If the tiger has consumed 48 pounds of food in 4 days that's \( \frac{48}{4} \) = 12 pounds of food per day. The tiger needs to consume 120 - 48 = 72 more pounds of food to reach 120 pounds total. At 12 pounds of food per day that's \( \frac{72}{12} \) = 6 more days.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{245mi}{35mph} \)
7 hours

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

4\( \sqrt{112} \) + 8\( \sqrt{7} \)
4\( \sqrt{16 \times 7} \) + 8\( \sqrt{7} \)
4\( \sqrt{4^2 \times 7} \) + 8\( \sqrt{7} \)
(4)(4)\( \sqrt{7} \) + 8\( \sqrt{7} \)
16\( \sqrt{7} \) + 8\( \sqrt{7} \)

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

First, solve for \( \left|a + 6\right| \):

\( \left|a + 6\right| \) + 8 = 1
\( \left|a + 6\right| \) = 1 - 8
\( \left|a + 6\right| \) = -7

The value inside the absolute value brackets can be either positive or negative so (a + 6) must equal - 7 or --7 for \( \left|a + 6\right| \) to equal -7:

So, a = 1 or a = -13.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{6} \) x \( \frac{4}{9} \) = \( \frac{3 x 4}{6 x 9} \) = \( \frac{12}{54} \) = \(\frac{2}{9}\)