If 12 cubic units fill the bottom layer of a box, and the box holds 3 layers, what is the volume of the box?

F(x)= 1/x-4, g(x)=4x+1/x a. use composition to prove whether or not the functions are inverses of each other. b. express the domain of the compositions using interval notation.

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) .

Geometry in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.