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LizzyLove<3

  • 2 years ago

Please help with geometry!!!

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  1. superraymond
    • 2 years ago
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    can you help me first

  2. LizzyLove<3
    • 2 years ago
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    |dw:1364254756475:dw| Find the area of ABCD.

  3. Hoa
    • 2 years ago
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    let CO is the height of the triangle, and let F is the point between A and O. redraw it. I guide you then

  4. LizzyLove<3
    • 2 years ago
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    Ok like this??|dw:1364255189854:dw|

  5. LizzyLove<3
    • 2 years ago
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    @Hoa

  6. Hoa
    • 2 years ago
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    perfect, now, you have 2 regions. right? and you have formula to get the answer, try, the first region is parralelogram ADCF, the area formula is????

  7. LizzyLove<3
    • 2 years ago
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    b*h = Area for rectangle and parallelogram

  8. jim_thompson5910
    • 2 years ago
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    are you sure that BC = 8?

  9. jim_thompson5910
    • 2 years ago
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    it would make things a lot easier if BC = 8

  10. jim_thompson5910
    • 2 years ago
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    i meant, BC = 6

  11. LizzyLove<3
    • 2 years ago
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    Yea:) @jim_thompson5910 It does!!

  12. jim_thompson5910
    • 2 years ago
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    ok one sec

  13. LizzyLove<3
    • 2 years ago
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    Oh i know what ur saying... @jim_thompson5910

  14. jim_thompson5910
    • 2 years ago
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    anyways, we need CO, which will give us the height needed to find the area of the paralleogram but before we find CO, we need FB

  15. jim_thompson5910
    • 2 years ago
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    that length is 32 |dw:1364255489567:dw|

  16. LizzyLove<3
    • 2 years ago
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    Yea...

  17. jim_thompson5910
    • 2 years ago
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    this length is 22 |dw:1364255516091:dw| so this remaining length here |dw:1364255533268:dw| must be 10

  18. jim_thompson5910
    • 2 years ago
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    since 22+10 = 32

  19. LizzyLove<3
    • 2 years ago
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    Huh?

  20. LizzyLove<3
    • 2 years ago
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    Nvm i know what urr doing:)

  21. jim_thompson5910
    • 2 years ago
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    We now have this triangle |dw:1364255559257:dw|

  22. LizzyLove<3
    • 2 years ago
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    And so u have to do the pythagoreum theorm thing...

  23. LizzyLove<3
    • 2 years ago
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    to find 'h'

  24. jim_thompson5910
    • 2 years ago
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    it's not drawn to scale because this is actually a right triangle with hypotenuse of 10 so it really looks like this |dw:1364255624494:dw|

  25. LizzyLove<3
    • 2 years ago
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    But u cant do tht, if it doesnt say in my HW...

  26. jim_thompson5910
    • 2 years ago
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    if x was this length |dw:1364255675546:dw|

  27. jim_thompson5910
    • 2 years ago
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    then 10-x must be this length here |dw:1364255697460:dw|

  28. LizzyLove<3
    • 2 years ago
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    Hold on there bro, let me see what ur doing, plz ... @jim_thompson5910

  29. jim_thompson5910
    • 2 years ago
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    so what this means is that we can say x^2 + h^2 = 6^2 and h^2 + (10-x)^2 = 8^2

  30. jim_thompson5910
    • 2 years ago
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    alright sorry

  31. LizzyLove<3
    • 2 years ago
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    |dw:1364255854635:dw| I dont get what u did here... @jim_thompson5910

  32. jim_thompson5910
    • 2 years ago
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    I broke up that length of 10 into two pieces

  33. jim_thompson5910
    • 2 years ago
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    one piece is x units long the other is 10-x units long

  34. jim_thompson5910
    • 2 years ago
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    both add back up to 10 (x) + (10-x) = x + 10-x = 10

  35. LizzyLove<3
    • 2 years ago
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    So y can t u just leave it as 10??

  36. LizzyLove<3
    • 2 years ago
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    @jim_thompson5910

  37. jim_thompson5910
    • 2 years ago
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    because breaking up this length of 10 will help us find the height h

  38. jim_thompson5910
    • 2 years ago
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    it's not the only way to find h, but it's probably one of the easier ways

  39. LizzyLove<3
    • 2 years ago
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    k hold on..

  40. jim_thompson5910
    • 2 years ago
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    alright

  41. LizzyLove<3
    • 2 years ago
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    |dw:1364256139846:dw|

  42. jim_thompson5910
    • 2 years ago
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    yes you break up the triangle like that and that will help you find h

  43. LizzyLove<3
    • 2 years ago
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    ok so now it makes sense...

  44. jim_thompson5910
    • 2 years ago
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    this first triangle here |dw:1364256244802:dw| has legs of x and h, with hypotenuse 6, so a^2 + b^2 = c^2 x^2 + h^2 = 6^2 x^2 + h^2 = 36

  45. jim_thompson5910
    • 2 years ago
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    this triangle here is a right triangle with leg1 = 10-x leg2 = h hypotenuse = 8 which means a^2 + b^2 = c^2 (10-x)^2 + h^2 = 8^2 (10-x)^2 + h^2 = 64

  46. jim_thompson5910
    • 2 years ago
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    with me so far?

  47. LizzyLove<3
    • 2 years ago
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    Kinda, i still dont get y u did 10 - x ?? lol sry

  48. jim_thompson5910
    • 2 years ago
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    well if you break up 10 into two pieces, then one piece is x units long the other must be 10-x units long

  49. jim_thompson5910
    • 2 years ago
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    example if x was say x = 2 inches, then the first piece would be 2 inches the remaining bit would be 10-x = 10-2 = 8 inches

  50. LizzyLove<3
    • 2 years ago
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    Yea i get it but y can u just split it in half??

  51. jim_thompson5910
    • 2 years ago
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    they must add back up to 10, and they do x + (10-x) 2 + (8) 10

  52. jim_thompson5910
    • 2 years ago
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    because we do NOT know whether the length h cuts the side 10 in half or not

  53. jim_thompson5910
    • 2 years ago
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    it could, but it could not (in this case, it doesn't) we just don't know

  54. jim_thompson5910
    • 2 years ago
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    so that's why we must go this route

  55. LizzyLove<3
    • 2 years ago
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    ok... sry for tht, its just i need to know how to do this, thxss :) so wats next?

  56. jim_thompson5910
    • 2 years ago
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    no need for sorries, questions are good

  57. LizzyLove<3
    • 2 years ago
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    lol

  58. jim_thompson5910
    • 2 years ago
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    ok we have these two equations x^2 + h^2 = 36 (10-x)^2 + h^2 = 64

  59. jim_thompson5910
    • 2 years ago
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    we can either use substitution or elimination to solve for x and h

  60. jim_thompson5910
    • 2 years ago
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    let's do substitution

  61. LizzyLove<3
    • 2 years ago
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    ok, i think there is a way simpler way... im pretty sure tht u can split tht in half, my teacher said tht we wouldn't need to use sub. or eli.

  62. LizzyLove<3
    • 2 years ago
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    Can we just assume, b/c it's a right angle??

  63. jim_thompson5910
    • 2 years ago
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    Start with equation 1 and isolate h^2 (not h, just h^2) x^2 + h^2 = 36 h^2 = 36 - x^2 ------------------------------------------------------- Now replace h^2 in equation 2 with 36 - x^2 (since h^2 = 36 - x^2 above) (10-x)^2 + h^2 = 64 (10-x)^2 + (36 - x^2) = 64 Now FOIL out, expand and simplify (10-x)^2 + (36 - x^2) = 64 100 - 20x + x^2 + 36 - x^2 = 64 100 - 20x + 36 = 64 136 - 20x = 64 -20x = 64-136 -20x = -72 x = -72/(-20) x = 18/5 x = 3.6

  64. jim_thompson5910
    • 2 years ago
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    This is why I asked if BC was 8 or not If BC = 6, then you could split the 10 into two equal pieces

  65. LizzyLove<3
    • 2 years ago
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    k let me get this down...

  66. jim_thompson5910
    • 2 years ago
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    alright

  67. LizzyLove<3
    • 2 years ago
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    So how did u get these two equations?? (10-x)^2 + h^2 = 64 x^2 + h^2 = 36

  68. LizzyLove<3
    • 2 years ago
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    @jim_thompson5910

  69. jim_thompson5910
    • 2 years ago
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    through the use of the pythagorean theorem

  70. jim_thompson5910
    • 2 years ago
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    a^2 + b^2 = c^2

  71. jim_thompson5910
    • 2 years ago
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    it's explained a bit more above

  72. LizzyLove<3
    • 2 years ago
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    where did u get 36 from?

  73. jim_thompson5910
    • 2 years ago
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    from squaring the 6

  74. LizzyLove<3
    • 2 years ago
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    So is it sub or elim tht ur doing ? @jim_thompson5910

  75. LizzyLove<3
    • 2 years ago
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    @jim_thompson5910 ??

  76. jim_thompson5910
    • 2 years ago
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    I'm doing substitution

  77. LizzyLove<3
    • 2 years ago
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    kk

  78. jim_thompson5910
    • 2 years ago
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    I isolated h^2 in the first equation and then replaced the other h^2 in the second equation with 36 - x^2

  79. jim_thompson5910
    • 2 years ago
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    notice how the h terms went away after that

  80. LizzyLove<3
    • 2 years ago
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    kk i need to write this

  81. jim_thompson5910
    • 2 years ago
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    alright

  82. LizzyLove<3
    • 2 years ago
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    Sry it took so long... but is this 3.6??

  83. jim_thompson5910
    • 2 years ago
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    good

  84. jim_thompson5910
    • 2 years ago
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    x = 3.6

  85. jim_thompson5910
    • 2 years ago
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    btw I showed how it's x = 3.6 above lol but I'm glad you got that on your own

  86. LizzyLove<3
    • 2 years ago
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    |dw:1364258514592:dw|

  87. LizzyLove<3
    • 2 years ago
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    Is tht 3.6 ??

  88. jim_thompson5910
    • 2 years ago
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    yep, that length you are pointing to is 3.6 units long

  89. jim_thompson5910
    • 2 years ago
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    so x^2 + h^2 = 6^2 x^2 + h^2 = 36 (3.6)^2 + h^2 = 36 12.96 + h^2 = 36 h^2 = 36 - 12.96 h^2 = 23.04 h = sqrt(23.04) h = 4.8

  90. LizzyLove<3
    • 2 years ago
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    kk

  91. jim_thompson5910
    • 2 years ago
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    So the height is 4.8

  92. LizzyLove<3
    • 2 years ago
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    So is tht for this one??

  93. LizzyLove<3
    • 2 years ago
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    |dw:1364258641203:dw|

  94. jim_thompson5910
    • 2 years ago
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    no this one here |dw:1364258674211:dw|

  95. jim_thompson5910
    • 2 years ago
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    that's what we wanted we really don't need x to find the area we only needed x to find h

  96. LizzyLove<3
    • 2 years ago
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    So, i thought u said that

  97. LizzyLove<3
    • 2 years ago
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    |dw:1364258753145:dw| trhis length is 10 - x ??

  98. LizzyLove<3
    • 2 years ago
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    *this

  99. jim_thompson5910
    • 2 years ago
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    yes

  100. jim_thompson5910
    • 2 years ago
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    but we found x, then used that to find h

  101. jim_thompson5910
    • 2 years ago
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    we don't need to know what 10-x is we just want h

  102. LizzyLove<3
    • 2 years ago
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    So the last equation u put was to find 'h' right??

  103. LizzyLove<3
    • 2 years ago
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    @jim_thompson5910

  104. jim_thompson5910
    • 2 years ago
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    exactly

  105. LizzyLove<3
    • 2 years ago
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    k hold on let me get tht down..

  106. jim_thompson5910
    • 2 years ago
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    I started with x^2 + h^2 = 36, plugged in x = 3.6, then solved for h

  107. LizzyLove<3
    • 2 years ago
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    OK!! lol i get what we did, so whats next?? Do we just do 32 * 4.8??

  108. LizzyLove<3
    • 2 years ago
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    @jim_thompson5910

  109. jim_thompson5910
    • 2 years ago
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    ok that's a lot of work to find h

  110. jim_thompson5910
    • 2 years ago
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    like I said, it would be a lot easier if BC = 6

  111. jim_thompson5910
    • 2 years ago
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    but it's still doable to find h even if BC wasn't 6

  112. LizzyLove<3
    • 2 years ago
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    so was i right?? or is there a different way to do this?

  113. jim_thompson5910
    • 2 years ago
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    anyways, this is a trapezoid with base1 = 32 base2 = 22 height = 4.8

  114. jim_thompson5910
    • 2 years ago
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    so we can find the area using this formula A = h*(b1+b2)/2 where in this case h = 4.8 b1 = 32 b2 = 22

  115. jim_thompson5910
    • 2 years ago
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    A = h*(b1+b2)/2 A = 4.8*(32+22)/2 A = 4.8*(54)/2 A = 4.8*27 A = 129.6

  116. LizzyLove<3
    • 2 years ago
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    kk hod it bro

  117. jim_thompson5910
    • 2 years ago
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    alright

  118. LizzyLove<3
    • 2 years ago
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    So thts it?? @jim_thompson5910

  119. jim_thompson5910
    • 2 years ago
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    yep pretty much, unless you want to convert that into a fraction

  120. LizzyLove<3
    • 2 years ago
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    No thank u, i perfer decimals:)

  121. jim_thompson5910
    • 2 years ago
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    ok great

  122. jim_thompson5910
    • 2 years ago
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    yeah decimals are more intuitive with area problems

  123. LizzyLove<3
    • 2 years ago
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    THANK THANK YOU SOOOOSOSOOOO MUCH:D:D:D:D: :):) UR THE BEST :D:D:D

  124. jim_thompson5910
    • 2 years ago
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    lol thx and glad to be of help

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