C Challenge

In Exercises 54–55, y varies directly with x. Explain your answer.

54. If x is doubled, what happens to y?
55. If x is divided by 7, what happens to y?
56. If z varies directly with the product of x and y (z = kxy), then z is said to vary jointly with x and y.
    1. Geometry The area of a triangle varies jointly with its base and height. What is the constant of variation?
    2. Suppose q varies jointly with v and s, and q = 24 q equals 24  when v = 2 v equals 2  and s = 3 . s equals 3 .  Find q when v = 4 v equals 4  and s = 2 . s equals 2 .
    3. Reasoning Suppose z varies jointly with x and y, and x varies directly with w. Show that z varies jointly with w and y.

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

57. A speed of 75 mi/h is equal to a speed of 110 ft/s. To the nearest mile per hour, what is the speed of an aircraft traveling at a speed of 1600 ft/s?
58. What number is a solution to both | x − 3 | = 2 vertical line x minus 3 vertical line equals 2  and | 9 − x | = 8 ? vertical line 9 minus x vertical line equals 8 question mark
59. If f ( x ) = 7 − 3 x f open x close equals 7 minus 3 x  and g ( x ) = 3 x − 7 , g open x close equals 3 x minus 7 comma  what is the value of f(1) + g(1)?

60. Look at the pattern. How many circles are in the 6th figure of this pattern?

    
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61. What is the solution of 4 ( x − 5 ) + x = 8 x − 10 − x ? 4 open x minus 5 close plus x equals 8 x minus 10 minus x question mark

Mixed Review

Graph each relation. Find the domain and range. See Lesson 2-1.

62. {(0, 1), ( 1 , − 3 ) , open 1 comma negative 3 close comma  ( − 2 , − 3 negative 2 comma negative 3 ), ( 3 , − 3 ) open 3 comma negative 3 close }
63. {(4, 0), (7, 0), ( 4 , − 1 ) , ( 7 , − 1 ) open 4 comma negative 1 close comma open 7 comma negative 1 close }
64. { ( 1 , − 2 ) , ( 2 , − 1 ) , open 1 comma negative 2 close comma open 2 comma negative 1 close comma  (4, 1), (5, 2)}
65. {(1, 7), (2, 8), (3, 9), (4, 10)}

Identify a pattern and find the next three numbers in the pattern. See Lesson 1-1.

66. 8, 16, 24, 32,…
67. 5, 3, 1, − 1 , negative 1 comma  …
68. 144, 132, 120, 108,…
69. 30, 45, 60, 75,…

Get Ready! To prepare for Lesson 2-3, do Exercises 70–73.

Evaluate each expression for x = − 2 , 0 , 1 , x equals negative 2 comma 0 comma 1 comma  and 4. See Lesson 1-3.

70. 2 3 x + 7 2 thirds , x plus 7
71. 3 5 x − 2 3 fifths , x minus 2
72. 3x + 1
73. 1 2 x − 8 1 half , x minus 8

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