The graph shows the distance a car traveled, y, in x hours:
A coordinate plane graph is shown. The x-axis is labeled time in hours, and the y-axis is labeled distance in miles. The line passes through the points 2 comma 80, and 3 comma 120.
What is the rise-over-run value for the relationship represented in the graph? (4 points)
40
80
1 over 40
1 over 80
To find the rise-over-run value, we need to calculate the change in y (rise) and the change in x (run) between the two points on the line.
The change in y is 120 - 80 = 40.
The change in x is 3 - 2 = 1.
So, the rise-over-run value is 40/1 = 40.
Therefore, the rise-over-run value for the relationship represented in the graph is 40.
hers the next one
The table shows the number of candies packed by Machine J. The equation shows the number of candies packed by Machine K. In both representations, x is a measure of the number of minutes and y is a measure of the number of candies packed.
Machine J Candy Packing
x (minutes) y (candies)
3 90
6 180
9 270
12 360
Machine K: y = 26x
How many more candies could machine J pack than machine K in 11 minutes? (4 points)
30
44
90
330
To find out how many more candies Machine J could pack than Machine K in 11 minutes, we need to calculate the number of candies packed by each machine at that time.
For Machine J, we can look up the value of y when x = 11. However, the table only provides data for x values of 3, 6, 9, and 12. We can estimate the value of y by finding the pattern in the data and interpolating.
From the table, we can observe that the y values for Machine J increase by 90 for every increase in x by 3. This means that the y values increase by 90/3 = 30 for every increase in x by 1.
To calculate the estimated value of y when x = 11, we can start with the value at x = 9 (270) and add 30 twice: 270 + 30 + 30 = 330. Therefore, Machine J would pack an estimated 330 candies in 11 minutes.
For Machine K, we need to calculate y when x = 11 using the equation y = 26x:
y = 26 * 11 = 286
Therefore, Machine K would pack 286 candies in 11 minutes.
To find the difference between the number of candies packed by Machine J and Machine K in 11 minutes, we subtract the value for Machine K from the value for Machine J:
330 - 286 = 44
Therefore, Machine J could pack 44 more candies than Machine K in 11 minutes.
next one
One triangle on a graph has a vertical side of 5 and a horizontal side of 11. Another triangle on a graph has a vertical side of 15 and a horizontal side of 33.
Could the hypotenuses of these two triangles lie along the same line? (4 points)
No, because they need to be the same size
No, because they are not similar triangles
Yes, because all triangles can fit along this line
Yes, because they are similar triangles
To determine if the hypotenuses of these two triangles could lie along the same line, we need to consider their proportions. If the two triangles are similar, then their corresponding sides are proportional to each other.
In the first triangle, the ratio of the vertical side to the horizontal side is 5/11.
In the second triangle, the ratio of the vertical side to the horizontal side is 15/33, which simplifies to 5/11.
Since the ratios of the corresponding sides in both triangles are equal to each other, the two triangles are similar triangles.
Therefore, the hypotenuses of these two triangles could lie along the same line. The correct answer is "Yes, because they are similar triangles."
another
The equation shows the relationship between x and y:
y = −2x + 11
What is the slope of the equation? (4 points)
−11
−2
9
11
The slope of the equation is the coefficient of the x term. In this case, the coefficient of x is -2.
Therefore, the slope of the equation is -2.
last 2
Mae sells newspaper subscriptions door-to-door. In addition to a fixed salary, she earns a commission for each subscription that she sells. The table shows Mae's total earnings, y (in dollars), from selling x newspaper subscriptions:
Subscriptions Sold and Earnings
Subscriptions Sold (x) Total Earnings (y)
1 135
2 145
3 155
Which equation best shows the relationship between x and y? (4 points)
y = 10x + 125
y = x + 135
y = 10x + 135
y = x + 10
To determine the equation that best shows the relationship between x and y in the given table, we can examine the patterns in the data.
From the table, we can observe that as the number of subscriptions sold (x) increases by 1, the total earnings (y) increase by 10.
This indicates that there is a constant rate of change of 10 between x and y.
Based on this pattern, the equation that best represents the relationship between x and y is y = 10x + 125.
Therefore, the equation "y = 10x + 125" is the correct answer.
last one
Sarah has been running a dog-walking business since 2010. She walks dogs twice a day, takes them to the park, and returns them to their homes. Each year, she has increased her fee by the same amount. The table shows what Sarah charged each customer for two given years of her business:
Year Annual Dog-walking Fee
2010 $350
2014 $750
A. What is the rate of change and initial value for Sarah's business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Sarah charges each year. (10 points)