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 6 meters so the equation becomes: 2w + 2h = 6.

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

2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h

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

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

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 + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

To add these radicals together their radicands must be the same:

5\( \sqrt{12} \) + 8\( \sqrt{3} \)
5\( \sqrt{4 \times 3} \) + 8\( \sqrt{3} \)
5\( \sqrt{2^2 \times 3} \) + 8\( \sqrt{3} \)
(5)(2)\( \sqrt{3} \) + 8\( \sqrt{3} \)
10\( \sqrt{3} \) + 8\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

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

9y⁷ - 6y⁷
(9 - 6)y⁷
3y⁷

The greatest common factor (GCF) is the greatest factor that divides two integers.