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Twice the sum of a number and 4 is equal to three times the difference of the number and 7. find the number.

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) = .

Tessa bought stock in a restaurant for $253.00. her stock is now worth $333.96. what is the percentage increase of the value of tessa's stock? a.) 81% b.) 32% c.) 24% d.) 76%