Question
The graph below shows the relationship between the side lengthwendy.Sadly, in feet of a square piece of carpet and it's price in dollars if s is the side length and p is the price.Which of these equations does the graft represent
P = 5s
p = 2.5s^2
p = 10s
p = s^2
P = 5s
p = 2.5s^2
p = 10s
p = s^2
Answers
Answered by
GPT-4o mini
To determine which equation represents the relationship between the side length \( s \) of a square piece of carpet and its price \( p \), we need to consider how the area of the carpet relates to the price.
For a square carpet:
- The area \( A \) is given by \( A = s^2 \).
- If the price per square foot of carpet is constant, then the price \( p \) would be proportional to the area.
If the price per square foot is \( k \), then the price can be expressed as:
\[
p = k \cdot A = k \cdot s^2
\]
Thus, we can identify the relationship depending on the constant \( k \).
Let's evaluate the options:
1. \( p = 5s \): This suggests a linear relationship, which typically would be incorrect for carpet pricing based on area.
2. \( p = 2.5s^2 \): This suggests that the price is directly proportional to the area of the carpet. This is a plausible equation depending on the price per square foot.
3. \( p = 10s \): Similar to option 1, this indicates a linear relationship.
4. \( p = s^2 \): This also indicates a direct relationship to the area but does not account for any price per square foot.
Given the typical relationship between area and price, the most likely equation from this list that represents the graph of the price versus the side length of a square piece of carpet is:
\[
p = 2.5s^2
\]
Thus, it suggests that the price increases with the area of the carpet, which is proportional to \( s^2 \).
For a square carpet:
- The area \( A \) is given by \( A = s^2 \).
- If the price per square foot of carpet is constant, then the price \( p \) would be proportional to the area.
If the price per square foot is \( k \), then the price can be expressed as:
\[
p = k \cdot A = k \cdot s^2
\]
Thus, we can identify the relationship depending on the constant \( k \).
Let's evaluate the options:
1. \( p = 5s \): This suggests a linear relationship, which typically would be incorrect for carpet pricing based on area.
2. \( p = 2.5s^2 \): This suggests that the price is directly proportional to the area of the carpet. This is a plausible equation depending on the price per square foot.
3. \( p = 10s \): Similar to option 1, this indicates a linear relationship.
4. \( p = s^2 \): This also indicates a direct relationship to the area but does not account for any price per square foot.
Given the typical relationship between area and price, the most likely equation from this list that represents the graph of the price versus the side length of a square piece of carpet is:
\[
p = 2.5s^2
\]
Thus, it suggests that the price increases with the area of the carpet, which is proportional to \( s^2 \).