Given the equation 2x2 - 5x + 7 = 0. find the discriminant. describe the roots and explain your reasoning.

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) = .

Suppose you are an avid reader and are looking to save money on the cost of books instead of paying about $20 for each book, you decide to look into purchasing a kindle for $120 you can purchase e-books for about $5 each 1. find the slope-intercept equation for the cost of the hard copy of books using x to represent the number of books 2. find the slope-intercept equation for the cost of the kindle with cost of e-books using x to represent the number of books

Three numbers x, y, and z are in the ratio 2: 7: 8. if 12 is subtracted from y, then three numbers form a geometric sequence (in the order x, y–12, z). find x, y, and z. there are 2 sets.