The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

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

4\( \sqrt{12} \) - 2\( \sqrt{3} \)
4\( \sqrt{4 \times 3} \) - 2\( \sqrt{3} \)
4\( \sqrt{2^2 \times 3} \) - 2\( \sqrt{3} \)
(4)(2)\( \sqrt{3} \) - 2\( \sqrt{3} \)
8\( \sqrt{3} \) - 2\( \sqrt{3} \)

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

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

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 18 meters so the equation becomes: 2w + 2h = 18.

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

2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h

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

w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3

Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m²

The factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48] and the factors of 16 are [1, 2, 4, 8, 16]. They share 5 factors [1, 2, 4, 8, 16] making 16 the greatest factor 48 and 16 have in common.