If the tiger has consumed 60 pounds of food in 6 days that's \( \frac{60}{6} \) = 10 pounds of food per day. The tiger needs to consume 100 - 60 = 40 more pounds of food to reach 100 pounds total. At 10 pounds of food per day that's \( \frac{40}{10} \) = 4 more days.

First, solve for \( \left|b - 5\right| \):

\( \left|b - 5\right| \) + 3 = -8
\( \left|b - 5\right| \) = -8 - 3
\( \left|b - 5\right| \) = -11

The value inside the absolute value brackets can be either positive or negative so (b - 5) must equal - 11 or --11 for \( \left|b - 5\right| \) to equal -11:

So, b = 16 or b = -6.

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

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 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.4km + 40.1km + 12.3km
total distance = 52.8km

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

3\( \sqrt{45} \) - 7\( \sqrt{5} \)
3\( \sqrt{9 \times 5} \) - 7\( \sqrt{5} \)
3\( \sqrt{3^2 \times 5} \) - 7\( \sqrt{5} \)
(3)(3)\( \sqrt{5} \) - 7\( \sqrt{5} \)
9\( \sqrt{5} \) - 7\( \sqrt{5} \)

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