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

9\( \sqrt{75} \) - 4\( \sqrt{3} \)
9\( \sqrt{25 \times 3} \) - 4\( \sqrt{3} \)
9\( \sqrt{5^2 \times 3} \) - 4\( \sqrt{3} \)
(9)(5)\( \sqrt{3} \) - 4\( \sqrt{3} \)
45\( \sqrt{3} \) - 4\( \sqrt{3} \)

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

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

\( \frac{30\sqrt{6}}{6\sqrt{3}} \)
\( \frac{30}{6} \) \( \sqrt{\frac{6}{3}} \)
5 \( \sqrt{2} \)

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

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

6,068,000 in scientific notation is 6.068 x 10⁶

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{7} \) ÷ \( \frac{1}{7} \) = \( \frac{1}{7} \) x \( \frac{7}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{7} \) x \( \frac{7}{1} \) = \( \frac{1 x 7}{7 x 1} \) = \( \frac{7}{7} \) = 1