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

- anonymous

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- Vocaloid

well, let's draw a picture of a 3*4 mirror with a frame that is x inches thick
|dw:1440372180188:dw|

- Vocaloid

now, let's see if we can write an expression, using x, for the width and length of the whole thing (mirror + frame)

- anonymous

So the answer would be C right?

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## More answers

- Vocaloid

hm, not C, let's keep going
|dw:1440372299021:dw|
any ideas?

- Vocaloid

can you tell me what the length and width are in terms of x?

- anonymous

\[x^3\]

- Vocaloid

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?

- Vocaloid

|dw:1440372540133:dw|

- anonymous

4x?

- Vocaloid

almost but not quite...
length of the mirror + width of the frame on each side = ?

- anonymous

0?

- Vocaloid

|dw:1440372618481:dw|
maybe just look at it from one dimension?

- Vocaloid

the length of the mirror is 4 and the width of the frame is x, so the total length is...?

- anonymous

4x^2?

- Vocaloid

nope, not quite...
|dw:1440372717991:dw|

- anonymous

Idk.

- Vocaloid

pretend that it's a straight line... add together length of mirror + width of frame = ?

- anonymous

Is the answer C?

- Vocaloid

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|

- Vocaloid

the length is 4, agreed?

- anonymous

144?

- Vocaloid

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|

- Plasmataco

... Y u so genius @Vocaloid

- anonymous

yes

- Vocaloid

ok, now let's put the frame around it now|dw:1440373034973:dw|

- Vocaloid

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|

- Vocaloid

just add: width of frame + length of mirror + width of frame = ?

- Vocaloid

your answer should involve x somehow

- anonymous

IS the answer D?

- Vocaloid

no, the answer isn't D, please stop guessing...

- Vocaloid

|dw:1440373181795:dw|

- Plasmataco

Lul

- anonymous

-.-

- Vocaloid

the length is 4 + x + x, agreed?

- Plasmataco

U sound like my mom when I do calculus. :3

- anonymous

Yes

- Vocaloid

alright, now can you find the width?|dw:1440373262344:dw|

- anonymous

3*4*x?

- Vocaloid

not quite.... just like before, we add
width of mirror + width of frame + width of frame = ?

- Vocaloid

|dw:1440373318819:dw|

- anonymous

3+2x

- Vocaloid

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?

- anonymous

So its B?

- Vocaloid

area = (width)*(length)
14 = (4 + 2x)(3 + 2x)
simplify that and you will get your answer....

- Vocaloid

start by doing FOIL on the right side

- anonymous

Is it A?

- Vocaloid

start by doing FOIL on the right side, please.....
(4 + 2x)(3 + 2x) = ??

- Plasmataco

@Vocaloid I believe she is correct

- Vocaloid

I already know the answer, I want her/him to learn so she/he can do this in the future without my guidance

- anonymous

I am a girl...

- Vocaloid

right, I figured as much, just making sure
so, start by doing FOIL on the right side...
(4 + 2x)(3 + 2x) = ?

- anonymous

@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?

- Vocaloid

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

- anonymous

You said it wasn't b...

- Vocaloid

do you understand FOIL?

- anonymous

Earlier

- anonymous

Yes. I am just in a big hurry

- Plasmataco

Lol... U sound real stressed

- anonymous

VERY

- anonymous

2x*2x+2x*3+4*2x+3*4-12

- Vocaloid

almost...
(2x + 3)(2x + 4) = (2x)(2x) + (4)(2x) + (3)(2x) + (3)(4)

- Vocaloid

there's no -12 at the end but other than that, you're on the right track... now start combining like terms

- anonymous

@Vocaloid I am in a bigggg hurrrryyy

- anonymous

My school starts tomorrow and i almost finsihed

- Vocaloid

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...

- anonymous

I am tring to get this done

- Vocaloid

4x^2 + 8x + 6x + 12 = 14

- anonymous

there is 40 more questions i have to do

- anonymous

So the answer is A.

- Vocaloid

right

- anonymous

Thank you.

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