Which quadratic equation is equivalent to (x – 4)2 – (x – 4) – 6 = 0?

I hope choices must be given in the problem.

I am showing the method to find the equivalent equation of the above equation. You can match with your given choices.

First step is to expand the first term. So,

(x-4)² = (x - 4)(x - 4) Since a²= a*a

= x² - 4x - 4x + 4 * 4 By multiplying.

= x² -8x + 16 Combine the like terms.

So, (x - 4)² - (x -4) - 6

= x² - 8x + 16 - x + 4 - 6

= x² - 9x + 14 Combine the like terms.

So, equivalent equation of the above equation is x² - 9x + 14 = 0.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq