Answer:
D. 4(2x² + 4x - 6); 130.0 inches
Step-by-step explanation:
Margot is sewing a ribbon on a seam along the perimeter of a square pillow. The side length of the pillow is 2x²+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x−7 inches. What expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3.5?
2x2+4x−6; 22.0 inches
2x2+4x−6; 32.5 inches
4(2x2+4x−6;) 88.0 inches
4(2x2+4x−6;) 130.0 inches
Perimeter of a square = 4 * side length
1- First square pillow
length = 2x²+1 in
Perimeter of first pillow = 4 * (2x²+1) in
Second square pillow
length = 4x-7 in
Perimeter of second pillow = 4(4x-7) in
Total ribbon length required = perimeter of first square pillow + perimeter of second square pillow
Total ribbon length required = 4(2x²+1) + 4(4x-7)
Factorise
4 is the common factor
=4(2x²+1)+(4x-7)
=4(2x²+1+4x-7)
=4(2x²+4x-6)
Total ribbon length required=4(2x²+4x-6)
If x=3.5
Total ribbon length required=4(2x²+4x-6)
=4{2(3.5)²+4(3.5)-6}
=4{2(12.25)+14-6)
=4(24.5+14-6)
=4(32.5)
=130.0 inches
