When eight is added to three times a number the result is sixty-eight. Write and solve an algebraic equation. Show all work.

The rumpart family is building a new room onto their house. the width of the new room will be 16 feet. the length of the room will be 4% greater than the width. write an expression to find the length of the new room. what will be the area of this new room?

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) = .

The marked price of an article is 25% above its selling price and the cost price is 30% less than its marked price . find the discount percent and gain percent. only a brainlest can solve it i will mark you brainlest