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

9\( \sqrt{6} \) x 3\( \sqrt{7} \)
(9 x 3)\( \sqrt{6 \times 7} \)
27\( \sqrt{42} \)

If the tiger has consumed 50 pounds of food in 10 days that's \( \frac{50}{10} \) = 5 pounds of food per day. The tiger needs to consume 70 - 50 = 20 more pounds of food to reach 70 pounds total. At 5 pounds of food per day that's \( \frac{20}{5} \) = 4 more days.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

There are 3 5-passenger taxis available so that's 3 x 5 = 15 total seats. There are 20 people needing transportation leaving 20 - 15 = 5 who will have to find other transportation.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 9}{5 x 9} \) + \( \frac{2 x 5}{9 x 5} \)

\( \frac{36}{45} \) + \( \frac{10}{45} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{36 + 10}{45} \) = \( \frac{46}{45} \) = 1\(\frac{1}{45}\)