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

To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{10 \text{ gallons}}{2 \text{ gallons}} \) = 5

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:

\( \frac{3a^8}{4a^3} \)
\( \frac{3}{4} \) a^{(8 - 3)}
\(\frac{3}{4}\)a⁵

The equation for this sequence is:

a_n = a_n-1 + 4

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 + 4
a₆ = 17 + 4
a₆ = 21

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

5 + (5 + 5) ÷ 5 x 4 - 5²
P: 5 + (10) ÷ 5 x 4 - 5²
E: 5 + 10 ÷ 5 x 4 - 25
MD: 5 + \( \frac{10}{5} \) x 4 - 25
MD: 5 + \( \frac{40}{5} \) - 25
AS: \( \frac{25}{5} \) + \( \frac{40}{5} \) - 25
AS: \( \frac{65}{5} \) - 25
AS: \( \frac{65 - 125}{5} \)
\( \frac{-60}{5} \)
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