A coordinate plane shows four quadrants with both the x-axis and the y-axis ranging from negative 10 to positive 10 in increments of 2. Two points are plotted and joined by a line. The plotted points are as follows: left parenthesis 4 comma 9 right parenthesis, left parenthesis 5 comma 0 right parenthesis. A line connects the two plotted points and extends beyond the points in both directions.

To find the slope of the graph, we need to calculate the change in y divided by the change in x between the two points.

The two points given are (4, 9) and (5, 0).

The change in y is 0 - 9 = -9.
The change in x is 5 - 4 = 1.

Therefore, the slope is -9/1 = -9.

If Chase runs 5 miles in 60 minutes, how far will he run in 3 hours if he continues to run at the same rate?(1 point)

Since Chase runs 5 miles in 60 minutes, we can find his running rate by dividing the distance he runs by the time it takes:

5 miles / 60 minutes = 0.0833 miles/minute.

If Chase runs at the same rate for 3 hours, which is equal to 3 * 60 = 180 minutes, we can find the distance he will run by multiplying his running rate by the time:

0.0833 miles/minute * 180 minutes = 14.994 miles.

Therefore, Chase will run approximately 14.994 miles in 3 hours.

its easy to solve, just multiply 5 by 3 and you have your answer.

Apologies for the confusion caused by my previous response. You are correct. To determine the distance Chase will run in 3 hours, we can simply multiply the distance he runs in 1 hour (5 miles) by the number of hours (3):

5 miles * 3 hours = 15 miles.

Therefore, Chase will run 15 miles in 3 hours. Thank you for pointing out the simpler solution.

A whale swims 200 miles in 5 days. Identify which equation could be used to find how many miles it swims in 16 days.(1 point)

To find how many miles the whale swims in 16 days, we can set up a proportion using the given information.

Let's assume x represents the number of miles the whale swims in 16 days. The proportion can be set up as:

200 miles / 5 days = x miles / 16 days.

To simplify the proportion, we cross-multiply:

5 * x = 200 * 16.

The equation that could be used to find how many miles the whale swims in 16 days is:

5x = 3200.

Wrong, solve the problem THEN tell me which equation can be used.

Apologies for the mistake. To find how many miles the whale swims in 16 days, we can set up a proportion using the given information.

We can use the concept of ratios to set up the proportion. The ratio of miles swum to days taken should be the same for both cases.

Let x represent the number of miles the whale swims in 16 days.

The proportion can be set up as:

200 miles / 5 days = x miles / 16 days.

To solve this proportion, we can cross-multiply:

5 * x = 200 * 16.

Now, we can simplify the equation:

5x = 3200.

Thus, the equation that can be used to find how many miles the whale swims in 16 days is:

5x = 3200.

The correct answer is y = 40 * 16

I apologize for the incorrect response. You are correct.

To find how many miles the whale swims in 16 days, we can set up a proportion using the given information:

200 miles / 5 days = x miles / 16 days.

To solve for x, we can cross multiply:

5 * x = 200 * 16.

Simplifying the expression:

5x = 3200.

To find the value of x, we divide both sides of the equation by 5:

x = 3200 / 5.

Simplifying the right side of the equation:

x = 640.

Therefore, the equation that represents the number of miles the whale swims in 16 days is:

y = 40 * 16.

Use the tables to answer the question.

Sonia
Number of Problems Minutes of Writing
6 120
18 360
25 500
60 1,200
Maryna
Number of Problems Minutes of Writing
8 200
15 375
20 500
50 1,250
Based on the tables showing the number of minutes two writers spent writing math problems for two different lessons, who spent more time writing per problem? Write the answer in unit rate form.

To determine who spent more time writing per problem, we can calculate the unit rate by dividing the number of minutes of writing by the number of problems.

For Sonia:

Unit rate = Minutes of writing / Number of problems

For the given data, the unit rates for Sonia are as follows:

For 6 problems: 120 minutes / 6 problems = 20 minutes per problem
For 18 problems: 360 minutes / 18 problems = 20 minutes per problem
For 25 problems: 500 minutes / 25 problems = 20 minutes per problem
For 60 problems: 1200 minutes / 60 problems = 20 minutes per problem

For Maryna:

Unit rate = Minutes of writing / Number of problems

The unit rates for Maryna are:

For 8 problems: 200 minutes / 8 problems = 25 minutes per problem
For 15 problems: 375 minutes / 15 problems = 25 minutes per problem
For 20 problems: 500 minutes / 20 problems = 25 minutes per problem
For 50 problems: 1250 minutes / 50 problems = 25 minutes per problem

Comparing the unit rates, we find that both Sonia and Maryna spent the same amount of time writing per problem, which is 20 minutes per problem or 25 minutes per problem.

Sonia and Maryna did NOT spend the same amount of time writing. Rethink your answer.

Apologies for the mistake in my previous response. Let's calculate the unit rates correctly to determine who spent more time writing per problem.

For Sonia:

Unit rate = Minutes of writing / Number of problems

For the given data, the unit rates for Sonia are as follows:

For 6 problems: 120 minutes / 6 problems = 20 minutes per problem
For 18 problems: 360 minutes / 18 problems = 20 minutes per problem
For 25 problems: 500 minutes / 25 problems = 20 minutes per problem
For 60 problems: 1200 minutes / 60 problems = 20 minutes per problem

For Maryna:

Unit rate = Minutes of writing / Number of problems

The unit rates for Maryna are:

For 8 problems: 200 minutes / 8 problems = 25 minutes per problem
For 15 problems: 375 minutes / 15 problems = 25 minutes per problem
For 20 problems: 500 minutes / 20 problems = 25 minutes per problem
For 50 problems: 1250 minutes / 50 problems = 25 minutes per problem

Upon recalculating, we find that both Sonia and Maryna spent the same amount of time writing per problem, which is 20 minutes per problem or 25 minutes per problem.

Maryna spent more time writing than Sonia.

Apologies for the confusion caused by my previous responses. You are correct.

Upon reevaluating the unit rates, we can see that Maryna spent more time writing per problem compared to Sonia.

For Maryna:
- For 8 problems: 200 minutes / 8 problems = 25 minutes per problem
- For 15 problems: 375 minutes / 15 problems = 25 minutes per problem
- For 20 problems: 500 minutes / 20 problems = 25 minutes per problem
- For 50 problems: 1250 minutes / 50 problems = 25 minutes per problem

For Sonia:
- For 6 problems: 120 minutes / 6 problems = 20 minutes per problem
- For 18 problems: 360 minutes / 18 problems = 20 minutes per problem
- For 25 problems: 500 minutes / 25 problems = 20 minutes per problem
- For 60 problems: 1200 minutes / 60 problems = 20 minutes per problem

As we can see, Maryna consistently spent 25 minutes per problem, while Sonia consistently spent 20 minutes per problem. Therefore, Maryna spent more time writing per problem compared to Sonia.

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 would reach 100 feet in the least amount of time?

To determine which object would reach 100 feet in the least amount of time, we need to find the slope of each line and compare them.

Line A passes through the points (0, 0) and (3, 6). The change in y is 6 - 0 = 6, and the change in x is 3 - 0 = 3. Therefore, the slope of line A is 6/3 = 2.

Line B passes through the points (0, 0) and (6, 6). The change in y is 6 - 0 = 6, and the change in x is 6 - 0 = 6. Therefore, the slope of line B is 6/6 = 1.

Line C passes through the points (0, 0) and (6, 3). The change in y is 3 - 0 = 3, and the change in x is 6 - 0 = 6. Therefore, the slope of line C is 3/6 = 1/2.

The slope represents the rate of change, or how quickly the distance increases with time. A larger slope indicates a steeper increase in distance over time.

Comparing the slopes, we find that line A has a slope of 2, line B has a slope of 1, and line C has a slope of 1/2.

Since line A has the largest slope, it indicates the fastest rate of increase in distance over time. Therefore, line A would reach 100 feet in the least amount of time compared to lines B and C.

The temperature is dropping throughout the day as a cold front comes in. In City A, the temperature is changing by −5°F per hour, and in City B the temperature is changing by −3°F per hour. If the temperatures in both cities started at 70°F , which city is warmer, and what is the difference in their temperatures after 5 hours?

To determine which city is warmer and find the difference in their temperatures after 5 hours, we need to calculate the final temperatures for both cities after 5 hours.

Starting with City A:
The temperature in City A is changing by -5°F per hour. If the initial temperature is 70°F, after 5 hours, the change in temperature would be:
-5°F * 5 hours = -25°F.

Therefore, the final temperature in City A after 5 hours would be:
70°F + (-25°F) = 45°F.

Moving on to City B:
The temperature in City B is changing by -3°F per hour. If the initial temperature is 70°F, after 5 hours, the change in temperature would be:
-3°F * 5 hours = -15°F.

Therefore, the final temperature in City B after 5 hours would be:
70°F + (-15°F) = 55°F.

Comparing the final temperatures, we can see that City B has a higher temperature of 55°F compared to City A's temperature of 45°F after 5 hours.

To find the difference in their temperatures after 5 hours, we can subtract the temperature of City A from the temperature of City B:
55°F - 45°F = 10°F.

Therefore, City B is warmer than City A by 10°F after 5 hours.

Jimmy reads 15 pages in 5 minutes. Carlo reads 12 pages in 6 minutes. Find each constant of proportionality, showing your work. Then write a sentence to compare the proportional relationships.(2 points)

To find the constant of proportionality for each scenario, we need to calculate the ratio of pages read to minutes spent for both Jimmy and Carlo.

For Jimmy:
Pages read: 15
Minutes spent: 5

Constant of proportionality = Pages read / Minutes spent = 15 / 5 = 3

For Carlo:
Pages read: 12
Minutes spent: 6

Constant of proportionality = Pages read / Minutes spent = 12 / 6 = 2

Therefore, the constant of proportionality for Jimmy is 3 and for Carlo is 2.

Now, let's compare the proportional relationships:

Jimmy's relationship: For every 1 minute, he reads 3 pages.
Carlo's relationship: For every 1 minute, he reads 2 pages.

From the comparison, we can see that Jimmy reads more pages per minute compared to Carlo. His rate of reading is faster with a constant of proportionality of 3, while Carlo's rate of reading has a constant of proportionality of 2.