Sides 4.6 km and 8930 m (Give the hypotenuse in kilometres.)

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth

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

Which answer choice listed below is thewhich answer choice listed below is the inverse function of ƒ(x) = x-3 x+3 , x ≠ -3? a) ƒ-1(x) = 3 ( x+1 x-1 ), x ≠ 1 b) ƒ-1(x) = -3 ( x+1 x-1 ), x ≠ 1 c) ƒ-1(x) = 3 ( x-1 x+1 ), x ≠ -1 d) ƒ-1(x) = -3 ( x-1 x+1 ), x ≠ -1inverse function of ƒ(x) = x-3 x+3 , x ≠ -3?