university math english 2 potx

74. Choice f is correct. Since YW is an altitude in an equilateral triangle, it bisects the opposite side. XW

and WZ are both 7 inches. See the diagram below.

An altitude also makes a right angle and, therefore, the Pythagorean theorem can be used to find the

length of the altitude. Refer to triangle WXY. The hypotenuse is 14 inches and one leg is 7 inches.

a2 + b2 = c2

72 + b2 = 142

49 + b2 = 196

b2 = 147

b = 147

b = 73

The length of the hypotenuse is 73.

75. Choice c is correct. The equation is quadratic. Set it equal to zero and factor.

2x2 − 2x − 12 = 0

2(x2 − x − 6) = 0

2(x − 3)(x + 2) = 0

Set each factor equal to zero and solve. (2 can be ignored because 2 ≠ 0).

x − 3 = 0 x + 2 = 0

x = 3 x = −2

The sum of the solutions is 3 + −2 = 1.

76. Choice j is correct. Use the identity sin2 A + cos2 A = 1.

sin2 A + (1

9

0

)2 = 1

sin2 A + 1

8

0

1

0

= 1

sin2 A = 1

1

0

9

0

sin A = 1

1

0

9

0  =

77. Choice d is correct. The triangle given is a 45-45-90 triangle so the sides are in the ratio 1:1:2.

Use a proportion to find x.

=

x = 10

2

x

1

19

10

14 in

14 in

Y

X 7 in W 7 in Z

–ACT MATH TEST PRACTICE–

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