Shannon's rectangular countertop is 33 feet wide. It is 33 times as long as it is wide. Find the length and area of Shannon's countertop. Use paper to show your work. Enter your answers in the boxes.

What is the vertex form of f(x) = x2 + 6x + 3

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Data from 2005 for various age groups show that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $105. also, for workers of ages 25 to 54 the median weekly income for whites was $676 and for blacks was $527. (a) let w represent the median weekly income for whites and b the median weekly income for blacks, and write the equation of the line that gives b as a linear function of w. b = (b) when the median weekly income for whites is $760, what does the equation in (a) predict for the median weekly income for blacks?