Jane bought a new rectangular placemat with an area of 126 square inches. The length of the placemat is four times the quantity of nine less than half its width. Complete the equation that models the area of the placemat, in terms of the width of the placemat, w.
let x------> the length of the placemat w------> the width of the placemat
we know that area of the rectangular placemat=x*w Area=126 in² so 126=x*w-----> x=126/w ----> equation 1 x=4*[9-w/2]----> x=4*[(18-w)/2]----> x=36-2w----> equation 2 equate equation 1 and equation 2 126/w=36-2w----> multiply by w both sides----> 126=36w-2w² 2w²-36w+126=0
using a graph tool see the attached figure
the solutions are w=4.757 in w=13.243 in
for w=4.76 in x=126/w----> x=126/4.76----> x=26.47 in
for w=13.24 in x=126/13.24-----> x=9.52 in
the answer is the equation that models the area of the placemat is 2w²-36w+126=0
