| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.73 |
| Score | 0% | 75% |
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = 7 |
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a = 7 or a = -7 |
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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).
Simplify \( \frac{28}{72} \).
| \( \frac{10}{11} \) | |
| \( \frac{8}{13} \) | |
| \( \frac{5}{7} \) | |
| \( \frac{7}{18} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{72} \) = \( \frac{\frac{28}{4}}{\frac{72}{4}} \) = \( \frac{7}{18} \)
How many hours does it take a car to travel 100 miles at an average speed of 20 miles per hour?
| 2 hours | |
| 9 hours | |
| 5 hours | |
| 8 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{100mi}{20mph} \)
5 hours
If \( \left|a + 5\right| \) + 6 = -4, which of these is a possible value for a?
| -2 | |
| 16 | |
| -15 | |
| -6 |
First, solve for \( \left|a + 5\right| \):
\( \left|a + 5\right| \) + 6 = -4
\( \left|a + 5\right| \) = -4 - 6
\( \left|a + 5\right| \) = -10
The value inside the absolute value brackets can be either positive or negative so (a + 5) must equal - 10 or --10 for \( \left|a + 5\right| \) to equal -10:
| a + 5 = -10 a = -10 - 5 a = -15 | a + 5 = 10 a = 10 - 5 a = 5 |
So, a = 5 or a = -15.
Which of the following is a mixed number?
\({7 \over 5} \) |
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\({a \over 5} \) |
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\({5 \over 7} \) |
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\(1 {2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.