The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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

5\( \sqrt{48} \) - 6\( \sqrt{3} \)
5\( \sqrt{16 \times 3} \) - 6\( \sqrt{3} \)
5\( \sqrt{4^2 \times 3} \) - 6\( \sqrt{3} \)
(5)(4)\( \sqrt{3} \) - 6\( \sqrt{3} \)
20\( \sqrt{3} \) - 6\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them:

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

\( \left|y - 2\right| \) - 3 = -6
\( \left|y - 2\right| \) = -6 + 3
\( \left|y - 2\right| \) = -3

The value inside the absolute value brackets can be either positive or negative so (y - 2) must equal - 3 or --3 for \( \left|y - 2\right| \) to equal -3:

So, y = 5 or y = -1.

You have 9 out of the total of 450 raffle tickets sold so you have a (\( \frac{9}{450} \)) x 100 = \( \frac{9 \times 100}{450} \) = \( \frac{900}{450} \) = 2% chance to win the raffle.

44% of the water consumption is industrial use and 28% is personal use so (44% - 28%) = 16% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{16}{100} \) x 10,000 gallons = 1,600 gallons.