| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
If \( \left|z - 9\right| \) + 9 = 4, which of these is a possible value for z?
| 14 | |
| -10 | |
| 8 | |
| -14 |
First, solve for \( \left|z - 9\right| \):
\( \left|z - 9\right| \) + 9 = 4
\( \left|z - 9\right| \) = 4 - 9
\( \left|z - 9\right| \) = -5
The value inside the absolute value brackets can be either positive or negative so (z - 9) must equal - 5 or --5 for \( \left|z - 9\right| \) to equal -5:
| z - 9 = -5 z = -5 + 9 z = 4 | z - 9 = 5 z = 5 + 9 z = 14 |
So, z = 14 or z = 4.
A bread recipe calls for 3\(\frac{3}{8}\) cups of flour. If you only have 1\(\frac{5}{8}\) cups, how much more flour is needed?
| 1\(\frac{3}{4}\) cups | |
| 2\(\frac{1}{2}\) cups | |
| 3\(\frac{1}{4}\) cups | |
| \(\frac{7}{8}\) cups |
The amount of flour you need is (3\(\frac{3}{8}\) - 1\(\frac{5}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{27}{8} \) - \( \frac{13}{8} \)) cups
\( \frac{14}{8} \) cups
1\(\frac{3}{4}\) cups
Convert b-2 to remove the negative exponent.
| \( \frac{-1}{-2b} \) | |
| \( \frac{2}{b} \) | |
| \( \frac{-2}{b} \) | |
| \( \frac{1}{b^2} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Simplify \( \sqrt{28} \)
| 2\( \sqrt{7} \) | |
| 9\( \sqrt{14} \) | |
| 3\( \sqrt{14} \) | |
| 9\( \sqrt{7} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{28} \)
\( \sqrt{4 \times 7} \)
\( \sqrt{2^2 \times 7} \)
2\( \sqrt{7} \)
| 1 | |
| 4.8 | |
| 2.8 | |
| 4.0 |
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