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anonymous

  • one year ago

Fan and Medal!! The area of a rectangular piece of land is 240 square meters. If the length of the land was 5 meters less and the width was 3 meters more, the shape of the land would be a square. Part A: Write an equation to find the width (x) of the land. Show the steps of your work. Part B: What is the width of the land in meters? Show the steps of your work.

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  1. DanJS
    • one year ago
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    A square would be X by X This rectangle is said to be (X-5) by (X+3)

  2. DanJS
    • one year ago
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    (X-5)(X+3) = 240

  3. anonymous
    • one year ago
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    (x+3)(x-5)=240?

  4. anonymous
    • one year ago
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    Okay I got that

  5. DanJS
    • one year ago
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    yes

  6. anonymous
    • one year ago
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    What do I do now?

  7. anonymous
    • one year ago
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    do you know how to find the area of a rectangle

  8. DanJS
    • one year ago
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    Solve for X, you will get 2 answers, the positive one is correct

  9. anonymous
    • one year ago
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    do I FOIL (x+3)(x-5)?

  10. DanJS
    • one year ago
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    yes

  11. anonymous
    • one year ago
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    I ended up getting x^2-2x-15

  12. DanJS
    • one year ago
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    move the 240 over now to get x^2 - 2x - 255 = 0

  13. DanJS
    • one year ago
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    factor that, or use the quadratic formula , since it is a book prob, it will probably factor nice

  14. anonymous
    • one year ago
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    Do I make that into two binomials?

  15. DanJS
    • one year ago
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    yep (x-17)(x+15)=0

  16. anonymous
    • one year ago
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    Wait how did you get the 17 and 15?

  17. DanJS
    • one year ago
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    255 = 17 * 15 and 15 - 17 = -2 (middle number)

  18. DanJS
    • one year ago
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    If you multiply that out, you get back to the original ax^2 + bx + c = 0

  19. anonymous
    • one year ago
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    Ohhh okay I understand that

  20. DanJS
    • one year ago
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    or you could always just apply the quadratic formula, and you would get the X values

  21. DanJS
    • one year ago
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    so now you have (x-17)(x+15)=0 which means either term can be zero, so (x-17)=0 or (x+15)=0 X=17 or X=-15

  22. DanJS
    • one year ago
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    The problem is a physical measure, so the positive value is the one that makes sense... X=17

  23. anonymous
    • one year ago
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    What do I write for part A and for Part B?

  24. DanJS
    • one year ago
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    First Part... Area of Land = Length * Width = 240 240 = (X-5)(X+3)

  25. anonymous
    • one year ago
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    And do I work it out until I get (x-17)(x+15) = 0?

  26. DanJS
    • one year ago
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    right, for the second part you solve it

  27. anonymous
    • one year ago
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    Thank you sososo much! You really helped a lot.

  28. DanJS
    • one year ago
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    yw

  29. anonymous
    • one year ago
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    Do you think you can check over some of my answers? If you have the time of course

  30. DanJS
    • one year ago
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    sure

  31. anonymous
    • one year ago
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    Thanks so much! They're quite long, so do you want me to screenshot it and attach it?

  32. DanJS
    • one year ago
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    Sure, i have a bit of time

  33. anonymous
    • one year ago
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  34. anonymous
    • one year ago
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  35. anonymous
    • one year ago
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    And that's it, since I don't want to have you check all of them, haha

  36. DanJS
    • one year ago
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    The first one looks good, what is the prob with that one?

  37. anonymous
    • one year ago
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    I just wanted to see if I got it correct or not

  38. DanJS
    • one year ago
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    That one looks good to me

  39. anonymous
    • one year ago
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    Thank you (:

  40. DanJS
    • one year ago
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    second one looks good too

  41. anonymous
    • one year ago
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    yay ^-^

  42. DanJS
    • one year ago
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    For the last one part C, it asks if they all have a common factor

  43. anonymous
    • one year ago
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    Yes, is it wrong?

  44. DanJS
    • one year ago
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    I don't see a common factor btw all 3 of those

  45. anonymous
    • one year ago
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    So it would be no because no common factor is consistent between the three polynomials?

  46. DanJS
    • one year ago
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    yeah i think so

  47. anonymous
    • one year ago
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    Do you think you could check 2 more?

  48. DanJS
    • one year ago
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    k, real quick, then i have to go... you can fan me for help later if you want

  49. anonymous
    • one year ago
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    Alright! Once I finish with these questions, I'll be done with Algebra for the year, aha

  50. DanJS
    • one year ago
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    haha

  51. anonymous
    • one year ago
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  52. anonymous
    • one year ago
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    And that's it!

  53. DanJS
    • one year ago
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    For the first, for the domain, be sure to call the variable 't' and not x, Since y is a function of t, in S(t)

  54. anonymous
    • one year ago
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    Okay

  55. anonymous
    • one year ago
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    anything else?

  56. DanJS
    • one year ago
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    nope, looks good to me

  57. anonymous
    • one year ago
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    Yay!

  58. anonymous
    • one year ago
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    Did you check the last one? or

  59. DanJS
    • one year ago
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    Part b asks what the maximum profit is, you dont say what that is

  60. anonymous
    • one year ago
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    How do I find the maximum?

  61. DanJS
    • one year ago
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    it would be at the vertex of the parabola, or axis of symmetry value

  62. anonymous
    • one year ago
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    How do I find that? Did my steps correspond to the question at all?

  63. DanJS
    • one year ago
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    It looks like you have P(n) written in vertex form in part b right... so you can use that to extract the vertex coordinate (h,k)

  64. anonymous
    • one year ago
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    Huh?

  65. DanJS
    • one year ago
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    vertex point - (h,k) Vertex Equation - y = a(x-h)^2+k

  66. anonymous
    • one year ago
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    Do I need to rewrite anything?

  67. DanJS
    • one year ago
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    so the vertex from your equation is at the point, (5, 2250)

  68. anonymous
    • one year ago
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    This is so confusing ._. I'm sorry that I'm so difficult to work with

  69. DanJS
    • one year ago
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    sorry i said year... the most profit is at (5,2250) price 5 and prfit 2250

  70. anonymous
    • one year ago
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    How do I find that with the steps I wrote down?

  71. DanJS
    • one year ago
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    which is also on the axis of symmetry

  72. DanJS
    • one year ago
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    The last thing you wrote, is the vertex equation for the parabola. vertex point - (h,k) Vertex Equation - y = a(x-h)^2+k The maximum profit 'k' is at that vertex point, you can just read it from your equation.

  73. anonymous
    • one year ago
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    Ahhh okay! So now I write that the maximum profit is 2250 ?

  74. DanJS
    • one year ago
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    yes, The vertex is at point (5,2250) When the tickets are sold at 5 dollars each, the profit is the most at 2250 dollars.

  75. anonymous
    • one year ago
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    Thank you sosososo much!! You're truly a lifesaver, I wish I could give you a thousand medals , haha

  76. DanJS
    • one year ago
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    |dw:1433203687682:dw|

  77. DanJS
    • one year ago
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    welcome,

  78. anonymous
    • one year ago
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    Take care!!

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