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 = \( 25mph \times 7h \)
175 miles

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

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

2\( \sqrt{175} \) + 2\( \sqrt{7} \)
2\( \sqrt{25 \times 7} \) + 2\( \sqrt{7} \)
2\( \sqrt{5^2 \times 7} \) + 2\( \sqrt{7} \)
(2)(5)\( \sqrt{7} \) + 2\( \sqrt{7} \)
10\( \sqrt{7} \) + 2\( \sqrt{7} \)

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

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{4!} \)
\( \frac{3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4} \)
\( \frac{1}{4} \)

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.