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anonymous

  • one year ago

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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  1. Vocaloid
    • one year ago
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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|

  2. Vocaloid
    • one year ago
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    now, let's see if we can write an expression, using x, for the width and length of the whole thing (mirror + frame)

  3. anonymous
    • one year ago
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    So the answer would be C right?

  4. Vocaloid
    • one year ago
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    hm, not C, let's keep going |dw:1440372299021:dw| any ideas?

  5. Vocaloid
    • one year ago
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    can you tell me what the length and width are in terms of x?

  6. anonymous
    • one year ago
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    \[x^3\]

  7. Vocaloid
    • one year ago
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    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?

  8. Vocaloid
    • one year ago
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    |dw:1440372540133:dw|

  9. anonymous
    • one year ago
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    4x?

  10. Vocaloid
    • one year ago
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    almost but not quite... length of the mirror + width of the frame on each side = ?

  11. anonymous
    • one year ago
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    0?

  12. Vocaloid
    • one year ago
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    |dw:1440372618481:dw| maybe just look at it from one dimension?

  13. Vocaloid
    • one year ago
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    the length of the mirror is 4 and the width of the frame is x, so the total length is...?

  14. anonymous
    • one year ago
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    4x^2?

  15. Vocaloid
    • one year ago
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    nope, not quite... |dw:1440372717991:dw|

  16. anonymous
    • one year ago
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    Idk.

  17. Vocaloid
    • one year ago
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    pretend that it's a straight line... add together length of mirror + width of frame = ?

  18. anonymous
    • one year ago
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    Is the answer C?

  19. Vocaloid
    • one year ago
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    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|

  20. Vocaloid
    • one year ago
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    the length is 4, agreed?

  21. anonymous
    • one year ago
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    144?

  22. Vocaloid
    • one year ago
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    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|

  23. Plasmataco
    • one year ago
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    ... Y u so genius @Vocaloid

  24. anonymous
    • one year ago
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    yes

  25. Vocaloid
    • one year ago
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    ok, now let's put the frame around it now|dw:1440373034973:dw|

  26. Vocaloid
    • one year ago
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    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|

  27. Vocaloid
    • one year ago
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    just add: width of frame + length of mirror + width of frame = ?

  28. Vocaloid
    • one year ago
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    your answer should involve x somehow

  29. anonymous
    • one year ago
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    IS the answer D?

  30. Vocaloid
    • one year ago
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    no, the answer isn't D, please stop guessing...

  31. Vocaloid
    • one year ago
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    |dw:1440373181795:dw|

  32. Plasmataco
    • one year ago
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    Lul

  33. anonymous
    • one year ago
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    -.-

  34. Vocaloid
    • one year ago
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    the length is 4 + x + x, agreed?

  35. Plasmataco
    • one year ago
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    U sound like my mom when I do calculus. :3

  36. anonymous
    • one year ago
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    Yes

  37. Vocaloid
    • one year ago
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    alright, now can you find the width?|dw:1440373262344:dw|

  38. anonymous
    • one year ago
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    3*4*x?

  39. Vocaloid
    • one year ago
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    not quite.... just like before, we add width of mirror + width of frame + width of frame = ?

  40. Vocaloid
    • one year ago
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    |dw:1440373318819:dw|

  41. anonymous
    • one year ago
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    3+2x

  42. Vocaloid
    • one year ago
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    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?

  43. anonymous
    • one year ago
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    So its B?

  44. Vocaloid
    • one year ago
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    area = (width)*(length) 14 = (4 + 2x)(3 + 2x) simplify that and you will get your answer....

  45. Vocaloid
    • one year ago
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    start by doing FOIL on the right side

  46. anonymous
    • one year ago
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    Is it A?

  47. Vocaloid
    • one year ago
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    start by doing FOIL on the right side, please..... (4 + 2x)(3 + 2x) = ??

  48. Plasmataco
    • one year ago
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    @Vocaloid I believe she is correct

  49. Vocaloid
    • one year ago
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    I already know the answer, I want her/him to learn so she/he can do this in the future without my guidance

  50. anonymous
    • one year ago
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    I am a girl...

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

  52. anonymous
    • one year ago
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    @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?

  53. Vocaloid
    • one year ago
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    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

  54. anonymous
    • one year ago
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    You said it wasn't b...

  55. Vocaloid
    • one year ago
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    do you understand FOIL?

  56. anonymous
    • one year ago
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    Earlier

  57. anonymous
    • one year ago
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    Yes. I am just in a big hurry

  58. Plasmataco
    • one year ago
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    Lol... U sound real stressed

  59. anonymous
    • one year ago
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    VERY

  60. anonymous
    • one year ago
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    2x*2x+2x*3+4*2x+3*4-12

  61. Vocaloid
    • one year ago
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    almost... (2x + 3)(2x + 4) = (2x)(2x) + (4)(2x) + (3)(2x) + (3)(4)

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

  63. anonymous
    • one year ago
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    @Vocaloid I am in a bigggg hurrrryyy

  64. anonymous
    • one year ago
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    My school starts tomorrow and i almost finsihed

  65. Vocaloid
    • one year ago
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    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...

  66. anonymous
    • one year ago
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    I am tring to get this done

  67. Vocaloid
    • one year ago
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    4x^2 + 8x + 6x + 12 = 14

  68. anonymous
    • one year ago
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    there is 40 more questions i have to do

  69. anonymous
    • one year ago
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    So the answer is A.

  70. Vocaloid
    • one year ago
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    right

  71. anonymous
    • one year ago
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    Thank you.

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