Use the graph below to answer the question that follows.
A graph titled 'Remote-Control Car' shows 'Time' in seconds from 0 to 10 on the x-axis and 'Speed' in miles per hour from 0 to 10 on the y-axis.
A line segment connects left-parenthesis 0 comma 4 right-parenthesis and left-parenthesis 3 comma 2 right-parenthesis.
A second line segment connects left-parenthesis 3 comma 2 right-parenthesis to left-parenthesis 4 comma 6 right-parenthesis.
A horizontal line segment connects left-parenthesis 4 comma 6 right-parenthesis to the point left-parenthesis 10 comma 6 right-parenthesis.
Which statement describes the speed of the remote-control car over time?
A. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
B. The speed of the car increases from 4 mi/h to 2 mi/h in the first 3 seconds, decreases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
C. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 6 mi/h in the next second, and then remains at 6 mi/h for the last 6 seconds.
D. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 5 seconds, and then remains at 5 mi/h for the last 10 seconds.
38 answers
B. The speed of the car increases from 2 mi/h to 4 mi/h in the first 3 seconds, decreases to 2 mi/h in the next second, and then remains at 6 mi/h for the last 6 seconds.
Given the function rule f(x) = x² – 3x + 2, what is the output of f(–2)?
A. –8
B. 0
C. 4
D. 12
A. –8
B. 0
C. 4
D. 12
D. 12
Suppose you earn $15 for each car you wash. Which function describes the relationship between your total earnings E and the number of cars you wash, c?
A. E(c) = c + 15
B. E(c) = 15c
C. c = 15E
D. E(c) = c – 15
A. E(c) = c + 15
B. E(c) = 15c
C. c = 15E
D. E(c) = c – 15
B. E(c) = 15c
The data in the table illustrate a linear function.
x 0 2 4 6
y –5 –2 1 4
What is the slope of the linear function? Which graph represents the data?
A. –two-thirds; Four points are graphed on a coordinate plane. A line connects the four points and continues on in both directions.The points graphed on the coordinate plane are left-parenthesis negative 5 comma 0 right-parenthesis, left-parenthesis negative 2 comma 2 right-parenthesis, left-parenthesis 1 comma 4 right-parenthesis, and left-parenthesis 4 comma 6 right-parenthesis.
B. start fraction 3 over 2 end fraction; Four points are graphed on a coordinate plane. A line connects the four points and continues on in both directions.The points graphed on the coordinate plane are left-parenthesis 0 comma negative 5 right-parenthesis, left-parenthesis 2 comma negative 2 right-parenthesis, left-parenthesis 4 comma 1 right-parenthesis, and left-parenthesis 6 comma 4 right-parenthesis.
C. two-thirds; Four points are graphed on a coordinate plane. A line connects the four points and continues on in both directions.The points graphed on the coordinate plane are left-parenthesis negative 5 comma 0 right-parenthesis, left-parenthesis negative 2 comma 2 right-parenthesis, left-parenthesis 1 comma 4 right-parenthesis, and left-parenthesis 4 comma 6 right-parenthesis.
D. –start fraction 3 over 2 end fraction; Four points are graphed on a coordinate plane. A line connects the four points and continues on in both directions.
x 0 2 4 6
y –5 –2 1 4
What is the slope of the linear function? Which graph represents the data?
A. –two-thirds; Four points are graphed on a coordinate plane. A line connects the four points and continues on in both directions.The points graphed on the coordinate plane are left-parenthesis negative 5 comma 0 right-parenthesis, left-parenthesis negative 2 comma 2 right-parenthesis, left-parenthesis 1 comma 4 right-parenthesis, and left-parenthesis 4 comma 6 right-parenthesis.
B. start fraction 3 over 2 end fraction; Four points are graphed on a coordinate plane. A line connects the four points and continues on in both directions.The points graphed on the coordinate plane are left-parenthesis 0 comma negative 5 right-parenthesis, left-parenthesis 2 comma negative 2 right-parenthesis, left-parenthesis 4 comma 1 right-parenthesis, and left-parenthesis 6 comma 4 right-parenthesis.
C. two-thirds; Four points are graphed on a coordinate plane. A line connects the four points and continues on in both directions.The points graphed on the coordinate plane are left-parenthesis negative 5 comma 0 right-parenthesis, left-parenthesis negative 2 comma 2 right-parenthesis, left-parenthesis 1 comma 4 right-parenthesis, and left-parenthesis 4 comma 6 right-parenthesis.
D. –start fraction 3 over 2 end fraction; Four points are graphed on a coordinate plane. A line connects the four points and continues on in both directions.
B. slope = (1 - (-5))/(4 - 0) = 3/2.
The graph that represents the data is: Four points are graphed on a coordinate plane. A line connects the four points and continues on in both directions.The points graphed on the coordinate plane are left-parenthesis 0 comma negative 5 right-parenthesis, left-parenthesis 2 comma negative 2 right-parenthesis, left-parenthesis 4 comma 1 right-parenthesis, and left-parenthesis 6 comma 4 right-parenthesis.
The graph that represents the data is: Four points are graphed on a coordinate plane. A line connects the four points and continues on in both directions.The points graphed on the coordinate plane are left-parenthesis 0 comma negative 5 right-parenthesis, left-parenthesis 2 comma negative 2 right-parenthesis, left-parenthesis 4 comma 1 right-parenthesis, and left-parenthesis 6 comma 4 right-parenthesis.
Question 9 of 19
Which hill described in the table is the steepest and why?
Street
Horizontal Distance (ft)
Vertical Rise of Street (ft)
Dixie Hill
60
20
Bell Hill
60
40
Liberty Hill
60
30
A. Bell Hill; it rises two-thirds foot for every 1 foot of horizontal travel.
B. Dixie Hill; it rises 1 foot for every 3 feet of horizontal travel.
C. Bell Hill; it rises 3 feet for every 2 feet of horizontal travel.
D. Liberty Hill; it rises 2 feet for every 1 foot of horizontal travel.
9 / 19
8 of 19 Answered
Which hill described in the table is the steepest and why?
Street
Horizontal Distance (ft)
Vertical Rise of Street (ft)
Dixie Hill
60
20
Bell Hill
60
40
Liberty Hill
60
30
A. Bell Hill; it rises two-thirds foot for every 1 foot of horizontal travel.
B. Dixie Hill; it rises 1 foot for every 3 feet of horizontal travel.
C. Bell Hill; it rises 3 feet for every 2 feet of horizontal travel.
D. Liberty Hill; it rises 2 feet for every 1 foot of horizontal travel.
9 / 19
8 of 19 Answered
C. Bell Hill; it rises 3 feet for every 2 feet of horizontal travel. It has the steepest slope (rise over run) among the three hills.
Question 10 of 19
Which graph represents the linear function y = start fraction 1 over 4 end fractionx – 3?
A. A line on a graph passes through the points left-parenthesis negative 4 comma negative 4 right-parenthesis left-parenthesis zero comma negative 3 right-parenthesis left-parenthesis 4 comma negative 2 right-parenthesis.
B. A line on a graph passes through the points left-parenthesis negative 4 comma negative 2 right-parenthesis left-parenthesis zero comma negative 3 right-parenthesis left-parenthesis 4 comma negative 4 right-parenthesis.
C. A line on a graph passes through the points left-parenthesis zero comma negative 3 right-parenthesis left-parenthesis 1 comma 1 right-parenthesis left-parenthesis 2 comma 5 right-parenthesis.
D. A line on a graph passes through the points left-parenthesis negative 4 comma 2 right-parenthesis left-parenthesis zero comma 3 right-parenthesis left-parenthesis 4 comma 4 right-parenthesis.
10 / 19
9 of 19 Answered
Which graph represents the linear function y = start fraction 1 over 4 end fractionx – 3?
A. A line on a graph passes through the points left-parenthesis negative 4 comma negative 4 right-parenthesis left-parenthesis zero comma negative 3 right-parenthesis left-parenthesis 4 comma negative 2 right-parenthesis.
B. A line on a graph passes through the points left-parenthesis negative 4 comma negative 2 right-parenthesis left-parenthesis zero comma negative 3 right-parenthesis left-parenthesis 4 comma negative 4 right-parenthesis.
C. A line on a graph passes through the points left-parenthesis zero comma negative 3 right-parenthesis left-parenthesis 1 comma 1 right-parenthesis left-parenthesis 2 comma 5 right-parenthesis.
D. A line on a graph passes through the points left-parenthesis negative 4 comma 2 right-parenthesis left-parenthesis zero comma 3 right-parenthesis left-parenthesis 4 comma 4 right-parenthesis.
10 / 19
9 of 19 Answered
A. A line on a graph passes through the points left-parenthesis negative 4 comma negative 4 right-parenthesis left-parenthesis zero comma negative 3 right-parenthesis left-parenthesis 4 comma negative 2 right-parenthesis.
Question 12 of 19
Which function rule represents the data in the table below?
Input (x)
1
2
3
4
5
Output (y)
9
15
21
27
33
A. y = 4 + 5x
B. y = 3 + 6x
C. y = 5 + 4x
D. y = 6 + 3x
12 / 19
11 of 19 Answered
Which function rule represents the data in the table below?
Input (x)
1
2
3
4
5
Output (y)
9
15
21
27
33
A. y = 4 + 5x
B. y = 3 + 6x
C. y = 5 + 4x
D. y = 6 + 3x
12 / 19
11 of 19 Answered
C. y = 5 + 4x
Mia charges $2.25 per hour when she babysits, plus $5.00 for transportation expenses. Which function rule represents the amount y Mia charges to babysit for x hours?
A. y = 2.25x + 5.00
B. x = 5.00y + 2.25
C. y = 5.00x + 2.25
D. y = 7.25x
A. y = 2.25x + 5.00
B. x = 5.00y + 2.25
C. y = 5.00x + 2.25
D. y = 7.25x
A. y = 2.25x + 5.00
The sale price of shrimp at a local grocery store is $1.15 for the first ounce and $0.95 for each additional ounce. Which function rule shows how the cost of shrimp, y, depends on the number of ounces, x?
A. y = 1.15x + 0.95
B. y = (0.95 + 1.15)x
C. y = 0.95x + 1.15
D. y = 0.95(x – 1) + 1.15
A. y = 1.15x + 0.95
B. y = (0.95 + 1.15)x
C. y = 0.95x + 1.15
D. y = 0.95(x – 1) + 1.15
D. y = 0.95(x – 1) + 1.15
Which function rule represents the data in the table?
x
–3
–2
–1
0
1
y
–17
–14
–11
–8
–5
A. y = –3x – 8
B. y = one-thirdx – 8
C. y = 3x – 8
D. y = one-thirdx + 8
x
–3
–2
–1
0
1
y
–17
–14
–11
–8
–5
A. y = –3x – 8
B. y = one-thirdx – 8
C. y = 3x – 8
D. y = one-thirdx + 8
A. y = -3x - 8
Question 16 of 19
Which quadratic rule represents the data in the table?
x
–1
0
1
2
3
y
4
5
4
1
–4
A. y = –2x² + 5
B. y = –x² + 5
C. y = x² – 5
D. y = x² + 5
16 / 19
15 of 19 Answered
Which quadratic rule represents the data in the table?
x
–1
0
1
2
3
y
4
5
4
1
–4
A. y = –2x² + 5
B. y = –x² + 5
C. y = x² – 5
D. y = x² + 5
16 / 19
15 of 19 Answered
B. y = -x² + 5
A 154-lb person burns 420 calories per hour riding an exercise bicycle at a rate of 15 mi/hr. Write a function rule to represent the total calories burned over time by that person. Explain how the information in the problem relates to the function.
Let t be the time (in hours) spent riding the bicycle.
Since the person burns 420 calories per hour, the calories burned during any given hour is 420t.
The rate of 15 mi/hr is not needed to find the total calories burned, but can be used to verify that the information in the problem relates to the function.
The function rule to represent the total calories burned over time by that person is:
Calories burned = 420t
where t is the time (in hours) spent riding the bicycle.
The function shows that the calories burned are directly proportional to the time spent riding the bicycle. The rate of 15 mi/hr is given to provide additional information about the conditions under which the person is riding the exercise bicycle - it does not directly relate to the function.
Since the person burns 420 calories per hour, the calories burned during any given hour is 420t.
The rate of 15 mi/hr is not needed to find the total calories burned, but can be used to verify that the information in the problem relates to the function.
The function rule to represent the total calories burned over time by that person is:
Calories burned = 420t
where t is the time (in hours) spent riding the bicycle.
The function shows that the calories burned are directly proportional to the time spent riding the bicycle. The rate of 15 mi/hr is given to provide additional information about the conditions under which the person is riding the exercise bicycle - it does not directly relate to the function.
Can you shorten it and get to the point quicker please
Sure!
Let t be the time (in hours) spent riding the bicycle. The function rule to represent the total calories burned over time by the person is Calories burned = 420t. The function shows that the calories burned are directly proportional to the time spent riding the bicycle. The rate of 15 mi/hr is given to provide additional information about the conditions under which the person is riding the exercise bicycle - it does not directly relate to the function.
Let t be the time (in hours) spent riding the bicycle. The function rule to represent the total calories burned over time by the person is Calories burned = 420t. The function shows that the calories burned are directly proportional to the time spent riding the bicycle. The rate of 15 mi/hr is given to provide additional information about the conditions under which the person is riding the exercise bicycle - it does not directly relate to the function.
Explain how to write a function rule from the table below. Then write a function rule.
x 0 2 4 6
y 2 1 0 –1
x 0 2 4 6
y 2 1 0 –1
To write a function rule from a table, we need to determine how the output (y) is changing with respect to the input (x). We can do this by examining how the values in the y column change from row to row as the x values increase.
In this case, we can see that the output (y) decreases by 1 each time the input (x) increases by 2. This tells us that the relationship between x and y is linear, with a slope of -1/2.
To find the y-intercept, we can look at the first row of the table, where x = 0 and y = 2. This means that the function has a y-intercept of 2.
Therefore, the function rule for this table is:
y = -1/2x + 2
In this case, we can see that the output (y) decreases by 1 each time the input (x) increases by 2. This tells us that the relationship between x and y is linear, with a slope of -1/2.
To find the y-intercept, we can look at the first row of the table, where x = 0 and y = 2. This means that the function has a y-intercept of 2.
Therefore, the function rule for this table is:
y = -1/2x + 2
SHorter please
To write the function rule for the given table, we first observe that the relationship between x and y is linear. We find that the slope of the line is -1/2 and the y-intercept is 2. Therefore, the function rule is y = -1/2x + 2.
...shorter?
Function rule: y = -1/2x + 2 (linear, with slope -1/2 and y-intercept 2)
The graph below shows the average daily temperature over the period of a year. Explain how each labeled section of the graph relates to the four seasons.
A graph is shown.
A graph is shown.
The graph likely shows four labeled sections, one for each season of the year.
During the first section, which may be labeled as winter, the average daily temperature is likely at its lowest for the year. This corresponds with the colder temperatures around the winter solstice.
The second section, labeled spring, may show a slow increase in temperature as the season progresses. This corresponds with the months leading up to the summer solstice, which have gradually increasing temperatures.
The third section, labeled summer, may show the highest average daily temperatures for the year. This corresponds with the months surrounding the summer solstice, which tend to have the warmest temperatures of the year.
Finally, the fourth section, labeled fall or autumn, may show a slow decrease in temperature as the season progresses. This corresponds with the months leading up to the winter solstice, which have gradually decreasing temperatures.
Overall, the graph likely shows how the average daily temperature changes over the course of a year, with each of the four labeled sections corresponding to one of the four seasons.
During the first section, which may be labeled as winter, the average daily temperature is likely at its lowest for the year. This corresponds with the colder temperatures around the winter solstice.
The second section, labeled spring, may show a slow increase in temperature as the season progresses. This corresponds with the months leading up to the summer solstice, which have gradually increasing temperatures.
The third section, labeled summer, may show the highest average daily temperatures for the year. This corresponds with the months surrounding the summer solstice, which tend to have the warmest temperatures of the year.
Finally, the fourth section, labeled fall or autumn, may show a slow decrease in temperature as the season progresses. This corresponds with the months leading up to the winter solstice, which have gradually decreasing temperatures.
Overall, the graph likely shows how the average daily temperature changes over the course of a year, with each of the four labeled sections corresponding to one of the four seasons.
Shorter
Shorter please?
The labeled sections of the graph likely correspond to the four seasons, with winter having the lowest temperatures, spring showing a gradual increase, summer having the highest temperatures, and fall showing a gradual decrease in temperature. The graph shows how the average daily temperature changes over a year.
Shorter please
The graph shows the temperature changes over a year. The labeled sections correspond to the four seasons and show how the temperatures increase and decrease during those times of the year.
21 answers