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calculusxy

  • one year ago

MEDAL!!! What values of m satisfies the equation m^2 - 5m = 36 ? A. -1 and 5 B. 2 and -3 C. 4 and -1 D. 6 and -6 E. 9 and -4

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  1. calculusxy
    • one year ago
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    \[m^2 - 5m = 36\]

  2. anonymous
    • one year ago
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    Sub and chug

  3. anonymous
    • one year ago
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    subtract 5m from both sides

  4. hartnn
    • one year ago
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    start by subtracting 36 from both sides, then it'll come in the form of \(ax^2+bx+c = 0\)

  5. anonymous
    • one year ago
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    its E.

  6. calculusxy
    • one year ago
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    I still don't understand @hartnn

  7. anonymous
    • one year ago
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    e) 9,-4

  8. hartnn
    • one year ago
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    |dw:1439831848970:dw|

  9. calculusxy
    • one year ago
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    Okay

  10. hartnn
    • one year ago
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    now there are several methods to solve it. lets use the easiest one, splitting the middle term can you think of 2 numbers whose sum is -5 but product is -36?

  11. hartnn
    • one year ago
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    hint : one of the number is positive

  12. calculusxy
    • one year ago
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    Well I can find 9 and -4 but if I add them, it is 5 not -5.

  13. hartnn
    • one year ago
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    right so change the signs of both the numbers and try :)

  14. calculusxy
    • one year ago
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    So that would be -9 and 4 right?

  15. hartnn
    • one year ago
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    correct! :) so we split our middle term -5m as -9m + 4m

  16. anonymous
    • one year ago
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    its 9 and -4

  17. hartnn
    • one year ago
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    \(m^2 -9m+4m -36 = 0 \) lets consider 1st 2 terms only m^2 -9m what do you see common from both these terms?

  18. calculusxy
    • one year ago
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    The variables are the same.

  19. hartnn
    • one year ago
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    Hi Ana, we really appreciate you helping the asker by giving them the answer, but this site is primarily for the purpose of learning which can be done only by interactions, like we are doing right now :)

  20. hartnn
    • one year ago
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    so, "m" is common right? can you factor out m from m^2-9m ?

  21. calculusxy
    • one year ago
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    I am not sure :\

  22. hartnn
    • one year ago
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    \(\large ☻☺+☻♥= ☻(☺+♥) \\ \text{this is factoring, } \\ \text{☻ was common from both terms and factored out.}\)

  23. hartnn
    • one year ago
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    \(m^2 -9m = m\times m - 9\times m = m \times (m-9)\) see if this makes sense :)

  24. calculusxy
    • one year ago
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    Yes :)

  25. hartnn
    • one year ago
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    cool, so lets test how much have you understood :P what is common from +4m -36 ?? factor that out!

  26. calculusxy
    • one year ago
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    4 and if you factor that out, then we can have \[4 \times m - (4 \times 9) = 4(m - 9)\]

  27. hartnn
    • one year ago
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    excellent! so now we have \(m (m-9) +4 (m-9) = 0\) what is common from 1st 2 terms!?? factor that out!

  28. calculusxy
    • one year ago
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    I don't understand what you mean

  29. hartnn
    • one year ago
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    \(\large ☻☺+☻♥= ☻(☺+♥) \\ \text{this is factoring, } \\ \text{☻ was common from both terms and factored out.}\) \(\large m(m-9) + 4(m-9) =0\\ \text {(m-9) is common from both therms!} \\ \Large (m-9)(m+4) =0 \)

  30. calculusxy
    • one year ago
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    Oh yes !

  31. hartnn
    • one year ago
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    so now we use the fact that if ab =0 a= 0 or b=0

  32. hartnn
    • one year ago
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    (m-9)(m+4) = 0 then ?

  33. calculusxy
    • one year ago
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    Would that mean that m = 0?

  34. hartnn
    • one year ago
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    (m-9)(m+4) = 0 means either one of (m-9) or (m+4) has to be 0, so that product becomes 0 means m-9 =0 OR m+4 = 0 makes sense?

  35. calculusxy
    • one year ago
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    Yes.

  36. hartnn
    • one year ago
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    m-9 = 0 what does m equal ?? m+4 = 0 what does m equal ??

  37. calculusxy
    • one year ago
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    m-9=0 m = 9 m+4 = 0 m = -4

  38. hartnn
    • one year ago
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    \(\huge \checkmark\)

  39. calculusxy
    • one year ago
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    Oh!!! Thank you so much!!! I get how it is 9 and -4 thank you!

  40. calculusxy
    • one year ago
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    I have another question.

  41. hartnn
    • one year ago
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    welcome ^_^ happy learning :)

  42. hartnn
    • one year ago
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    sure, ask

  43. calculusxy
    • one year ago
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    |dw:1439833174185:dw|

  44. calculusxy
    • one year ago
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    In the figure about, point A is the center of the circle and a vertex of the right triangle, which has an area of 12 square units and where angle BAC is the right. Point D (not shown) is the point of intersection of the perimeter of circle A and segment An. The ratio of Ab to AC is 2 to 3 and the ratio of AD and AB is 1 to 2. What is the area of the shaded region, in square units?

  45. calculusxy
    • one year ago
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    @hartnn

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