Question 1

Match the inequality with a graph.
-$$7 - 3 x > y$$

A)

B)

C)

D)

Accepted Answer

The answer of Match the inequality with a graph.
-\[7 -...

Question 2

Provide an appropriate response.
-Equating the numerators in the process of partial fraction decomposition, your friend has obtained the algebraic expression $5 x - 8 = A ( 3 x - 3 ) + B ( x + 4 )$. From this equation, what can you say about the original expression?
A) The denominator of the original expression is $3 x ^ { 2 } + 9 x - 12$.
B) The original expression has repeated linear factors in the denominator.
C) The original expression has a non-reducible quadratic factor in the denominator.
D) The numerator of the original expression is $3 x ^ { 2 } + 9 x - 12$.

Accepted Answer

The given algebraic expression for partial fraction decomposition suggests that the denominator of the original expression was factored into linear factors, $3x-3$ and $x+4$, indicating that the original denominator is the product of these factors, which simplifies to $3x^2 + 9x - 12$.

Question 3

Rewrite the expression using a determinant. Show all your work.
-$$\frac { a + b } { c }$$

Accepted Answer

The answer of Rewrite the expression using a determinant. Show...

Question 4

Find the graph that matches the given system of equations.
-$$\begin{array} { l } 
3 x + 4 y = - 7 \
2 x - 3 y = - 16
\end{array}$$
A)

B)

C)

D)

Accepted Answer

The answer of Find the graph that matches the given...

Question 5

Provide an appropriate answer.
-$$\text { Let } A = \left[ \begin{array} { c c } 
- 1 & 3 \
- 3 & 1
\end{array} \right] \text { and } B = \left[ \begin{array} { c c } 
- 5 & - 1 \
- 5 & - 4
\end{array} \right] \text {. Show that } A B \neq B A \text {. Show all your work. }$$

Accepted Answer

The answer of Provide an appropriate answer.
-\[\text { Let }...

Question 6

Match the system of inequalities with a graph.
- 
A)

B)

C)

D)

Accepted Answer

The answer of Match the system of inequalities with a...

Question 7

Match the system of inequalities with a graph.
-

A)

B)

C)

D)

Accepted Answer

The answer of Match the system of inequalities with a...

Question 8

Provide an appropriate response.
-You are finding the partial fraction decomposition of the expression $\frac { x ^ { 3 } - 7 x + 12 } { x ^ { 2 } - 13 x + 40 }$.
You should ...
A) Solve the equation $x ^ { 3 } - 7 x + 12 = A ( x - 5 ) + B ( x - 8 )$
B) Solve the equation $x ^ { 3 } - 7 x + 12 = ( A x + B ) \left( x ^ { 2 } - 13 x + 40 \right)$
C) Solve the equation $x ^ { 2 } - 13 x + 40 = ( A x + B ) \left( x ^ { 3 } - 7 x + 12 \right)$
D) Use long division to divide the numerator by the denominator

Accepted Answer

The numerator is of higher degree than the denominator, so you should use long division to simplify the expression before finding the partial fraction decomposition.

Question 9

Solve the problem.
-Evaluate $| \mathrm { A } |$ by expanding across the third row. Show all your work.
$$A = \left[ \begin{array} { r r r r } 
- 1 & 1 & 0 & 2 \
- 5 & 2 & 4 & - 5 \
0 & 5 & 0 & - 1 \
1 & 2 & - 1 & 0
\end{array} \right]$$

Accepted Answer

The answer of Solve the problem.
-Evaluate \(| \mathrm { A...

Question 10

Find the graph that matches the given system of equations.
-$$\begin{array} { l } 
3 x - y = 13 \
- 6 x + 2 y = - 26
\end{array}$$
A)

B)

C)

D)

Accepted Answer

The answer of Find the graph that matches the given...

Question 11

Match the inequality with a graph.
-$2 x+5 y>-4$

A)

B)

C)

D)

Accepted Answer

The answer of Match the inequality with a graph.
-\(2 x+5...

Question 12

Provide an appropriate response.
-The partial fraction decomposition of an expression is $2 x + \frac { 4 } { 2 x - 7 } - \frac { 6 } { 2 x ^ { 2 } - 7 }$. From this decomposition, what can you say about the original expression?
A) The numerator of the original expression was $2 x ^ { 2 } + 4 x - 6$.
B) The numerator of the original expression was of a degree greater than the denominator of the original expression.
C) The denominator of the original expression contained a nonreducible quadratic factor.
D) The denominator of the original expression contained repeated linear factors.

Accepted Answer

The answer of Provide an appropriate response.
-The partial fraction decomposition...

Question 13

Provide an appropriate response.
-You are graphing $2 x ^ { 2 } + 3 y ^ { 2 } > 5$. You have drawn the graph of $2 x ^ { 2 } + 3 y ^ { 2 } = 5$. What single point will allow you to determine the correct region?
A) $( 3,5 )$
B) $( 2,5 )$
C) The origin
D) $( 2,3 )$

Accepted Answer

The origin (0,0) is the most effective point to test because it is easy to substitute into the inequality. If the origin satisfies the inequality, then the region containing the origin is the solution. For this inequality, substituting (0,0) gives $2(0)^2 + 3(0)^2 > 5$, which simplifies to $0 > 5$, which is false. Therefore, the correct region is the one not containing the origin.

Question 14

Find the graph that matches the given system of equations.
-$$\begin{array} { l } 
2 x + y = 8 \
y = 2 x + 0
\end{array}$$
A)

B)

C)

D)

Accepted Answer

The answer of Find the graph that matches the given...

Question 15

Match the system of inequalities with a graph.
-$$\begin{array} { l } 
3 y - x \leq - 4 , \
y + 4 x \leq 6 \
- y \geq x - 3
\end{array}$$

A)

B)
 
C)

D)

Accepted Answer

The answer of Match the system of inequalities with a...

Question 16

Provide an appropriate response.
-Which one of the following is a description of the graph of the inequality? $( x + 4 ) ^ { 2 } + ( y - 7 ) ^ { 2 } < 4$
A) the region inside the circle with center $( 4 , - 7 )$ and radius 2
B) the region outside a circle with center $( 4 , - 7 )$ and radius 2
C) the region outside a circle with center $( - 4,7 )$ and radius 2
D) the region inside a circle with center $( - 4,7 )$ and radius 2

Accepted Answer

The equation $( x + 4 ) ^ { 2 } + ( y - 7 ) ^ { 2 } < 4$ represents the region inside a circle with center $(-4, 7)$ and radius $2$, because the inequality sign "<" indicates inside the circle, and the equation is in the form $(x - h)^2 + (y - k)^2 < r^2$, where $(h, k)$ is the center and $r$ is the radius.

Question 17

Provide an appropriate response.
-Which one of the following is a description of the graph of the inequality?
$$( x + 9 ) ^ { 2 } + ( y - 2 ) ^ { 2 } > 16$$
A) the region inside a circle with center $( - 9,2 )$ and radius 4
B) the region outside a circle with center $( 9 , - 2 )$ and radius 4
C) the region inside the circle with center $( 9 , - 2 )$ and radius 4
D) the region outside a circle with center $( - 9,2 )$ and radius 4

Accepted Answer

The inequality describes the region outside a circle with center $(-9,2)$ and radius 4, because the equation is in the form $(x - h)^2 + (y - k)^2 > r^2$, where $(h,k)$ is the center and $r$ is the radius.

Question 18

Provide an appropriate response.
-You are finding the partial fraction decomposition of the expression $\frac { x ^ { 2 } - 11 x + 24 } { \left( x ^ { 2 } - 10 x + 21 \right) ( x + 7 ) }$. You should ...
A) Solve the equation $x ^ { 2 } - 11 x + 24 = A ( x + 7 ) + B ( x - 3 ) + C ( x + 7 )$
B) Use long division to divide the numerator by the denominator
C) Solve the equation $x ^ { 2 } - 11 x + 24 = A ( x - 7 ) + B ( x - 3 ) + C ( x + 7 )$
D) Solve the equation $x ^ { 2 } - 11 x + 24 = ( A x + B ) \left( x ^ { 2 } - 10 x + 21 \right) + C ( x + 7 )$

Accepted Answer

The answer of Provide an appropriate response.
-You are finding the...

Question 19

Provide an appropriate response.
-When using the substitution or elimination method to solve a system of two equations, you
end up with an equation stating 0 = 0. What does this indicate to you about the system of
equations?

Accepted Answer

The answer of Provide an appropriate response.
-When using the substitution...

Question 20

Provide an appropriate answer.
-$$\text { Let } A = \left[ \begin{array} { r r } 
- 1 & 3 \
- 3 & - 3
\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 
- 3 & 3 \
4 & - 4
\end{array} \right] \text {. Show that } A ( A + B ) = A ^ { 2 } + A B \text {. Show all your work. }$$

Accepted Answer

The answer of Provide an appropriate answer.
-\[\text { Let }...

Quiz 6: Systems of Equations and Matrices

Match the inequality with a graph. - $7 - 3 x > y$

Provide an appropriate response. -Equating the numerators in the process of partial fraction decomposition, your friend has obtained the algebraic expression $5 x - 8 = A ( 3 x - 3 ) + B ( x + 4 )$ . From this equation, what can you say about the original expression?

Rewrite the expression using a determinant. Show all your work. - $\frac { a + b } { c }$

Find the graph that matches the given system of equations. - $\begin{array} { l } 3 x + 4 y = - 7 \\2 x - 3 y = - 16\end{array}$

Provide an appropriate answer. - $\text { Let } A = \left[ \begin{array} { c c } - 1 & 3 \\- 3 & 1\end{array} \right] \text { and } B = \left[ \begin{array} { c c } - 5 & - 1 \\- 5 & - 4\end{array} \right] \text {. Show that } A B \neq B A \text {. Show all your work. }$

Match the system of inequalities with a graph. -

Match the system of inequalities with a graph. -

Provide an appropriate response. -You are finding the partial fraction decomposition of the expression $\frac { x ^ { 3 } - 7 x + 12 } { x ^ { 2 } - 13 x + 40 }$ . You should ...

Solve the problem. -Evaluate $| \mathrm { A } |$ by expanding across the third row. Show all your work. $A = \left[ \begin{array} { r r r r } - 1 & 1 & 0 & 2 \\- 5 & 2 & 4 & - 5 \\0 & 5 & 0 & - 1 \\1 & 2 & - 1 & 0\end{array} \right]$

Find the graph that matches the given system of equations. - $\begin{array} { l } 3 x - y = 13 \\- 6 x + 2 y = - 26\end{array}$

Match the inequality with a graph. - $2 x+5 y>-4$

Provide an appropriate response. -The partial fraction decomposition of an expression is $2 x + \frac { 4 } { 2 x - 7 } - \frac { 6 } { 2 x ^ { 2 } - 7 }$ . From this decomposition, what can you say about the original expression?

Provide an appropriate response. -You are graphing $2 x ^ { 2 } + 3 y ^ { 2 } > 5$ . You have drawn the graph of $2 x ^ { 2 } + 3 y ^ { 2 } = 5$ . What single point will allow you to determine the correct region?

Find the graph that matches the given system of equations. - $\begin{array} { l } 2 x + y = 8 \\y = 2 x + 0\end{array}$

Match the system of inequalities with a graph. - $\begin{array} { l } 3 y - x \leq - 4 , \\y + 4 x \leq 6 \\- y \geq x - 3\end{array}$ $Match the system of inequalities with a graph. - \begin{array} { l } 3 y - x \leq - 4 , \\ y + 4 x \leq 6 \\ - y \geq x - 3 \end{array} A) B) C) D)$

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x + 4 ) ^ { 2 } + ( y - 7 ) ^ { 2 } < 4$

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x + 9 ) ^ { 2 } + ( y - 2 ) ^ { 2 } > 16$

Provide an appropriate response. -You are finding the partial fraction decomposition of the expression $\frac { x ^ { 2 } - 11 x + 24 } { \left( x ^ { 2 } - 10 x + 21 \right) ( x + 7 ) }$ . You should ...

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Provide an appropriate answer. - $\text { Let } A = \left[ \begin{array} { r r } - 1 & 3 \\- 3 & - 3\end{array} \right] \text { and } B = \left[ \begin{array} { r r } - 3 & 3 \\4 & - 4\end{array} \right] \text {. Show that } A ( A + B ) = A ^ { 2 } + A B \text {. Show all your work. }$

Quiz 6: Systems of Equations and Matrices

Match the inequality with a graph. - 7−3x>y7 - 3 x > y7−3x>y

Rewrite the expression using a determinant. Show all your work. - a+bc\frac { a + b } { c }ca+b​

Find the graph that matches the given system of equations. - 3x+4y=−72x−3y=−16\begin{array} { l } 3 x + 4 y = - 7 \\2 x - 3 y = - 16\end{array}3x+4y=−72x−3y=−16​

Match the system of inequalities with a graph. -

Match the system of inequalities with a graph. -

Provide an appropriate response. -You are finding the partial fraction decomposition of the expression x3−7x+12x2−13x+40\frac { x ^ { 3 } - 7 x + 12 } { x ^ { 2 } - 13 x + 40 }x2−13x+40x3−7x+12​ . You should ...

Find the graph that matches the given system of equations. - 3x−y=13−6x+2y=−26\begin{array} { l } 3 x - y = 13 \\- 6 x + 2 y = - 26\end{array}3x−y=13−6x+2y=−26​

Match the inequality with a graph. - 2x+5y>−42 x+5 y>-42x+5y>−4

Provide an appropriate response. -The partial fraction decomposition of an expression is 2x+42x−7−62x2−72 x + \frac { 4 } { 2 x - 7 } - \frac { 6 } { 2 x ^ { 2 } - 7 }2x+2x−74​−2x2−76​ . From this decomposition, what can you say about the original expression?

Provide an appropriate response. -You are graphing 2x2+3y2>52 x ^ { 2 } + 3 y ^ { 2 } > 52x2+3y2>5 . You have drawn the graph of 2x2+3y2=52 x ^ { 2 } + 3 y ^ { 2 } = 52x2+3y2=5 . What single point will allow you to determine the correct region?

Find the graph that matches the given system of equations. - 2x+y=8y=2x+0\begin{array} { l } 2 x + y = 8 \\y = 2 x + 0\end{array}2x+y=8y=2x+0​

Match the system of inequalities with a graph. - 3y−x≤−4,y+4x≤6−y≥x−3\begin{array} { l } 3 y - x \leq - 4 , \\y + 4 x \leq 6 \\- y \geq x - 3\end{array}3y−x≤−4,y+4x≤6−y≥x−3​

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? (x+4) 2+(y−7) 2<4( x + 4 ) ^ { 2 } + ( y - 7 ) ^ { 2 } < 4(x+4) 2+(y−7) 2<4

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? (x+9) 2+(y−2) 2>16( x + 9 ) ^ { 2 } + ( y - 2 ) ^ { 2 } > 16(x+9) 2+(y−2) 2>16

Provide an appropriate response. -You are finding the partial fraction decomposition of the expression x2−11x+24(x2−10x+21) (x+7) \frac { x ^ { 2 } - 11 x + 24 } { \left( x ^ { 2 } - 10 x + 21 \right) ( x + 7 ) }(x2−10x+21) (x+7) x2−11x+24​ . You should ...

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Match the inequality with a graph. - $7 - 3 x > y$

Rewrite the expression using a determinant. Show all your work. - $\frac { a + b } { c }$

Find the graph that matches the given system of equations. - $\begin{array} { l } 3 x + 4 y = - 7 \\2 x - 3 y = - 16\end{array}$

Provide an appropriate response. -You are finding the partial fraction decomposition of the expression $\frac { x ^ { 3 } - 7 x + 12 } { x ^ { 2 } - 13 x + 40 }$ . You should ...

Find the graph that matches the given system of equations. - $\begin{array} { l } 3 x - y = 13 \\- 6 x + 2 y = - 26\end{array}$

Match the inequality with a graph. - $2 x+5 y>-4$

Provide an appropriate response. -The partial fraction decomposition of an expression is $2 x + \frac { 4 } { 2 x - 7 } - \frac { 6 } { 2 x ^ { 2 } - 7 }$ . From this decomposition, what can you say about the original expression?

Provide an appropriate response. -You are graphing $2 x ^ { 2 } + 3 y ^ { 2 } > 5$ . You have drawn the graph of $2 x ^ { 2 } + 3 y ^ { 2 } = 5$ . What single point will allow you to determine the correct region?

Find the graph that matches the given system of equations. - $\begin{array} { l } 2 x + y = 8 \\y = 2 x + 0\end{array}$

Match the system of inequalities with a graph. - $\begin{array} { l } 3 y - x \leq - 4 , \\y + 4 x \leq 6 \\- y \geq x - 3\end{array}$ $Match the system of inequalities with a graph. - \begin{array} { l } 3 y - x \leq - 4 , \\ y + 4 x \leq 6 \\ - y \geq x - 3 \end{array} A) B) C) D)$

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x + 4 ) ^ { 2 } + ( y - 7 ) ^ { 2 } < 4$

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x + 9 ) ^ { 2 } + ( y - 2 ) ^ { 2 } > 16$

Provide an appropriate response. -You are finding the partial fraction decomposition of the expression $\frac { x ^ { 2 } - 11 x + 24 } { \left( x ^ { 2 } - 10 x + 21 \right) ( x + 7 ) }$ . You should ...