Mrs. Gonzales spent $58 on groceries. She had $13 left after paying for the food.
How much money did she have before she
bought the groceries?

Math each whole number with a rational,exponential expression

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) = .

Formulate alisha has a number in mind. if she adds three to her number the result is less than five. use this information to write and solve an inequality about alisha's number. then graph the solution set.