To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{4z^7}{6z^4} \)
\( \frac{4}{6} \) z^{(7 - 4)}
\(\frac{2}{3}\)z³

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (3 + 5) ÷ 2 x 2 - 4²
P: 4 + (8) ÷ 2 x 2 - 4²
E: 4 + 8 ÷ 2 x 2 - 16
MD: 4 + \( \frac{8}{2} \) x 2 - 16
MD: 4 + \( \frac{16}{2} \) - 16
AS: \( \frac{8}{2} \) + \( \frac{16}{2} \) - 16
AS: \( \frac{24}{2} \) - 16
AS: \( \frac{24 - 32}{2} \)
\( \frac{-8}{2} \)
-4

By buying two shirts, Ezra will save $12 x \( \frac{25}{100} \) = \( \frac{$12 x 25}{100} \) = \( \frac{$300}{100} \) = $3.00 on the second shirt.

So, his total cost will be
$12.00 + ($12.00 - $3.00)
$12.00 + $9.00
$21.00

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 42 meters so the equation becomes: 2w + 2h = 42.

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

2w + 2h = 42
w + h = \( \frac{42}{2} \)
w + h = 21
w = 21 - h

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

w = 21 - 2w
3w = 21
w = \( \frac{21}{3} \)
w = 7

Since h = 2w that makes h = (2 x 7) = 14 and the area = h x w = 7 x 14 = 98 m²

First, solve for \( \left|x + 0\right| \):

\( \left|x + 0\right| \) + 2 = -2
\( \left|x + 0\right| \) = -2 - 2
\( \left|x + 0\right| \) = -4

The value inside the absolute value brackets can be either positive or negative so (x + 0) must equal - 4 or --4 for \( \left|x + 0\right| \) to equal -4:

So, x = 4 or x = -4.