| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.46 |
| Score | 0% | 69% |
How many hours does it take a car to travel 420 miles at an average speed of 70 miles per hour?
| 5 hours | |
| 6 hours | |
| 9 hours | |
| 3 hours |
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 time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{420mi}{70mph} \)
6 hours
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 54 | |
| 49 | |
| 46 | |
| 55 |
The equation for this sequence is:
an = an-1 + 3(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
|
commutative property for division |
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distributive property for multiplication |
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distributive property for division |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.
What is \( \frac{-4x^8}{2x^2} \)?
| -\(\frac{1}{2}\)x6 | |
| -2x6 | |
| -2x\(\frac{1}{4}\) | |
| -2x10 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-4x^8}{2x^2} \)
\( \frac{-4}{2} \) x(8 - 2)
-2x6
What is \( \frac{3}{2} \) + \( \frac{9}{10} \)?
| 1 \( \frac{6}{15} \) | |
| 2\(\frac{2}{5}\) | |
| 2 \( \frac{5}{11} \) | |
| \( \frac{5}{13} \) |
To add 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:
\( \frac{3 x 5}{2 x 5} \) + \( \frac{9 x 1}{10 x 1} \)
\( \frac{15}{10} \) + \( \frac{9}{10} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{15 + 9}{10} \) = \( \frac{24}{10} \) = 2\(\frac{2}{5}\)