In the parallelogram shown, AE = p − 8, CE = 2p − 58, and DE = p + 15. Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E.

What is the length of line segment EB?

42 units
50 units
65 units
73 units

the third picture

step-by-step explanation:

you need to rotate this triangle about the origin 270 degrees clockwise to create the full square.

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.