tailieunhanh - – ACT MATH TEST PRACTICE – 74. Choice f is correct. Since YW is an altitude in an equilateral

– ACT MATH TEST PRACTICE – 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. Y i 14 14 i n n X 7 in W 7 in Z 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=7 3 The length. | ---------------------------- ACT MATH TEST PRACTICE ------------------------------- 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. Y X 7 in W 7 in Z 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 V147 b 7V3 The length of the hypotenuse is 7V3. 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 q9f 2 1 sin2 A wo 1 sin2 A wo si A Hl sin A wo w 77. Choice d is correct. The triangle given is a 45-45-90 triangle so the sides are in the ratio 1 1 V2. Use a proportion to find x. V2 x I x VĨÕ 199 -------------------------------- ACT MATH TEST PRACTICE ------------------------------------------- 78. Choice f is correct. An ellipse is defined by an equation such as ị ệ 1- Therefore answer choices f and i are possibilities. Choice f is the correct choice because the square root of the number under the x is where the ellipse crosses the x-axis. Another way to check is to substitute the given ordered pairs into the equations to see which one works. 79. Choice b is correct. Notice that the y-intercept is 2 and the slope is -3. Thus the equation must be y - 3x 2. Answer choices b and c are possibilities. The shading will determine which one. Substitute 0 0 in for x and y. Since the shading is over the point 0 0 0 0 must be a solution to the inequality. 0 - 3 0 2 0 2 TRUE Therefore choice b is the correct answer. 80. Choice j is correct. The only constraint on this function is that the denominator must not be zero.