| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.46 |
| Score | 0% | 69% |
What is 8y6 - 3y6?
| -5y-6 | |
| 5y6 | |
| 11y36 | |
| 11y6 |
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:
8y6 - 3y6
(8 - 3)y6
5y6
What is the distance in miles of a trip that takes 6 hours at an average speed of 55 miles per hour?
| 375 miles | |
| 450 miles | |
| 280 miles | |
| 330 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 55mph \times 6h \)
330 miles
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 32,000 seats in a stadium are filled, how many home fans are in attendance?
| 26,667 | |
| 33,600 | |
| 24,667 | |
| 20,667 |
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:
32,000 fans x \( \frac{5}{6} \) = \( \frac{160000}{6} \) = 26,667 fans.
What is the greatest common factor of 32 and 44?
| 24 | |
| 2 | |
| 4 | |
| 18 |
The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 the greatest factor 32 and 44 have in common.
If \( \left|y - 4\right| \) + 4 = 6, which of these is a possible value for y?
| -2 | |
| 2 | |
| -24 | |
| 14 |
First, solve for \( \left|y - 4\right| \):
\( \left|y - 4\right| \) + 4 = 6
\( \left|y - 4\right| \) = 6 - 4
\( \left|y - 4\right| \) = 2
The value inside the absolute value brackets can be either positive or negative so (y - 4) must equal + 2 or -2 for \( \left|y - 4\right| \) to equal 2:
| y - 4 = 2 y = 2 + 4 y = 6 | y - 4 = -2 y = -2 + 4 y = 2 |
So, y = 2 or y = 6.