| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.27 |
| Score | 0% | 65% |
What is -3a2 x 7a3?
| 4a5 | |
| 4a3 | |
| -21a5 | |
| -21a2 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-3a2 x 7a3
(-3 x 7)a(2 + 3)
-21a5
What is (z3)2?
| z5 | |
| z-1 | |
| z6 | |
| 2z3 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(z3)2In a class of 27 students, 8 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 8 | |
| 11 | |
| 14 | |
| 23 |
The number of students taking German or Spanish is 8 + 14 = 22. Of that group of 22, 3 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 22 - 3 = 19 who are taking at least one language. 27 - 19 = 8 students who are not taking either language.
Find the average of the following numbers: 13, 5, 13, 5.
| 5 | |
| 9 | |
| 11 | |
| 10 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{13 + 5 + 13 + 5}{4} \) = \( \frac{36}{4} \) = 9
What is \( 4 \)\( \sqrt{63} \) + \( 2 \)\( \sqrt{7} \)
| 14\( \sqrt{7} \) | |
| 8\( \sqrt{7} \) | |
| 8\( \sqrt{9} \) | |
| 6\( \sqrt{441} \) |
To add these radicals together their radicands must be the same:
4\( \sqrt{63} \) + 2\( \sqrt{7} \)
4\( \sqrt{9 \times 7} \) + 2\( \sqrt{7} \)
4\( \sqrt{3^2 \times 7} \) + 2\( \sqrt{7} \)
(4)(3)\( \sqrt{7} \) + 2\( \sqrt{7} \)
12\( \sqrt{7} \) + 2\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
12\( \sqrt{7} \) + 2\( \sqrt{7} \)