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Danielle has $127.02 in her account before making any transactions. over the course of a week, danielle makes the following transactions: transaction debit ($) credit ($) birthday check 75.00 night out 66.14 garage sale proceeds 121.58 charitable donation 42.25 doctor’s appointment 115.30 at the end of the week, how much money is in danielle’s account? a. $99.91 b. $27.11 c. $184.41 d. $142.16 select the best answer from the choices provided a b c d

Which system of linear inequalities is represented by the graph? x-3y > 6 and y? 2x + 4 x + 3y > 6 and y? 2x - 4 x - 3y > 6 and y? 2 - 4 x + 3y > 6 and y > 2x + 4 no be 2 -1.1 1 2 3 4 5 submit save and exit next mark this and retum be

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) = .