The point: (0,600), (10,400) , (20,200) , (30,0)
(1 point)
Responses
The balloon takes 0 minutes to descend 600 feet.
The balloon takes 0 minutes to descend 600 feet.
The balloon starts its descent at 600 feet.
The balloon starts its descent at 600 feet.
It will take the balloon 600 minutes to descend.
It will take the balloon 600 minutes to descend.
The balloon rises 600 feet.
9 answers
The y-intercept of a graph represents the value of the dependent variable when the independent variable is zero. In this case, the y-intercept is (0,600), which means that at 0 minutes, the hot air balloon is at 600 feet.
Therefore, the correct response is:
The balloon starts its descent at 600 feet.
To determine which points would appear on the graph of the function \( C = 1.25m + 25 \), we can substitute the values of \( m \) (miles driven) into the equation.
For the point (2, C): \[ C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \] This gives us the point (2, 27.5).
For the point (4, C): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \] This gives us the point (4, 30).
None of the provided options match these calculated points exactly. However, if we check through the options:
(2, 2.5) and (4, 5) - Incorrect.
(2, 22.5) and (4, 20) - Incorrect.
(4, 30) and (8, 35) - Let's check (8): \[ C = 1.25(8) + 25 = 10 + 25 = 35 \] This gives us the point (8, 35) which is correct.
(30, 4) and (35, 8) - Incorrect.
The closest and correct points from your provided options are:
(4, 30) and (8, 35).
To interpret the slope of the graph, we can look at the changes in the values of the points provided. The points given are:
We can analyze how much the balloon rises (the y-coordinate) for each increase in time (the x-coordinate):
From (4, 2) to (8, 4):
From (8, 4) to (12, 6):
From (12, 6) to (16, 8):
The pattern shows that for every 4 minutes that pass, the balloon rises 2 units.
To convert these units into feet (if we assume they represent feet, as is common in such scenarios):
To find the rate per minute:
However, among your provided choices, the closest interpretation of the slope according to the rise and run calculation is:
For every four minutes that pass, the balloon rises 200 feet.
(Note: If the units are not in feet, the interpretation should be adjusted accordingly, but it seems the focus is on the change per 4 minutes.)
To model the slope of the balance remaining on Barton's car loan after each payment, you'll want to calculate the change in the remaining balance over the change in payments made.
Barton took out a loan of $2,625 and makes monthly payments of $175. The remaining balance decreases with each payment he makes. Thus, the slope of the line representing the remaining balance can be determined by:
Let's analyze each of your provided responses:
\( m = \frac{525 - 700}{11 - 12} \):
\( m = \frac{9 - 8}{1,050 - 1,225} \):
\( m = \frac{2,450 - 2,625}{0 - 1} \):
\( m = \frac{1,050 - 1,225}{9 - 8} \):
Among these choices, option 4 seems to be the correct model for the slope because it represents the decrease in the remaining balance after a payment, as the balance goes down by $175 per month.
Therefore, the correct answer is:
\( m = \frac{1,050 - 1,225}{9 - 8} \).
To find the correct slope that models Barton's car loan payments over time, we need to understand how the remaining balance changes after each payment made.
Given:
The slope \( m \) in this context represents the change in the remaining balance for each payment made. Specifically, the remaining balance decreases by $175 each month.
Let's analyze each of the provided responses to find the one that accurately represents this slope:
\( m = \frac{525 - 700}{11 - 12} \):
\( m = \frac{9 - 8}{1,050 - 1,225} \):
\( m = \frac{2,450 - 2,625}{0 - 1} \):
\( m = \frac{1,050 - 1,225}{9 - 8} \):
Given these analyses, the most straightforward option that correctly models the slope reflecting the change in the loan balance per payment is:
\( m = \frac{2,450 - 2,625}{0 - 1} \).
This represents the decrease in balance after the first payment accurately and directly corresponds to the monthly payment of $175.
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