| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.46 |
| Score | 0% | 69% |
If a car travels 180 miles in 3 hours, what is the average speed?
| 60 mph | |
| 50 mph | |
| 55 mph | |
| 30 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)The __________ is the smallest positive integer that is a multiple of two or more integers.
greatest common factor |
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absolute value |
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least common factor |
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least common multiple |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
If a rectangle is twice as long as it is wide and has a perimeter of 36 meters, what is the area of the rectangle?
| 162 m2 | |
| 128 m2 | |
| 2 m2 | |
| 72 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 36 meters so the equation becomes: 2w + 2h = 36.
Putting these two equations together and solving for width (w):
2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6
Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m2
a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
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distributive property for multiplication |
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distributive property for division |
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commutative 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 the distance in miles of a trip that takes 8 hours at an average speed of 35 miles per hour?
| 240 miles | |
| 90 miles | |
| 280 miles | |
| 390 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 = \( 35mph \times 8h \)
280 miles