Triangle abc is similar to triangle def. using the image below, prove that lines bc and ef have the same slope. you must show all of your work to receive credit. triangle abc and def are shown. a is at negative 2, 1. b is at negative 2, 4. c is at 1, 1. d is at 4, 2. e is at 4, 4. f is at 6, 2.

You are designing a rectangular pet pen for your new baby puppy. you have 30 feet of fencing you would like the fencing to be 6 1/3 feet longer than the width

[15 points]find the least common multiple of the expressions: 1. 3x^2, 6x - 18 2. 5x, 5x(x +2) 3. x^2 - 9, x + 3 4. x^2 - 3x - 10, x + 2 explain if possible

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) = .