2.A truck driver maintains a constant speed of 65 miles per hour on a stretch of highway that lasts 130 miles. Graph the remaining distance as a function of the time driven in hours.(1 point)a.The horizontal axis labeled Hours Driven goes from 0 to 15 in increments of 1 and the vertical axis labeled Miles Remaining goes from 0 to 150 in increments of 10. The line segment starts at left parenthesis 0 comma 130 right parenthesis, passes through left parenthesis 1 comma 65 right parenthesis, and ends at left parenthesis 2 comma 0 right parenthesis.
b.The horizontal axis labeled Hours Driven goes from 0 to 15 in increments of 1 and the vertical axis labeled Miles Remaining goes from 0 to 150 in increments of 10. The line starts at left parenthesis 2 comma 0 right parenthesis, and passes through left parenthesis 3 comma 65 right parenthesis and left parenthesis 4 comma 130 right parenthesis.
c.The horizontal axis labeled Hours Driven goes from 0 to 15 in increments of 1 and the vertical axis labeled Miles Remaining goes from 0 to 150 in increments of 10. The line starts at left parenthesis 0 comma 0 right parenthesis, and passes through left parenthesis 1 comma 65 right parenthesis and left parenthesis 2 comma 130 right parenthesis.
d.The horizontal axis labeled Hours Driven goes from 0 to 15 in increments of 1 and the vertical axis labeled Miles Remaining goes from 0 to 150 in increments of 10. The line segment starts at left parenthesis 0 comma 130 right parenthesis, passes through left parenthesis 2 comma 65 right parenthesis, and ends at left parenthesis 4 comma 0 right parenthesis.
3.Tayson walked for 8 minutes before running n laps around a track. Tayson takes 1 minute and 45 seconds to run each lap. What is the graph of the function that relates the amount of time, T, in minutes Tayson walked or ran after running n laps?(1 point)
A.A function is graphed on a first quadrant coordinate plane. The horizontal axis labeled Laps goes from 0 to 10 in increments of 1. The vertical axis labeled Time in minutes goes from 0 to 35 in increments of 1. A line starts at (0, 5) and passes through (2, 17) and (5, 35).
B.A function is graphed on a first quadrant coordinate plane. The horizontal axis labeled Laps goes from 0 to 10 in increments of 1. The vertical axis labeled Time in minutes goes from 0 to 35 in increments of 1. A line starts at (0, 8), and passes through (4, 11) and (8, 14).
C.A function is graphed on a first quadrant coordinate plane. The horizontal axis labeled Laps goes from 0 to 10 in increments of 1. The vertical axis labeled Time in minutes goes from 0 to 35 in increments of 1. A line starts at (0, 8), and passes through (4, 15).
D.A function is graphed on a first quadrant coordinate plane. The horizontal axis labeled Laps goes from 0 to 10 in increments of 1. The vertical axis labeled Time in minutes goes from 0 to 35 in increments of 1. A line starts at (0, 1.75), and passes through (1, 9.75). All coordinates are approximate.
4.Function f(x) has a slope of 32 and a y-intercept of 6. Explain how the graph of f(x) could be used to find the x-intercept.(1 point)
A.Find the x-coordinate of the point that crosses the x-axis. The x-intercept is −4.
B.Find the y-coordinate of the point where x=1. The x-intercept is 152.
C.Use the value of riserun for the function, which is 32.
D.Find the y-coordinate of the point that crosses the y-axis. The x-intercept is 6.
5.Alma's mobile phone is charged to 80% when she takes the phone off the charger. The phone's charge decreases by 15% every 2 hours. Which graph could be used to show the charge of Alma's phone, C, as a percentage as a function of t hours after Alma takes the phone off the charger?(1 point)
A.A function is graphed on a first quadrant coordinate plane. The horizontal axis labeled Time in hours goes from 0 to 12 in increments of 1. The vertical axis labeled Battery Charge in percent goes from 0 to 100 in increments of 2. A line starts at (0, 80), passes through (2, 50) and (4, 20), and ends at approximately (5.3, 0).
B.A function is graphed on a first quadrant coordinate plane. The horizontal axis labeled Time in hours goes from 0 to 12 in increments of 1. The vertical axis labeled Battery Charge in percent goes from 0 to 100 in increments of 2. A line starts at (0, 20), and passes through (4, 50).
C.A function is graphed on a first quadrant coordinate plane. The horizontal axis labeled Time in hours goes from 0 to 12 in increments of 1. The vertical axis labeled Battery Charge in percent goes from 0 to 100 in increments of 2. A line starts at (0, 80), and passes approximately through (2, 95).
D.A function is graphed on a first quadrant coordinate plane. The horizontal axis labeled Time in hours goes from 0 to 12 in increments of 1. The vertical axis labeled Battery Charge in percent goes from 0 to 100 in increments of 2. A line starts at (0, 80), passes through (4, 50) and (8, 20), and ends at approximately (10.7, 0).
2. The correct answer is option b. The graph should start at (2, 0), pass through (3, 65), and (4, 130) because the truck driver maintains a constant speed of 65 miles per hour for a stretch of highway that lasts 130 miles.
For question 2:
To determine the correct graph, we need to consider the information given in the problem. It states that the truck driver maintains a constant speed of 65 miles per hour, and the stretch of highway is 130 miles long.
We are asked to graph the remaining distance as a function of the time driven in hours. Since the driver is maintaining a constant speed, the remaining distance will decrease linearly with time.
Let's look at the options:
a. The line segment starts at (0, 130), passes through (1, 65), and ends at (2, 0). This graph represents the correct relationship between time driven and remaining distance.
b. This graph does not represent a constant speed, as the remaining distance does not decrease linearly with time.
c. This graph starts at (0, 0), which does not align with the given information that the truck driver starts with 130 miles remaining.
d. This graph starts at (0, 130) and ends at (4, 0), but the middle point does not align with the given constant speed.
Therefore, the correct answer is option a.
For question 3:
We are given that Tayson walked for 8 minutes before running n laps around a track. It takes Tayson 1 minute and 45 seconds to run each lap.
To graph the function that relates the amount of time Tayson walked or ran after running n laps, we need to consider the following:
- The time Tayson spent walking is constant and does not change with the number of laps.
- The time taken to run each lap (1 minute and 45 seconds) is proportional to the number of laps (n).
Let's analyze the options:
A. This graph starts at (0, 5) and passes through (2, 17) and (5, 35). The time values increase with the number of laps, which aligns with the given information.
B. This graph does not represent the given information that the time spent walking is constant.
C. This graph does not represent the given information that the time taken to run each lap is proportional to the number of laps.
D. This graph does not represent the given information that the time taken to run each lap is proportional to the number of laps.
Therefore, the correct answer is option A.
For question 4:
We are given that the function f(x) has a slope of 32 and a y-intercept of 6. We need to explain how the graph of f(x) could be used to find the x-intercept.
To find the x-intercept, we need to determine the value of x when f(x) equals zero. In other words, we need to find the point where the graph of f(x) crosses the x-axis.
Let's analyze the options:
A. This option suggests finding the x-coordinate of the point that crosses the x-axis, which is what we need to find to determine the x-intercept.
B. This option suggests finding the y-coordinate of the point where x=1, which does not help in finding the x-intercept.
C. This option mentions the "riserun" for the function, but it does not explain how it can be used to find the x-intercept.
D. This option suggests finding the y-coordinate of the point that crosses the y-axis, which does not help in finding the x-intercept.
Therefore, the correct answer is option A.
For question 5:
We are given that Alma's mobile phone is charged to 80% when she takes the phone off the charger. The phone's charge decreases by 15% every 2 hours.
To graph the function that relates the charge of Alma's phone as a percentage to the time in hours after taking the phone off the charger, we need to consider the following:
- The initial charge is 80%.
- The charge decreases by 15% every 2 hours.
Let's analyze the options:
A. This graph starts at (0, 80), passes through (2, 50), ends at approximately (5.3, 0). The charge decreases by 15% every 2 hours, which aligns with the given information.
B. This graph does not represent the given information that the charge decreases by 15% every 2 hours.
C. This graph does not represent the given information that the charge decreases by 15% every 2 hours.
D. This graph starts at (0, 80), passes through (4, 50), (8, 20), and ends at approximately (10.7, 0). The charge decreases by more than 15% every 2 hours, which does not align with the given information.
Therefore, the correct answer is option A.