For each expression, select all equivalent expressions from the list. (a) 4(5x-2)

1) 20x-2
2) 20x - 8
3) 9x-2
4) 4.5x-4.2

(b) 8y + 5y + 7y

1) 8y+12y
2) 12y-8y
3) 20y
4) 20+ y

Valentina is subtracting from . she finds the lcd to be 15y2. what is valentina's next step?

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) = .

Janice determined there were 10 possible outcomes when tossing two coins and spinning a spinner numbered 1 through 6. what is the correct number? what might have been janice's error?