Find the equation of the line that contains the given point and is perpendicular to the given line . write the equation in slope intercept form. (4,1) y= -4x-7 show work

Astudent draws two parabolas both parabolas cross the x axis at (-4,0) and (6,0) the y intercept of the first parabolas 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

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

15 oranges weigh 3.75 kilograms (kg). if each orange weighs approximately the same, approximately how much does each orange weigh?