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Katie wants to hang a painting in a gallery. The painting and frame must have an area of 45 square feet. The painting is 6 feet wide by 7 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (5 points)

4x^2 + 26x + 45 = 0
4x^2 + 26x − 3 = 0
x^2 + 13x − 3 = 0
x^2 + 13x + 45 = 0

Respuesta :

CastleRook
This is the concept of quadratic equation;
The area  of rectangle is given by:
area=length*width
The dimensions of the paint is 6 ft by 7 ft

the thickness of the frame is x cm

the length of the frame= (2x+7) cm
the width of the frame = (2x+6) cm
the area of the frame is:

Area=45=(2x+7)(2x+6)

45=4x^2+14x+12x+42
45=4x^2+26x+42

this can be written as a quadratic form:

4x^2+26x+42-45=0

4x^2+26x-3=0

The quadratic equation that can be used to determine the thickness of the frame,x, is:

4x^2+26x-3=0

The quadratic equation can be used to determine the thickness of the frame, x is 4x^2 + 26x − 3 = 0, the correct option is B.

Area of the rectangle

The area of the rectangle is given by the product of the length and width.

Given information

Katie wants to hang a painting in a gallery.

The painting and frame must have an area of 45 square feet.

The painting is 6 feet wide by 7 feet long.

Let, the length of painting and frame = 7 + 2x

The breadth of painting and frame= 6 + 2x

The area of the rectangle is;

[tex]\rm Area \ of \ rectangle=length \times width\\\\Area \ of \ rectangle=(7+2x)(6+2x)\\\\45=7(6+2x)+2x(6+2x)\\\\45=42+14x+12x+4x^2\\\\ 4x^2+26x+42-45=0\\\\4x^2+26x-3=0\\\\[/tex]

Hence, the quadratic equation can be used to determine the thickness of the frame, x is 4x^2 + 26x − 3 = 0.

To know more about the area of the rectangle click the link is given below.

https://brainly.com/question/1418582

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