To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-6b⁵ - 7b⁵
(-6 - 7)b⁵
-13b⁵

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{60}{100} \) = \( \frac{60 x 10}{100} \) = \( \frac{600}{100} \) = 6 shots

The center makes 50% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{6}{\frac{50}{100}} \) = 6 x \( \frac{100}{50} \) = \( \frac{6 x 100}{50} \) = \( \frac{600}{50} \) = 12 shots

to make the same number of shots as the guard and thus score the same number of points.

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 36 meters so the equation becomes: 2w + 2h = 36.

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

2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h

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

w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6

Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m²

Betty scored 80% on the test meaning she earned 80% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.8 = 96 points. Each question is worth 3 points so she got \( \frac{96}{3} \) = 32 questions right.

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

8\( \sqrt{3} \) x 3\( \sqrt{2} \)
(8 x 3)\( \sqrt{3 \times 2} \)
24\( \sqrt{6} \)