A test is worth 50 points. Multiple-choice questions are worth 1 point, and short-answer questions are worth 3 points. If the test has 20 questions, how
many multiple-choice questions are there?
A. m + s = 50
B. m + 2s = 20
C. m. s= 20
D. m + s = 20

The distributive property allows you to say that 3(x − 1) = 3x −

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) = .

25) 56(1) = 5b a. identity property of addition b. identity property of multiplication c. commutative property of multiplication d. commutative property of addition