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)inconsistent C)   D)   E)
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30
Solve for x given the following equation involving a determinant. <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
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31
Find the equation of the circle <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   that passes through the points <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
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32
Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form. <strong>Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.  </strong> A)row-echelon form and reduced row-echelon form B)row-echelon form C)neither

A)row-echelon form and reduced row-echelon form
B)row-echelon form
C)neither
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33
An airplane flying into a headwind travels 432 miles in 3 hours and 36 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

A)plane speed = 147 mph; wind speed = 12 mph
B)plane speed = 109 mph; wind speed = 12 mph
C)plane speed = 109 mph; wind speed = 121 mph
D)plane speed = 147 mph; wind speed = 139 mph
E)plane speed = 132 mph; wind speed = 12 mph
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34
During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 218 tickets and collected $1410. If adult tickets sold for $7 and children's tickets sold for $6, how many of each type of ticket were sold?

A)adult tickets sold = 80; children's tickets sold = 141
B)adult tickets sold = 94; children's tickets sold = 80
C)adult tickets sold = 102; children's tickets sold = 116
D)adult tickets sold = 116; children's tickets sold = 102
E)adult tickets sold = 80; children's tickets sold = 94
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35
Use Cramer's Rule to solve the following system of linear equations: <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)

A) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
B) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
C) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
D) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
E) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
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36
Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. <strong>Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.  </strong> A)x = 5, y = -2, z = -6 B)x = 2, y = -5, z = 6 C)x = -2, y = -5, z = 6 D)no solution E)x = 2, y = 5, z = 6

A)x = 5, y = -2, z = -6
B)x = 2, y = -5, z = 6
C)x = -2, y = -5, z = 6
D)no solution
E)x = 2, y = 5, z = 6
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37
Solve the system by the method of elimination. <strong>Solve the system by the method of elimination.  </strong> A)inconsistent B)   C)   D)   E)

A)inconsistent
B) <strong>Solve the system by the method of elimination.  </strong> A)inconsistent B)   C)   D)   E)
C) <strong>Solve the system by the method of elimination.  </strong> A)inconsistent B)   C)   D)   E)
D) <strong>Solve the system by the method of elimination.  </strong> A)inconsistent B)   C)   D)   E)
E) <strong>Solve the system by the method of elimination.  </strong> A)inconsistent B)   C)   D)   E)
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38
An object moving vertically is at the given heights at the specified times. Find the position equation <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)   for the object. At t = 1 second, s = 284 feet
At t = 2 seconds, s = 221 feet
At t = 3 seconds, s = 126 feet

A) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)
B) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)
C) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)
D) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)
E) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 284 feet At t = 2 seconds, s = 221 feet At t = 3 seconds, s = 126 feet</strong> A)   B)   C)   D)   E)
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39
Find the determinant of the matrix <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
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40
Write the augmented matrix for the system of linear equations. <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)

A) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
B) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
C) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
D) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
E) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
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41
An airplane flying into a headwind travels 216 miles in 2 hours and 42 minutes. On the return flight, the distance is traveled in 2 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

A)plane speed = 109 mph; wind speed = 101 mph
B)plane speed = 109 mph; wind speed = 14 mph
C)plane speed = 71 mph; wind speed = 83 mph
D)plane speed = 71 mph; wind speed = 14 mph
E)plane speed = 94 mph; wind speed = 14 mph
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42
If possible, find AB. <strong>If possible, find AB.  </strong> A)not possible B)   C)   D)   E)

A)not possible
B) <strong>If possible, find AB.  </strong> A)not possible B)   C)   D)   E)
C) <strong>If possible, find AB.  </strong> A)not possible B)   C)   D)   E)
D) <strong>If possible, find AB.  </strong> A)not possible B)   C)   D)   E)
E) <strong>If possible, find AB.  </strong> A)not possible B)   C)   D)   E)
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43
Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.) <strong>Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)  </strong> A)782 units B)782 units or 852 units C)852 units D)831 units E)no real solution

A)782 units
B)782 units or 852 units
C)852 units
D)831 units
E)no real solution
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44
Solve the system by the method of substitution. <strong>Solve the system by the method of substitution.  </strong> A)(4, 3) B)(-3, 4) C)(3, 4) D)(4, -3) E)(-4, 3)

A)(4, 3)
B)(-3, 4)
C)(3, 4)
D)(4, -3)
E)(-4, 3)
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45
Determine which one of the ordered triples below is a solution of the given system of equations. <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)

A) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
B) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
C) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
D) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
E) <strong>Determine which one of the ordered triples below is a solution of the given system of equations.  </strong> A)   B)   C)   D)   E)
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46
If possible, find 5A - 4B. <strong>If possible, find 5A - 4B.  </strong> A)   B)not possible C)   D)   E)

A) <strong>If possible, find 5A - 4B.  </strong> A)   B)not possible C)   D)   E)
B)not possible
C) <strong>If possible, find 5A - 4B.  </strong> A)   B)not possible C)   D)   E)
D) <strong>If possible, find 5A - 4B.  </strong> A)   B)not possible C)   D)   E)
E) <strong>If possible, find 5A - 4B.  </strong> A)   B)not possible C)   D)   E)
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47
Solve using any method. <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent

A) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
B) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
C) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
D) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
E)inconsistent
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48
An object moving vertically is at the given heights at the specified times. Find the position equation <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)   for the object. At t = 1 second, s = 161 feet
At t = 2 seconds, s = 98 feet
At t = 3 seconds, s = 3 feet

A) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)
B) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)
C) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)
D) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)
E) <strong>An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet</strong> A)   B)   C)   D)   E)
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49
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible

A) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
B) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
C) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
D) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
E)not possible
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50
Find the inverse of the matrix <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)   (if it exists).

A) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)
B) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)
C)does not exist
D) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)
E) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)does not exist D)   E)
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51
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)   C)not possible D)   E)

A) <strong>Evaluate the expression.  </strong> A)   B)   C)not possible D)   E)
B) <strong>Evaluate the expression.  </strong> A)   B)   C)not possible D)   E)
C)not possible
D) <strong>Evaluate the expression.  </strong> A)   B)   C)not possible D)   E)
E) <strong>Evaluate the expression.  </strong> A)   B)   C)not possible D)   E)
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52
Use Cramer's Rule to solve the following system of linear equations: <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)

A) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
B) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
C) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
D) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
E) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
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53
During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 200 tickets and collected $1372. If adult tickets sold for $8 and children's tickets sold for $6, how many of each type of ticket were sold?

A)adult tickets sold = 97; children's tickets sold = 125
B)adult tickets sold = 86; children's tickets sold = 114
C)adult tickets sold = 114; children's tickets sold = 86
D)adult tickets sold = 125; children's tickets sold = 97
E)adult tickets sold = 97; children's tickets sold = 99
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54
Solve using any method. <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent

A) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
B) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
C) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
D) <strong>Solve using any method.  </strong> A)   B)   C)   D)   E)inconsistent
E)inconsistent
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55
Solve the system by the method of elimination. <strong>Solve the system by the method of elimination.  </strong> A)   B)   C)   D)   E)inconsistent

A) <strong>Solve the system by the method of elimination.  </strong> A)   B)   C)   D)   E)inconsistent
B) <strong>Solve the system by the method of elimination.  </strong> A)   B)   C)   D)   E)inconsistent
C) <strong>Solve the system by the method of elimination.  </strong> A)   B)   C)   D)   E)inconsistent
D) <strong>Solve the system by the method of elimination.  </strong> A)   B)   C)   D)   E)inconsistent
E)inconsistent
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56
Find the determinant of the matrix <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
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57
Solve for x given the following equation involving a determinant. <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
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58
The currents in an electrical network are given by the solutions of the system <strong>The currents in an electrical network are given by the solutions of the system   where I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are measured in amperes. Solve the system of equations using matrices.</strong> A)I<sub>1</sub> = 4, I<sub>2</sub> = 5, I<sub>3</sub> = 9 B)I<sub>1</sub> = 2, I<sub>2</sub> = 3, I<sub>3</sub> = 6 C)I<sub>1</sub> = 2, I<sub>2</sub> = 3, I<sub>3</sub> = 5 D)I<sub>1</sub> = 4, I<sub>2</sub> = 9, I<sub>3</sub> = 5 E)no solution where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

A)I1 = 4, I2 = 5, I3 = 9
B)I1 = 2, I2 = 3, I3 = 6
C)I1 = 2, I2 = 3, I3 = 5
D)I1 = 4, I2 = 9, I3 = 5
E)no solution
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59
Find the determinant of <strong>Find the determinant of   .</strong> A)-828 B)512 C)-768 D)-736 E)-64 .

A)-828
B)512
C)-768
D)-736
E)-64
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60
Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand
Supply <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent

A) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent
B) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent
C) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent
D) <strong>Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand Supply    </strong> A)   B)   C)   D)   E)inconsistent
E)inconsistent
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61
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible

A) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
B) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
C) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
D) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
E)not possible
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62
If possible, find AB. <strong>If possible, find AB.  </strong> A)   B)   C)   D)   E)not possible

A) <strong>If possible, find AB.  </strong> A)   B)   C)   D)   E)not possible
B) <strong>If possible, find AB.  </strong> A)   B)   C)   D)   E)not possible
C) <strong>If possible, find AB.  </strong> A)   B)   C)   D)   E)not possible
D) <strong>If possible, find AB.  </strong> A)   B)   C)   D)   E)not possible
E)not possible
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63
Determine which ordered pair is a solution of the system. <strong>Determine which ordered pair is a solution of the system.  </strong> A)(8, 1) B)(-9, 3) C)(-9,8) D)(8, -1) E)(1, -8)

A)(8, 1)
B)(-9, 3)
C)(-9,8)
D)(8, -1)
E)(1, -8)
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64
Evaluate the expression. <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible

A) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
B) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
C) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
D) <strong>Evaluate the expression.  </strong> A)   B)   C)   D)   E)not possible
E)not possible
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65
Solve for x given the following equation involving a determinant. <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve for x given the following equation involving a determinant.  </strong> A)   B)   C)   D)   E)
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66
Determine which ordered pair is a solution of the system. <strong>Determine which ordered pair is a solution of the system.  </strong> A)(-3, 6) B)(-1, -2) C)(-2, -1) D)(1, -2) E)(6, 3)

A)(-3, 6)
B)(-1, -2)
C)(-2, -1)
D)(1, -2)
E)(6, 3)
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67
Use Cramer's Rule to solve the following system of linear equations: <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)

A) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
B) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
C) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
D) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
E) <strong>Use Cramer's Rule to solve the following system of linear equations:  </strong> A)   B)   C)   D)   E)
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68
Find the determinant of <strong>Find the determinant of   .</strong> A)14 B)7 C)12 D)-8 E)6 .

A)14
B)7
C)12
D)-8
E)6
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69
Write the augmented matrix for the system of linear equations. <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)

A) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
B) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
C) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
D) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
E) <strong>Write the augmented matrix for the system of linear equations.  </strong> A)   B)   C)   D)   E)
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70
The currents in an electrical network are given by the solutions of the system <strong>The currents in an electrical network are given by the solutions of the system   where I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are measured in amperes. Solve the system of equations using matrices.</strong> A)I<sub>1</sub> = 5, I<sub>2</sub> = 8, I<sub>3</sub> = 3 B)I<sub>1</sub> = 5, I<sub>2</sub> = 3, I<sub>3</sub> = 8 C)I<sub>1</sub> = 3, I<sub>2</sub> = 5, I<sub>3</sub> = 9 D)I<sub>1</sub> = 3, I<sub>2</sub> = 5, I<sub>3</sub> = 8 E)no solution where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

A)I1 = 5, I2 = 8, I3 = 3
B)I1 = 5, I2 = 3, I3 = 8
C)I1 = 3, I2 = 5, I3 = 9
D)I1 = 3, I2 = 5, I3 = 8
E)no solution
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71
Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form. <strong>Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.  </strong> A)row-echelon form B)row-echelon form and reduced row-echelon form C)neither

A)row-echelon form
B)row-echelon form and reduced row-echelon form
C)neither
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72
Solve the system. <strong>Solve the system.  </strong> A)   B)   C)   D)   E)no solution

A) <strong>Solve the system.  </strong> A)   B)   C)   D)   E)no solution
B) <strong>Solve the system.  </strong> A)   B)   C)   D)   E)no solution
C) <strong>Solve the system.  </strong> A)   B)   C)   D)   E)no solution
D) <strong>Solve the system.  </strong> A)   B)   C)   D)   E)no solution
E)no solution
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73
Find the inverse of the matrix <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)   D)   E)does not exist (if it exists).

A) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)   D)   E)does not exist
B) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)   D)   E)does not exist
C) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)   D)   E)does not exist
D) <strong>Find the inverse of the matrix   (if it exists).</strong> A)   B)   C)   D)   E)does not exist
E)does not exist
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74
Applying Kirchhoff's Laws to the electrical network in the figure, the currents I1, I2, and I3 are the solution of the system <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       Find the currents. <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)

A) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
B) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
C) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
D) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
E) <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)       <strong>Applying Kirchhoff's Laws to the electrical network in the figure, the currents I<sub>1</sub>, I<sub>2</sub>, and I<sub>3</sub> are the solution of the system   Find the currents.    </strong> A)       B)       C)       D)       E)
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75
Solve the system by substitution, if possible. <strong>Solve the system by substitution, if possible.  </strong> A)(4, 8) B)(8, 4) C)(-4, 13) D)(12, -3) E)no solutions

A)(4, 8)
B)(8, 4)
C)(-4, 13)
D)(12, -3)
E)no solutions
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76
Find the equation of the circle <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   that passes through the points <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the equation of the circle   that passes through the points   .</strong> A)   B)   C)   D)   E)
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77
Find the determinant of the matrix <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
B) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
C) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
D) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
E) <strong>Find the determinant of the matrix   .</strong> A)   B)   C)   D)   E)
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78
Solve the system of equations by graphing. <strong>Solve the system of equations by graphing.  </strong> A)(-4, 6) B)(-5, 5) C)(6, 1) D)(5, -5) E)(3, 13)

A)(-4, 6)
B)(-5, 5)
C)(6, 1)
D)(5, -5)
E)(3, 13)
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79
If possible, find 2A - 5B. <strong>If possible, find 2A - 5B.  </strong> A)   B)   C)   D)   E)not possible

A) <strong>If possible, find 2A - 5B.  </strong> A)   B)   C)   D)   E)not possible
B) <strong>If possible, find 2A - 5B.  </strong> A)   B)   C)   D)   E)not possible
C) <strong>If possible, find 2A - 5B.  </strong> A)   B)   C)   D)   E)not possible
D) <strong>If possible, find 2A - 5B.  </strong> A)   B)   C)   D)   E)not possible
E)not possible
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80
Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. <strong>Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.  </strong> A)x = -5, y = -3, z = 2 B)x = 5, y = -3, z = 2 C)x = 5, y = 3, z = 2 D)x = 3, y = -5, z = -2 E)no solution

A)x = -5, y = -3, z = 2
B)x = 5, y = -3, z = 2
C)x = 5, y = 3, z = 2
D)x = 3, y = -5, z = -2
E)no solution
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