Use the image to answer the question.
An illustration shows quadrant four of a coordinate plane where the x-axis ranges from 0 to 6 in increments of one and the y-axis ranges from 0 to negative 6 in increments of one. The line passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 4 comma negative 6 right parenthesis.
What is the rate of this graph?(1 point)
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The rate of the graph is the change in y-coordinates divided by the change in x-coordinates.
In this case, the change in y-coordinates is -6 (from 0 to -6), and the change in x-coordinates is 4 (from 0 to 4).
Therefore, the rate of the graph is -6/4 = -3/2.
To compare the cost of the two memberships for a year, we can write two equations in the form of y = kx, where y represents the cost and x represents the number of months.
For Gym A, the equation is y = kx, where y is the cost of the Gym A membership and x is the number of months. Since Gym A costs $50 for 5 months, we can substitute these values into the equation: 50 = 5k.
Simplifying the equation, we get 10 = k.
For Gym B, the equation is y = kx, where y is the cost of the Gym B membership and x is the number of months. Since Gym B costs $40 for 3 months, we can substitute these values into the equation: 40 = 3k.
Simplifying the equation, we get 13.33 = k.
To find the value of k for the cheaper membership, we compare 10 and 13.33. Since 10 is smaller than 13.33, the value of k for the cheaper membership is 10.
To find the unit cost from the graph, we need to determine the cost per marker.
The unit cost is given by the slope of the line, which is the change in y-coordinates divided by the change in x-coordinates.
In this case, the change in y-coordinates is 3 (from 0 to 3), and the change in x-coordinates is 4 (from 0 to 4).
Therefore, the unit cost from the graph is $3/4 per marker.
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled total cost in dollars and the x-axis is titled number of markers. A line is marked on the graph, passing through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 4 comma 3 right parenthesis.
What is the unit cost from the graph?(1 point)
$
per marker
A membership at Gym A costs $50 for 5 months. A membership at Gym B down the street costs $40 for 3 months. You write two equations in the form of y=kx to try and figure out which membership would be cheaper for a year. What is the value of k for the cheaper membership?(1 point)
Two equations are written to express how far a car can go when driving on different roads. On Road 1, the car can go 60 miles in 2 hours. On Road 2, the car can go 90 miles in 4 hours. Write an equation where y
is the distance in miles and x is the time in hours to represent the motion of the faster car.(1 point)
are you sure
Apologies for the previous incorrect response. Let's correct it:
To find the equation for the motion of the faster car, we need to determine the rate at which it travels in miles per hour. We can do this by calculating the average speed for each road.
For Road 1, the car travels 60 miles in 2 hours. Therefore, the average speed is 60 miles divided by 2 hours, which is 30 miles per hour.
For Road 2, the car travels 90 miles in 4 hours. Therefore, the average speed is 90 miles divided by 4 hours, which is 22.5 miles per hour.
Since the car travels faster on Road 1, the equation for the motion of the faster car would be y = 30x, where y represents the distance in miles and x represents the time in hours.
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Which of these objects is moving at a rate of 2 feet per second?
(1 point)
Responses
object C
object C
object A
object A
all of the objects
all of the objects
object B
object B
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To determine which object is moving at a rate of 2 feet per second, we need to find the slope of each line on the graph. The slope represents the rate of change of distance with respect to time.
For line A, the slope is the change in y-coordinates divided by the change in x-coordinates. In this case, the change in y-coordinates is 6 (from 0 to 6), and the change in x-coordinates is 3 (from 0 to 3). Therefore, the slope of line A is 6/3 = 2 feet per second.
For line B, the slope is also 2 feet per second because the line has a constant slope and passes through coordinates (0,0) and (6,6).
For line C, the slope is the change in y-coordinates divided by the change in x-coordinates. In this case, the change in y-coordinates is 3 (from 0 to 3), and the change in x-coordinates is 6 (from 0 to 6). Therefore, the slope of line C is 3/6 = 1/2 feet per second.
Based on this analysis, the only object moving at a rate of 2 feet per second is object A.
Compare Proportions from Graphs & Equations Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled total cost in dollars and the x-axis is titled number of markers. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Predict what the total cost would be for buying 10 of the type A markers.
(1 point)
Responses
$0.50
$0.50
$5.00
$5.00
$2.00
$2.00
$20.00
$20.00
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To predict the total cost of buying 10 of the type A markers, we can use the equation for the line A.
From the graph, we can see that the line passes through coordinates (0,0) and (3,6). This means that when the number of markers is 0, the total cost is 0, and when the number of markers is 3, the total cost is 6.
We can write the equation for line A as y = mx, where y represents the total cost and x represents the number of markers. To find the value of m (the slope), we can use the coordinates (0,0) and (3,6).
The slope (m) is equal to the change in y-coordinates divided by the change in x-coordinates. In this case, the change in y-coordinates is 6 (from 0 to 6), and the change in x-coordinates is 3 (from 0 to 3). Therefore, the slope is 6/3 = 2.
Now we have the equation for line A: y = 2x.
To find the total cost for buying 10 markers, we substitute x = 10 into the equation: y = 2(10) = 20.
Therefore, the total cost for buying 10 of the type A markers is $20.
You are going to drive to another state for a vacation. One route will take 8 hours to drive 400 miles, and the other route will take 7 hours to drive 420 miles. You write two equations to try and figure out the average rate of speed you would travel on each route. How much higher will your average speed be on the faster route?(1 point)
Responses
20 mph
20 mph
60 mph
60 mph
10 mph
10 mph
50 mph
To calculate the average speed for each route, we need to divide the total distance by the total time taken for each route.
For the first route, the distance is 400 miles and the time taken is 8 hours. Therefore, the average speed for the first route is 400 miles divided by 8 hours, or 50 mph.
For the second route, the distance is 420 miles and the time taken is 7 hours. Therefore, the average speed for the second route is 420 miles divided by 7 hours, or 60 mph.
To find the difference in average speed between the two routes, we subtract the average speed of the slower route from the average speed of the faster route: 60 mph - 50 mph = 10 mph.
Therefore, the average speed will be 10 mph higher on the faster route.
A candy store sells different types of candy by the ounce. Red Snaps cost $0.25 per ounce, and Blue Tarts cost $0.30 per ounce. You decide to buy 8 ounces of candy to share with your friends. How much more expensive would it be to get a bag of Blue Tarts instead of a bag of Red Snaps?(1 point)
Responses
$0.40
$0.40
$4.40
$4.40
$2.00
$2.00
$2.40
To calculate how much more expensive it would be to get a bag of Blue Tarts instead of a bag of Red Snaps, we need to compare the cost per ounce of each type of candy.
Red Snaps cost $0.25 per ounce, so for 8 ounces, the total cost would be 8 * $0.25 = $2.00.
Blue Tarts cost $0.30 per ounce, so for 8 ounces, the total cost would be 8 * $0.30 = $2.40.
To find out the difference in cost, we subtract the cost of Red Snaps from the cost of Blue Tarts: $2.40 - $2.00 = $0.40.
Therefore, it would be $0.40 more expensive to get a bag of Blue Tarts instead of a bag of Red Snaps.
You are training twice a week for a race. On Monday, you go 4 miles in 40 minutes. Then on Wednesday you go 2 miles in 16 minutes. Write an equation where y is the number of miles and x is the time in minutes for the day you ran the fastest for the week.(1 point)
Responses
y=8x
y equals 8 x
y=0.1x
y equals 0.1x
y=10x
y equals 10 x
y=0.125x
To determine which equation represents the relationship between the number of miles (y) and the time in minutes (x) on the day you ran the fastest for the week, we need to compare the rates of motion for each run. The fastest run would have the highest rate.
The rate of motion is calculated by dividing the distance by the time.
For the Monday run, you went 4 miles in 40 minutes. The rate of motion for this run is 4 miles / 40 minutes = 0.1 miles per minute.
For the Wednesday run, you went 2 miles in 16 minutes. The rate of motion for this run is 2 miles / 16 minutes = 0.125 miles per minute.
Since the Wednesday run had a higher rate of motion, we can conclude that it represents the day you ran the fastest for the week.
Therefore, the correct equation is y = 0.125x. This means that the number of miles (y) is equal to 0.125 times the time in minutes (x) on the day you ran the fastest for the week.
What happened when Cortés and his soldiers first arrived in the Aztec capital of Tenochtitlán?
(1 point)
Responses
The Spanish army became ill with smallpox.
The Spanish army became ill with smallpox.
The Aztec ruler Moctezuma welcomed them as guests at first.
The Aztec ruler Moctezuma welcomed them as guests at first.
The Aztec army attacked Cortés and his soldiers.
The Aztec army attacked Cortés and his soldiers.
Cortés immediately killed the Aztec leader Moctezuma and burned the city.
Cortés immediately killed the Aztec leader Moctezuma and burned the city.
The correct response is: The Aztec ruler Moctezuma welcomed them as guests at first.
What happened to American Indians as a result of the Spanish conquest of the Americas?
(1 point)
Responses
Those who converted to Christianity were given freedom.
Those who converted to Christianity were given freedom.
Many died from disease and mistreatment.
Many died from disease and mistreatment.
Many migrated north to escape Spanish rule.
Many migrated north to escape Spanish rule.
They learned new ways to farm their land.
The correct response is: Many died from disease and mistreatment.
Use the drop-down menu to complete the sentence.(1 point)
In Spanish colonial society, the group in the highest position were the
Choose
Peninsulares
To represent the motion of the faster car, we will use the equation y = kx, where y represents the distance in miles and x represents the time in hours.
Given that the car can go 60 miles in 2 hours on Road 1, we can substitute these values into the equation to find the value of k: 60 = 2k.
Simplifying the equation, we get k = 30.
Therefore, the equation for the motion of the faster car is y = 30x.