To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{72} \) = \( \frac{\frac{28}{4}}{\frac{72}{4}} \) = \( \frac{7}{18} \)

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

6\( \sqrt{80} \) + 7\( \sqrt{5} \)
6\( \sqrt{16 \times 5} \) + 7\( \sqrt{5} \)
6\( \sqrt{4^2 \times 5} \) + 7\( \sqrt{5} \)
(6)(4)\( \sqrt{5} \) + 7\( \sqrt{5} \)
24\( \sqrt{5} \) + 7\( \sqrt{5} \)

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

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 4 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 4 x 3 = 12 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 12 - 6 = 6 new staff for the busy season.

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 factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 the greatest factor 28 and 60 have in common.