the graph of 2x + 3y = 8 is shown on the grid. which ordered pair is in the solution set of 2x + 3y = 8?

The table shows a pattern of exponents. what is the pattern as the exponents decrease?

Find the pattern and use it to list the nth term in the sequence. 6, 12, 20, 30, 42, 56, the nth term of the sequence is

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) = .