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anonymous

  • one year ago

I have 5 questions i really need help with!!! Please help me! attached in comments

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  1. anonymous
    • one year ago
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  2. mathstudent55
    • one year ago
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    1. Use the formula in the figure to find x |dw:1436809516866:dw|

  3. anonymous
    • one year ago
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    so 8+15=6+x?

  4. mathstudent55
    • one year ago
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    |dw:1436809633896:dw|

  5. mathstudent55
    • one year ago
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    Almost, but keep in mind that two variables written together mean multiplication, not addition.

  6. mathstudent55
    • one year ago
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    8 * 15 = 6 * x

  7. anonymous
    • one year ago
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    so 8x15= 120 and 120/6=20 correct?

  8. mathstudent55
    • one year ago
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    Exactly. 1 down, 4 to go.

  9. mathstudent55
    • one year ago
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    |dw:1436809837663:dw|

  10. anonymous
    • one year ago
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    Yay :)

  11. mathstudent55
    • one year ago
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    Let's do 2 now.

  12. mathstudent55
    • one year ago
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    Here is the rule for problem 2. |dw:1436809889123:dw|

  13. mathstudent55
    • one year ago
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    One external segment times its entire secant equals the other external segment times its entire secant.

  14. anonymous
    • one year ago
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    So (10*6)10=(8*x)8

  15. mathstudent55
    • one year ago
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    |dw:1436810128136:dw|

  16. mathstudent55
    • one year ago
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    No. Here you DO need some additions.

  17. anonymous
    • one year ago
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    16*10=(8+x)8

  18. mathstudent55
    • one year ago
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    The upper secant has an external segment of length 10. The entire upper secant has length 10 + 6. The lower secant has an external segment of 8. The entire lower secant has a length of 8 + x. That means: 10(10 + 6) = 8(8 + x) Yes, you are correct now.

  19. mathstudent55
    • one year ago
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    We need to solve this for x: 10(16) = 8(8 + x)

  20. anonymous
    • one year ago
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    160=64+8x?

  21. mathstudent55
    • one year ago
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    yes

  22. anonymous
    • one year ago
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    96=8x because 160-64=96?

  23. mathstudent55
    • one year ago
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    yes

  24. anonymous
    • one year ago
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    so the answer is x=12

  25. mathstudent55
    • one year ago
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    correct

  26. mathstudent55
    • one year ago
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    Ready for problem 3?

  27. anonymous
    • one year ago
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    yes :)

  28. mathstudent55
    • one year ago
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    |dw:1436810571796:dw|

  29. mathstudent55
    • one year ago
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    Use the same idea for the secant as before: the external segment times the entire secant. For the tangent, just square its length.

  30. mathstudent55
    • one year ago
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    |dw:1436810702662:dw|

  31. anonymous
    • one year ago
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    So 2x= 36?

  32. mathstudent55
    • one year ago
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    Be careful here. The right side 36 is correct bec that is 6^2. Now let's look at the left side. What is the length of the external segment?

  33. mathstudent55
    • one year ago
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    |dw:1436810831719:dw|

  34. anonymous
    • one year ago
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    x

  35. mathstudent55
    • one year ago
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    Good. What is the length of the entire secant? |dw:1436810876026:dw|

  36. anonymous
    • one year ago
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    x(2x) the entire secant is x+x which

  37. anonymous
    • one year ago
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    3x=36

  38. anonymous
    • one year ago
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    x=12?

  39. mathstudent55
    • one year ago
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    You need to be careful with algebra. External segment of secant: x Entire secant: x + x = 2x Product: x(2x) = 2xx = 2x^2, not 3x

  40. mathstudent55
    • one year ago
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    There is a big difference between adding x to 2x which is 3x, and multiplying x by 2x which is 2x^2.

  41. mathstudent55
    • one year ago
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    The equation then is: \(x(x + x) = 6^2\) \(x(2x) = 36\) \(2x^2 = 36\) Now divide both sides by 2.

  42. anonymous
    • one year ago
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    x^2= 6

  43. mathstudent55
    • one year ago
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    ??? What is 36/2 = ???

  44. anonymous
    • one year ago
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    oh! 18! I was thinking square root it

  45. mathstudent55
    • one year ago
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    \(2x^2 = 36\) \(\dfrac{2x^2}{2} = \dfrac{36}{2} \)

  46. mathstudent55
    • one year ago
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    Good. Now we have this. Now take square root of both sides. \(x^2 = 18\)

  47. anonymous
    • one year ago
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    3 rad 2?

  48. mathstudent55
    • one year ago
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    Yes! Correct.

  49. mathstudent55
    • one year ago
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    |dw:1436811486694:dw|

  50. anonymous
    • one year ago
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    Thank you soo much. Im afraid i have to go But you helped me a lot!

  51. anonymous
    • one year ago
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    I need to take my final!

  52. mathstudent55
    • one year ago
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    Let's check on that: Is this true? \(3\sqrt 2(3\sqrt 2 + 3 \sqrt 2) = 6^2\) \(3 \sqrt 2(6 \sqrt 2) = 36\) \(18 \times 2 = 36\) \(36 = 36\) Yes, \(3 \sqrt 2\) is correct.

  53. mathstudent55
    • one year ago
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    You're welcome.

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