anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Vocaloid
  • Vocaloid
well, let's draw a picture of a 3*4 mirror with a frame that is x inches thick |dw:1440372180188:dw|
Vocaloid
  • 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
  • anonymous
So the answer would be C right?

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More answers

Vocaloid
  • Vocaloid
hm, not C, let's keep going |dw:1440372299021:dw| any ideas?
Vocaloid
  • Vocaloid
can you tell me what the length and width are in terms of x?
anonymous
  • anonymous
\[x^3\]
Vocaloid
  • 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
  • Vocaloid
|dw:1440372540133:dw|
anonymous
  • anonymous
4x?
Vocaloid
  • Vocaloid
almost but not quite... length of the mirror + width of the frame on each side = ?
anonymous
  • anonymous
0?
Vocaloid
  • Vocaloid
|dw:1440372618481:dw| maybe just look at it from one dimension?
Vocaloid
  • Vocaloid
the length of the mirror is 4 and the width of the frame is x, so the total length is...?
anonymous
  • anonymous
4x^2?
Vocaloid
  • Vocaloid
nope, not quite... |dw:1440372717991:dw|
anonymous
  • anonymous
Idk.
Vocaloid
  • Vocaloid
pretend that it's a straight line... add together length of mirror + width of frame = ?
anonymous
  • anonymous
Is the answer C?
Vocaloid
  • 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
  • Vocaloid
the length is 4, agreed?
anonymous
  • anonymous
144?
Vocaloid
  • 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
  • Plasmataco
... Y u so genius @Vocaloid
anonymous
  • anonymous
yes
Vocaloid
  • Vocaloid
ok, now let's put the frame around it now|dw:1440373034973:dw|
Vocaloid
  • 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
  • Vocaloid
just add: width of frame + length of mirror + width of frame = ?
Vocaloid
  • Vocaloid
your answer should involve x somehow
anonymous
  • anonymous
IS the answer D?
Vocaloid
  • Vocaloid
no, the answer isn't D, please stop guessing...
Vocaloid
  • Vocaloid
|dw:1440373181795:dw|
Plasmataco
  • Plasmataco
Lul
anonymous
  • anonymous
-.-
Vocaloid
  • Vocaloid
the length is 4 + x + x, agreed?
Plasmataco
  • Plasmataco
U sound like my mom when I do calculus. :3
anonymous
  • anonymous
Yes
Vocaloid
  • Vocaloid
alright, now can you find the width?|dw:1440373262344:dw|
anonymous
  • anonymous
3*4*x?
Vocaloid
  • Vocaloid
not quite.... just like before, we add width of mirror + width of frame + width of frame = ?
Vocaloid
  • Vocaloid
|dw:1440373318819:dw|
anonymous
  • anonymous
3+2x
Vocaloid
  • 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
  • anonymous
So its B?
Vocaloid
  • Vocaloid
area = (width)*(length) 14 = (4 + 2x)(3 + 2x) simplify that and you will get your answer....
Vocaloid
  • Vocaloid
start by doing FOIL on the right side
anonymous
  • anonymous
Is it A?
Vocaloid
  • Vocaloid
start by doing FOIL on the right side, please..... (4 + 2x)(3 + 2x) = ??
Plasmataco
  • Plasmataco
@Vocaloid I believe she is correct
Vocaloid
  • 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
  • anonymous
I am a girl...
Vocaloid
  • Vocaloid
right, I figured as much, just making sure so, start by doing FOIL on the right side... (4 + 2x)(3 + 2x) = ?
anonymous
  • 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
  • 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
  • anonymous
You said it wasn't b...
Vocaloid
  • Vocaloid
do you understand FOIL?
anonymous
  • anonymous
Earlier
anonymous
  • anonymous
Yes. I am just in a big hurry
Plasmataco
  • Plasmataco
Lol... U sound real stressed
anonymous
  • anonymous
VERY
anonymous
  • anonymous
2x*2x+2x*3+4*2x+3*4-12
Vocaloid
  • Vocaloid
almost... (2x + 3)(2x + 4) = (2x)(2x) + (4)(2x) + (3)(2x) + (3)(4)
Vocaloid
  • Vocaloid
there's no -12 at the end but other than that, you're on the right track... now start combining like terms
anonymous
  • anonymous
@Vocaloid I am in a bigggg hurrrryyy
anonymous
  • anonymous
My school starts tomorrow and i almost finsihed
Vocaloid
  • 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
  • anonymous
I am tring to get this done
Vocaloid
  • Vocaloid
4x^2 + 8x + 6x + 12 = 14
anonymous
  • anonymous
there is 40 more questions i have to do
anonymous
  • anonymous
So the answer is A.
Vocaloid
  • Vocaloid
right
anonymous
  • anonymous
Thank you.

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