The equation for this sequence is:

a_n = a_n-1 + 7

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 7
a₆ = 29 + 7
a₆ = 36

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 18 meters so the equation becomes: 2w + 2h = 18.

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

2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h

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

w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3

Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m²

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

4 + (5 + 2) ÷ 5 x 3 - 4²
P: 4 + (7) ÷ 5 x 3 - 4²
E: 4 + 7 ÷ 5 x 3 - 16
MD: 4 + \( \frac{7}{5} \) x 3 - 16
MD: 4 + \( \frac{21}{5} \) - 16
AS: \( \frac{20}{5} \) + \( \frac{21}{5} \) - 16
AS: \( \frac{41}{5} \) - 16
AS: \( \frac{41 - 80}{5} \)
\( \frac{-39}{5} \)
-7\(\frac{4}{5}\)

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

By buying two shirts, Alex will save $22 x \( \frac{15}{100} \) = \( \frac{$22 x 15}{100} \) = \( \frac{$330}{100} \) = $3.30 on the second shirt.

So, his total cost will be
$22.00 + ($22.00 - $3.30)
$22.00 + $18.70
$40.70