9514 1404 393
Answer:
x = 16
Step-by-step explanation:
Corresponding sides are proportional.
BE/CD = AE/AD
20/(3x+8) = (x-1)/(x-1+27)
20(x+26) = (3x+8)(x -1)
In standard form, this is ...
3x^2 -15x -528 = 0
x^2 -5x -176 = 0 . . . . . . divide by 3
(x -16)(x +11) = 0 . . . . . . . factor
x = 16
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This is the positive value that makes the product zero. x=-11 will also make the product 0, but gives negative segment lengths in the geometry. It is an extraneous solution.
Answer:
2
Step-by-step explanation:
-13 x 2 = -26
-4 x 2 = -8
14 x 2 = 28
-26 + -8 + 28 +-9 = -15
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We have two points describing the diameter of a circumference, these are:

Recall that the equation for the standard form of a circle is:

Where (h,k) is the coordinate of the center of the circle, to find this coordinate, we find the midpoint of the diameter, that is, the midpoint between points A and B.
For this we use the following equation:

Now, we replace and solve:

The center of the circle is (-8,-7), so:

On the other hand, we must find the radius of the circle, remember that the radius of a circle goes from the center of the circumference to a point on its arc, for this we use the following equation:

In this case, we will solve the delta with the center coordinate and the B coordinate.

Therefore, the equation for the standard form of a circle is:

In conclusion, the equation is the following: