63. Open-Ended Choose a fraction to use as a value for the variable a. Find the values of a − 1 , a 2 , eh super negative 1 end super , comma , eh squared , comma  and a − 2 . eh super negative 2 end super , .
64. Manufacturing A company is making metal rods with a target diameter of 1.5 mm. A rod is acceptable when its diameter is within 10 − 3 10 super negative 3 end super  mm of the target diameter. Write an inequality for the acceptable range of diameters.
65. Reasoning Are 3 x − 2 3 x super negative 2 end super  and 3 x 2 3 x squared  reciprocals? Explain.

C Challenge

Simplify each expression.

66. ( r − 7 b − 8 t − 4 w 1 ) 0 open . fraction r super negative 7 end super . b super negative 8 end super , over t super negative 4 end super . w to the first end fraction . close to the
67. ( − 5 ) 2 − ( 0.5 ) − 2 open negative 5 close squared . minus . open 0.5 close super negative 2 end super
68. 6 m 2 + 5 m − 2 3 − 3 fraction 6 , over m squared end fraction , plus . fraction 5 , m super negative 2 end super , over 3 super negative 3 end super end fraction
69. 2 3 ( 5 0 − 6 m 2 ) 2 cubed , open , 5 to the , minus , 6 m squared , close
70. 2 x − 5 y 3 n 2 ÷ r 2 y 5 2 n fraction 2 , x super negative 5 end super . y cubed , over n squared end fraction . divides . fraction r squared , y to the fifth , over 2 n end fraction

71. 2 − 1 − 1 3 − 2 + 5 ( 1 2 2 ) 2 super negative 1 end super , minus . fraction 1 , over 3 super negative 2 end super end fraction . plus 5 . open , fraction 1 , over 2 squared end fraction , close

72. For what value or values of n is n − 3 = ( 1 n ) 5 ? n super negative 3 end super , equals . open , 1 over n , close to the fifth . question mark

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

73. What is the simplified form of − 6 ( − 6 ) − 1 ? negative 6 . open negative 6 close super negative 1 end super . question mark
74. Segment CD represents the flight of a bird that passes through the points (1, 2) and (5, 4). What is the slope of a line that represents the flight of a second bird that flew perpendicular to the first bird?
75. What is the solution of the equation 1.5 ( x − 2.5 ) = 3 ? 1.5 open x minus 2.5 close equals 3 question mark
76. What is the simplified form of | 3.5 − 4.7 | + 5.6 ? vertical line 3.5 minus 4.7 vertical line plus 5.6 question mark
77. What is the y-intercept of the graph of 3 x − 2 y = − 8 ? 3 x minus 2 y equals negative 8 question mark

Mixed Review

See Lesson 6-6.

Solve each system by graphing.

78. y > 3 x + 4 y ≤ − 3 x + 1 table with 2 rows and 1 column , row1 column 1 , y greater than 3 x plus 4 , row2 column 1 , y less than or equal to negative 3 x plus 1 , end table
79. y ≤ − 2 x + 1 y < 2 x − 1 table with 2 rows and 1 column , row1 column 1 , y less than or equal to negative 2 x plus 1 , row2 column 1 , y less than 2 x minus 1 , end table
80. y ≥ 0.5 x y ≤ x + 2 table with 2 rows and 1 column , row1 column 1 , y greater than or equal to 0.5 x , row2 column 1 , y less than or equal to x plus 2 , end table

See Lesson 5-3.

Write an equation in slope-intercept form for the line with the given slope m and y-intercept b.

81. m = − 1 , b = 4 m equals negative 1 comma b equals 4
82. m = 5 , b = − 2 m equals 5 comma b equals negative 2
83. m = 2 5 , b = − 3 m equals , 2 fifths , comma b equals negative 3
84. m = − 3 11 , b = − 17 m equals negative , 3 elevenths , comma b equals negative 17
85. m = 5 9 , b = 1 3 m equals , 5 ninths , comma b equals , 1 third
86. m = 1.25 , b = − 3.79 m equals , 1.25 , comma b equals negative , 3.79

Get Ready! To prepare for Lesson 7-2, do Exercises 87–91.

See Lesson 7-1.

Simplify each expression.

87. 6 · 10 4 6 middle dot , 10 to the fourth
88. 7 · 10 − 2 7 middle dot , 10 super negative 2 end super
89. 8.2 · 10 5 8.2 middle dot , 10 to the fifth
90. 3 · 10 − 3 3 middle dot , 10 super negative 3 end super
91. 3.4 · 10 5 3.4 middle dot , 10 to the fifth

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