If a polynomial has three terms, x2 + 12x + 36, which factoring method can be considered?
a) perfect-square trinomial
b) difference of squares
c) sum of cubes
d) difference of cubes

Aprobability experiment is conducted in which the sample space of the experiment is s={7,8,9,10,11,12,13,14,15,16,17,18 }, event f={7,8,9,10,11,12}, and event g={11,12,13,14}. assume that each outcome is equally likely. list the outcomes in f or g. find p(f or g) by counting the number of outcomes in f or g. determine p(f or g) using the general addition rule.

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

Given: lkm jkm, clmk prove: alkmajkm jmk. choose the word that completes the sentence correctly. proof: lkm jkm and lmk * umk are given. km km by the property of congruence. equivalence symmetric reflexive transitive