Answer: 
The cable car’s elevation will be 750 feet after 15 minutes or 65 minutes.
Step-by-step explanation:
Given: A cable car begins its trip by moving up a hill. As it moves up, it gains elevation at a constant rate of 50 feet/minute until it reaches the peak at 2,000 feet.
Then, total time taken to reach the peak = (Distance) ÷ (speed)
= (2,000 feet) ÷ ( 50 feet/minute)
= 40 minutes
Then, as the car moves down to the hill’s base, its elevation drops at the same rate.
The equation that models the cable car’s elevation, e, after t minutes is
e= (constant rate)|t- time to reach peak |+ Peak's height
When the cable car’s elevation will be 750 feet after minutes, then we have
Time cannot be negative, so the cable car’s elevation will be 750 feet after 15 minutes or 65 minutes.
Answer:
3.8 percent
Step-by-step explanation:
To find his average return over n years, we sum all of his returns, and divide by n.
In this problem:
5 years.
The sum is (12 + 15 - 15 + 19 - 12) = 19
19/5 = 3.8
So the correct answer is:
3.8 percent
Step OneUse the vertex to determine the basic equation for the parabola.
y = a(x - 2)^2 + 7 Notice the sign change for x. I have provided a graph to show how this would look with a = 1 (in red.)
What it means is the 2 has to be minus in order that the vertex will shift 2 units in the x direction.
Step TwoUse the point to solve for a.
y = a(x - 2)^2 + 7
When x = - 1
Then y = 3
3 = a(-1 - 2)^2 + 7 combine -1 with - 2
3 = a (-3)^2 + 7
3 = 9a + 7 Subtract 7 from both sides
3 - 7 = 9a
-4 = 9a Divide by 9.
a = -4/9
or
a = - 0.4444
y = -0.4444(x + 2)^2 + 7 <<<<<
answer
y = - 4/9 (x + 2)^2 + 7
Note: if you have choices, list them please.
Note: The red graph is y = (x - 2)^2 + 7 ; a = 1
The blue graph is y = - 4/9(x - 2)^2 + 7 ; a = - 0.44444
You should notice that the a does 3 things to the graph. Before you read the answer, what are those three things? The answer is in the comments.
