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MeowLover17

  • one year ago

The lengths of two sides of a triangle are shown below: Side 1: 8x2 − 5x − 2 Side 2: 7x − x2 + 3 The perimeter of the triangle is 4x3 − 3x2 + 2x − 6. Part A: What is the total length of the two sides, 1 and 2, of the triangle? Part B: What is the length of the third side of the triangle? Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.

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  1. MeowLover17
    • one year ago
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    @welshfella

  2. Hero
    • one year ago
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    @MeowLover17, What is (8x^2 - 5x - 2) + (7x - x^2 + 3) ?

  3. MeowLover17
    • one year ago
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    One moment

  4. Jhannybean
    • one year ago
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    Rearrange your terms to combine like terms with eachother. It makes it easier to evaluate.

  5. MeowLover17
    • one year ago
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    I got +6x^2+2x+1 @Hero

  6. MeowLover17
    • one year ago
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    Sorry my computer died

  7. MeowLover17
    • one year ago
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    @Jhannybean

  8. MeowLover17
    • one year ago
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    Hello hero i got what i wrote above

  9. MeowLover17
    • one year ago
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    So would that be the total length of the two sides??

  10. Hero
    • one year ago
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    You should have gotten 7x^2 + 2x + 1

  11. MeowLover17
    • one year ago
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    Oh sorry yes i see

  12. MeowLover17
    • one year ago
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    So hero 7x^2 + 2x + 1 <- This is my answer for part A correct?

  13. MeowLover17
    • one year ago
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    how would i find the length of the third side?

  14. Hero
    • one year ago
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    To find the length of the third side subtract the result you got for part A from the perimeter.

  15. MeowLover17
    • one year ago
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    That's what i was thinking let me do that

  16. MeowLover17
    • one year ago
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    so i would receive -4x^3+10^2+7?

  17. MeowLover17
    • one year ago
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    for the length of the third side

  18. Hero
    • one year ago
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    Subtract this way: |dw:1441579511663:dw|

  19. MeowLover17
    • one year ago
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    ok

  20. MeowLover17
    • one year ago
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    -4x^3 -4x^2-5x-3

  21. MeowLover17
    • one year ago
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    Is what i got

  22. MeowLover17
    • one year ago
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    and if thats correct please help me with part C because i dont understand what its asking.

  23. Hero
    • one year ago
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    What is 4x^3 minus zero?

  24. Hero
    • one year ago
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    |dw:1441579942249:dw|

  25. MeowLover17
    • one year ago
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    +4x^3

  26. MeowLover17
    • one year ago
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    4x^3 -4x^2-5x-3

  27. Hero
    • one year ago
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    What is -3x^2 -(-x^2) ?

  28. MeowLover17
    • one year ago
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    -2x^2

  29. Hero
    • one year ago
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    Yes. When you're subtracting one expression from the other, you have to flip the signs.

  30. MeowLover17
    • one year ago
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    Oh i understand i forgot to change the signs

  31. MeowLover17
    • one year ago
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    Yes :/

  32. MeowLover17
    • one year ago
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    so i get 4x^3-2x^2-5x-9

  33. MeowLover17
    • one year ago
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    For the third side

  34. mathstudent55
    • one year ago
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    |dw:1441580340586:dw|

  35. mathstudent55
    • one year ago
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    |dw:1441580483756:dw|

  36. mathstudent55
    • one year ago
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    To find the third side, subtract the sum of the lengths of the first two sides (Part A) from the perimeter.

  37. MeowLover17
    • one year ago
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    Okay so i would recieve 4x^3-10x^2-7

  38. MeowLover17
    • one year ago
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    Right?

  39. Hero
    • one year ago
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    Somehow I wrote the second term incorrectly.

  40. MeowLover17
    • one year ago
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    I just noticed that lol

  41. MeowLover17
    • one year ago
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    But hero now that i have done gotten part B how do i do part 3?

  42. MeowLover17
    • one year ago
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    Part B is 4x^3-10x^2-7 correct?

  43. mathstudent55
    • one year ago
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    |dw:1441580817818:dw|

  44. mathstudent55
    • one year ago
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    Correct. Your Part B is good. 4x^3 - 10x^2 - 7 is correct.

  45. MeowLover17
    • one year ago
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    yes now how do i do part C?

  46. MeowLover17
    • one year ago
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    please help

  47. mathstudent55
    • one year ago
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    For Part C, you need to understand what this sentence means: "polynomials are closed under addition and subtraction"

  48. MeowLover17
    • one year ago
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    i don't understand what it means :/

  49. mathstudent55
    • one year ago
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    Here is an example. The set of integers is closed under addition, subtraction and multiplication. That means that when you add two integers, or when you subtract integers, or when you multiply integers, the answer is an integer. Integers are not closed under division because when you divide integers, you may get a non-integer answer. For example, 3/4 is not an integer.

  50. MeowLover17
    • one year ago
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    oh i see

  51. mathstudent55
    • one year ago
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    Now think of your problem and the set of all polynomials. If you add two polynomials, is the sum always a polynomial?

  52. MeowLover17
    • one year ago
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    So yes part A and B are closed under subtraction and addition since when i receive the sum of one problem it is still an integer.

  53. MeowLover17
    • one year ago
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    Is that answer correct for part c?

  54. mathstudent55
    • one year ago
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    Above, for Part A, we did add two polynomials. The sum was a polynomial. This leads you to think that adding any polynomials together will result is a polynomial.

  55. mathstudent55
    • one year ago
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    In Part B, we subtracted polynomials and the difference was a polynomial. That makes us think that polynomials are closed under subtraction.

  56. MeowLover17
    • one year ago
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    yes the sum is always a polynomial isnt it?

  57. mathstudent55
    • one year ago
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    Your statement shows you have the right idea, but we are dealing with polynomials, not integers, so I'd modify it this way: "Parts A and B show that polynomials are closed under addition and subtraction since when I added or subtracted polynomials, the result is still a polynomial."

  58. MeowLover17
    • one year ago
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    Thanks you :)

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