| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
What is -5x6 - 8x6?
| 3x12 | |
| -13x6 | |
| 13x-6 | |
| 3x-12 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
-5x6 - 8x6
(-5 - 8)x6
-13x6
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 or a = -7 |
|
a = 7 |
|
a = -7 |
|
none of these is correct |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
A triathlon course includes a 300m swim, a 40.3km bike ride, and a 9.7km run. What is the total length of the race course?
| 50.3km | |
| 61.1km | |
| 60.6km | |
| 36.8km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.3km + 40.3km + 9.7km
total distance = 50.3km
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 60% of his shots. If the guard takes 10 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 10 | |
| 16 | |
| 11 | |
| 13 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{60}{100} \) = \( \frac{60 x 10}{100} \) = \( \frac{600}{100} \) = 6 shots
The center makes 45% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{6}{\frac{45}{100}} \) = 6 x \( \frac{100}{45} \) = \( \frac{6 x 100}{45} \) = \( \frac{600}{45} \) = 13 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{7}{6} \) + \( \frac{3}{8} \)?
| 1 \( \frac{6}{24} \) | |
| 1\(\frac{13}{24}\) | |
| 1 \( \frac{2}{24} \) | |
| \( \frac{9}{24} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 4}{6 x 4} \) + \( \frac{3 x 3}{8 x 3} \)
\( \frac{28}{24} \) + \( \frac{9}{24} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{28 + 9}{24} \) = \( \frac{37}{24} \) = 1\(\frac{13}{24}\)