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

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

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well, let's draw a picture of a 3*4 mirror with a frame that is x inches thick |dw:1440372180188:dw|
now, let's see if we can write an expression, using x, for the width and length of the whole thing (mirror + frame)
So the answer would be C right?

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Other answers:

hm, not C, let's keep going |dw:1440372299021:dw| any ideas?
can you tell me what the length and width are in terms of x?
\[x^3\]
uh, not quite... let's just look at the length first, ok? do you see how the length of the whole thing is just the length of the mirror + x on each side?
|dw:1440372540133:dw|
4x?
almost but not quite... length of the mirror + width of the frame on each side = ?
0?
|dw:1440372618481:dw| maybe just look at it from one dimension?
the length of the mirror is 4 and the width of the frame is x, so the total length is...?
4x^2?
nope, not quite... |dw:1440372717991:dw|
Idk.
pretend that it's a straight line... add together length of mirror + width of frame = ?
Is the answer C?
the answer isn't C.... hm, maybe I can break it down another way... let's just go back to our mirror, without the frame for now|dw:1440372900669:dw|
the length is 4, agreed?
144?
let's just forget about the frame for a sec and just look at the mirror... the mirror is 4 feet long, agreed?|dw:1440372976654:dw|
... Y u so genius @Vocaloid
yes
ok, now let's put the frame around it now|dw:1440373034973:dw|
can you tell me what this length is now? (we don't know what x is yet, but we can write an expression using x)|dw:1440373076022:dw|
just add: width of frame + length of mirror + width of frame = ?
your answer should involve x somehow
IS the answer D?
no, the answer isn't D, please stop guessing...
|dw:1440373181795:dw|
Lul
-.-
the length is 4 + x + x, agreed?
U sound like my mom when I do calculus. :3
Yes
alright, now can you find the width?|dw:1440373262344:dw|
3*4*x?
not quite.... just like before, we add width of mirror + width of frame + width of frame = ?
|dw:1440373318819:dw|
3+2x
fantastic! so our length is 4 + 2x our width is 3 + 2x our area (stated in the problem is 14) so, do you think you can take it from here?
So its B?
area = (width)*(length) 14 = (4 + 2x)(3 + 2x) simplify that and you will get your answer....
start by doing FOIL on the right side
Is it A?
start by doing FOIL on the right side, please..... (4 + 2x)(3 + 2x) = ??
@Vocaloid I believe she is correct
I already know the answer, I want her/him to learn so she/he can do this in the future without my guidance
I am a girl...
right, I figured as much, just making sure so, start by doing FOIL on the right side... (4 + 2x)(3 + 2x) = ?
@Vocaloid Am i correct there is no way it can be D. And i already asked about B and C. So only possible can be is A? Am i correct?
the point is to get the correct answer by actually doing the math, not by guessing... the answer is either A or B, I'll give you that
You said it wasn't b...
do you understand FOIL?
Earlier
Yes. I am just in a big hurry
Lol... U sound real stressed
VERY
2x*2x+2x*3+4*2x+3*4-12
almost... (2x + 3)(2x + 4) = (2x)(2x) + (4)(2x) + (3)(2x) + (3)(4)
there's no -12 at the end but other than that, you're on the right track... now start combining like terms
@Vocaloid I am in a bigggg hurrrryyy
My school starts tomorrow and i almost finsihed
your deadline =/= my problem (2x)(2x) + (4)(2x) + (3)(2x) + (3)(4) 4x^2 + 8x + 6x + 12 = 4x^2 + 8x + 6x + 12 now we set that equal to 14...
I am tring to get this done
4x^2 + 8x + 6x + 12 = 14
there is 40 more questions i have to do
So the answer is A.
right
Thank you.

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