In parallelogram abcd , diagonals ac and bd intersect at point e, ae=2x2−3x , and ce=x2+4 . what is ac ?

Given that ABCD is a parallelogram.

And diagonals AC and BD intersect at E point.

Therefore, AE = CE , because the diagonals of a parallelogram bisect each other.

Given AE=2x^2−3x , and CE=x^2+4.

Putting them equal.

Factoring quadratic

(x-4)(x+1)=0

.

We can't take a negative value.

Therefore plugging x=4 in AE=2x^2−3x, we get

AE = 2(4)^2 - 3(4) = 32 - 12 = 20.

AC= 2 × 20 = 40.

Therefore, AC = 40 units.

Best answer that i found on yahoo ok   set :   x= length of 2nd piece in cm  x- 3= length of 1st piece in cm  x-4= length of 3rd piece in cm  then since you know they all came from the 20 cm ribbon you add them together and set them equal to 20x+ x-3 +x-4 = 20  3x - 7= 20  3x= 27  x= 9  the shortest piece is the third piece which is x- 4  x-4  9-4 = 5  the length of the smallest piece is 5 cm.  the other lengths are  9 cm  6 cm