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

5 + (4 + 2) ÷ 3 x 5 - 3²
P: 5 + (6) ÷ 3 x 5 - 3²
E: 5 + 6 ÷ 3 x 5 - 9
MD: 5 + \( \frac{6}{3} \) x 5 - 9
MD: 5 + \( \frac{30}{3} \) - 9
AS: \( \frac{15}{3} \) + \( \frac{30}{3} \) - 9
AS: \( \frac{45}{3} \) - 9
AS: \( \frac{45 - 27}{3} \)
\( \frac{18}{3} \)
6

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

5\( \sqrt{112} \) + 7\( \sqrt{7} \)
5\( \sqrt{16 \times 7} \) + 7\( \sqrt{7} \)
5\( \sqrt{4^2 \times 7} \) + 7\( \sqrt{7} \)
(5)(4)\( \sqrt{7} \) + 7\( \sqrt{7} \)
20\( \sqrt{7} \) + 7\( \sqrt{7} \)

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

The greatest common factor (GCF) is the greatest factor that divides two integers.

If a single cook can bake 4 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 4 x 2 = 8 large cakes during that time. 31 large cakes are needed for the party so \( \frac{31}{8} \) = 3\(\frac{7}{8}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 16 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 16 x 2 = 32 small cakes during that time. 470 small cakes are needed for the party so \( \frac{470}{32} \) = 14\(\frac{11}{16}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 15 = 19 cooks.

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.