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

3\( \sqrt{75} \) + 9\( \sqrt{3} \)
3\( \sqrt{25 \times 3} \) + 9\( \sqrt{3} \)
3\( \sqrt{5^2 \times 3} \) + 9\( \sqrt{3} \)
(3)(5)\( \sqrt{3} \) + 9\( \sqrt{3} \)
15\( \sqrt{3} \) + 9\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (3 + 5) ÷ 2 x 3 - 3²
P: 4 + (8) ÷ 2 x 3 - 3²
E: 4 + 8 ÷ 2 x 3 - 9
MD: 4 + \( \frac{8}{2} \) x 3 - 9
MD: 4 + \( \frac{24}{2} \) - 9
AS: \( \frac{8}{2} \) + \( \frac{24}{2} \) - 9
AS: \( \frac{32}{2} \) - 9
AS: \( \frac{32 - 18}{2} \)
\( \frac{14}{2} \)
7

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

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 35mph \times 2h \)
70 miles