The equation for the circle is: x2+y2+16x−24y+159=0 . what is the center of the circle?

x^2 + y^2 +16x - 24y +159 = 0

Rearrange:

x^2 +16x + y^2 - 24y = -159

(16x/2)^2 = 64

(-24y/2)^2 = 144

x^2 + 16x + 64 + y^2 - 24y + 144 = -159 + 144 + 64

x^2 + 16x + 64 + y^2 - 24y + 144 = 49

Reduce the trinomials to binomials:

(x + 8)^2 + (y - 12)^2 = 49

Thus the center point is (-8, 12) and the radius is 7

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: