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

\( \frac{12\sqrt{35}}{4\sqrt{5}} \)
\( \frac{12}{4} \) \( \sqrt{\frac{35}{5}} \)
3 \( \sqrt{7} \)

Diane scored 90% on the test meaning she earned 90% of the possible points on the test. There were 90 possible points on the test so she earned 90 x 0.9 = 81 points. Each question is worth 3 points so she got \( \frac{81}{3} \) = 27 questions right.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{35}{100} \) = \( \frac{35 x 25}{100} \) = \( \frac{875}{100} \) = 8 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 = \( \frac{8}{\frac{30}{100}} \) = 8 x \( \frac{100}{30} \) = \( \frac{8 x 100}{30} \) = \( \frac{800}{30} \) = 27 shots

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

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

The equation for this sequence is:

a_n = a_n-1 + 8

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 8
a₆ = 33 + 8
a₆ = 41