Question

Mary wants to hang a mirror in her room. the mirror and frame must have an area of 7 square feet. the mirror is 2 feet wide and 3 feet long. which quadratic equation can be used to determine the thickness of the frame, x? square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. arrow on the bottom frame with an x and an arrow on the right frame with an x. x2 14x − 2 = 0 2x2 10x − 7 = 0 3x2 12x − 7 = 0 4x2 10x − 1 = 0

Answer 1

The quadratic equation use to determine the thickness of the frame, x is 4x² + 10x - 1 = 0.

The correct option is D.

What is a quadratic equation ?

A quadratic equation is an algebraic equation of the second degree in x.. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

According to the given information:

Total area  = 7 square feet

and,

Total area = Length x Width

So,

7 = (2x + 3)(2x + 2)

7 = 4x2 + 4x + 6x + 6

7 = 4x2 + 10x + 6

4x2 + 10x + 6 - 7 = 0

4x2 + 10x - 1 = 0

Hence,

The quadratic equation use to determine the thickness of the frame, x is 4x² + 10x - 1 = 0.

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I understand that the question you are looking for is:

Mary wants to hang a mirror in her room. the mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long.  Square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x. Which quadratic equation can be used to determine the thickness of the frame, x?

A. x² + 14x - 2 = 0

B. 2x² + 10x - 7 = 0

C. 3x² + 12x - 7 = 0

D. 4x² + 10x - 1 = 0