| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.41 |
| Score | 0% | 68% |
If a rectangle is twice as long as it is wide and has a perimeter of 48 meters, what is the area of the rectangle?
| 128 m2 | |
| 32 m2 | |
| 50 m2 | |
| 72 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 48 meters so the equation becomes: 2w + 2h = 48.
Putting these two equations together and solving for width (w):
2w + 2h = 48
w + h = \( \frac{48}{2} \)
w + h = 24
w = 24 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 24 - 2w
3w = 24
w = \( \frac{24}{3} \)
w = 8
Since h = 2w that makes h = (2 x 8) = 16 and the area = h x w = 8 x 16 = 128 m2
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 25% off." If Charlie buys two shirts, each with a regular price of $11, how much will he pay for both shirts?
| $14.30 | |
| $19.25 | |
| $8.25 | |
| $11.55 |
By buying two shirts, Charlie will save $11 x \( \frac{25}{100} \) = \( \frac{$11 x 25}{100} \) = \( \frac{$275}{100} \) = $2.75 on the second shirt.
So, his total cost will be
$11.00 + ($11.00 - $2.75)
$11.00 + $8.25
$19.25
How many 12-passenger vans will it take to drive all 82 members of the football team to an away game?
| 4 vans | |
| 6 vans | |
| 7 vans | |
| 10 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{82}{12} \) = 6\(\frac{5}{6}\)
So, it will take 6 full vans and one partially full van to transport the entire team making a total of 7 vans.
A factor is a positive __________ that divides evenly into a given number.
integer |
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mixed number |
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fraction |
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improper fraction |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
Simplify \( \frac{16}{48} \).
| \( \frac{1}{3} \) | |
| \( \frac{1}{2} \) | |
| \( \frac{5}{19} \) | |
| \( \frac{4}{15} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{48} \) = \( \frac{\frac{16}{16}}{\frac{48}{16}} \) = \( \frac{1}{3} \)