In exercise 27, (a) write an equation that represents the sum of the angle measures of the triangle and (b) use your equation and the question shown to find the value of x and y.

Solve for x by completing the square. 2x^2-4x+7=0

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) = .

There were 25 students who answered to a survey about sports. four-fifths of them like football. how many students like football?