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

6\( \sqrt{12} \) + 7\( \sqrt{3} \)
6\( \sqrt{4 \times 3} \) + 7\( \sqrt{3} \)
6\( \sqrt{2^2 \times 3} \) + 7\( \sqrt{3} \)
(6)(2)\( \sqrt{3} \) + 7\( \sqrt{3} \)
12\( \sqrt{3} \) + 7\( \sqrt{3} \)

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

If the tiger has consumed 26 pounds of food in 2 days that's \( \frac{26}{2} \) = 13 pounds of food per day. The tiger needs to consume 117 - 26 = 91 more pounds of food to reach 117 pounds total. At 13 pounds of food per day that's \( \frac{91}{13} \) = 7 more days.

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

\( \frac{1}{8} \) x \( \frac{2}{5} \) = \( \frac{1 x 2}{8 x 5} \) = \( \frac{2}{40} \) = \(\frac{1}{20}\)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{16} \) = 2\(\frac{5}{16}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 19 x 4 = 76 small cakes during that time. 480 small cakes are needed for the party so \( \frac{480}{76} \) = 6\(\frac{6}{19}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 7 = 10 cooks.