Rebecca bought x pairs of socks and receive a 20% discount. each pair of socks cost $4.99.her total cost without tax $55.08, which included an 8% tax. what was the price of each meal, not including tax?

Sam makes his sales calls according to a pattern. he travels either north or south depending on the calendar. some of his past trips were as follows: on february 17, april 24, june 10, september 19, and november 3 he drove north. on february 28, may 25, august 22, november 20, and december 18, he drove south. describe sams' pattern. in which direction will sam drive on oct4 and oct 24?

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) = .

Given: m zade = 60° and m2cdf = (3x + 15) prove: x = 15