First, solve for \( \left|a + 9\right| \):

\( \left|a + 9\right| \) - 2 = 8
\( \left|a + 9\right| \) = 8 + 2
\( \left|a + 9\right| \) = 10

The value inside the absolute value brackets can be either positive or negative so (a + 9) must equal + 10 or -10 for \( \left|a + 9\right| \) to equal 10:

So, a = -19 or a = 1.

By buying two shirts, Bob will save $20 x \( \frac{5}{100} \) = \( \frac{$20 x 5}{100} \) = \( \frac{$100}{100} \) = $1.00 on the second shirt.

So, his total cost will be
$20.00 + ($20.00 - $1.00)
$20.00 + $19.00
$39.00

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

2\( \sqrt{50} \) + 9\( \sqrt{2} \)
2\( \sqrt{25 \times 2} \) + 9\( \sqrt{2} \)
2\( \sqrt{5^2 \times 2} \) + 9\( \sqrt{2} \)
(2)(5)\( \sqrt{2} \) + 9\( \sqrt{2} \)
10\( \sqrt{2} \) + 9\( \sqrt{2} \)

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

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:

\( \frac{6 x 9}{5 x 9} \) - \( \frac{5 x 5}{9 x 5} \)

\( \frac{54}{45} \) - \( \frac{25}{45} \)

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

\( \frac{54 - 25}{45} \) = \( \frac{29}{45} \) = \(\frac{29}{45}\)

39% of the water consumption is industrial use and 12% is personal use so (39% - 12%) = 27% more water is used for industrial purposes. 15,000 gallons are consumed daily so industry consumes \( \frac{27}{100} \) x 15,000 gallons = 4,050 gallons.