The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,000
i = 0.06 x $1,000
i = $60

First, solve for \( \left|c - 7\right| \):

\( \left|c - 7\right| \) + 4 = -8
\( \left|c - 7\right| \) = -8 - 4
\( \left|c - 7\right| \) = -12

The value inside the absolute value brackets can be either positive or negative so (c - 7) must equal - 12 or --12 for \( \left|c - 7\right| \) to equal -12:

So, c = 19 or c = -5.

A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

31,000 fans x \( \frac{4}{5} \) = \( \frac{124000}{5} \) = 24,800 fans.

If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 22 large cakes are needed for the party so \( \frac{22}{16} \) = 1\(\frac{3}{8}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 13 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 13 x 4 = 52 small cakes during that time. 320 small cakes are needed for the party so \( \frac{320}{52} \) = 6\(\frac{2}{13}\) 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 2 + 7 = 9 cooks.

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:

-2b² - 3b²
(-2 - 3)b²
-5b²