C Challenge

64. Assume that a, b, and c are integers and a ≠ 0 . eh not equal to 0 .
    1. Proof Prove that the solution of the linear equation a x − b = c eh x minus b equals c  must be a rational number.
    2. Writing Describe the values of a, b, and c for which the solutions of a x 2 + b = c eh , x squared , plus b equals c  are rational.
65. A tortoise crawling at a rate of 0.1 mi/h passes a resting hare. The hare wants to rest another 30 min before chasing the tortoise at a rate of 5 mi/h. How many feet must the hare run to catch the tortoise?

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

66. A mural made of triangular tiles has an area of 1750 square centimeters. Each triangle has a height that is 3 centimeters longer than its base of 2 centimeters. How many triangular tiles are there?
67. The table shows the population of bacteria in a petri dish at various times. If the pattern continues, what will the bacteria population be at 6:00 p.m.?

    Bacteria Population
    Time	8:00 A.M.	10:00 A.M.	12:00 P.M.	2:00 P.M.
    Population	100	200	400	800

68. To the nearest tenth, what is the value of t in the following equation? 4 ( t − 30 ) = 5 − 3 t 4 open t minus 30 close equals 5 minus 3 t
69. A 10-foot-tall basketball hoop is 4 feet shorter than twice the height of a flag pole. What is the height in feet of the flag pole?

Mixed Review

See Lesson 1-3.

Evaluate each expression for x = − 4 x equals negative 4  and y = 3.

70. x − 2 y + 3 x minus 2 y plus 3
71. x + x ÷ y x plus x divides y
72. 3 x − 4 y − x 3 x minus 4 y minus x
73. x + 2 y ÷ x x plus 2 y divides x

See Lesson 1-3.

Write an algebraic expression for each phrase.

74. 5 more than a number x
75. the product of 16 and a number x
76. 3 times the difference of 12 and a number x

Get Ready! To prepare for Lesson 1-5, do Exercises 77-79.

See Lesson 1-2.

State whether each inequality is true or false.

77. 5 < 12 5 less than 12
78. 5 < − 12 5 less than negative 12
79. 5 ≥ 5 5 greater than or equal to 5

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