Look at Mia’s work. 83 + n = 110

83 + 83 + n = 110 + 83

n = 193

What was Mia’s error?

1. Mia’s work is correct.
2. Mia made an addition error when adding 110 and 83.
3. Mia only needed to add 83 to 110.
4. Mia should have subtracted 83 from both sides of the equation.

Arecipe uses 2 cups of sugar to make 32 brownies. how many cups of sugar are needed to make 72 brownies?

Prove that quadrilateral is a rhombus.

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) = .