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

\( \frac{15\sqrt{49}}{3\sqrt{7}} \)
\( \frac{15}{3} \) \( \sqrt{\frac{49}{7}} \)
5 \( \sqrt{7} \)

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.3km + 20.8km + 15.9km
total distance = 37km

By buying two shirts, Frank will save $45 x \( \frac{5}{100} \) = \( \frac{$45 x 5}{100} \) = \( \frac{$225}{100} \) = $2.25 on the second shirt.

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 24 meters so the equation becomes: 2w + 2h = 24.

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

2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h

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

w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4

Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m²

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

7z² - 9z²
(7 - 9)z²
-2z²