Final answer:
The total length of ribbon needed is the sum of the perimeters of both squares, represented by the expression (4 × (2x² + 1)) + (4 × (4x - 7)). If x=3.5, the total length required is 130 inches.
Step-by-step explanation:
The question asks for the expression to determine the length of ribbon Margot needs for both a square pillow with a side length of 2x² + 1 inch and a ribbon with a side length of 4x - 7 inches. To find the total length of ribbon required, we need to calculate the perimeter of the square represented by the pillow and add it to the perimeter of the square represented by the ribbon.
For the pillow, the perimeter is the sum of all sides, given by the formula P = 4 × (side length). So the perimeter of the pillow is:
4 × (2x² + 1).
For the ribbon, we use the same perimeter formula, which gives us:
4 × (4x - 7).
Adding these expressions together gives us the total length of ribbon needed:
(4 × (2x² + 1)) + (4 × (4x - 7)).
If x=3.5, we substitute this value into the expression to find the total length:
4(2(3.5)² + 1) + 4(4(3.5) - 7),
which simplifies to:
4(2(12.25) + 1) + 4(14 - 7),
= 4(24.5 + 1) + 4(7),
= 4(25.5) + 28,
= 102 + 28,
= 130 inches.