C Challenge

Simplify each radical expression.

74. 24 · 2 x · 3 x square root of 24 middle dot , square root of 2 x end root , middle dot , square root of 3 x end root
75. 2 b ( 5 b ) 2 2 b . open , square root of 5 b end root , close squared
76. 45 a 7 · 20 a square root of 45 , eh to the seventh end root . middle dot , square root of 20 eh end root
77. Geometry The equation r = A π r equals , square root of eh over pi end root  gives the radius r of a circle with area A. What is the radius of a circle with the given area? Write your answer as a simplified radical and as a decimal rounded to the nearest hundredth.
    1. 50   ft 2 50 , ft squared
    2. 32  in . 2 32 , in , . squared
    3. 10   m 2 10 , m squared
78. For a linear equation in standard form Ax + By = C, where A ≠ 0 eh not equal to 0  and B ≠ 0 , b not equal to 0 comma  the distance d between the x- and y-intercepts is given by d = ( C A ) 2 + ( C B ) 2 . d equals . square root of open , c over eh , close squared . plus . open , c over b , close squared end root . .  What is the distance between the x- and y-intercepts of the graph of 4 x − 3 y = 2 ? 4 x minus 3 y equals 2 question mark

Standardized Test Prep

SAT/ACT

79. What is the simplified form of 12 y 5 ? square root of 12 , y to the fifth end root . question mark
    1. 2 3 y 5 2 , square root of 3 , y to the fifth end root
    2. 4 y 4 3 y 4 , y to the fourth , square root of 3 y end root
    3. 2 y 2 3 y 2 , y squared , square root of 3 y end root
    4. 3 y 3 3 , y cubed
80. In the proportion 3 b = 7 8 − b , 3 over b , equals . fraction 7 , over 8 minus b end fraction . comma  what is the value of b?
    6. 6
    7. 21 8 21 over 8
    8. 12 5 12 over 5
    9. 5 12 5 twelfths

81. The area of the triangle below is 24  in . 2 . 24 , in , . squared , .  What is the height of the triangle?

    

    1. 1.8 in.
    2. 3 in.
    3. 7 in.
    4. 16 in.

82. Short Response An architect is sketching a line on a coordinate grid showing the location of a pipe. The line has an x-intercept of − 2 negative 2  and a y-intercept of 3. What is an equation of the architect's line?

Mixed Review

See Lesson 10-1.

Determine whether the given lengths can be side lengths of a right triangle.

83. 7, 24, 25
84. 1 ,   4 3 , 5 3 1 comma , 4 thirds , comma , 5 thirds
85. 5, 13, 14

See Lesson 8-7.

Factor each expression.

86. 64 y 2 − 9 64 , y squared , minus 9
87. a 2 − 81 eh squared , minus 81
88. 25 −   16 b 2 25 minus 16 , b squared

Get Ready! To prepare for Lesson 10-3, do Exercises 89–91.

See Lesson 8-3.

Simplify each product.

89. ( 3 a − 4 ) ( 2 a + 1 ) open , 3 eh minus 4 , close . open , 2 eh plus 1 , close
90. ( 2 m − 3 n )   ( 4 n − 2 m ) open 2 m minus 3 n close open 4 n minus 2 m close
91. ( 5   +   2 x )   ( 2 x   +   3 ) open 5 plus 2 x close open 2 x plus 3 close

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