| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.55 |
| Score | 0% | 71% |
Simplify \( \sqrt{27} \)
| 4\( \sqrt{6} \) | |
| 3\( \sqrt{3} \) | |
| 5\( \sqrt{6} \) | |
| 6\( \sqrt{6} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{27} \)
\( \sqrt{9 \times 3} \)
\( \sqrt{3^2 \times 3} \)
3\( \sqrt{3} \)
Which of the following is not a prime number?
7 |
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2 |
|
9 |
|
5 |
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
4! = ?
5 x 4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
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4 x 3 |
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4 x 3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
Simplify \( \frac{16}{68} \).
| \( \frac{6}{19} \) | |
| \( \frac{3}{8} \) | |
| \( \frac{7}{15} \) | |
| \( \frac{4}{17} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{68} \) = \( \frac{\frac{16}{4}}{\frac{68}{4}} \) = \( \frac{4}{17} \)
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
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a = 7 or a = -7 |
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none of these is correct |
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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).