w varies directly as r cubed and inversely as s. If w = 24 when r = 4 and s = 8, find r when w = 81 and s = 27.

Mary beth used the mapping rule to find the coordinates of a point that had been rotated 90° counterclockwise around the origin. examine the steps to determine whether she made an error. m (3, –6) is rotated 90° counterclockwise. (x, y) → (–y, x) 1. switch the x- and y-coordinates: (6, –3) 2. multiply the new x-coordinate by –1: (6(–1), –3) 3. simplify: (–6, –3) .

Rewrite the following quadratic functions in intercept or factored form. show your work. y = 9 + 12x + 4x^2

In δabc, m∠acb = 90°, cd ⊥ ab and m∠acd = 45°. find: a find cd, if bc = 3 in