C Challenge

69. Antennas Guy wires are attached to an antenna tower at the heights h shown below. Use the expression h 2 + ( 0.55 h ) 2 square root of h squared , plus . open , 0.55 , h , close squared end root  to estimate the wire length for each height. If three wires are attached at each height, what is the minimum total amount of wire needed?

    

70. Reasoning Sometimes the product of two positive numbers is less than either number. Describe the numbers for which this is true.
71. Cube Roots The number a is the cube root of a number b if a 3 = b . eh cubed , equals b .  For example, the cube root of 8 is 2 because 2 3 = 8 . 2 cubed , equals 8 .  Find the cube root of each number.
    1. 64
    2. 1000
    3. 343
    4. 2197

Standardized Test Prep

SAT/ACT

72. A square picture has an area of 225 in. 2 . 225 , in. squared , .  What is the side length of the picture?
    1. 5 in.
    2. 15 in.
    3. 25 in.
    4. 225 in.
73. To simplify the expression 9 · ( 33 − 5 2 ) ÷ 2 , 9 middle dot open 33 minus , 5 squared , close divides 2 comma  what do you do first?
    6. Divide by 2.
    7. Subtract 5.
    8. Multiply by 9.
    9. Square 5.
74. The table below shows the number of pages you can read per minute. Which algebraic expression gives a rule for finding the number of pages read in any number of minutes m?

    Reading

    Minutes	Pages Read
    1	2
    2	4
    3	6
    m	□ white square

    1. m
    2. 2m
    3. m + 2
    4. m 2 m over 2

Mixed Review

See Lesson 1-2.

Evaluate each expression for the given values of the variables.

75. ( r − t ) 2 ; r = 11 , t = 7 open r minus t close squared . semicolon r equals 11 comma t equals 7
76. 3 m 2 + n ; m = 5 , n = 3 3 , m squared , plus n semicolon m equals 5 comma n equals 3
77. ( 2 x ) 2 y ; x = 4 , y = 8 open 2 x close squared . y semicolon x equals 4 comma y equals 8

See Lesson 1-1.

Write an algebraic expression for each word phrase.

78. the sum of 14 and x
79. 4 multiplied by the sum of y and 1
80. 3880 divided by z
81. the product of t and the quotient of 19 and 3

Get Ready! To prepare for Lesson 1-4, do Exercises 82–85.

See Lesson 1-2.

Simplify each expression.

82. 4 + 7 · 2 4 plus 7 middle dot 2
83. (7 + 1)9
84. 2 + 22 · 20 2 plus 22 middle dot 20
85. 6 + 18 ÷ 6 6 plus 18 divides 6

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