| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.91 |
| Score | 0% | 58% |
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
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least common factor |
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greatest common factor |
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least common multiple |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
What is \( \frac{35\sqrt{20}}{5\sqrt{5}} \)?
| \(\frac{1}{4}\) \( \sqrt{7} \) | |
| 7 \( \sqrt{\frac{1}{4}} \) | |
| 7 \( \sqrt{4} \) | |
| \(\frac{1}{7}\) \( \sqrt{\frac{1}{4}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{35\sqrt{20}}{5\sqrt{5}} \)
\( \frac{35}{5} \) \( \sqrt{\frac{20}{5}} \)
7 \( \sqrt{4} \)
If a rectangle is twice as long as it is wide and has a perimeter of 12 meters, what is the area of the rectangle?
| 50 m2 | |
| 162 m2 | |
| 8 m2 | |
| 128 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 12 meters so the equation becomes: 2w + 2h = 12.
Putting these two equations together and solving for width (w):
2w + 2h = 12
w + h = \( \frac{12}{2} \)
w + h = 6
w = 6 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 6 - 2w
3w = 6
w = \( \frac{6}{3} \)
w = 2
Since h = 2w that makes h = (2 x 2) = 4 and the area = h x w = 2 x 4 = 8 m2
Convert a-5 to remove the negative exponent.
| \( \frac{-1}{-5a} \) | |
| \( \frac{1}{a^{-5}} \) | |
| \( \frac{1}{a^5} \) | |
| \( \frac{-1}{a^{-5}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 42,000 seats in a stadium are filled, how many home fans are in attendance?
| 31,500 | |
| 25,600 | |
| 28,000 | |
| 25,833 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
42,000 fans x \( \frac{3}{4} \) = \( \frac{126000}{4} \) = 31,500 fans.