Answer:
Alan: 200 m/min
Brian: 150 m/min
Step-by-step explanation:
Given : Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same point. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes.
To find : What are their rates, in meters per minute?
Solution :
Let n represent the number of laps that Alan completes in 9 minutes.
Then n-1 is the number of laps Brian completes.
45 seconds = 3/4 minutes.
The difference in their lap times in minutes per lap is

Solving the equation we get,








Neglecting n=-3
So, n=4
Then Alan's speed in m/min is



Brian completes 3 laps in that 9-minute time, so his rate is


Therefore, Alan: 200 m/min
Brian: 150 m/min
Answer:
(w^2 - 4w + 16)
Step-by-step explanation:
Note that w^3 +64 is the sum of two perfect cubes, which are (w)^3 and (4)^3. The corresponding factors are (w + 4)(w^2 - 4w + 16).
Therefore,
(w^3 +64)/(4+ w) reduces as follows:
(w^3 +64)/(4+ w) (4 + w)(w^2 - 4w + 16)
--------------------------- = --------------------------------- = (w^2 - 4w + 16)
4 + w 4 + w
Answer:
-5
Step-by-step explanation:
Remember the slope intercept form:
y = mx + b
m = Slope value
b = y-intercept
So in this case,
y = (-5)x + b
m = -5
b = 1
Thus the answer is -5
Step-by-step explanation:
2x = y-10
Rewrite as: 2x + 10 = y
Therefore:
2x+10 = y
2x +7 = 2y
Subtract the equations:
2x + 10 = y
- 2x + 7 = 2y
______________
3 = -y
Therefore y = -3
Substiture y = -3 into the second equation:
2x + 7 = 2(-3)
2x + 7 = -6
2x = -13
x= -6.5
Answer : (-6.5, -3)
Answer:
The mixed number 5 1/4 is equal to the improper fraction 21/4.