1. The graph shows the distance a ghost crab can run over time.
A graph is shown in the xy-plane. The x-axis is labeled as Time in seconds and the y-axis is labeled as Distance in Meters. The values on the x-axis ranges from 0 to 9 in increments of 1 and the values on the y-axis ranges from 0 to 45 in increments of 5. A line starts from the origin, goes up, and passes through the points (3, 5), (6, 10), and so on.
Let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation for this relationship?
A. d= 3/5t
b. d=5/3t
c. t=5/3d
d. t=2/5d
2.Which of the following graphs shows a direct variation?
3.Which graph displays equivalent ratios? Select all that apply.
4.The relationship between the number of girls who are in the middle school and high school jazz bands is proportional. What is the constant of proportionality?
Jazz Band Number of Girls Total Members
Middle School 6 15
High School 8 20
a. 3/10
b. 2/5
c. 8/15
d. 3/4
5.A real estate agent received a $17,500 commission on the sale of a $350,000 house on Walnut Street. The same agent received a $20,000 commission on the sale of a house on Center Avenue. What was the sale price of the house on Center Avenue?
A.
$100,000
B.
$370,000
C.
$400,000
D.
$450,000
6.The number of pages Cameron reads varies directly with time in minutes. He can read 15 pages in 60 minutes. What is the constant of proportionality for the number of minutes to read 1 page.
A. 1/4
B. 1/2
C. 2
D. 4
7.In the graph, the amount of sales tax (t) is proportional to the price (p) of an item.
A graph is shown in the xy-plane. The x-axis is labeled as Price left parenthesis dollars right parenthesis and the y-axis is labeled as Tax left parenthesis cents right parenthesis. The values on the x-axis ranges from 0 to 4 in increments of 1 and the values on the y-axis ranges from 0 to 0 decimal point 4 0 in increments of 0 decimal point 1 0. A line starts from the origin, goes up and Five points are marked on the line with coordinates (0, 0), (1, 0 decimal point 0 6), (2, 0 decimal point 1 2), (3, 0 decimal point 1 8), and (4, 0 decimal point 2 4).
Which equation represents this relationship?
A. T=0.05P
B. T=0.06P
C. T=0.96P
D. T=1.6P
8.Consider the graph shown.
A graph is shown in the xy-plane. The values on the x-axis ranges from 0 to 1 decimal point 5 in increments of 0 decimal point 5 and the values on the y-axis ranges from 0 to 800 in increments of 200. A line starts from a point 100 on the y-axis, goes up, and passes through the points (0, 100), (0 decimal point 3, 200), (0 decimal point 9, 400), and (1 decimal point 5, 600).
Determine if the graph shows two quantities that vary directly. If possible, determine the constant of proportionality. Explain your reasoning.
9.Determine the constant of proportionality for the graph.
A graph is shown in the xy-plane. The x-axis is labeled as Items and the y-axis is labeled as Profit left parenthesis dollars right parenthesis. The values on the x-axis ranges from 0 to 40 in increments of 10 and the values on the y-axis ranges from 0 to 8 in increments of 2. Five points are marked on the graph with coordinates (0, 0), (10, 2), (20, 4), (30, 6), and (40, 8).
A. 1/5
B. 2
C. 5
D.10
10.Tanya polled boys and girls in her grade to determine how many prefer math to other subjects. Her results are shown in the table.
Students Prefer Math Total Students
Boys 14 30
Girls 16 32
Which is a true statement?
A. the relationship is prportional because
16-4=2 and 32-30=2
B. the relationship is prportional because
30-14=16 and 32-16=16
C. the relationship is not prportional because
14/16=7/8 and 30/35=15/16
D. the relationship is not prportional because
14/30=7/15 and 16/32=1/2
if i get an f il absolutely get the full force of angry mom
1. The direct variation equation for this relationship is option C: t = 5/3d. This equation states that the time t varies directly with the distance d, with a constant of proportionality of 5/3.
2. Without a visual representation, it is not possible to determine which of the following graphs shows a direct variation.
3. Without the given graphs, it is not possible to determine which graph displays equivalent ratios.
4. The constant of proportionality for the relationship between the number of girls in the middle school and high school jazz bands is option a: 3/10. This can be found by calculating the ratio of the number of girls to the total members for both bands: (6/15) = (8/20) = 3/10.
5. The sale price of the house on Center Avenue can be calculated using the given information. Since the agent received a $17,500 commission on a $350,000 house, the commission rate is 5% (17,500/350,000). Therefore, if the agent received a $20,000 commission on the house on Center Avenue, the sale price of that house would be $400,000. The correct answer is option C.
6. The constant of proportionality for the number of minutes to read 1 page is option D: 4. This can be found by calculating the ratio of the number of pages to the time in minutes: (15/60) = (1/4).
7. The equation that represents the relationship between the amount of sales tax (t) and the price (p) of an item is option A: T=0.05P. The equation shows a constant of proportionality of 0.05, indicating that the amount of sales tax is 5% of the price.
8. The graph shows two quantities that vary directly. The line passes through the origin, indicating a direct variation relationship. The constant of proportionality can be determined by calculating the ratio of the y-values to the x-values for any two points on the line. For example, (0.3/0.1) = (200/100) = 2. Therefore, the constant of proportionality is 2.
9. The constant of proportionality for the given graph is option C: 5. This can be found by calculating the ratio of the y-values to the x-values for any two points on the graph. For example, (2/10) = (0.2/1) = 5.
10. The relationship between the number of boys and girls who prefer math is not proportional. The statement in option D correctly states that the relationship is not proportional because the fraction (14/30) is not equal to the fraction (16/32).
1. To determine the direct variation equation for the relationship between distance and time, we can use the formula for direct variation, which is in the form of y = kx, where y represents the dependent variable, x represents the independent variable, and k is the constant of variation. In this case, let d represent the distance and t represent the time. We can find the equation by identifying two corresponding points on the graph.
From the graph, we can see that at time t = 3, the distance is d = 5, and at time t = 6, the distance is d = 10. We can use these two points to find the constant of variation.
First, calculate the value of k: k = d / t
k = (10 - 5) / (6 - 3)
k = 5 / 3
Now we can write the direct variation equation:
d = (5/3) * t
Therefore, the correct direct variation equation for this relationship is B. d = (5/3)t.
2. To determine which graph shows a direct variation, you need to understand the characteristics of a direct variation. In a direct variation, as one variable increases, the other variable also increases or decreases proportionally. This relationship is represented by a straight line passing through the origin (0,0) on a graph.
Examine the given graphs and look for a straight line passing through the origin. The graph that satisfies this criterion represents a direct variation.
3. To determine which graph displays equivalent ratios, you need to compare the ratios for each graph. Equivalent ratios have the same value when simplified to the lowest terms.
Examine the given graphs and identify the ratios represented by each point or line in the graph. Compare these ratios to see if any are equivalent.
4. To find the constant of proportionality for the relationship between the number of girls and total members in the jazz bands, we can use the formula k = y / x, where k is the constant of proportionality, y is the dependent variable (number of girls), and x is the independent variable (total members).
In this case, we can find the constant of proportionality by comparing the ratios between the number of girls and total members for each jazz band.
For the middle school jazz band, the ratio is 6 girls / 15 total members, which simplifies to 2/5.
For the high school jazz band, the ratio is 8 girls / 20 total members, which also simplifies to 2/5.
Since the ratios are the same for both jazz bands, the constant of proportionality is 2/5. Therefore, the correct answer is B. 2/5.
5. To find the sale price of the house on Center Avenue, we can use the concept of proportionality. Commission is directly proportional to the sale price.
The agent received a $17,500 commission on a $350,000 house, and a $20,000 commission on the Center Avenue house. We can set up a proportion to find the sale price:
Commission1 / Price1 = Commission2 / Price2
17500 / 350000 = 20000 / Price2
Cross-multiplying, we get:
17500 * Price2 = 20000 * 350000
Price2 = (20000 * 350000) / 17500
Price2 = 400000
Therefore, the sale price of the house on Center Avenue is $400,000. The correct answer is C. $400,000.
6. To find the constant of proportionality for the number of minutes it takes Cameron to read 1 page, we can use the formula k = y / x, where k is the constant of proportionality, y is the dependent variable (number of pages), and x is the independent variable (time in minutes).
In this case, we are given that Cameron can read 15 pages in 60 minutes. To find the constant of proportionality, we can divide the number of pages by the time in minutes:
k = 15 pages / 60 minutes
Simplifying this ratio, we get:
k = 1/4 pages per minute
Therefore, the constant of proportionality for the number of minutes to read 1 page is A. 1/4.
7. To determine the equation that represents the relationship between the amount of sales tax (t) and the price (p) of an item, we need to analyze the given graph.
The line on the graph represents a proportional relationship, as a straight line passing through the origin indicates direct variation.
Based on the graph, we can see that as the price increases, the amount of sales tax also increases. The equation that represents this relationship is:
t = 0.06p
Therefore, the correct equation that represents this relationship is B. t = 0.06p.
8. To determine if the given graph shows two quantities that vary directly, we need to examine if the graph represents a straight line passing through the origin (0,0).
From the description of the graph, it starts from a point on the y-axis and passes through several points on the line. If the points on the line form a straight line passing through the origin, then the graph shows two quantities that vary directly.
By examining the given graph, if it indeed forms a straight line passing through the origin, then the quantities represented on the graph vary directly. If it does not form a straight line passing through the origin, then the quantities do not vary directly.
To determine the constant of proportionality, we need to find the ratio between the two variables at any two points on the line and simplify it. If the ratios are equal, then that value should be the constant of proportionality.
9. To find the constant of proportionality for the graph, we can identify two points that lie on the line and calculate the ratio of the y-values to the x-values.
Using the given points (0, 0) and (10, 2), we can calculate the constant of proportionality:
k = Δy / Δx
= (2 - 0) / (10 - 0)
= 2 / 10
= 1/5
Therefore, the constant of proportionality for the graph is A. 1/5.
10. To determine if the relationship between the number of students who prefer math and the total number of students is proportional, we can compare the ratios between the number of boys and the total number of students, and the number of girls and the total number of students.
For the boys, the ratio is 14/30, and for the girls, the ratio is 16/32. Simplifying both ratios, we get 7/15 for the boys and 1/2 for the girls.
Since the two ratios are not equal, the relationship is not proportional.
Therefore, the correct statement is D. The relationship is not proportional because 14/30 = 7/15 and 16/32 = 1/2.
Remember, it's important to always give your best effort and if you are struggling, seek help from a teacher or tutor. Your parents might be disappointed if you don't do well, but it's important to remember that learning is a process, and everyone makes mistakes.