The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 3 crews so there are \( \frac{6}{3} \) = 2 workers on a crew. 6 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 6 x 2 = 12 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 12 - 6 = 6 new staff for the busy season.

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

2 + (4 + 3) ÷ 3 x 5 - 3²
P: 2 + (7) ÷ 3 x 5 - 3²
E: 2 + 7 ÷ 3 x 5 - 9
MD: 2 + \( \frac{7}{3} \) x 5 - 9
MD: 2 + \( \frac{35}{3} \) - 9
AS: \( \frac{6}{3} \) + \( \frac{35}{3} \) - 9
AS: \( \frac{41}{3} \) - 9
AS: \( \frac{41 - 27}{3} \)
\( \frac{14}{3} \)
4\(\frac{2}{3}\)

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

3\( \sqrt{75} \) + 4\( \sqrt{3} \)
3\( \sqrt{25 \times 3} \) + 4\( \sqrt{3} \)
3\( \sqrt{5^2 \times 3} \) + 4\( \sqrt{3} \)
(3)(5)\( \sqrt{3} \) + 4\( \sqrt{3} \)
15\( \sqrt{3} \) + 4\( \sqrt{3} \)

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

If the tiger has consumed 120 pounds of food in 8 days that's \( \frac{120}{8} \) = 15 pounds of food per day. The tiger needs to consume 165 - 120 = 45 more pounds of food to reach 165 pounds total. At 15 pounds of food per day that's \( \frac{45}{15} \) = 3 more days.