What construction does the image below demonstrate?

the circumcenter of a regular hexagon

the incenter of a regular hexagon

a regular hexagon circumscribed about a circle

a regular hexagon inscribed in a circle

The correct answer is:

The circumcenter of a regular hexagon.

Explanation:

The incenter of a regular hexagon would be found by constructing the angle bisectors of each vertex and finding their intersection point. This would not involve circles.

We can see from the diagram that the hexagon is not circumscribed about the circle.

Construction of a regular hexagon inscribed in a circle involves creating 6 arcs the length of the radius of the circle; we would not draw this many circles.

This leaves the circumcenter of a regular hexagon as our answer.

2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

Ithink the answer is d. not sure but don’t answer it.