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help_people

  • one year ago

Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? Image of a frame 7 feet wide by 8 feet long, with an of x on the bottom and right sides x2 + 15x − 2 = 0 x2 + 15x + 58 = 0 4x2 + 30x − 2 = 0 4x2 + 30x + 58 = 0

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  1. help_people
    • one year ago
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    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
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    |dw:1442710030323:dw|

  3. jim_thompson5910
    • one year ago
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    |dw:1442710064925:dw|

  4. jim_thompson5910
    • one year ago
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    can you tell me what this length is? |dw:1442710140915:dw|

  5. help_people
    • one year ago
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    15?

  6. jim_thompson5910
    • one year ago
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    no the 7 is the vertical dimension I'm asking for the total horizontal dimension

  7. jim_thompson5910
    • one year ago
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    hint: |dw:1442710233263:dw|

  8. help_people
    • one year ago
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    30?

  9. jim_thompson5910
    • one year ago
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    idk how you're getting that

  10. jim_thompson5910
    • one year ago
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    do you see the stuff I circled?

  11. help_people
    • one year ago
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    yes

  12. jim_thompson5910
    • one year ago
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    add them up to get ???

  13. help_people
    • one year ago
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    2x or x^2

  14. jim_thompson5910
    • one year ago
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    x + 8 + x = ???

  15. help_people
    • one year ago
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    7

  16. jim_thompson5910
    • one year ago
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    think of it like this `apple + apple = 2 apples` so `x + x = 2x` right?

  17. help_people
    • one year ago
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    yeah x8x?

  18. jim_thompson5910
    • one year ago
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    so if x+x = 2x, then x+x+8 turns into what?

  19. help_people
    • one year ago
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    2x+8

  20. jim_thompson5910
    • one year ago
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    good

  21. jim_thompson5910
    • one year ago
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    |dw:1442710945434:dw|

  22. jim_thompson5910
    • one year ago
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    so hopefully you see how that total length marked in the drawing is 2x+8 feet?

  23. help_people
    • one year ago
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    i finally do :D

  24. jim_thompson5910
    • one year ago
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    ok great

  25. jim_thompson5910
    • one year ago
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    what is this marked length here? |dw:1442711082155:dw|

  26. help_people
    • one year ago
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    2x+7?

  27. jim_thompson5910
    • one year ago
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    good

  28. jim_thompson5910
    • one year ago
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    |dw:1442711337192:dw|

  29. jim_thompson5910
    • one year ago
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    now if the length was 2x+8 and the width was 2x+7, then what is the area of the rectangle?

  30. help_people
    • one year ago
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    4x+15?

  31. jim_thompson5910
    • one year ago
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    you have to multiply (2x+8) with (2x+7) FOIL it out

  32. help_people
    • one year ago
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    could you show me ?

  33. jim_thompson5910
    • one year ago
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    have you learned the box method? that's actually better than FOIL

  34. help_people
    • one year ago
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    4x^2+30x+56?

  35. jim_thompson5910
    • one year ago
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    good, you used the box method to get that? or some other method?

  36. help_people
    • one year ago
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    box method

  37. jim_thompson5910
    • one year ago
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    ok great

  38. jim_thompson5910
    • one year ago
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    so the entire area of the rectangle (larger rectangle) is `4x^2+30x+56` they tell us that "The painting and frame must have an area of 58 square feet." so equate the two areas 4x^2+30x+56 = 58

  39. jim_thompson5910
    • one year ago
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    now get everything to one side

  40. help_people
    • one year ago
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    how

  41. jim_thompson5910
    • one year ago
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    subtract 58 from both sides

  42. jim_thompson5910
    • one year ago
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    |dw:1442712284053:dw|

  43. jim_thompson5910
    • one year ago
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    |dw:1442712322065:dw|

  44. jim_thompson5910
    • one year ago
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    |dw:1442712342649:dw|

  45. help_people
    • one year ago
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    4x^2+30x-2

  46. help_people
    • one year ago
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    @jim_thompson5910

  47. jim_thompson5910
    • one year ago
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    correct

  48. jim_thompson5910
    • one year ago
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    0 be left on the other side (since 58-58 = 0) so we have this answer `4x^2 + 30x - 2 = 0`

  49. help_people
    • one year ago
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    ok wow

  50. help_people
    • one year ago
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    tahnks alot for everything :)

  51. jim_thompson5910
    • one year ago
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    no problem

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