Prove the divisibility of the following expressions: 10^6−5^7 is divisible by 59
81^7−27^9−9^13 by 45

Adecorative window is made up of a rectangle with semicircles at either end. the ratio of ad to ab is 3: 2 and ab is 30 inches. what is the ratio of the area of the rectangle to the combined area of the semicircles? possible answers: a. 2: 3 b. 3: 2 c. 6: π d. 9: π e. 30: π

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.

Given the numbers c = –3 and d = 4, which statement is true? a. |–c| = 3 and |–d| = –4 b. |–c| = 3 and –|d| = –4 c. –|c| = –4 and –|d| = 3 d. |–c| = 3 and –|d| = 4