Answer :
Let's translate the situation described into mathematical terms.
1. Width of the cake: The width of the cake is 4 inches more than the width of the photo. If [tex]\( x \)[/tex] represents the width of the photo, then the width of the cake is [tex]\( x + 4 \)[/tex].
2. Length of the cake: The length of the cake is twice its width. Since the width of the cake is [tex]\( x + 4 \)[/tex], the length of the cake is [tex]\( 2(x + 4) \)[/tex].
3. Area of the cake: The area of a rectangle is given by the product of its width and length. Therefore, the area of the cake is:
[tex]\[ \text{Area} = \text{Width} \times \text{Length} = (x + 4) \times 2(x + 4) \][/tex]
4. Simplify the expression for the area:
[tex]\[ \text{Area} = (x + 4) \times 2(x + 4) = 2(x + 4)^2 \][/tex]
5. Inequality representing the area constraint: The area of the cake must be at least 254 square inches, so we write the inequality as:
[tex]\[ 2(x + 4)^2 \geq 254 \][/tex]
The correct inequality that represents the situation is:
[tex]\[ 2(x + 4)^2 \geq 254 \][/tex]
This is most similar to option D if we consider the expanded form incorrectly. However, since we are looking for the direct form that matches [tex]\(2*(x + 4)^2 \geq 254\)[/tex]:
None of the listed options directly match [tex]\(2(x + 4)^2 \geq 254\)[/tex]. But the closest correct transformation of this would be in option D considering the sources.
Therefore, the correct answer is:
E. None of the listed options are direct fits.
1. Width of the cake: The width of the cake is 4 inches more than the width of the photo. If [tex]\( x \)[/tex] represents the width of the photo, then the width of the cake is [tex]\( x + 4 \)[/tex].
2. Length of the cake: The length of the cake is twice its width. Since the width of the cake is [tex]\( x + 4 \)[/tex], the length of the cake is [tex]\( 2(x + 4) \)[/tex].
3. Area of the cake: The area of a rectangle is given by the product of its width and length. Therefore, the area of the cake is:
[tex]\[ \text{Area} = \text{Width} \times \text{Length} = (x + 4) \times 2(x + 4) \][/tex]
4. Simplify the expression for the area:
[tex]\[ \text{Area} = (x + 4) \times 2(x + 4) = 2(x + 4)^2 \][/tex]
5. Inequality representing the area constraint: The area of the cake must be at least 254 square inches, so we write the inequality as:
[tex]\[ 2(x + 4)^2 \geq 254 \][/tex]
The correct inequality that represents the situation is:
[tex]\[ 2(x + 4)^2 \geq 254 \][/tex]
This is most similar to option D if we consider the expanded form incorrectly. However, since we are looking for the direct form that matches [tex]\(2*(x + 4)^2 \geq 254\)[/tex]:
None of the listed options directly match [tex]\(2(x + 4)^2 \geq 254\)[/tex]. But the closest correct transformation of this would be in option D considering the sources.
Therefore, the correct answer is:
E. None of the listed options are direct fits.
