| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.44 |
| Score | 0% | 69% |
If \( \left|z - 2\right| \) - 4 = -8, which of these is a possible value for z?
| -6 | |
| -10 | |
| -27 | |
| -2 |
First, solve for \( \left|z - 2\right| \):
\( \left|z - 2\right| \) - 4 = -8
\( \left|z - 2\right| \) = -8 + 4
\( \left|z - 2\right| \) = -4
The value inside the absolute value brackets can be either positive or negative so (z - 2) must equal - 4 or --4 for \( \left|z - 2\right| \) to equal -4:
| z - 2 = -4 z = -4 + 2 z = -2 | z - 2 = 4 z = 4 + 2 z = 6 |
So, z = 6 or z = -2.
What is the greatest common factor of 36 and 28?
| 21 | |
| 15 | |
| 22 | |
| 4 |
The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 28 are [1, 2, 4, 7, 14, 28]. They share 3 factors [1, 2, 4] making 4 the greatest factor 36 and 28 have in common.
Which of these numbers is a factor of 20?
| 15 | |
| 10 | |
| 24 | |
| 17 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 20 are 1, 2, 4, 5, 10, 20.
What is the least common multiple of 2 and 8?
| 14 | |
| 13 | |
| 8 | |
| 5 |
The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 have in common.
If \( \left|z - 2\right| \) - 4 = -8, which of these is a possible value for z?
| -6 | |
| -10 | |
| -27 | |
| -2 |
First, solve for \( \left|z - 2\right| \):
\( \left|z - 2\right| \) - 4 = -8
\( \left|z - 2\right| \) = -8 + 4
\( \left|z - 2\right| \) = -4
The value inside the absolute value brackets can be either positive or negative so (z - 2) must equal - 4 or --4 for \( \left|z - 2\right| \) to equal -4:
| z - 2 = -4 z = -4 + 2 z = -2 | z - 2 = 4 z = 4 + 2 z = 6 |
So, z = 6 or z = -2.