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)
Skip to navigation
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
Skip to navigation
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.