Question
The length of a garden plot is 6 meters less than 5 times the width. Which equation describes the relationship between the width `w` of the plot in meters, and the area `A` in square meters?(1 point)
Responses
A=5w2−6w
cap A is equal to 5 w squared minus 6 w
A=5w2
cap A is equal to 5 w squared
A=5w−6
cap A is equal to 5 w minus 6
A=5(w2−6)
Responses
A=5w2−6w
cap A is equal to 5 w squared minus 6 w
A=5w2
cap A is equal to 5 w squared
A=5w−6
cap A is equal to 5 w minus 6
A=5(w2−6)
Answers
GPT-4o mini
To describe the relationship between the width \( w \) of the garden plot and the area \( A \), we first need to establish the relationship given in the problem.
The length \( L \) of the garden plot is defined as:
\[ L = 5w - 6 \]
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{width} \]
So, substituting the expression for length:
\[ A = (5w - 6) \times w \]
Now, distributing \( w \):
\[ A = 5w^2 - 6w \]
Thus, the equation that describes the relationship is:
\[
A = 5w^2 - 6w
\]
The correct response is:
**A = 5w² - 6w**
The length \( L \) of the garden plot is defined as:
\[ L = 5w - 6 \]
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{width} \]
So, substituting the expression for length:
\[ A = (5w - 6) \times w \]
Now, distributing \( w \):
\[ A = 5w^2 - 6w \]
Thus, the equation that describes the relationship is:
\[
A = 5w^2 - 6w
\]
The correct response is:
**A = 5w² - 6w**