The associative and commutative properties can be applied only to problems with addition. Juan had to change the subtraction to addition by adding the additive inverse.

Terri makes a quilt using three sizes of fabric squares the side lenght of each fabric square is the square root of the area

When using the linear combination metho e linear combination method to solve a system of linear equations, the four options are:

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) = .