Final answer:
The correct answer is option c. The inequality that represents this situation is x²+4x≥254.
Step-by-step explanation:
Given that the width of the cake is 4 inches more than the width of the photo, and the length is two times its width, let's denote the width of the photo as x, then the width of the cake is x + 4 inches, and the length of the cake is 2(x + 4). The area of the rectangle is the width times the length accordingly. So the area A is A = (x + 4) × 2(x + 4), simplifying to A = 2x² + 16x + 32. Since the area must be at least 254 square inches, the inequality is 2x² + 16x + 32 ≥ 254.
The correct answer is option c. The inequality that represents this situation is x²+4x≥254.
Let's break down the problem step by step:
1. The width of the cake is 4 inches more than the width of the photo, so the width of the cake is x + 4 inches.
2. The length of the cake is two times its width, so the length of the cake is 2(x + 4) inches.
3. The area of the cake is given by multiplying the width and length, so Area = (x + 4)(2(x + 4)).
4. We are given that the area is at least 254 square inches, so the inequality is (x + 4)(2(x + 4)) ≥ 254.
5. Simplifying the inequality gives us x² + 4x ≥ 254.
Therefore, the correct inequality is x² + 4x ≥ 254.