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Question 721266: A rectangular picture has a length of 2x+2 and a width of x-4 inches. You decide to frame the picture with a frame that is x units wide. Find the dimension of the framed picture. (Ialready did this one and got the answer
(3x-4)(4x+2). Next, I had to write an expression in terms of the framed picture. I got the answer 12x^2-10x-8. Is this correct? Finally, I was asked to find the area in terms of x of the frame alone. I have no clue how to solve this... Please help??
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular picture has a length of 2x+2 and a width of x-4 inches. You decide to frame the picture with a frame that is x units wide. Find the dimension of the framed picture. (Ialready did this one and got the answer
(3x-4)(4x+2). Next, I had to write an expression in terms of the framed picture. I got the answer 12x^2-10x-8. Is this correct? Finally, I was asked to find the area in terms of x of the frame alone.
:
you got the overall area, find the area of just the picture
(2x+2)(x-4) = 2x^2 - 6x - 8, is the area of the picture
:
The area of the frame = the overall area - the picture area
f(x) = (12x^2-10x-8) - (2x^2 - 6x - 8)
remove the brackets
f(x) = 12x^2 - 10x - 8 - 2x^2 + 6x + 8
combine like terms
f(x) = 12x^2 - 2x^2 - 10x + 6x - 8 + 8
f(x) = 10x^2 - 4x is the area of the picture frame
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