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

5\( \sqrt{112} \) - 2\( \sqrt{7} \)
5\( \sqrt{16 \times 7} \) - 2\( \sqrt{7} \)
5\( \sqrt{4^2 \times 7} \) - 2\( \sqrt{7} \)
(5)(4)\( \sqrt{7} \) - 2\( \sqrt{7} \)
20\( \sqrt{7} \) - 2\( \sqrt{7} \)

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

The amount of flour you need is (2\(\frac{3}{4}\) - \(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{22}{8} \) - \( \frac{2}{8} \)) cups
\( \frac{20}{8} \) cups
2\(\frac{1}{2}\) cups

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:

-4b⁵ - 2b⁵
(-4 - 2)b⁵
-6b⁵

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 55mph \times 6h \)
330 miles

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.