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jaylelile

  • one year ago

AB:BC is 3:4. Solve for x. A.11 B.14 C.120 D.140

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  1. jaylelile
    • one year ago
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  2. jaylelile
    • one year ago
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  3. mathstudent55
    • one year ago
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    You are given this, right? \(\dfrac{AB}{BC} = \dfrac{3}{4} \)

  4. jaylelile
    • one year ago
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    right..

  5. mathstudent55
    • one year ago
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    Now replace AB and BC with the lengths given in the figure. What do you get?

  6. jaylelile
    • one year ago
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    |dw:1433800191984:dw|

  7. mathstudent55
    • one year ago
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    \(\dfrac{90}{10x-20} = \dfrac{3}{4}\) Ok?

  8. jaylelile
    • one year ago
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    oh okay

  9. mathstudent55
    • one year ago
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    -20 is not the length of BC. The entire expression 10x - 20 is. See my equation above?

  10. mathstudent55
    • one year ago
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    Now we solve that equation.

  11. mathstudent55
    • one year ago
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    When you have a fraction equal to a fraction, you can cross multiply.

  12. mathstudent55
    • one year ago
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    |dw:1433800210299:dw|

  13. jaylelile
    • one year ago
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    so x=14?????

  14. mathstudent55
    • one year ago
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    |dw:1433800248981:dw|

  15. jaylelile
    • one year ago
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    x=14 right?

  16. jaylelile
    • one year ago
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    I just have a hard time making the equations.

  17. jaylelile
    • one year ago
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    Can you help me with a few more questions?

  18. mathstudent55
    • one year ago
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    Now we cross multiply in our problem. \(3(10x - 20) = 4(90) \) \(30x - 60 = 360\) \(30x = 420\) \(x = 14\) You are correct.

  19. jaylelile
    • one year ago
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    yay! Thank you so much! Can you help me with a few more? I get confused when it comes to setting up the equations.

  20. mathstudent55
    • one year ago
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    Let's see if our answer makes sense. Sides AB and BC are in a 3:4 ratio. Side AB measures 90. Side BC measures 10(x) - 20. We know x = 14, so side BC measure 10(14) - 20 = 140 - 20 = 120. Side BC measures 120. Since AB:BC = 3:4, then 90:120 also has to be a 3:4 ratio. \(\dfrac{90}{120} = \dfrac{30 \times 3}{30 \times 4} = \dfrac{3}{4]\) We are correct. x = 14 makes sense.

  21. jaylelile
    • one year ago
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    Find the value of x. A. 7 B. 9 C. 11 D. 12

  22. mathstudent55
    • one year ago
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    Do you know the triangle angle bisector theorem?

  23. mathstudent55
    • one year ago
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    The angle bisector of an angle of a triangle divides the opposite side in two segments whose lengths are proportional to the lengths of the other sides of the triangle, each segment to its adjacent side.

  24. jaylelile
    • one year ago
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    I just don't know how to write an equation to solve.

  25. mathstudent55
    • one year ago
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    That is a very cumbersome way to express this: |dw:1433800821218:dw|

  26. mathstudent55
    • one year ago
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    Compare the above figure to your problem.

  27. mathstudent55
    • one year ago
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    |dw:1433801007502:dw|

  28. mathstudent55
    • one year ago
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    Here is the fugure from your problem with the letter "y" added.

  29. mathstudent55
    • one year ago
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    The angle at the right was bisected. That means look at the segments on the opposite side. The segments are x and y. Ok?

  30. jaylelile
    • one year ago
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    I'm not really following....

  31. jaylelile
    • one year ago
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    wait! So it would be 9??? I think I'm understanding.

  32. mathstudent55
    • one year ago
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    According tot he theorem, the segments are proportional to the adjacent sides, so you can write this: \(\dfrac{36}{x} = \dfrac{28}{y} \)

  33. jaylelile
    • one year ago
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    so it isn't 9?

  34. mathstudent55
    • one year ago
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    Now we need to express y in terms of x. Notice the left side is 16. One segment in it is x, so the other segment is 16 - x. That is the segment I called y. \(\dfrac{36}{x} = \dfrac{28}{16 - x} \) Now you cross multiply and solve for x.

  35. mathstudent55
    • one year ago
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    28x = 36(16 - x) 28x = 576 - 36x 64x = 576 x = 9

  36. mathstudent55
    • one year ago
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    You are correct.

  37. jaylelile
    • one year ago
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    YAY!!! Thanks! can you help me with one more?

  38. jaylelile
    • one year ago
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    last one: Find the value of each variable. A. a = 15, b = 5, c = 8, d = 4 B. a = 15, b = 4, c = 8, d = 5 C. a = 14.5, b = 5, c = 6, d = 4 D. a = 14.5, b = 4, c = 6, d = 5

  39. mathstudent55
    • one year ago
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    Ok, here there is another thing at work. If you have two lines that are cut by parallel lines, the segments are of proportional lengths. That means \(\dfrac{d}{5} = \dfrac{12}{15} = \dfrac{c}{10} \)

  40. mathstudent55
    • one year ago
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    Use the left two fractions as a proportion and solve for d. Then use the right two fractions as a proportion and solve for c

  41. mathstudent55
    • one year ago
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    Do you understand what to do?

  42. jaylelile
    • one year ago
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    yes! Thank you very much for all your help!

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

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