16x^2 + 16x + 4 = 4(1 + 4x + 4x^2) = 4(2x + 1)^2

To find the length of the hypotenuse in a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

Given that the lengths of the legs are 5 and abs(2) (which is also 2), we can substitute these values into the Pythagorean theorem:

Hypotenuse^2 = Leg1^2 + Leg2^2

Hypotenuse^2 = 5^2 + 2^2
Hypotenuse^2 = 25 + 4
Hypotenuse^2 = 29

To find the length of the hypotenuse, we need to take the square root of both sides:

Hypotenuse = sqrt(29)

Using a calculator, we find that the square root of 29 is approximately 5.385.

Therefore, the length of the hypotenuse in the right triangle with legs 5 and abs(2) is approximately 5.385 units.

To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is ((x1 + x2) / 2, (y1 + y2) / 2).

Let's apply the formula to the given endpoints (-3, 8) and (7, 4):

Center = ((-3 + 7) / 2, (8 + 4) / 2)
Center = (4 / 2, 12 / 2)
Center = (2, 6)

So, the center of the circle is at the point (2, 6).

y(y + 4) - y^2 = 6 is a quadratic equation. TRUE