| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.30 |
| Score | 0% | 66% |
Simplify \( \sqrt{75} \)
| 5\( \sqrt{3} \) | |
| 4\( \sqrt{6} \) | |
| 6\( \sqrt{3} \) | |
| 2\( \sqrt{6} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{75} \)
\( \sqrt{25 \times 3} \)
\( \sqrt{5^2 \times 3} \)
5\( \sqrt{3} \)
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = 7 or a = -7 |
|
a = 7 |
|
a = -7 |
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).
Simplify \( \frac{40}{64} \).
| \( \frac{8}{13} \) | |
| \( \frac{5}{8} \) | |
| \( \frac{4}{19} \) | |
| \( \frac{1}{2} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{40}{64} \) = \( \frac{\frac{40}{8}}{\frac{64}{8}} \) = \( \frac{5}{8} \)
What is \( \frac{1}{8} \) ÷ \( \frac{3}{5} \)?
| \(\frac{5}{8}\) | |
| \(\frac{3}{35}\) | |
| 1\(\frac{2}{3}\) | |
| \(\frac{5}{24}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{1}{8} \) ÷ \( \frac{3}{5} \) = \( \frac{1}{8} \) x \( \frac{5}{3} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{8} \) x \( \frac{5}{3} \) = \( \frac{1 x 5}{8 x 3} \) = \( \frac{5}{24} \) = \(\frac{5}{24}\)
If all of a roofing company's 9 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 5 complete crews out on jobs?
| 6 | |
| 4 | |
| 7 | |
| 18 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 9 workers at the company now and that's enough to staff 3 crews so there are \( \frac{9}{3} \) = 3 workers on a crew. 5 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 5 x 3 = 15 total workers to staff the crews during the busy season. The company already employs 9 workers so they need to add 15 - 9 = 6 new staff for the busy season.