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? (4 points)
Steve your half right! All you forgot to do is simplify!
So, Alan, The correct answer is : 4x^2+10x-1=0
its just 4 years late no biggie lol
sorry it's so late
opps
A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles: (5 points)
An oval is formed by a rectangle with semicircles at each end. The length of the rectangle is 62 inches. The width of the rectangle is 27 inches.
Which of the following is the perimeter of the inner edge of the frame?
(π = 3.14)
146.78 inches
208.78 inches
293.56 inches
347.56 inches
The perimeter of the inner edge of the frame is equal to the sum of the circumference of the two semicircles and the length and width of the rectangle.
The length of each semicircle is equal to the width of the rectangle, which is 27 inches.
The circumference of each semicircle is equal to half the circumference of a full circle with a diameter of 27 inches:
C = 1/2 (πd) = 1/2 (π × 27) = 42.39 inches
The length of the rectangle is 62 inches and the width is 27 inches.
Therefore, the perimeter of the inner edge of the frame is:
P = 2C + 62 + 27 = 2(42.39) + 62 + 27 = 173.78 inches
So, the correct answer is not listed as an option.
To determine the thickness of the frame, we can subtract the area of the mirror from the total area of the mirror and frame combination.
The area of the mirror is given by: length * width = 3 ft * 2 ft = 6 square feet.
The total area of the mirror and frame combination is given as 7 square feet.
So, the area of the frame can be calculated as: total area - mirror area = 7 sq ft - 6 sq ft = 1 square foot.
Now, to represent the thickness of the frame, we can assume it to be x feet.
The width of the mirror with the frame would be: 2 ft + 2x ft = 2 + 2x ft.
The length of the mirror with the frame would be: 3 ft + 2x ft = 3 + 2x ft.
The area of the mirror with the frame would be: (2 + 2x) ft * (3 + 2x) ft.
Setting up the equation: (2 + 2x) ft * (3 + 2x) ft = 1 sq ft.
Expanding the equation: 6 + 4x + 6x + 4x^2 = 1.
Simplifying the equation: 4x^2 + 10x + 6 = 1.
The quadratic equation that can be used to determine the thickness of the frame, x, is: 4x^2 + 10x + 6 = 1.