Question
The graph below shows the relationship between the side length in feet of a square piece of carpet and its price in dollars. If s is the side length and p is the price, which of these equations does the graph represent?
(1 point)
Responses
p=10s
p is equal to 10 s
p=5s
p is equal to 5 s
p=2.5s2
p is equal to 2 point 5 s squared
p=s2
p is equal to s squared
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(1 point)
Responses
p=10s
p is equal to 10 s
p=5s
p is equal to 5 s
p=2.5s2
p is equal to 2 point 5 s squared
p=s2
p is equal to s squared
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Answers
Answered by
GPT-4o mini
To determine the correct equation that the graph represents, we need to understand the relationship between the side length of a square piece of carpet (s) and its price (p).
The area (A) of a square is calculated as:
\[ A = s^2 \]
Since the price is often related to the area of the carpet (assuming a price per square foot), we might expect that the price varies with the area. It is common for problems of this nature to relate the price to the area in terms of a price per unit area.
1. If the price \( p \) is directly proportional to the side length \( s \), then we would use a linear equation, which might imply a price per foot of length (like \( p = 10s \) or \( p = 5s \)). However, since the relationship is quadratic due to the area, we can likely dismiss these options.
2. The option \( p = s^2 \) indicates that the price is directly proportional to the area (with a price of 1 dollar per square foot).
3. The option \( p = 2.5s^2 \) suggests that the price is proportional to the area with a different price per square foot (specifically 2.5 dollars per square foot).
Since we expect the price of a square carpet to relate to its area, we should examine these equations more closely.
If the graph has a quadratic shape (e.g., a parabola) then the most likely choices would be either \( p = s^2 \) or \( p = 2.5s^2 \).
If the graph indicates that price increases significantly with a small increase in side length, then \( p = 2.5s^2 \) should be the equation represented by the graph.
If the graph shows a straightforward increase but not as steep, \( p = s^2 \) might fit.
To select the correct answer without a visual, we would likely favor the equation that represents price relative to area, which is often the case in such problems.
**Based on this reasoning, the equations that represent the price in relation to the area would likely be:**
- **p = 2.5s^2** is the most probable choice if the price increases quickly relative to the size of the carpet.
- Alternatively, **p = s^2** is suitable for a direct \(1\) dollar per square foot price.
Please choose based on these insights or review the graph for confirmation.
The area (A) of a square is calculated as:
\[ A = s^2 \]
Since the price is often related to the area of the carpet (assuming a price per square foot), we might expect that the price varies with the area. It is common for problems of this nature to relate the price to the area in terms of a price per unit area.
1. If the price \( p \) is directly proportional to the side length \( s \), then we would use a linear equation, which might imply a price per foot of length (like \( p = 10s \) or \( p = 5s \)). However, since the relationship is quadratic due to the area, we can likely dismiss these options.
2. The option \( p = s^2 \) indicates that the price is directly proportional to the area (with a price of 1 dollar per square foot).
3. The option \( p = 2.5s^2 \) suggests that the price is proportional to the area with a different price per square foot (specifically 2.5 dollars per square foot).
Since we expect the price of a square carpet to relate to its area, we should examine these equations more closely.
If the graph has a quadratic shape (e.g., a parabola) then the most likely choices would be either \( p = s^2 \) or \( p = 2.5s^2 \).
If the graph indicates that price increases significantly with a small increase in side length, then \( p = 2.5s^2 \) should be the equation represented by the graph.
If the graph shows a straightforward increase but not as steep, \( p = s^2 \) might fit.
To select the correct answer without a visual, we would likely favor the equation that represents price relative to area, which is often the case in such problems.
**Based on this reasoning, the equations that represent the price in relation to the area would likely be:**
- **p = 2.5s^2** is the most probable choice if the price increases quickly relative to the size of the carpet.
- Alternatively, **p = s^2** is suitable for a direct \(1\) dollar per square foot price.
Please choose based on these insights or review the graph for confirmation.