Jennifer bought a piece of wire for a crafts project that was
8

9
of a yard
long. she used
1

2
of a yard. how long was the wire she had left?

The base of a triangle exceeds the height by 9 inches. if the area is 180 square inches, find the length of the base and the height of the triangle.

Which of the following transformations will always produce a congruent figure?

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) = .