Timothy has the following ingredients to mix together to make packages of fruit snacks: 1/ 1/12
pounds of apricots, 3/ 1/2 pounds of grapes, and 2 pounds of raspberries.
How many 1/4-pound packages can he make?

Marya wants to factor the polynomial 36x^3 -22x^2 - 144x. which term can she add to the polynomial that would not change its grestest common factor? check all that apply

James adds two numbers a + b. sally adds the same two numbers but reverse the order b + a what property of addition assures us that james and sally will get the same sum

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) = .