The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 12 meters so the equation becomes: 2w + 2h = 12.

Putting these two equations together and solving for width (w):

2w + 2h = 12
w + h = \( \frac{12}{2} \)
w + h = 6
w = 6 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 6 - 2w
3w = 6
w = \( \frac{6}{3} \)
w = 2

Since h = 2w that makes h = (2 x 2) = 4 and the area = h x w = 2 x 4 = 8 m²

You have 14 out of the total of 350 raffle tickets sold so you have a (\( \frac{14}{350} \)) x 100 = \( \frac{14 \times 100}{350} \) = \( \frac{1400}{350} \) = 4% chance to win the raffle.

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

6\( \sqrt{8} \) - 7\( \sqrt{2} \)
6\( \sqrt{4 \times 2} \) - 7\( \sqrt{2} \)
6\( \sqrt{2^2 \times 2} \) - 7\( \sqrt{2} \)
(6)(2)\( \sqrt{2} \) - 7\( \sqrt{2} \)
12\( \sqrt{2} \) - 7\( \sqrt{2} \)

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

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 divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{56\sqrt{12}}{8\sqrt{3}} \)
\( \frac{56}{8} \) \( \sqrt{\frac{12}{3}} \)
7 \( \sqrt{4} \)