| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
If \( \left|y + 4\right| \) - 4 = -4, which of these is a possible value for y?
| -18 | |
| 9 | |
| -4 | |
| 14 |
First, solve for \( \left|y + 4\right| \):
\( \left|y + 4\right| \) - 4 = -4
\( \left|y + 4\right| \) = -4 + 4
\( \left|y + 4\right| \) = 0
The value inside the absolute value brackets can be either positive or negative so (y + 4) must equal + 0 or -0 for \( \left|y + 4\right| \) to equal 0:
| y + 4 = 0 y = 0 - 4 y = -4 | y + 4 = 0 y = 0 - 4 y = -4 |
So, y = -4 or y = -4.
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 or a = -7 |
|
a = -7 |
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a = 7 |
|
none of these is correct |
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).
In a class of 19 students, 5 are taking German and 11 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 19 | |
| 7 | |
| 10 |
The number of students taking German or Spanish is 5 + 11 = 16. Of that group of 16, 4 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 16 - 4 = 12 who are taking at least one language. 19 - 12 = 7 students who are not taking either language.
If the ratio of home fans to visiting fans in a crowd is 2:1 and all 44,000 seats in a stadium are filled, how many home fans are in attendance?
| 24,000 | |
| 29,333 | |
| 37,500 | |
| 34,500 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
44,000 fans x \( \frac{2}{3} \) = \( \frac{88000}{3} \) = 29,333 fans.
The __________ is the greatest factor that divides two integers.
least common multiple |
|
absolute value |
|
greatest common multiple |
|
greatest common factor |
The greatest common factor (GCF) is the greatest factor that divides two integers.