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anonymous

  • one year ago

The SneakerRama Company makes and sells sneakers. They have one linear function that represents the cost of producing sneakers and another linear function that models how much income they get from those sneakers. Describe the key features that would determine if these linear functions ever intercepted.

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  1. anonymous
    • one year ago
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    @Michele_Laino @mathstudent55 @mathmate

  2. Michele_Laino
    • one year ago
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    any linear function can be described by this formula: \[y = kx + h\] where k and h are coefficients, and x, and y are two variables

  3. Michele_Laino
    • one year ago
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    now, in your first case y is the cost of producing sneakers and for second linear function y is the income for sneakers

  4. Michele_Laino
    • one year ago
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    what can be x?

  5. anonymous
    • one year ago
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    um..the sneakers?

  6. Michele_Laino
    • one year ago
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    yes! the number of sneakers

  7. anonymous
    • one year ago
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    Yay:) Now what?

  8. Michele_Laino
    • one year ago
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    we have to consider one functionat a time. So for first function if x=0, we have: y=h, namely if we have not produced sneakers then the cost is h

  9. anonymous
    • one year ago
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    Ok, i see

  10. anonymous
    • one year ago
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    so what would be the key features to determine if they intersected?

  11. Michele_Laino
    • one year ago
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    I rewrite the two functions as below: \[\begin{gathered} f\left( x \right) = {a_1}x + {b_1} \hfill \\ g\left( x \right) = {a_2}x + {b_2} \hfill \\ \end{gathered} \]

  12. Michele_Laino
    • one year ago
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    we have intersection if: \[\begin{gathered} f\left( x \right) = g\left( x \right) \hfill \\ {a_1}x + {b_1} = {a_2}x + {b_2} \hfill \\ \left( {{a_1} - {a_2}} \right)x = {b_2} - {b_1} \hfill \\ \end{gathered} \]

  13. anonymous
    • one year ago
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    alright, but how would I type that in word form?

  14. Michele_Laino
    • one year ago
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    and we have no solutions, if and only if: \[\large {a_1} - {a_2} = 0,\;{b_2} - {b_1} \ne 0\]

  15. Michele_Laino
    • one year ago
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    namely, if the producing rate is equal to the earning rate and the cost for producing no sneakers is different from the earning for no sneakers sold, then we have no intersection

  16. anonymous
    • one year ago
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    ok but we have to determine the key features if they ever intersceted?

  17. anonymous
    • one year ago
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    "Describe the key features that would determine if these linear functions ever intercepted." See?

  18. Michele_Laino
    • one year ago
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    yes!

  19. anonymous
    • one year ago
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    so what would be the answer?

  20. anonymous
    • one year ago
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    Can I ask another question please?

  21. Michele_Laino
    • one year ago
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    I think that the requested key can be this: the producing rate has to be different from the earning rate

  22. anonymous
    • one year ago
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    OK:)

  23. Michele_Laino
    • one year ago
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    :)

  24. anonymous
    • one year ago
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    Your boss hands you the monthly data that show the number of orders coming in to and out of the warehouse. The data are in the table below. Explain to your boss, in complete sentences, the solution to this system and what the solution represents. Month No. of orders in No. of orders out January (1) 3 3 February (2) 6 4 March (3) 9 5 April (4) 12 6

  25. anonymous
    • one year ago
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    # of orders in: 3 6 9 12

  26. anonymous
    • one year ago
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    #of orders out: 3 4 5 6

  27. Michele_Laino
    • one year ago
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    we can write the relationship between the orders out y, as a function of the orders in x, like below: \[\Large y = \left( {x - 1} \right) + 3\]

  28. anonymous
    • one year ago
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    ok:)

  29. Michele_Laino
    • one year ago
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    please wait

  30. anonymous
    • one year ago
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    Alright:P)

  31. Michele_Laino
    • one year ago
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    no, I my formula is wrong

  32. Michele_Laino
    • one year ago
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    my fromula is wrong

  33. anonymous
    • one year ago
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    that's okay:)

  34. anonymous
    • one year ago
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    we can always start over

  35. Michele_Laino
    • one year ago
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    we have two linear equations. Namely the relationship between months x and orders out f(x), which is: \[\Large f\left( x \right) = \left( {x - 1} \right) + 3\]

  36. Michele_Laino
    • one year ago
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    the second relationship is between the months x and the orders in g(x): \[\Large g\left( x \right) = 3x\]

  37. anonymous
    • one year ago
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    ok:) I see

  38. Michele_Laino
    • one year ago
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    the solution of your system is given solving this equation: \[\Large \begin{gathered} f\left( x \right) = g\left( x \right) \hfill \\ \\ \left( {x - 1} \right) + 3 = 3x \hfill \\ \end{gathered} \] solve please, for x

  39. anonymous
    • one year ago
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    ux x- I got x+2=3x, then I got 2x+2

  40. Michele_Laino
    • one year ago
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    I got: 2x=2

  41. Michele_Laino
    • one year ago
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    so, x=?

  42. anonymous
    • one year ago
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    1

  43. Michele_Laino
    • one year ago
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    that's right!

  44. Michele_Laino
    • one year ago
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    it means that at first month the orders in are equal to the orders out

  45. Michele_Laino
    • one year ago
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    more precisely: the number of orders in is equal to the number of orders out

  46. anonymous
    • one year ago
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    Thanks! S :P)

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