To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-4y³ + 9y³
(-4 + 9)y³
5y³

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 48 meters so the equation becomes: 2w + 2h = 48.

Putting these two equations together and solving for width (w):

2w + 2h = 48
w + h = \( \frac{48}{2} \)
w + h = 24
w = 24 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 24 - 2w
3w = 24
w = \( \frac{24}{3} \)
w = 8

Since h = 2w that makes h = (2 x 8) = 16 and the area = h x w = 8 x 16 = 128 m²

First, solve for \( \left|z - 3\right| \):

\( \left|z - 3\right| \) + 9 = -8
\( \left|z - 3\right| \) = -8 - 9
\( \left|z - 3\right| \) = -17

The value inside the absolute value brackets can be either positive or negative so (z - 3) must equal - 17 or --17 for \( \left|z - 3\right| \) to equal -17:

So, z = 20 or z = -14.

To simplify a radical, factor out the perfect squares:

\( \sqrt{175} \)
\( \sqrt{25 \times 7} \)
\( \sqrt{5^2 \times 7} \)
5\( \sqrt{7} \)

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.