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 30 meters so the equation becomes: 2w + 2h = 30.

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

2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h

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

w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5

Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m²

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

38,000 fans x \( \frac{2}{3} \) = \( \frac{76000}{3} \) = 25,333 fans.

To multiply terms with radicals, multiply the coefficients and radicands separately:

3\( \sqrt{7} \) x 2\( \sqrt{7} \)
(3 x 2)\( \sqrt{7 \times 7} \)
6\( \sqrt{49} \)

Now we need to simplify the radical:

6\( \sqrt{49} \)
6\( \sqrt{7^2} \)
(6)(7)
42

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.