with same slope and different y-intercepts are parallel and never intersect, so when t and v
are not equal, you’ll get two parallel lines, so the answer must be (D).
42 . F Because you are finding the side opposite the 34° angle and are given the hypotenuse, use
SOHCAHTOA or the sine function, eliminating (G), (H), and (K). Since sin 34° = ,
you solve for the distance by multiplying 40, not dividing and thus eliminating (J).
43 . D Because 6th graders comprise 22% of the total number of students, 100 − 22 = 78% of the
students are not in 6th grade. The odds is the ratio of 22:78, which reduces to 11:39. Choice
(E) incorrectly calculates the ratio of 6th graders to the total number of students. Choices
(A), (B), and (C) are approximations of 22%; however, not as accurate as (D).
44 . H Lines of symmetry cut the figure into two mirror images.
Since each of the divisions above creates two mirror images, the figure has four lines of
symmetry.
45 . D Because a square has right angles, you can determine the diagonal length using the
Pythagorean theorem: 3^2 + 3^2 = d^2 . The diagonal is 3 meters ≈ 4.2 meters. Choices (A)
and (C) take the square root of 6 and 12, rather than 18. Choices (B) and (E) incorrectly
calculate the diagonal without the Pythagorean theorem.
46 . G Because the office wall is shorter, you can eliminate (J) and (K) immediately. Calculate 20%
of the length of the current mosaic: 0.20 × 3 meters = 0.6 meters. Since the length is 20%
shorter, subtract 0.6 meters from the original 3 meters. Choice (F) is a partial answer, but it
does not give the actual length of the office wall. Choice (H) subtracts 0.2 rather than 20%.
47 . B Because DG bisects HDE, HDG = EDG = 68°. Since DE || FG, FGD = EDG = 68°.
Since HG bisects FGD, DGH = 34° and DHG + HDG + DGH = 180°, thus =
DHG = 78°.
