The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 have in common.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{45}{14} \) = 3\(\frac{3}{14}\)

So, it will take 3 full vans and one partially full van to transport the entire team making a total of 4 vans.

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

There are 2 3-passenger taxis available so that's 2 x 3 = 6 total seats. There are 8 people needing transportation leaving 8 - 6 = 2 who will have to find other transportation.

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

7\( \sqrt{175} \) - 8\( \sqrt{7} \)
7\( \sqrt{25 \times 7} \) - 8\( \sqrt{7} \)
7\( \sqrt{5^2 \times 7} \) - 8\( \sqrt{7} \)
(7)(5)\( \sqrt{7} \) - 8\( \sqrt{7} \)
35\( \sqrt{7} \) - 8\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them: