| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.46 |
| Score | 0% | 49% |
If a rectangle is twice as long as it is wide and has a perimeter of 24 meters, what is the area of the rectangle?
| 32 m2 | |
| 98 m2 | |
| 128 m2 | |
| 8 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 24 meters so the equation becomes: 2w + 2h = 24.
Putting these two equations together and solving for width (w):
2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4
Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m2
What is \( \frac{6}{2} \) - \( \frac{2}{10} \)?
| 2\(\frac{4}{5}\) | |
| 2 \( \frac{6}{9} \) | |
| \( \frac{3}{10} \) | |
| 2 \( \frac{8}{14} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 5}{2 x 5} \) - \( \frac{2 x 1}{10 x 1} \)
\( \frac{30}{10} \) - \( \frac{2}{10} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{30 - 2}{10} \) = \( \frac{28}{10} \) = 2\(\frac{4}{5}\)
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 45,000 seats in a stadium are filled, how many home fans are in attendance?
| 22,000 | |
| 38,333 | |
| 37,500 | |
| 36,750 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
45,000 fans x \( \frac{5}{6} \) = \( \frac{225000}{6} \) = 37,500 fans.
Which of the following statements about exponents is false?
b1 = b |
|
b1 = 1 |
|
all of these are false |
|
b0 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
What is 2\( \sqrt{7} \) x 3\( \sqrt{8} \)?
| 5\( \sqrt{56} \) | |
| 12\( \sqrt{14} \) | |
| 6\( \sqrt{15} \) | |
| 6\( \sqrt{7} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
2\( \sqrt{7} \) x 3\( \sqrt{8} \)
(2 x 3)\( \sqrt{7 \times 8} \)
6\( \sqrt{56} \)
Now we need to simplify the radical:
6\( \sqrt{56} \)
6\( \sqrt{14 \times 4} \)
6\( \sqrt{14 \times 2^2} \)
(6)(2)\( \sqrt{14} \)
12\( \sqrt{14} \)