Mr. hawk cuts a square matte board that is 15 1/2 inches on each side. he wants to cut an
equal border that is 2 3/4 inches wide. what will be the dimensions of the square hole?

Explain step-by-step how to simplify -5(2x – 3y + 6z – 10).

(50 points) drag each description to the correct location on the table. each description can be used more than once. some systems of equations and their graphs are given in the table. for each system, place the description(s) in the box that correctly describe the type of system shown. :

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0