| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.49 |
| Score | 0% | 70% |
What is x4 - 9x4?
| 10x16 | |
| -8x4 | |
| 8x4 | |
| 8x-4 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
1x4 - 9x4
(1 - 9)x4
-8x4
What is the next number in this sequence: 1, 7, 13, 19, 25, __________ ?
| 27 | |
| 36 | |
| 31 | |
| 30 |
The equation for this sequence is:
an = an-1 + 6
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 6
a6 = 25 + 6
a6 = 31
If \( \left|z + 2\right| \) + 6 = 7, which of these is a possible value for z?
| 5 | |
| 16 | |
| -1 | |
| -7 |
First, solve for \( \left|z + 2\right| \):
\( \left|z + 2\right| \) + 6 = 7
\( \left|z + 2\right| \) = 7 - 6
\( \left|z + 2\right| \) = 1
The value inside the absolute value brackets can be either positive or negative so (z + 2) must equal + 1 or -1 for \( \left|z + 2\right| \) to equal 1:
| z + 2 = 1 z = 1 - 2 z = -1 | z + 2 = -1 z = -1 - 2 z = -3 |
So, z = -3 or z = -1.
Simplify \( \sqrt{80} \)
| 2\( \sqrt{10} \) | |
| 4\( \sqrt{5} \) | |
| 9\( \sqrt{10} \) | |
| 3\( \sqrt{10} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{80} \)
\( \sqrt{16 \times 5} \)
\( \sqrt{4^2 \times 5} \)
4\( \sqrt{5} \)
In a class of 30 students, 14 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 6 | |
| 11 | |
| 10 | |
| 15 |
The number of students taking German or Spanish is 14 + 14 = 28. Of that group of 28, 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 28 - 4 = 24 who are taking at least one language. 30 - 24 = 6 students who are not taking either language.