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pooja195

  • one year ago

@mathmate

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  1. pooja195
    • one year ago
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    @mathmate

  2. pooja195
    • one year ago
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    Chapter 9 ;-;

  3. mathmate
    • one year ago
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    Chapter 9 ======

  4. mathmate
    • one year ago
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    |dw:1433627905280:dw| Find x (hypotenuse) shown in the above drawing.

  5. pooja195
    • one year ago
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    a^2 + b^2 = c^2?

  6. mathmate
    • one year ago
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    Yep, now evaluate x numerically, please.

  7. pooja195
    • one year ago
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    12^2+5^2=c^ 144+25=169 13^2

  8. mathmate
    • one year ago
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    So x=13 (is the final answer).

  9. mathmate
    • one year ago
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    which two consecutive integers does sqrt(200) fall between?

  10. pooja195
    • one year ago
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    idk this ;-;

  11. mathmate
    • one year ago
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    10^2=100 11^2=121 12^2=144 13^2=169 14^2=196 15^2=225 16^2=256 ... which two consecutive integers does sqrt(200) fall between?

  12. pooja195
    • one year ago
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    no .-.

  13. pooja195
    • one year ago
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    *none

  14. mathmate
    • one year ago
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    "between" is the keyword. We know that 14^2=196, and 15^2=225 or sqrt(196)=14, sqrt(225)=15, so sqrt(200) falls between which integer numbers?

  15. pooja195
    • one year ago
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    Decimals? .-.

  16. pooja195
    • one year ago
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    wait no

  17. mathmate
    • one year ago
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    no, we are looking for two integer numbers! lol

  18. pooja195
    • one year ago
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    This si confusing T_T lets skip this

  19. mathmate
    • one year ago
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    the answer is 14 and 15. In fact sqrt(200)=14.1421356237309.... (never ends). So we know that sqrt(200) falls between 14 and 15! You were probably thinking that it's more complicated than this!

  20. pooja195
    • one year ago
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    -_-

  21. mathmate
    • one year ago
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    The hint is 14^2=196, so too small, 15^2=225, so too big. Therefore sqrt(200) must fall between 14 and 15. Is that ok?

  22. pooja195
    • one year ago
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    yes

  23. mathmate
    • one year ago
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    Solve the equation 27-3y^2=0

  24. pooja195
    • one year ago
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    Would you like the work or is it ok to put in the answer?

  25. mathmate
    • one year ago
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    put in the work, but LaTeX is not required.

  26. pooja195
    • one year ago
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    first find a GCF 27-3y^2=0 -3 is the gcf then square root answer: −3(y+3)(y−3) set values to 0 y=3 or y=−3

  27. pooja195
    • one year ago
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    /.\

  28. mathmate
    • one year ago
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    Very good, shows that you're comfortable with factoring. It will help in the later sections. You can also solve by isolating y, -3y^2=-27 y^2=9 y=\(\pm 3\)

  29. mathmate
    • one year ago
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    Ready for the next one?

  30. mathmate
    • one year ago
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    an engineering student is a contestant in an egg dropping contest. The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking. The model for the egg's height, h (in feet), at time t seconds since release, is h = -16t^2 + 32. Calculate the time at whic the egg is at a height of 10 feet above ground. Give answer to 2 decimal places.

  31. pooja195
    • one year ago
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    10=-16t^2+32 subtract 32 from both sides then divide by 16 1.375= t^2 idk where to go after this

  32. mathmate
    • one year ago
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    Take out your ti-83 to finish!

  33. mathmate
    • one year ago
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    "give answer to 2 decimal places" is a hint you might need your ti-83!

  34. mathmate
    • one year ago
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    sqrt(1.375)=?

  35. pooja195
    • one year ago
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    1.172604

  36. mathmate
    • one year ago
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    exactly! (1.17 for 2 decimal places).

  37. mathmate
    • one year ago
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    Any questions before we move to simplifying radicals?

  38. pooja195
    • one year ago
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    no

  39. mathmate
    • one year ago
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    Simplifying radicals basically is to pull things out of the square-root sign, whenever possible. For example, sqrt(4)=2 is rather straight-forward.

  40. mathmate
    • one year ago
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    But sqrt(18) is less obvious, since we write sqrt(18)=sqrt(3^2 *2)=3sqrt(2)

  41. mathmate
    • one year ago
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    So I'll let your try sqrt(48) while I take a meal break!

  42. pooja195
    • one year ago
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    48 6 8 3 2 42 \[2\sqrt{12}\]

  43. mathmate
    • one year ago
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    almost, just one step further sqrt(48)=sqrt(4*12)=sqrt(16*3)=sqrt(4^2 * 3)=4sqrt(3)

  44. mathmate
    • one year ago
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    Simplify (1) sqrt(98) [98=2*7*7]

  45. mathmate
    • one year ago
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    So every factor that appears twice inside the radical you take one outside. So sqrt(98)=sqrt(2*7*7)=7sqrt(2)

  46. pooja195
    • one year ago
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    Dance club.

  47. pooja195
    • one year ago
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    Dance club is the method my teacher taught me because teens like to think like that

  48. mathmate
    • one year ago
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    Oh! Can you show me that?

  49. pooja195
    • one year ago
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    Ok its been a while but eh :P 56 8 7 4 2 2 2 2 and 2 are a couble so they leave the dance club 2 squrt 2 idk if its right

  50. mathmate
    • one year ago
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    Yes, I get the part for the leaving dance club part (ingeneous!) Then we have to keep 2*7 in the club, so we get 2sqrt(14)

  51. pooja195
    • one year ago
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    lel :3

  52. pooja195
    • one year ago
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    Are we done with this section ?

  53. mathmate
    • one year ago
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    I usually like to see you do at least one perfect answer, like (2) sqrt(60) [60=2*2 * 3 * 5] then there is rationalize the denominator.

  54. pooja195
    • one year ago
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    T_T

  55. pooja195
    • one year ago
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    ok

  56. mathmate
    • one year ago
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    (2) sqrt(60) [60=2*2 * 3 * 5]

  57. pooja195
    • one year ago
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    im confused whats the question? .-.

  58. mathmate
    • one year ago
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    simplify sqrt(60)

  59. pooja195
    • one year ago
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    60 10 6 5 2 3 2 2 sqrt 15

  60. pooja195
    • one year ago
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    T_T say im right!

  61. pooja195
    • one year ago
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    Princess demands it!

  62. mathmate
    • one year ago
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    Yes, you're right, I don't think you have problem with that.

  63. mathmate
    • one year ago
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    Now we move onto rationalizing the denominator.

  64. mathmate
    • one year ago
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    Mathematicians traditionally do not like to see square roots in the denominator, because that would make the common denominator very messy.

  65. pooja195
    • one year ago
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    Just multiply by the root

  66. pooja195
    • one year ago
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    *in the denominator

  67. mathmate
    • one year ago
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    Do you want me to explain, or jump to pretest?

  68. pooja195
    • one year ago
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    Pretest

  69. mathmate
    • one year ago
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    Rationalize 9sqrt(1/3)

  70. pooja195
    • one year ago
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    9 squrt 3

  71. pooja195
    • one year ago
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    ^LOL

  72. mathmate
    • one year ago
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    Sure?

  73. mathmate
    • one year ago
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    The question was \(9\sqrt{\frac{1}{3}}\)

  74. pooja195
    • one year ago
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    :/

  75. pooja195
    • one year ago
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    this is diffrent .-.

  76. mathmate
    • one year ago
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    Example: \(sqrt(\frac{2}{5}) = \frac{\sqrt2}{\sqrt5}=\frac{\sqrt2\times \sqrt5}{\sqrt5^2}=\frac{\sqrt{10}}{5}\)

  77. mathmate
    • one year ago
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    just a recap, we were working on simplify 9sqrt(1/3). I sent this previous example to help.

  78. pooja195
    • one year ago
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    sqrt 3/ 3

  79. mathmate
    • one year ago
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    9 sqrt(1/3) = 9(sqrt(1)/sqrt(3)) = 9(sqrt(1)*sqrt(3)/(sqrt(3)^2)=9sqrt(3)/3=3sqrt(3)

  80. mathmate
    • one year ago
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    or \(9\sqrt{1/3}=3\frac{\sqrt3 \times \sqrt3}{\sqrt3}=3\sqrt3\)

  81. pooja195
    • one year ago
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    IM IRGHT??

  82. pooja195
    • one year ago
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    *RIGHT?

  83. mathmate
    • one year ago
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    no, you had the 3 as denominator, and not multiplied.

  84. pooja195
    • one year ago
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    >:(

  85. pooja195
    • one year ago
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    9

  86. pooja195
    • one year ago
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    .-.

  87. mathmate
    • one year ago
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    not 9, it's \(3\sqrt3\) :)

  88. pooja195
    • one year ago
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    >:(

  89. mathmate
    • one year ago
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    ok, try this one: Simplify \(\Large \sqrt{\frac{25}{3}}\)

  90. pooja195
    • one year ago
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    \[\huge~\frac{ 5\sqrt{3} }{ 3 }\]

  91. pooja195
    • one year ago
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    Am i right?

  92. pooja195
    • one year ago
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    >:(

  93. mathmate
    • one year ago
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    Excellent! It's correct!

  94. pooja195
    • one year ago
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    :O YAY!!! :D

  95. mathmate
    • one year ago
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    Yep! any questions before we move on?

  96. pooja195
    • one year ago
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    Nope

  97. mathmate
    • one year ago
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    Graphing parabolas (quadratic functions)

  98. pooja195
    • one year ago
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    No we ahvent learned this

  99. mathmate
    • one year ago
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    We need to be able to find the vertex of a parabola.

  100. pooja195
    • one year ago
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    ,-,

  101. mathmate
    • one year ago
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    no?

  102. pooja195
    • one year ago
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    ^no

  103. mathmate
    • one year ago
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    ok, next case!

  104. pooja195
    • one year ago
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    kk

  105. mathmate
    • one year ago
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    Do you know the shape of a quadratic function? (concave up, concave down)

  106. mathmate
    • one year ago
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    When the leading coefficient is positive, it's concave up.

  107. pooja195
    • one year ago
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    We havent learned this

  108. mathmate
    • one year ago
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    |dw:1433641575278:dw| Here coef. of x^2=1 (positive), so it is drawn concave up.

  109. mathmate
    • one year ago
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    sure?

  110. pooja195
    • one year ago
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    yea im sure .-.

  111. mathmate
    • one year ago
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    ok, next case!

  112. mathmate
    • one year ago
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    Solving quadratic equations by graphing, guess not learned!

  113. pooja195
    • one year ago
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    ^exactly

  114. mathmate
    • one year ago
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    Using a graphics calculator?

  115. pooja195
    • one year ago
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    nopee

  116. mathmate
    • one year ago
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    Quadratic formula, no?

  117. mathmate
    • one year ago
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    Si!

  118. pooja195
    • one year ago
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    :3

  119. pooja195
    • one year ago
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    lets avoid that ;)

  120. pooja195
    • one year ago
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    Next case!

  121. mathmate
    • one year ago
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    because you already know it, or because you don't?

  122. pooja195
    • one year ago
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    because i know it :P

  123. pooja195
    • one year ago
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    but i get the feeling yr gonna end up giving a problem anyways :P

  124. mathmate
    • one year ago
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    Right! I believe you, but I am sure you can solve this in a flash!

  125. mathmate
    • one year ago
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    You know me toooooooo well!

  126. mathmate
    • one year ago
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    Use the quadratic formula to solve the equation 2x^2+x-10=0

  127. mathmate
    • one year ago
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    show work!

  128. mathmate
    • one year ago
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    El cheapo, no LaTeX

  129. pooja195
    • one year ago
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    i cant do it without latex

  130. mathmate
    • one year ago
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    ok then!

  131. pooja195
    • one year ago
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    a=2 b=1 c=-1 \[\huge~x=\frac{ -(1) \pm \sqrt{(1)^2-4(2)(-1)} }{ 2(2) } \] \[\huge~x=\frac{ 1 \pm \sqrt{(9} }{ 4 } \]

  132. pooja195
    • one year ago
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    Right so far?

  133. pooja195
    • one year ago
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    \[\huge~x=\frac{ -1 \pm \sqrt{9\times 1} }{ 4 } \]

  134. pooja195
    • one year ago
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    i meant -1 on the top sorry!

  135. mathmate
    • one year ago
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    But you have -1 on top! Can you simplify further?

  136. pooja195
    • one year ago
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    \[\huge~x=\frac{-1 \pm 3\sqrt{1} }{ 4 }\]

  137. pooja195
    • one year ago
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    Set up two of the equations + and - and then i get x=0.5 x=−1

  138. mathmate
    • one year ago
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    sorry, the question was: 2x^2+x-10=0 Can you make some adjustments? such as : \(\huge~x=\frac{-1 \pm 3\sqrt{1-4(2)(-10)} }{ 4 } = ...\)

  139. pooja195
    • one year ago
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    OMG NO T_T

  140. pooja195
    • one year ago
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    cant i just link u to a one ive done today T_T

  141. mathmate
    • one year ago
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    ok, I believe you, I have seen you work before!

  142. pooja195
    • one year ago
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    Thank you! :D

  143. mathmate
    • one year ago
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    ok, discriminants!

  144. mathmate
    • one year ago
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    Please tell me how many roots does this equation have: -x^2+2x-1=0

  145. pooja195
    • one year ago
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    2^2−4(−1)(1)=8 2 roots

  146. mathmate
    • one year ago
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    Excellent! how about this one? \(2x^2-2x+3=0\)

  147. pooja195
    • one year ago
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    (−2)^2−4(2)(3)=−20 no solution OR 2 imaginary roots

  148. mathmate
    • one year ago
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    Excellent! now this one, you can almost answer without looking: \(x^2+2x+1=0\)

  149. pooja195
    • one year ago
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    2 equal solutions :P

  150. mathmate
    • one year ago
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    The answer (I mean guess) is correct. Please justify your response!

  151. pooja195
    • one year ago
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    -.-

  152. pooja195
    • one year ago
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    2^2−4(1)(1)=0

  153. mathmate
    • one year ago
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    Excellent. I would also guess the same answer, because there are only three possible cases! lol Your books calls it "one solution", but I like yours better, "two equal solutions", or better still, two "coincident roots". So use any appropriate one of your choice.

  154. pooja195
    • one year ago
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    kk

  155. mathmate
    • one year ago
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    Graphing quadratic inequalities?

  156. pooja195
    • one year ago
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    no

  157. mathmate
    • one year ago
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    |dw:1433643467187:dw|

  158. pooja195
    • one year ago
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    we havent learned it

  159. mathmate
    • one year ago
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    still no?

  160. mathmate
    • one year ago
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    ok, next case!

  161. mathmate
    • one year ago
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    ...more like next chapter!

  162. pooja195
    • one year ago
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    lol :)

  163. mathmate
    • one year ago
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    Chapter 10 Polynomials and factoring ========================

  164. mathmate
    • one year ago
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    x^2 is a monomial (x+2) is a binomial (x^2+3x-1) is a trinomial. Is x a polynomial?

  165. pooja195
    • one year ago
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    no

  166. mathmate
    • one year ago
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    "ERROR", the computer game says!

  167. pooja195
    • one year ago
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    O_o

  168. mathmate
    • one year ago
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    A polynomial includes all degrees, including x (first degree, one term only).

  169. mathmate
    • one year ago
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    What is the degree of the polynomial 4.

  170. pooja195
    • one year ago
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    linear/

  171. mathmate
    • one year ago
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    linear is like 2x, 5x, which are abbreviations of \(2x^1, 5x^1\)

  172. pooja195
    • one year ago
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    in that case i havent learned this ..-..

  173. mathmate
    • one year ago
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    \(4=4x^0\), so the degree is zero! (see p.569), perhaps the teacher went through it fast.

  174. pooja195
    • one year ago
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    hmm ok

  175. mathmate
    • one year ago
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    Do you know how to add, subtract, multiply and divide polynomials?

  176. pooja195
    • one year ago
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    maybe >:) maybe not

  177. mathmate
    • one year ago
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    We'll see!

  178. pooja195
    • one year ago
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    of course

  179. mathmate
    • one year ago
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    add: \((x^2-7)-(x+2)=?\)

  180. mathmate
    • one year ago
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    *subtract

  181. pooja195
    • one year ago
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    \[x^2-7-x-2\] \[x^2-x-9\]

  182. mathmate
    • one year ago
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    Excellent! now|dw:1433644413460:dw| Find the perimeter and area of the swimming pool shown.

  183. pooja195
    • one year ago
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    .-.not this

  184. pooja195
    • one year ago
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    ;-;

  185. mathmate
    • one year ago
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    You find it hard, or too easy?

  186. pooja195
    • one year ago
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    4x+3+4x+3+x-2+x-2 8x^2+2x+2

  187. pooja195
    • one year ago
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    Next case!

  188. mathmate
    • one year ago
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    sorry, not quite yet!

  189. pooja195
    • one year ago
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    T_T

  190. mathmate
    • one year ago
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    add like terms perimeter =4x+3+4x+3+x-2+x-2 =4x+4x+x+x +3+3-2-2 =10x+2

  191. mathmate
    • one year ago
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    |dw:1433644752391:dw|

  192. pooja195
    • one year ago
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    is that a question?

  193. mathmate
    • one year ago
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    The first post was the corrected calculation for the perimeter. The second post is to calculate the area using FOIL, to be completed by you!

  194. pooja195
    • one year ago
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    4x^2−5x−6

  195. mathmate
    • one year ago
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    Excellent! For a rectangle: perimeter = 2 times the sum of two adjacent sides. Area = product of two adjacent sides.

  196. pooja195
    • one year ago
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    ok

  197. mathmate
    • one year ago
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    Have you done division? (called long division, or synthetic division).

  198. pooja195
    • one year ago
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    no

  199. mathmate
    • one year ago
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    Like Divide \(20x^2+17x+3\) by 5x+3.

  200. pooja195
    • one year ago
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    no

  201. mathmate
    • one year ago
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    ok, but can you do it using chapter 11?

  202. pooja195
    • one year ago
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    omg no i hate that chapter >::( no no no ;(

  203. mathmate
    • one year ago
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    \(\Large \frac{20x^2+17x+3}{5x+3}\)

  204. mathmate
    • one year ago
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    But you were good at it, if I remember right!

  205. pooja195
    • one year ago
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    I dont like that stuff T_T princess says skip

  206. mathmate
    • one year ago
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    Teacher says "you pay now, or you pay later!" xD

  207. pooja195
    • one year ago
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    T_T

  208. pooja195
    • one year ago
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    skip

  209. mathmate
    • one year ago
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    ok, for now!

  210. pooja195
    • one year ago
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    >:) princess wins!

  211. mathmate
    • one year ago
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    as always!

  212. mathmate
    • one year ago
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    Now back to multiplication! \((m^2+2m-9)(m-4)= \ ?\)

  213. pooja195
    • one year ago
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    \[\huge~m^3−2m^2−17m+36 \]

  214. mathmate
    • one year ago
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    Excellent! You're as good as a calculator!

  215. pooja195
    • one year ago
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    :)

  216. mathmate
    • one year ago
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    Good so far?

  217. pooja195
    • one year ago
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    yes next case!

  218. mathmate
    • one year ago
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    10.3 special products of polynomials ========================

  219. mathmate
    • one year ago
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    @pooja195

  220. mathmate
    • one year ago
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    @pooja195

  221. pooja195
    • one year ago
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    +_=

  222. mathmate
    • one year ago
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    gimme a minute to find the page

  223. mathmate
    • one year ago
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    ok, special products of polynomials. First, if you can, commit to memory the following: Factoring difference of two squares (a+b)(a-b)=a^2-b^2 Example: x^2-y^2=(x+y)(x-y)

  224. mathmate
    • one year ago
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    But life is not always simple like that. the problem may come up as: 4p^2-9q^2

  225. pooja195
    • one year ago
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    2p+3)(2p-3)

  226. mathmate
    • one year ago
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    You will have to _try_ to factorize each term into a perfect square before proceeding, 4p^2-9q^2 = (2p)^2-(3q)^2 (remember the law of exponents?

  227. mathmate
    • one year ago
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    Yes, pretty close, you only lost your q..lol

  228. pooja195
    • one year ago
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    oops

  229. mathmate
    • one year ago
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    (2p+3q)(2p-3q)

  230. mathmate
    • one year ago
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    Expand (a+2b)(a-2b)

  231. pooja195
    • one year ago
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    a^2−4b^2

  232. mathmate
    • one year ago
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    Excellent! You get the idea, and I'm sure you can do it backwards.

  233. mathmate
    • one year ago
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    like factor (16a^2-4b^2 ).

  234. pooja195
    • one year ago
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    (4a+2b)(4a-2b)

  235. mathmate
    • one year ago
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    Very good! Now we move on to the perfect squares. Commit to memory the following patterns: (a+b)^2 = a^2 + 2ab + b^2 (a-b)^2 = a^2 - 2ab + b^2

  236. mathmate
    • one year ago
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    Example: (backwards of FOIL) 9x^2-24x+16 = (3x)^2 - 2 (3x)(4) + (4^2) = (3x-4)^2

  237. mathmate
    • one year ago
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    Note that perfect squares have three terms, and both the square terms are ALWAYS positive. The middle term may be positive or negative, depending on the pattern.

  238. mathmate
    • one year ago
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    I'll give you a couple of problems, but I have to go after that, perhaps for 50 minutes. factor 1. 9x^2+30x+25 2. 4x^2-12x+9

  239. pooja195
    • one year ago
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    :D ok!

  240. mathmate
    • one year ago
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    gtg, but hope you have the answers by the time I'm back!

  241. pooja195
    • one year ago
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    ok :)

  242. pooja195
    • one year ago
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    \(\huge\color{blue}{1.~~ (3x+5)(3x+5)}\) \(\huge\color{blue}{2.~~(2x−3)(2x−3) }\)

  243. mathmate
    • one year ago
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    @pooja195 Yes, excellent. I would have written them as squres, so that it is easier to read. \( \huge\color{blue}{1.~~ (3x+5)^2}\) \(\huge\color{blue}{2.~~(2x−3)^2 }\)

  244. mathmate
    • one year ago
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    * squares

  245. mathmate
    • one year ago
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    No you don't have to do foil to get the answer, but it's a good idea to do FOIL to _check_ the answer.

  246. mathmate
    • one year ago
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    If there are no questions on 11.3, then next case. 11.4 ZERO PRODUCT PROPERTY Let a and b be real number. If ab=0, then a=0 or b=0. If the product of two factors is zero, then at least one of the factors must be zero.

  247. pooja195
    • one year ago
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    thats eaasy

  248. mathmate
    • one year ago
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    So if (x-3)(2x-5)=0, what are the possible values of x?

  249. pooja195
    • one year ago
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    x=3 x=5/2

  250. mathmate
    • one year ago
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    Excellent! Solve by factoring: \(\Large x^2-x-3=0\)

  251. pooja195
    • one year ago
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    Cant do it .-.

  252. mathmate
    • one year ago
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    sorry, it: \(\Large x^2-x-6=0\)

  253. pooja195
    • one year ago
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    x=−2 or x=3

  254. mathmate
    • one year ago
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    yes! perfect!

  255. pooja195
    • one year ago
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    Are we done? :D

  256. mathmate
    • one year ago
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    no

  257. mathmate
    • one year ago
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    brb

  258. mathmate
    • one year ago
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    sorry!

  259. mathmate
    • one year ago
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    Do you need more practice on factoring a quadratic?

  260. pooja195
    • one year ago
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    No

  261. mathmate
    • one year ago
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    ...apart from word problems?

  262. pooja195
    • one year ago
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    No i think i have it all

  263. mathmate
    • one year ago
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    Just to make sure, try factor \(2x^2-9x-35\)

  264. pooja195
    • one year ago
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    (2x+5)(x−7)

  265. mathmate
    • one year ago
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    Why, that's too fast!? Are you sure of your answer?

  266. pooja195
    • one year ago
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    (2x+5)=0 (x−7)=0 x=-5/2 x=7

  267. mathmate
    • one year ago
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    ok, now factor 3p^2+36p+108

  268. mathmate
    • one year ago
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    Do you remember the first step in factoring?

  269. pooja195
    • one year ago
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    GCF

  270. pooja195
    • one year ago
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    in this case its 3

  271. mathmate
    • one year ago
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    Excellent!!!!!!!

  272. pooja195
    • one year ago
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    3(p+6)(p+6)

  273. mathmate
    • one year ago
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    faster than I can type! Is the calculator there somewhere? lol

  274. pooja195
    • one year ago
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    maybe ;) but not for the whole problem :P

  275. mathmate
    • one year ago
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    xD

  276. pooja195
    • one year ago
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    How did u know ? :P

  277. pooja195
    • one year ago
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    too fast? :P xD

  278. pooja195
    • one year ago
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    i didnt use it for the whole thing just to find the factors :/

  279. mathmate
    • one year ago
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    Aren't you on your laptop with a camera?

  280. pooja195
    • one year ago
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    xD yesh :P

  281. mathmate
    • one year ago
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    xD

  282. mathmate
    • one year ago
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    next: factor \(\large 4x^3+20x^2+24x\)

  283. pooja195
    • one year ago
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    4x(x+2)(x+3)

  284. mathmate
    • one year ago
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    Excellent!

  285. mathmate
    • one year ago
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    I like it when you actually sweat it out!

  286. pooja195
    • one year ago
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    xD

  287. mathmate
    • one year ago
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    Now real cubic factors: \((x+y)^3 = (x+y)(x^2-xy+y^2)\) \((x-y)^3 = (x-y)(x^2+xy+y^2)\) I'll sho you the SOAP rule Nnesha taught me today!

  288. pooja195
    • one year ago
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    i havent learned this ,-,

  289. mathmate
    • one year ago
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    Sorry, wrong formulas: \(x^3+y^3 = (x+y)(x^2-xy+y^2)\) \(x^3-y^3 = (x-y)(x^2+xy+y^2)\)

  290. mathmate
    • one year ago
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    Sure?

  291. pooja195
    • one year ago
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    yes

  292. mathmate
    • one year ago
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    ok, then Ch 10 is done!

  293. pooja195
    • one year ago
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    O_O

  294. pooja195
    • one year ago
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    lets learn SOAP

  295. mathmate
    • one year ago
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    It has to do with the cubic factoring, you really want it?

  296. pooja195
    • one year ago
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    yes yes

  297. mathmate
    • one year ago
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    k, gimme a minute.

  298. mathmate
    • one year ago
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    |dw:1433700122466:dw|

  299. mathmate
    • one year ago
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    The same SOAP rule applies to x^3-y^3 and x^3+y^3.

  300. mathmate
    • one year ago
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    It's all about signs only.

  301. pooja195
    • one year ago
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    oooo ok

  302. mathmate
    • one year ago
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    Pretty cute, isn't it?

  303. pooja195
    • one year ago
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    yesh :3

  304. mathmate
    • one year ago
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    So, shall we start Ch 11?

  305. pooja195
    • one year ago
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    Maybe we should do more quadratic factoring

  306. mathmate
    • one year ago
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    ok!

  307. mathmate
    • one year ago
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    Find the product \(\large (d+2)(d^2-3d-10)\)

  308. pooja195
    • one year ago
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    \[\huge~d^3−d^2−16d−20\]

  309. mathmate
    • one year ago
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    Exactly! Have you done the grid method of multiplication?

  310. pooja195
    • one year ago
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    nope

  311. mathmate
    • one year ago
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    It makes your life easier, even without a calculator!

  312. pooja195
    • one year ago
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    O-o

  313. mathmate
    • one year ago
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    Here's how it works. Nothing magical, just helps you organize.

  314. mathmate
    • one year ago
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    |dw:1433700861581:dw|

  315. pooja195
    • one year ago
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    ooo thats neat :o

  316. mathmate
    • one year ago
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    Yep!

  317. pooja195
    • one year ago
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    whats next? :)

  318. mathmate
    • one year ago
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    find product: (3x^3-5z^2+8)(z+2)

  319. mathmate
    • one year ago
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    Be careful if you use the grid method, and treat the first factor as: (3z^3-5z^2+0+8) to fill the gap. and the first term is 3z^3, not 3x^3, sorry.

  320. pooja195
    • one year ago
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    3x^3z+6x^3−5z^3−10z^2+8z+16

  321. mathmate
    • one year ago
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    and simplify...

  322. mathmate
    • one year ago
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    You mean 3x^4 at the beginning. :)

  323. pooja195
    • one year ago
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    Right..

  324. mathmate
    • one year ago
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    How about factor \(\large 30x^2+38x+12\)

  325. pooja195
    • one year ago
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    2(5x+3)(3x+2)

  326. mathmate
    • one year ago
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    Very good!

  327. mathmate
    • one year ago
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    Last one for chapter 10 (if you get it without calculator) Factor \(\large 4x^2+44x+121\)

  328. pooja195
    • one year ago
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    (2x+11)(2x+11)

  329. mathmate
    • one year ago
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    Yep, excellent.

  330. mathmate
    • one year ago
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    Unless there are questions, that's it for Ch 10.

  331. pooja195
    • one year ago
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    nope thats all :P

  332. pooja195
    • one year ago
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    mm chapter 11

  333. mathmate
    • one year ago
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    11.1 Proportions ==========

  334. mathmate
    • one year ago
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    solve \(\Large \frac{3}{y}=\frac{5}{8}\)

  335. mathmate
    • one year ago
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    brb

  336. pooja195
    • one year ago
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    8*3=24 5y 5y=24 y=24/5

  337. mathmate
    • one year ago
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    Yep, that's good. That's cross multiplication.

  338. mathmate
    • one year ago
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    We can extend the idea...

  339. mathmate
    • one year ago
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    Solve \(\Large \frac{2}{x-3}=\frac{7}{x+2}\)

  340. pooja195
    • one year ago
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    2(x+2) = 7(x-3) 2x+4=7x-21 2x=7x-25 -5x=-25 x=5

  341. mathmate
    • one year ago
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    Excellent. Now try solve \(\Large \frac{x}{x-4}=\frac{6x}{x+1}\)

  342. pooja195
    • one year ago
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    x(x+1)=6x(x-4) x^2+1x=6x^2-24x -7x^2+1x=-24x not sure...

  343. mathmate
    • one year ago
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    x^2+1x=6x^2-24x is good, work from here.

  344. pooja195
    • one year ago
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    idkk :/

  345. mathmate
    • one year ago
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    x^2+1x=6x^2-24x subtract x^2+x on each side: x^2+x - (x^2-x) = 6x^2-24x -x^2 -x 0 = 5x^2-25x 0=5x(x-5) so x=0 or x=5

  346. pooja195
    • one year ago
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    :/

  347. mathmate
    • one year ago
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    Solve \(\Large \frac{5}{x+2}=\frac{3x-1}{x^2-1}\)

  348. pooja195
    • one year ago
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    5(x^2-1) = (3x-1)(x+2) 5x^2−5=3x^2+5x−2 5x^2−5−(3x^2+5x−2)=3x^2+5x−2−(3x^2+5x−2) 2x^2−5x−3=0 (2x+1)(x−3)=0 2x+1=0 or x−3=0 x= -1/2 or x=3

  349. mathmate
    • one year ago
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    Excellent, like a pro!

  350. mathmate
    • one year ago
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    Any question on proportions?

  351. pooja195
    • one year ago
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    nope

  352. mathmate
    • one year ago
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    11.2 Direct and inverse variations. =====================

  353. mathmate
    • one year ago
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    It's important to know what's what.

  354. mathmate
    • one year ago
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    Can you give me an example of one of each?

  355. mathmate
    • one year ago
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    Usually it's in the form y=.....

  356. mathmate
    • one year ago
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    Direct variation: y=kx, example y=x, y=x/2, y=3.2x Inverse variation: xy=k, or y=k/x Example y=4/x, or xy=10

  357. mathmate
    • one year ago
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    |dw:1433706731769:dw|

  358. mathmate
    • one year ago
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    |dw:1433706794615:dw|

  359. pooja195
    • one year ago
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    Direct variation: rule y=kx (when x is greater, y is greater) Inverse variation: rule xy=k (when x increases, y decreases, that's why inverse) right? This is from the other post.

  360. mathmate
    • one year ago
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    That's true, exactly!

  361. mathmate
    • one year ago
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    So if I give you: x y 1 3 2 6 3 9 Is this direct or inverse variation?

  362. pooja195
    • one year ago
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    >_< can we not do these .-.

  363. mathmate
    • one year ago
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    These are needed to solve word problems!

  364. pooja195
    • one year ago
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    O_O

  365. mathmate
    • one year ago
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    Say x=4/y, direct or inverse?

  366. mathmate
    • one year ago
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    Ok, I'll put it another way. When the function is in the slope-intercept form, with \(b=0\), then it is direct variation.

  367. mathmate
    • one year ago
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    if it is something to do with xy=something, it is inverse.

  368. mathmate
    • one year ago
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    If it is in slope-intercept with intercept NOT equal to zero, it's partial (neither direct, nor inverse)