Write each phrase as a mathematical expression the sum of 6 less than a number and 3​

What is the perimeter of a rectangular building that is 80 feet wide and 140 feet deep?

What is the range of the function? f(x)=-2|x+1|? a. all real numbers. b. all real numbers less than or equal to 0. c. all real numbers less than or equal to 1. d. all real numbers greater than or equal to 1

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) = .