Solve this application problem using a system of equations: quick mart recently sold a bag of
oranges for $0.76 and a bag of grapes for $3.68. at the end of that day, so bags of oranges and
grapes were sold for a total of $128.52. how many bags of each were sold?

Find the height of a square pyramid that has the volume of 32 ft.³ and a base lengthof 4 feet

Pranza plotted point a in the coordinate plane below.

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) = .