The ratio of the money that Jane, Lucy, Carl, Micheal got is 2:3:1:4. What is the ratio between Lucy and Micheal?

Which of the following quartic functions has x = –1 and x = –2 as its only two real zeroes?

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) = .

Polygon abcde is reflected to produce polygon a′b′c′d′e′. what is the equation for the line of reflection?