Deck 11: Comprehensive Algebra and Functions Problem Set: Concepts, Graphs, and Equations

Question 1

Perform the indicated operation.
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Answer 1

Question 2

Perform the indicated operation.
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Answer 2

Question 3

Perform the indicated operation.
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Answer 3

Question 4

Perform the indicated operation.
-Write $8.3 \times 10^{-4}$ without exponents.

Question 5

Perform the indicated operation.
-Graph $y = \frac34x$ .

Question 6

Solve each system of equations
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Question 7

Solve each system of equations
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Question 8

Solve each system of equations
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Question 9

Simplify.
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Question 10

Simplify.
-9 - 24 ÷ 4(2)

Question 11

Simplify.
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Question 12

Simplify.
-Combine $x-3 + \frac2{x-2}$

Question 13

Solve each logarithmic equation for x. Give an exact solution
-log₈ (2x + 14) = 2

Question 14

Solve each logarithmic equation for x. Give an exact solution
-log x + log (x -15) = 2

Question 15

Solve each logarithmic equation for x. Give an exact solution
-Solve ln (3x + 11) = 1.57 accurate to four decimal places.

Question 16

Solve each logarithmic equation for x. Give an exact solution
-Find the vertex of the graph of g(x) = -4x² + 24x + 3 .

Question 17

Solve each logarithmic equation for x. Give an exact solution
-Graph (x + 4)² + ( y + 5)² = 9.

Question 18

Raise to the power or take the root. Assume that all variables represent positive numbers.
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Question 19

Raise to the power or take the root. Assume that all variables represent positive numbers.
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Question 20

Solve each system using matrices.
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Question 21

Solve each system using matrices.
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Question 22

Solve each system using matrices.
-The product of one less than a number and three times its reciprocal is 21/8 . Find the number.

Question 23

Solve each system using matrices.
-Simplify

Question 24

Solve each system using matrices.
-Find the slope of the line that passes through (8, -2) and (-1, -5).

Question 25

Find the equation of the line in standard form satisfying the conditions given.
-Though (-4, -1) and (2, 5)

Question 26

Find the equation of the line in standard form satisfying the conditions given.
-Vertical; through (-3, 9)

Question 27

Find the equation of the line in standard form satisfying the conditions given.
-Through (3, -2) and parallel to 4x - y = 18.

Question 28

Find the equation of the line in standard form satisfying the conditions given.
-Name the property illustrated: (3 $\cdot$ x) $\cdot$ y = 3 $\cdot$ ( x $\cdot$ y)

Question 29

Find the equation of the line in standard form satisfying the conditions given.
-Graph 4x - 2y = 5

Question 30

Factor each polynomial completely.
-4 y² - 12 y + 9

Question 31

Factor each polynomial completely.
-49x² - 25 y²

Question 32

Factor each polynomial completely.
-4x³ + 24x² + 32x

Question 33

Factor each polynomial completely.
-x³ - 27 y³

Question 34

Solve each equation for the variable.
-5x² - 44x + 63 = 0

Question 35

Solve each equation for the variable.
-u² - 3u - 2 = 0

Question 36

Solve each equation for the variable.
-4x² + 8x + 27 = 0

Question 37

Solve each equation for the variable.
-x² + 18x + 86 = 0

Question 38

Solve each equation for the variable.
-Graph 2x + y > -2.

Question 39

Solve each equation for the variable.
-The graph of x = y² + 2 y - 15 is a(n)

Question 40

Solve each equation for the variable.
-If f (x) = 3x + 1 and g(x) = 2x - 6 , find ( f $\circ$ g)(x)

Question 41

Perform the indicated operations. Assume that all variables represent positive numbers.
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Question 42

Perform the indicated operations. Assume that all variables represent positive numbers.
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Question 43

Solve each inequality.
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Question 44

Solve each inequality.
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Question 45

Solve each inequality.
-Solve the system of equations.

Question 46

Solve each inequality.
-Solve 5^2x-3 = 4 for x. Approximate the solution to four decimal places

Question 47

Solve each inequality.
-Simplify:

Question 48

Solve each inequality.
-Write in lowest terms.

Question 49

Solve each inequality.
-Graph f (x) = |x + 2| - 3.

Question 50

Write each statement using mathematical notation.
-The square of the sum of y and two, minus three, is greater than six.

Question 51

Write each statement using mathematical notation.
-Four times the quotient of x and three is equal to the difference of x and one.

Question 52

Solve each inequality. Give the answer in interval notation
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Question 53

Solve each inequality. Give the answer in interval notation
--4 < 2 x + 8 < 12

Question 54

Solve each inequality. Give the answer in interval notation
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Question 55

Solve each inequality. Give the answer in interval notation
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Question 56

Solve each inequality. Give the answer in interval notation
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Question 57

Solve each inequality. Give the answer in interval notation
-Divide:

Question 58

Solve each inequality. Give the answer in interval notation
-Rationalize the denominator:

Question 59

Solve each inequality. Give the answer in interval notation
-Find the slope and the y-intercept of the line 4x + 9y = -2.

Question 60

Evaluate each expression when m = -1, n = 4, and p = 5.
-3(m - n) + 2(n + p)²

Question 61

Evaluate each expression when m = -1, n = 4, and p = 5.
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Question 62

Evaluate each expression when m = -1, n = 4, and p = 5.
-Use a calculator to approximate 251^3/4 to three decimal places.

Question 63

Evaluate each expression when m = -1, n = 4, and p = 5.
-Solve

Question 64

Evaluate each expression when m = -1, n = 4, and p = 5.
-The graph of 36x² - 25y² = 900 is a(n)

Question 65

Evaluate each expression when m = -1, n = 4, and p = 5.
-Approximate log₄17 to four decimal places.

Question 66

Evaluate each expression when m = -1, n = 4, and p = 5.
-Graph f (x) = -2( x - 2)² + 3 .

Question 67

Perform the indicated operation and simplify.
-(3+12i) - (7-9i)

Question 68

Perform the indicated operation and simplify.
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Question 69

Perform the indicated operation and simplify.
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Question 70

Perform the indicated operation and simplify.
-The graph of 3x² + 12x + 8y² - 16y = 30 is a(n)____________.

Question 71

Perform the indicated operation and simplify.
-f (x) = 3x - 10 is a one-to-one function. Find its inverse.

Question 72

Perform the indicated operation and simplify.
-Find the exact distance between $(\sqrt3, -6)$ and $(3\sqrt3, 4)$ .

Question 73

Perform the indicated operation and simplify.
-Graph

Question 74

Solve each equation.
-2( x - 5) = 7 - 4(3 - x)

Question 75

Solve each equation.
-4n + 9 = 3(n - 6) + n

Question 76

Solve each equation.
-7x + 12 = 5x + 26

Question 77

Solve each equation.
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Question 78

Solve each equation.
-|5 - 2x| = 3

Question 79

Solve each equation.
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Question 80

Solve each equation.
-Find an equation of the line perpendicular to 5x + 2y = -6 that passes through (2, 6) in function notation.