Question
Over the summer, you text a bunch. Let’s say you make 50 texts every 2 days.
(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Fill in the missing parts of the table:
x - # of days 0 a. 7 b.
y - # of texts c. 75 d. 300
(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Fill in the missing parts of the table:
x - # of days 0 a. 7 b.
y - # of texts c. 75 d. 300
Answers
Answer
c is 50 and d is wrong, we have 50, 75, BLANK, 300
Answer
The image is a line chart displaying water use over time. The x-axis represents time in minutes, while the y-axis represents water used in gallons. The line on the chart shows a decreasing trend of water usage over time. 10 gallons are used in 2 minutes, 15 in 3, 35 in 7, and 50 in 9. Use the graph to answer the questions.
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a. The constant of proportionality is Response area
b. Write an equation that represents the linear graph. Response area
c. This is a proportional relationship because the graph shows
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a. The constant of proportionality is Response area
b. Write an equation that represents the linear graph. Response area
c. This is a proportional relationship because the graph shows
Answer
options for c are:
A. A constant rate of change
B. Linear with a y-intercept at (0, 0)
C. The points are connected
D. A linear relationship
A. A constant rate of change
B. Linear with a y-intercept at (0, 0)
C. The points are connected
D. A linear relationship
Answered by
GPT-4o mini
To fill in the missing parts of your table, let's determine the rate of texting first. Given that you make 50 texts every 2 days, we can find the number of texts made in terms of days.
1. **Finding the rate of texting**:
- 50 texts every 2 days means:
\[
\text{Rate per day} = \frac{50 \text{ texts}}{2 \text{ days}} = 25 \text{ texts/day}
\]
2. **Using the rate to find the values**:
- For each day **x**, the number of texts **y** can be calculated using the formula:
\[
y = 25 \cdot x
\]
Now, we can fill in the missing parts of the table based on the above calculations:
- **For x = 0** (the start):
\[
y = 25 \cdot 0 = 0 \quad \Rightarrow \, \text{(c) = 0}
\]
- **For x = 2** (the first 2 days):
\[
y = 25 \cdot 2 = 50 \quad \Rightarrow \, \text{(a) = 2}
\]
- **For x = 7** (after 7 days):
\[
y = 25 \cdot 7 = 175 \quad \Rightarrow \, \text{(b) = 7}
\]
- **For x = 12** (after 12 days):
\[
y = 25 \cdot 12 = 300 \quad \Rightarrow \, \text{(d) = 300}
\]
Now, we can summarize the table:
| x - # of days | 0 | a. (2) | 7 | b. (12) |
|--------------------|----|--------|-----|-------|
| y - # of texts | 0 | 50 | 175 | 300 |
So, the final assignment is:
- (a) = 2
- (b) = 12
- (c) = 0
- (d) = 300
1. **Finding the rate of texting**:
- 50 texts every 2 days means:
\[
\text{Rate per day} = \frac{50 \text{ texts}}{2 \text{ days}} = 25 \text{ texts/day}
\]
2. **Using the rate to find the values**:
- For each day **x**, the number of texts **y** can be calculated using the formula:
\[
y = 25 \cdot x
\]
Now, we can fill in the missing parts of the table based on the above calculations:
- **For x = 0** (the start):
\[
y = 25 \cdot 0 = 0 \quad \Rightarrow \, \text{(c) = 0}
\]
- **For x = 2** (the first 2 days):
\[
y = 25 \cdot 2 = 50 \quad \Rightarrow \, \text{(a) = 2}
\]
- **For x = 7** (after 7 days):
\[
y = 25 \cdot 7 = 175 \quad \Rightarrow \, \text{(b) = 7}
\]
- **For x = 12** (after 12 days):
\[
y = 25 \cdot 12 = 300 \quad \Rightarrow \, \text{(d) = 300}
\]
Now, we can summarize the table:
| x - # of days | 0 | a. (2) | 7 | b. (12) |
|--------------------|----|--------|-----|-------|
| y - # of texts | 0 | 50 | 175 | 300 |
So, the final assignment is:
- (a) = 2
- (b) = 12
- (c) = 0
- (d) = 300
Answered by
GPT-4o mini
Thank you for the clarification. Based on the corrected values provided, let’s work through it again to fill in the correct table with the given structure.
We know:
- You're sending 50 texts every 2 days, which means you send 25 texts per day.
Let's complete the table with the given values:
### Existing Values
- **For x = 0 days:**
\( y = 0 \) texts
- **For x = 2 days:**
\( y = 25 \times 2 = 50 \) texts
- **For x = 7 days:**
\( y = 25 \times 7 = 175 \) texts
- **For x = b (we need to identify the missing x for 75 texts):**
To find this, we calculate:
\( 75 = 25 \times x \)
\( x = \frac{75}{25} = 3 \) days
- **For x where y is 300:**
\( 300 = 25 \times x \)
\( x = \frac{300}{25} = 12 \) days
### Filling in the Missing Parts
Now, we can fill the missing parts as follows:
| x - # of days | 0 | 3 | 7 | 12 |
|---------------------|----|----|----|----|
| y - # of texts | 0 | 75 | 175 | 300 |
### Summary of Values
- (a) = 3 (for 75 texts)
- (b) = 12 (for 300 texts)
- (c) = 50
- (d) = 175
So the missing values identified are:
- **(a) = 3**
- **(b) = 12**
- **(c) = 50**
- **(d) = 175**
This completes the table correctly based on your clarification!
We know:
- You're sending 50 texts every 2 days, which means you send 25 texts per day.
Let's complete the table with the given values:
### Existing Values
- **For x = 0 days:**
\( y = 0 \) texts
- **For x = 2 days:**
\( y = 25 \times 2 = 50 \) texts
- **For x = 7 days:**
\( y = 25 \times 7 = 175 \) texts
- **For x = b (we need to identify the missing x for 75 texts):**
To find this, we calculate:
\( 75 = 25 \times x \)
\( x = \frac{75}{25} = 3 \) days
- **For x where y is 300:**
\( 300 = 25 \times x \)
\( x = \frac{300}{25} = 12 \) days
### Filling in the Missing Parts
Now, we can fill the missing parts as follows:
| x - # of days | 0 | 3 | 7 | 12 |
|---------------------|----|----|----|----|
| y - # of texts | 0 | 75 | 175 | 300 |
### Summary of Values
- (a) = 3 (for 75 texts)
- (b) = 12 (for 300 texts)
- (c) = 50
- (d) = 175
So the missing values identified are:
- **(a) = 3**
- **(b) = 12**
- **(c) = 50**
- **(d) = 175**
This completes the table correctly based on your clarification!
Answered by
GPT-4o mini
To answer your questions based on the water usage chart you've described, we'll follow the steps to determine the constant of proportionality, formulate the equation for the linear graph, and confirm the nature of the relationship.
### a. The constant of proportionality
The constant of proportionality can be found by calculating the ratio of the gallons used to the minutes for one of the data points. Let's calculate it from the first data point.
- For 10 gallons in 2 minutes:
\[
k = \frac{\text{gallons}}{\text{minutes}} = \frac{10}{2} = 5
\]
So, **the constant of proportionality is 5**.
### b. Write an equation that represents the linear graph
The linear relationship can be expressed in the form of the equation \(y = kx\), where \(y\) is the water used (in gallons), \(x\) is time (in minutes), and \(k\) is the constant we calculated.
From our previous calculation:
\[
y = 5x
\]
### c. This is a proportional relationship because the graph shows
This is a proportional relationship because the graph shows a constant ratio of water usage to time, indicating that water used is directly proportional to time. When one quantity changes, the other quantity changes at a constant rate.
### Summary of Responses
- **a:** The constant of proportionality is **5**.
- **b:** Write an equation that represents the linear graph: **y = 5x**.
- **c:** This is a proportional relationship because the graph shows **a constant ratio of water usage to time**.
Please input the answers in the respective response areas as described above. If you need additional help with formatting or moving the responses, let me know!
### a. The constant of proportionality
The constant of proportionality can be found by calculating the ratio of the gallons used to the minutes for one of the data points. Let's calculate it from the first data point.
- For 10 gallons in 2 minutes:
\[
k = \frac{\text{gallons}}{\text{minutes}} = \frac{10}{2} = 5
\]
So, **the constant of proportionality is 5**.
### b. Write an equation that represents the linear graph
The linear relationship can be expressed in the form of the equation \(y = kx\), where \(y\) is the water used (in gallons), \(x\) is time (in minutes), and \(k\) is the constant we calculated.
From our previous calculation:
\[
y = 5x
\]
### c. This is a proportional relationship because the graph shows
This is a proportional relationship because the graph shows a constant ratio of water usage to time, indicating that water used is directly proportional to time. When one quantity changes, the other quantity changes at a constant rate.
### Summary of Responses
- **a:** The constant of proportionality is **5**.
- **b:** Write an equation that represents the linear graph: **y = 5x**.
- **c:** This is a proportional relationship because the graph shows **a constant ratio of water usage to time**.
Please input the answers in the respective response areas as described above. If you need additional help with formatting or moving the responses, let me know!
Answered by
GPT-4o mini
Given the options for part (c), the best choice to describe why this is a proportional relationship is:
### c. This is a proportional relationship because the graph shows
**A. A constant rate of change**
While "B. Linear with a y-intercept at (0, 0)" can also describe characteristics of proportional relationships, the most direct answer based on the nature of proportional relationships is the constant rate of change, as it emphasizes the constant ratio involved in the linear relationship.
### Final Summary of Responses
- **a:** The constant of proportionality is **5**.
- **b:** Write an equation that represents the linear graph: **y = 5x**.
- **c:** This is a proportional relationship because the graph shows **A. A constant rate of change**.
Feel free to ask if you have any further questions!
### c. This is a proportional relationship because the graph shows
**A. A constant rate of change**
While "B. Linear with a y-intercept at (0, 0)" can also describe characteristics of proportional relationships, the most direct answer based on the nature of proportional relationships is the constant rate of change, as it emphasizes the constant ratio involved in the linear relationship.
### Final Summary of Responses
- **a:** The constant of proportionality is **5**.
- **b:** Write an equation that represents the linear graph: **y = 5x**.
- **c:** This is a proportional relationship because the graph shows **A. A constant rate of change**.
Feel free to ask if you have any further questions!