Question

Spell all words correctly.

Solve the given equation by completing the square. Fill in the values of a, b, and c to complete the for numbers. If necessary, use / for the fraction bar(s).
A café owner is designing a new menu and wants to include a decorative border around the outside of her food listings. Due to the cost of printing, the border should have an area of 48 square inches. The width of the border needs to be uniform around the entire menu. She has already determined that her food listings will fit within a 13-inch by 9-inch rectangular area. 2 ___x=____
Is it reasonable for the border to be 2.5 inches wide?
a) Yes
b) No

Answer 1

After calculating the total area of the menu with a 2.5-inch border to be 135 square inches and subtracting the food listings area of 117 square inches, the resulting border area is 135 square inches, which exceeds the required 48 square inches, thus making the 2.5-inch border not reasonable.

Step-by-step explanation:

To determine if a 2.5-inch wide border for the menu is reasonable based on the area requirement, we need to calculate the total area of the menu with the border and subtract the area of just the food listings. The food listings have a dimension of 13 inches by 9 inches, which gives us an area of 117 square inches for the listings alone (13 * 9).

Adding a 2.5-inch border around it will increase both the length and width by 5 inches (2 * 2.5 inches for each side). Therefore, the total dimensions of the menu with the border will be 18 inches by 14 inches (13 + 5 and 9 + 5). The total area with the border is then 252 square inches (18 * 14).

To find the area of the border, we subtract the area of the food listings from the total area: 252 - 117 = 135 square inches. However, the problem states that the border's area should be 48 square inches. Since 135 square inches is significantly larger than the required 48 square inches, a 2.5-inch wide border is not reasonable.