43 . D The quadratic equation is x = . In this equation, a = 2, b = 3, and c = −10.
Start by looking at the −b. Since b = 3, (A) and (B) can be eliminated. Choice (E) can be
eliminated because it incorrectly suggests that c = 10. Of the remaining choices, only (D)
correctly puts a subtraction sign in the middle of the radical.
44 . K The midpoint formula is . Start with the x-coordinate, −2 = , and
solve for x 2 . Multiply both sides by 2: −4 = −7 + x 2 , then add −7 to both sides to get x 2 = 3.
Eliminate (F), (G), and (H), all of which have the incorrect x-coordinate. Do the same with
the y-coordinate: 5 = . Multiply by 2, 10 = 3 + y 2 , then subtract 3, y 2 = 7. Choice (K),
(3,7) is correct.
45 . A Since the unknown side is adjacent to the 55° angle, and the height of the lamppost is known,
use tan 55° = to get tan 55° = . Multiply both sides by x, x tan 55° = 4, then
divide both sides by tan 55°, x = .
46 . J Because the line shown crosses the y-axis above the origin, the y-intercept, or b in the slope-
intercept equation y = mx + b must be positive. Choice (K) can be eliminated because it
gives a negative value for b. Because the line shown slopes down, the slope, or m, must be
negative. Choices (F) and (G) can be eliminated because they have positive values for m.
Because m = and the line crosses the x-axis at about 1, a slope of −2 is appropriate,
and (J) is correct.
47 . C Divide the quadrilateral into a rectangle and a triangle by drawing a horizontal line from
point D across to the point (2,4). To find the dimensions of the rectangle, count the number of
units from point A to point B, which is 5, and the number of units from point A to point D,
which is 7. The area of the rectangle is A = l × w = 5 × 7 = 35. Add to that the area of the
