Help please: A bus and a train leave a station at the same time, t = 0. The graph shows the bus's distance to the next station o
ver time. The train moves more quickly than the bus. Write an equation of a function that could represent the train's distance to the next station.
1 answer:
Answer:
y = (5/2)x + 20
Step-by-step explanation:
Since the bus and train are both at the station at time 0, the y-intercept for the new equation is 20. That is one point on the new graph: (0,20) The question said that the train travels faster, that means it spends less time getting to the next station. The existing graph shows the bus got to the next station in 10 minutes, so maybe the train got there in 8 minutes. So another point on the graph is (8,0) We can use a slope formula to calculate the slope of a new line. Or just count squares on the graph (se image) to find the slope. Slope tells how steep a line is, whether the line is going up or down, but also the slope is like directions how to get from one point to another point on the line.
All you need to write an equation is the slope, m and the y-intercept, b and fill those two numbers into the formula y=mx+b Here slope is 5/2 and y-intercept is 20. So you get
y=(5/2)x +20
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<u>Scenario 1</u>
It is given that on Albert's favorite shoe website, the prices for a pair of the shoes range from $80 to $180 and the delivery fee is one-twentieth of the price of the basketball shoes.
We know that Albert has $105 to spend on new basketball shoes.
From the above pieces of information we see that the minimum that Albert will have to spend is dollars.
Now, we know that Albert can spend a maximum of $105 including the delivery fee. Let the upper limit of the price of the shoe Albert can buy be . So, the upper limit of the domain can be found as:
dollars.
Thus, in the first scenario, the domain of the total cost function, f(c) will be [86.67,96.92].
<u>Scenario 2</u>
After receiving $42 from his friend, Albert's total buying power becomes $147. Albert can now buy a costlier pair of shoes.
Thus, the maximum that Albert can buy is again given by:
Solving this we get: dollars
The lower limit will remain the same as the lowest price point in the website is $80. Therefore, in the second scenario the domain is:
[86.67, 135.69]