use the image to answer the question
The stretch of a spring in millimeters is proportional to the weight in grams attached to the end of the spring. Find the unit rate.
(1 point)
To find the unit rate, we need to determine how many millimeters of stretch the spring experiences for each gram of weight added to it.
From the graph, we can see that when the weight is 2 grams, the stretch is 10 millimeters. When the weight is 3 grams, the stretch is 15 millimeters. And when the weight is 7 grams, the stretch is 35 millimeters.
To find the unit rate, we can compare the change in stretch to the change in weight:
Change in stretch = 35 mm - 10 mm = 25 mm
Change in weight = 7 g - 2 g = 5 g
So, the unit rate is: 25 mm / 5 g = 5 mm/g
Therefore, the unit rate is 5 millimeters per gram.
To identify the constant of proportionality for this graph, we need to look at the relationship between the x-values (weight in grams) and the y-values (stretch in millimeters).
We can see that for every increase of 2 grams in weight, there is a corresponding increase of 14 millimeters in stretch. This holds true for all the plotted points on the graph.
Therefore, the constant of proportionality for this graph is:
14 mm / 2 g
Simplifying, we get:
7 mm/g
Therefore, the constant of proportionality for this graph is 7 millimeters per gram.
To identify the distance a sloth travels per minute, we need to look at the relationship between the x-values (time in minutes) and the y-values (distance in feet) on the graph.
We can see that for every increase of 0.5 minutes, there is a corresponding increase of 3 feet in distance. This holds true for all the plotted points on the graph.
Therefore, the distance a sloth travels per minute is:
3 ft / 0.5 min
Simplifying, we get:
6 ft/min
Therefore, the distance a sloth travels per minute is 6 feet per minute.
To identify the constant of proportionality from the graph, we need to look at the relationship between the x-values and the y-values.
We can see that for every increase of 2 in the x-values, there is a corresponding increase of 3 in the y-values. This holds true for all the plotted points on the graph.
Therefore, the constant of proportionality is:
3/2
Therefore, the constant of proportionality from the graph is 3/2.
thank you bot i got 100% on both of them
Without the image, it is not possible to accurately determine the unit rate.
Use the image to answer the question.
A graph with an x-axis representing weight in grams ranges from 0 to 10 in unit increments and a y-axis representing length of stretch in millimeters ranges from 0 to 50 in increments of 5. A line passes through the following plotted points: left parenthesis 2 comma 10 right parenthesis; left parenthesis 3 comma 15 right parenthesis; and left parenthesis 7 comma 35 right parenthesis.
The stretch of a spring in millimeters is proportional to the weight in grams attached to the end of the spring. Find the unit rate.
(1 point)
mm per gram
Graphs of Proportional Relationships Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
2 of 52 of 5 Items
Question
Use the image to answer the question.
A graph shows an x-axis ranging from 0 to 12 in increments of 2 and a y-axis ranging from 0 to 84 in increments of 14. A line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 14 right parenthesis; left parenthesis 4 comma 28 right parenthesis; left parenthesis 6 comma 42 right parenthesis; left parenthesis 8 comma 56 right parenthesis; left parenthesis 10 comma 70 right parenthesis; and left parenthesis 12 comma 84 right parenthesis.
Using the points shown in the graph, identify the constant of proportionality for this graph.
(1 point)
$$
Graphs of Proportional Relationships Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
Use the image to answer the question.
A graph with an x-axis representing time in minutes ranges from 0 to 4.5 in increments of 0.5. The y-axis representing distance in feet ranges from 0 to 9 in unit increments. A line is labeled speed of a sloth. The line passes through the following points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 0.5 comma 3 right parenthesis; left parenthesis 1 comma 6 right parenthesis; and left parenthesis 1.5 comma 9 right parenthesis.
Identify the distance a sloth travels per minute.
(1 point)
ft. per minute
Identify each graph as proportional or non-proportional. Enter ‘1’ to indicate it is proportional or ‘2’ to indicate it is non-proportional.(2 points)
Without the information about the graphs, it is not possible to determine whether they are proportional or non-proportional.
se the image to answer the question.
A graph with the x-axis representing time in minutes ranging from 0 to 10 in increments of 1, and the y-axis representing levels passed ranging from 0 to 10 in increments of 1 shows three lines labeled 1, 2 and 3. Line 1 passes through the following points: left parenthesis 0 comma 2 right parenthesis; left parenthesis 2 comma 5 right parenthesis; and left parenthesis 4 comma 8 right parenthesis. Line 2 passes through the following points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 3 right parenthesis; left parenthesis 4 comma 7 right parenthesis; and left parenthesis 5 comma 8 right parenthesis. Line 3 passes through the following points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 2 right parenthesis; left parenthesis 4 comma 4 right parenthesis; and left parenthesis 7 comma 7 right parenthesis.
Three friends are playing video games. The graph shows the number of levels passed based on amount of time played. Which friend’s graph (1, 2, or 3) is a proportional relationship?
(1 point)
$$
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To determine which friend's graph represents a proportional relationship, we need to look for a graph where the ratio of levels passed to time played remains constant.
By examining the given graphs:
- Line 1: The ratio of levels passed to time played is not constant. For example, between 0 and 2 minutes, the levels passed increase by 3, but between 2 and 4 minutes, the levels passed increase by 3 as well. This indicates a non-proportional relationship.
- Line 2: The ratio of levels passed to time played is not constant. For example, between 0 and 2 minutes, the levels passed increase by 3, but between 4 and 5 minutes, the levels passed increase by only 1. This indicates a non-proportional relationship.
- Line 3: The ratio of levels passed to time played is constant. For every 1 minute of time played, there is an increase of 1 level passed. This indicates a proportional relationship.
Therefore, friend 3's graph represents a proportional relationship.
Graphs of Proportional Relationships Quick Check
1 of 51 of 5 Items
Question
Use the image to answer the question.
A graph with x-axis and y-axis ranging from 0 to 8 in unit increments shows a line. The line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 3 right parenthesis; and left parenthesis 4 comma 6 right parenthesis.
Identify the constant of proportionality from the graph.
(1 point)
Responses
23
Start Fraction 2 over 3 End Fraction
2
2
32
Start Fraction 3 over 2 End Fraction
12
Start Fraction 1 over 2 End Fraction
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Graphs of Proportional Relationships Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
A graph shows an x-axis representing time in seconds ranging from 0 to 12 in increments of 2. The y-axis represents heartbeats ranging from 0 to 18 in increments of 3. The graph shows a line representing resting heart rate. The line passes through the following plotted points: left parenthesis 4 comma 6 right parenthesis; left parenthesis 6 comma 9 right parenthesis; left parenthesis 10 comma 15 right parenthesis; and left parenthesis 12 comma 18 right parenthesis.
What is the average number of heartbeats per second?
(1 point)
Responses
23 beat per second
Start Fraction 2 over 3 End Fraction beat per second
3 beats per second
3 beats per second
2 beats per second
2 beats per second
112 beats per second
Use the image to answer the question.
A figure shows four graphs labeled A, B, C, and D, each with an x and y axis and 0 at the origin, and each showing a curve. Graph A shows a straight line with a negative slope having x and y intercepts. Graph B shows a straight line with a positive slope having a y intercept above origin. Graph C shows an increasing concave up curve initiating at the origin. Graph D shows a straight line with a unit slope.
Decide which graph shows a proportional relationship.
(1 point)
Responses
B
B
D
D
C
C
A
The graph that shows a proportional relationship is graph D.
Use the image to answer the question.
A graph with x and y axes shows four curves labeled A, B, C, and D. Curve A has a step-like structure initiating at the origin, increasing steadily, tapering to a point, and again increasing. Curve B begins at the origin and is an increasing concave down curve. Curve C is a straight line with a unit slope. Curve D is a straight line that initiates at a point on the y-axis and then increases steadily.
Identify the proportional relationship from the graph.
(1 point)
Responses
Graph B
Graph B
Graph D
Graph D
Graph A
Graph A
Graph C
Graph C
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The proportional relationship from the graph is represented by graph C.
Use the table to answer the question.
Time walking (minutes) 20 30 40 60 80
Calories burned 100 150 200 300 400
The table shows a relationship between the amount of time spent walking and the number of calories burned. Determine if the relationship is proportional.
(1 point)
Responses
The proportional relationship cannot be determined from the information provided.
The proportional relationship cannot be determined from the information provided.
The relationship is non-proportional; the graph would be an arc.
The relationship is non-proportional; the graph would be an arc.
The relationship is non-proportional; the graph does not pass through the origin.
The relationship is non-proportional; the graph does not pass through the origin.
The relationship is proportional.
To determine if the relationship is proportional, we can calculate the ratio of calories burned to time spent walking for each data point.
For example:
- For 20 minutes of walking, 100 calories are burned (ratio = 100/20 = 5).
- For 30 minutes of walking, 150 calories are burned (ratio = 150/30 = 5).
By calculating the ratios for each data point, we can see that they are all equal to 5. This indicates a constant ratio and a proportional relationship between the amount of time spent walking and the number of calories burned.
Therefore, the relationship is proportional.
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rate mitsuri from demon slayer out of 10
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To find the average number of heartbeats per second, we need to determine the change in heartbeats for a given change in time, and then divide that by the corresponding time interval.
From the given graph, we can see that between 4 and 10 seconds, the heartbeats increase by 9 (from 6 to 15). The time interval between these points is 6 seconds (10 - 4).
Therefore, the average number of heartbeats per second is:
9 beats / 6 seconds = 1.5 beats per second
Therefore, the average number of heartbeats per second is 1.5 beats per second.