Answer:
x = 2
distributive property of equality, subtraction property of equality, and division property of equality
Step-by-step explanation:
(Proof is in parenthesis)
4(x + 3) = 20 (Given)
4x + 12 = 20 (distributive property of equality)
4x = 8 (subtraction property of equality)
x = 2 (division property of equality)
With this problem, you should first look at the equation for the area of a trapezoid. That is A = (1/2)(B1 + B2)*H. We know what A, B1, and B2 are so you just need to solve for height. So, based on the equation:
![3x^{3} -16 x^{2} + 31x-20 = (1/2)(x+5+ x^{2} -5x)*h](https://tex.z-dn.net/?f=%203x%5E%7B3%7D%20-16%20x%5E%7B2%7D%20%2B%2031x-20%20%3D%20%281%2F2%29%28x%2B5%2B%20x%5E%7B2%7D%20-5x%29%2Ah)
Next, you would have:
![6x^{3} -32x^{2} +62x-40=(x^{2}-4x+5)*h](https://tex.z-dn.net/?f=6x%5E%7B3%7D%20-32x%5E%7B2%7D%20%2B62x-40%3D%28x%5E%7B2%7D-4x%2B5%29%2Ah%20)
Next solve for h by dividing the polynomials like so:
![h = (6 x^{3}-32 x^{2} +62x-40)/( x^{2} -4x+5)](https://tex.z-dn.net/?f=h%20%3D%20%286%20x%5E%7B3%7D-32%20x%5E%7B2%7D%20%2B62x-40%29%2F%28%20x%5E%7B2%7D%20-4x%2B5%29%20)
Using long division you get:
The commutative property, because you are simply moving the terms around without actually changing the overall value.