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

3\( \sqrt{3} \) x 3\( \sqrt{7} \)
(3 x 3)\( \sqrt{3 \times 7} \)
9\( \sqrt{21} \)

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

If 59% of the town's 42,000 voters cast ballots the number of votes cast is:

(\( \frac{59}{100} \)) x 42,000 = \( \frac{2,478,000}{100} \) = 24,780

The mayor got 62% of the votes cast which is:

(\( \frac{62}{100} \)) x 24,780 = \( \frac{1,536,360}{100} \) = 15,364 votes.

The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 the greatest factor 24 and 76 have in common.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{90mi}{30mph} \)
3 hours