Section 7

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Harvard University *

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Mathematics

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Jan 9, 2024

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61. Solve the equation 2(4 −3)=202(4 x −3)=20 . Answer : =4 x =4 . 62. Calculate the value of y in the equation 3 2−4=10 23 y −4=10 . Answer : =14 y =14 . 63. Find the volume of a rectangular prism with length 66 units, width 44 units, and height 55 units. Answer : Volume = length×width×height=6×4×5=120length×width×height=6×4×5=120 cubic units. 64. Determine the value of z if 4 +3=234 z +3=23 . Answer : =5 z =5 . 65. Solve the equation 5 3+2=12 35 x +2=12 . Answer : =6 x =6 . 66. Evaluate the expression: 82−6×48 2 −6×4 . Answer : 82−6×4=64−24=408 2 −6×4=64−24=40 . 67. Calculate the area of a circle with a radius of 77 units (use =3.14 π =3.14 ). Answer : Area = × 2=3.14×72=153.86 π × r 2 =3.14×7 2 =153.86 square units. 68. Solve the inequality: 2 −5<92 x −5<9 . Answer : <7 x <7 . 69. Find the slope of the line parallel to =12 −3 y = 21 x −3 . Answer : The slope of a line parallel to this line is also 12 21 . 70. Solve for y in the equation 3 −2=133 y −2=13 . Answer : =5 y =5 .
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