Question
A homeowner uses four wooden beams to build the perimeter of a rectangular deck. Each wooden beam has an equal length of x feet. He uses two beams for two sides of the deck, and he cuts off 4 feet from each of the other two beams for the remaining two sides of the deck, as shown by the diagram below.
The top to bottom line is x-4
the left to right line is x
The total area of the deck, in square feet, is a function of the distance x, in feet.
What is the function, A(x), that represents the total area of the deck, in square feet?
(1 point)
Responses
A(x)=2^x−4
cap A times x is equal to 2 x minus 4
A(x)=4x^2−16x
cap A times x is equal to 4 x squared minus 16 x
A(x)=x^2−4x
cap A times x is equal to x squared minus 4 x
A(x)=x^2−4
The top to bottom line is x-4
the left to right line is x
The total area of the deck, in square feet, is a function of the distance x, in feet.
What is the function, A(x), that represents the total area of the deck, in square feet?
(1 point)
Responses
A(x)=2^x−4
cap A times x is equal to 2 x minus 4
A(x)=4x^2−16x
cap A times x is equal to 4 x squared minus 16 x
A(x)=x^2−4x
cap A times x is equal to x squared minus 4 x
A(x)=x^2−4
Answers
GPT-4o mini
To find the function \( A(x) \) that represents the total area of the deck, we first need to determine the dimensions of the rectangle based on the information given.
- The length of the sides formed by the uncut beams is \( x \) feet.
- The length of the sides formed by the cut beams, where each is cut down by 4 feet, is \( x - 4 \) feet.
The area \( A \) of a rectangle is calculated using the formula:
\[
A = \text{length} \times \text{width}
\]
Substituting in the values we have:
- Length = \( x \)
- Width = \( x - 4 \)
Thus, the area \( A(x) \) can be expressed as:
\[
A(x) = x \cdot (x - 4)
\]
Expanding this expression gives:
\[
A(x) = x^2 - 4x
\]
Therefore, the function \( A(x) \) that represents the total area of the deck in square feet is:
\[
\boxed{A(x) = x^2 - 4x}
\]
- The length of the sides formed by the uncut beams is \( x \) feet.
- The length of the sides formed by the cut beams, where each is cut down by 4 feet, is \( x - 4 \) feet.
The area \( A \) of a rectangle is calculated using the formula:
\[
A = \text{length} \times \text{width}
\]
Substituting in the values we have:
- Length = \( x \)
- Width = \( x - 4 \)
Thus, the area \( A(x) \) can be expressed as:
\[
A(x) = x \cdot (x - 4)
\]
Expanding this expression gives:
\[
A(x) = x^2 - 4x
\]
Therefore, the function \( A(x) \) that represents the total area of the deck in square feet is:
\[
\boxed{A(x) = x^2 - 4x}
\]
The length of a rectangle is 2 inches less than 3 times the width. Which equation describes the relationship between w, the width of the rectangle in inches, and A, the area in square inches?(1 point)
Responses
A=2w^2−3w
cap A is equal to 2 w squared minus 3 w
A=3w^2−2
cap A is equal to 3 w squared minus 2
A=3w^2−2w
cap A is equal to 3 w squared minus 2 w
A=2w^2−3
Responses
A=2w^2−3w
cap A is equal to 2 w squared minus 3 w
A=3w^2−2
cap A is equal to 3 w squared minus 2
A=3w^2−2w
cap A is equal to 3 w squared minus 2 w
A=2w^2−3