To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-6y⁶ + 7y⁶
(-6 + 7)y⁶
y⁶

First, solve for \( \left|a + 4\right| \):

\( \left|a + 4\right| \) + 2 = -1
\( \left|a + 4\right| \) = -1 - 2
\( \left|a + 4\right| \) = -3

The value inside the absolute value brackets can be either positive or negative so (a + 4) must equal - 3 or --3 for \( \left|a + 4\right| \) to equal -3:

So, a = -1 or a = -7.

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

31,000 fans x \( \frac{3}{4} \) = \( \frac{93000}{4} \) = 23,250 fans.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{37}{14} \) = 2\(\frac{9}{14}\)

So, it will take 2 full vans and one partially full van to transport the entire team making a total of 3 vans.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 9}{5 x 9} \) - \( \frac{5 x 5}{9 x 5} \)

\( \frac{27}{45} \) - \( \frac{25}{45} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{27 - 25}{45} \) = \( \frac{2}{45} \) = \(\frac{2}{45}\)