Test Prep SAT2-MATHEMATICS - Questions & Answers

Cross multiply and solve for x:

Explanation:
Point B is the same distance from the y-axis as point A, so the x-coordinate of point B is the same as the x- coordinate of point A: -1. Point B is the same distance from the x-axis as point C, so the y-coordinate of point B is the same as the y-coordinate of point C: 4. The coordinates of point B are (-1,4).

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. The slope of the line given is
2/1.

The negative reciprocal of 2/1 is 1/2. Every line with a slope of -3/4 is perpendicular to the given line; y= 3/2x + i5 is perpendicular to y = 2/3x - i.

9. 9 is equal to 75% of s. If 0.75s = 9, then s =
12. 50% of s = (0.50)(12) =
6.

Explanation:

30 men X 42 square feet = 1,260 square feet of space; 1,260 square feet ÷ 35 men = 36 square feet; 42 - 36 = 6, so each man will have 6 less square feet of space.

The order of the four songs is important. The orderings A, B, C, D and A, C, B, D contain the same four songs, but in different orders. Both orderings must be counted. The number of six-choose-four orderings is equal to (6)(5)(4)(3)= 360.

The statement "Raphael runs every Sunday" is equivalent to "If it is Sunday, Raphael runs." The contrapositive of a true statement is also true. The contrapositive of "If it is Sunday, Raphael runs" is "If Raphael does not run, it is not Sunday."

Line AB is perpendicular to line BC, which makes triangle ABC a right triangle. Angles DAF and DCH are alternating angles -- angles made by a pair of parallel lines cut by a transversal. Angle DAF angle DCH, therefore, angle DCH = 120 degrees. Angles DCH and ACB form a line. There are 180 degrees in a line, so the measure of angle ACB = 180 ?120 = 60 degrees. Triangle ABC is a 30-60-90 right triangle, which means that the length of the hypotenuse, AC, is equal to twice the length of the leg opposite the 30-degree angle, BC. Therefore, the length of BC is 10/2, or 5. The length of the leg opposite the 60-degree angle, AB, is 3 times the length of the other leg, BC. Therefore, the length of AB is.

The midpoint of a line is equal to the average x-coordinates and the average y-coordinates of the line's endpoints:

The other endpoint of this line is at (9,-1).

The number of roses, 5x, plus the number of tulips, 6x, is equal to 242 total flowers: 5x + 6x = 242, 11x = 242, x = 22. There are 5(22) = 110 roses and 6(22) = 132 tulips in Lindsay's garden.