Rob has six songs on his portable music player. How many different four-song orderings can Rob create?
Answer(s): D
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 always true. Which of the following statements is also true?
Answer(s): A
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."
In the diagram above, lines EF and GH are parallel, and line AB is perpendicular to lines EF and GH.What is the length of line AB?
Answer(s): C
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 is10/2, or 5. The length of the leg opposite the 60- degree angle, AB, is3times the length of the other leg, BC. Therefore, the length of AB is.
The expression is equivalent to
Factor the numerator and denominator and cancel like factors:
The point (2, 1) is the midpoint of a line with endpoints at (5, 3) and
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).
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