Each week ms jones does estimates that he will spend $120 when he goes to the grocery store this week. he actually spends $94.what is the percent of changhe

The triangles in the diagram are congruent. if mzf = 40°, mza = 80°, and mzg = 60°, what is mzb?

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) = .

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