The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 40 and 48 have in common.

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

7c⁵ + 9c⁵
(7 + 9)c⁵
16c⁵

There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 17 people needing transportation leaving 17 - 16 = 1 who will have to find other transportation.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{50}{100} \) = \( \frac{50 x 15}{100} \) = \( \frac{750}{100} \) = 7 shots

The center makes 30% 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 = \( \frac{7}{\frac{30}{100}} \) = 7 x \( \frac{100}{30} \) = \( \frac{7 x 100}{30} \) = \( \frac{700}{30} \) = 23 shots

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

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

8\( \sqrt{3} \) x 7\( \sqrt{3} \)
(8 x 7)\( \sqrt{3 \times 3} \)
56\( \sqrt{9} \)

Now we need to simplify the radical:

56\( \sqrt{9} \)
56\( \sqrt{3^2} \)
(56)(3)
168