| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.33 |
| Score | 0% | 67% |
If \( \left|a + 4\right| \) + 2 = -3, which of these is a possible value for a?
| 24 | |
| 6 | |
| 2 | |
| -9 |
First, solve for \( \left|a + 4\right| \):
\( \left|a + 4\right| \) + 2 = -3
\( \left|a + 4\right| \) = -3 - 2
\( \left|a + 4\right| \) = -5
The value inside the absolute value brackets can be either positive or negative so (a + 4) must equal - 5 or --5 for \( \left|a + 4\right| \) to equal -5:
| a + 4 = -5 a = -5 - 4 a = -9 | a + 4 = 5 a = 5 - 4 a = 1 |
So, a = 1 or a = -9.
Convert b-5 to remove the negative exponent.
| \( \frac{1}{b^5} \) | |
| \( \frac{-1}{-5b} \) | |
| \( \frac{-1}{-5b^{5}} \) | |
| \( \frac{-1}{b^{-5}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
11 members of a bridal party need transported to a wedding reception but there are only 2 5-passenger taxis available to take them. How many will need to find other transportation?
| 6 | |
| 2 | |
| 7 | |
| 1 |
There are 2 5-passenger taxis available so that's 2 x 5 = 10 total seats. There are 11 people needing transportation leaving 11 - 10 = 1 who will have to find other transportation.
Simplify \( \sqrt{112} \)
| 9\( \sqrt{14} \) | |
| 2\( \sqrt{14} \) | |
| 7\( \sqrt{7} \) | |
| 4\( \sqrt{7} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{112} \)
\( \sqrt{16 \times 7} \)
\( \sqrt{4^2 \times 7} \)
4\( \sqrt{7} \)
The __________ is the greatest factor that divides two integers.
least common multiple |
|
greatest common multiple |
|
absolute value |
|
greatest common factor |
The greatest common factor (GCF) is the greatest factor that divides two integers.