First, solve for \( \left|y + 2\right| \):

\( \left|y + 2\right| \) - 6 = -6
\( \left|y + 2\right| \) = -6 + 6
\( \left|y + 2\right| \) = 0

The value inside the absolute value brackets can be either positive or negative so (y + 2) must equal + 0 or -0 for \( \left|y + 2\right| \) to equal 0:

So, y = -2 or y = -2.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

4,713,000 in scientific notation is 4.713 x 10⁶

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{75mi}{15mph} \)
5 hours

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. 28 large cakes are needed for the party so \( \frac{28}{8} \) = 3\(\frac{1}{2}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 19 x 2 = 38 small cakes during that time. 430 small cakes are needed for the party so \( \frac{430}{38} \) = 11\(\frac{6}{19}\) 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 + 12 = 16 cooks.