Jensen wants to hang a mirror in his boat and put a frame around it. The mirror and frame must have an area of 19.75 square feet
. The mirror is 4 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (2 points) 2x2 + 6x − 19.25 = 0
The frame will have the same thickness on both sides of the mirror. Therefore we add 5+x+x to get the total length, and we have 4+x+x to get the total width.
The area is found by multiplying the total width and total length:
A=(5+x+x)(4+x+x) A=(5+2x)(4+2x)
Multiplying the binomials, we have: A=5*4+5*2x+2x*4+2x*2x A=20+10x+8x+4x² A=20+18x+4x²
We know that the area is 19.75: 19.75=20+18x+4x²
We need quadratics set equal to 0, so subtract 19.75 from each side: 19.75-19.75 = 20+18x+4x²-19.75 0=0.25+18x+4x²
