| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.29 |
| Score | 0% | 66% |
The __________ is the greatest factor that divides two integers.
greatest common multiple |
|
least common multiple |
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greatest common factor |
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absolute value |
The greatest common factor (GCF) is the greatest factor that divides two integers.
What is (a5)5?
| 5a5 | |
| a10 | |
| a0 | |
| a25 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(a5)5If a rectangle is twice as long as it is wide and has a perimeter of 18 meters, what is the area of the rectangle?
| 8 m2 | |
| 98 m2 | |
| 128 m2 | |
| 18 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 18 meters so the equation becomes: 2w + 2h = 18.
Putting these two equations together and solving for width (w):
2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3
Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m2
What is \( \frac{15\sqrt{6}}{5\sqrt{2}} \)?
| \(\frac{1}{3}\) \( \sqrt{3} \) | |
| 3 \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{3}} \) | |
| 3 \( \sqrt{\frac{1}{3}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{15\sqrt{6}}{5\sqrt{2}} \)
\( \frac{15}{5} \) \( \sqrt{\frac{6}{2}} \)
3 \( \sqrt{3} \)
In a class of 26 students, 13 are taking German and 11 are taking Spanish. Of the students studying German or Spanish, 8 are taking both courses. How many students are not enrolled in either course?
| 10 | |
| 13 | |
| 15 | |
| 24 |
The number of students taking German or Spanish is 13 + 11 = 24. Of that group of 24, 8 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 24 - 8 = 16 who are taking at least one language. 26 - 16 = 10 students who are not taking either language.