| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.87 |
| Score | 0% | 57% |
If a rectangle is twice as long as it is wide and has a perimeter of 6 meters, what is the area of the rectangle?
| 98 m2 | |
| 2 m2 | |
| 32 m2 | |
| 50 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 6 meters so the equation becomes: 2w + 2h = 6.
Putting these two equations together and solving for width (w):
2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1
Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m2
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 40% off." If Alex buys two shirts, each with a regular price of $26, how much money will he save?
| $3.90 | |
| $7.80 | |
| $11.70 | |
| $10.40 |
By buying two shirts, Alex will save $26 x \( \frac{40}{100} \) = \( \frac{$26 x 40}{100} \) = \( \frac{$1040}{100} \) = $10.40 on the second shirt.
What is \( 8 \)\( \sqrt{48} \) - \( 9 \)\( \sqrt{3} \)
| 23\( \sqrt{3} \) | |
| 72\( \sqrt{16} \) | |
| 72\( \sqrt{144} \) | |
| -1\( \sqrt{48} \) |
To subtract these radicals together their radicands must be the same:
8\( \sqrt{48} \) - 9\( \sqrt{3} \)
8\( \sqrt{16 \times 3} \) - 9\( \sqrt{3} \)
8\( \sqrt{4^2 \times 3} \) - 9\( \sqrt{3} \)
(8)(4)\( \sqrt{3} \) - 9\( \sqrt{3} \)
32\( \sqrt{3} \) - 9\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
32\( \sqrt{3} \) - 9\( \sqrt{3} \)What is \( \frac{5}{3} \) + \( \frac{9}{9} \)?
| 2\(\frac{2}{3}\) | |
| \( \frac{2}{9} \) | |
| 1 \( \frac{6}{9} \) | |
| \( \frac{2}{5} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 3}{3 x 3} \) + \( \frac{9 x 1}{9 x 1} \)
\( \frac{15}{9} \) + \( \frac{9}{9} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{15 + 9}{9} \) = \( \frac{24}{9} \) = 2\(\frac{2}{3}\)
Which of the following is an improper fraction?
\(1 {2 \over 5} \) |
|
\({2 \over 5} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.