Emily wants to hang a painting in a gallery, The painting and frame must have an area of 31 square feet. The painting is 5 feet wide by 6 feet lone, Which quadratic equation can be used to determine the thickness of the frame, x? (5 points) 511 42.22x+31 - 0 4x22x - 1.0 OX.11.31 - 0 O x + 11-1-0

4x² + 22x - 1 = 0

Step-by-step explanation:

The painting is in the form of a rectangle with measurement of 5 feet width and 6 feet length. Let us assume that the frame has a thickness of x feet, hence:

Length of painting and frame = 6 + 2x, breadth of painting and frame = 5 + 2x

Therefore:

Area of painting and frame = length of painting and frame * breadth of painting and frame

Given that the area of painting and frame is 31 ft², substituting gives:

31 = (6 + 2x)(5 + 2x)

31 = 30 + 12x + 10x + 4x²

31 = 30 + 22x + 4x²

4x² + 22x + 30 = 31

4x² + 22x - 1 = 0

step-by-step explanation:

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