A nearby pond has 5 frogs, and the population doubles every year. Which inequality, where t is the number of years, models when the population of frogs will be greater than 75?

Angela is buying a dress that is on sale for 20% off. if the original price of the dress is $40.00, how much money is angela saving on the dress? a. $0.80 b. $3.20 c. $32.00 d. $8.00

The measure of an angle is 117°. what is the measure of a supplementary angle?

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) = .