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

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You are given this, right? \(\dfrac{AB}{BC} = \dfrac{3}{4} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now replace AB and BC with the lengths given in the figure. What do you get?

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433800191984:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\dfrac{90}{10x20} = \dfrac{3}{4}\) Ok?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.120 is not the length of BC. The entire expression 10x  20 is. See my equation above?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we solve that equation.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1When you have a fraction equal to a fraction, you can cross multiply.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433800210299:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433800248981:dw

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1I just have a hard time making the equations.

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1Can you help me with a few more questions?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we cross multiply in our problem. \(3(10x  20) = 4(90) \) \(30x  60 = 360\) \(30x = 420\) \(x = 14\) You are correct.

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1yay! Thank you so much! Can you help me with a few more? I get confused when it comes to setting up the equations.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Let'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.

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1Find the value of x. A. 7 B. 9 C. 11 D. 12

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Do you know the triangle angle bisector theorem?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The 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.

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1I just don't know how to write an equation to solve.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1That is a very cumbersome way to express this: dw:1433800821218:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Compare the above figure to your problem.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433801007502:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Here is the fugure from your problem with the letter "y" added.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The angle at the right was bisected. That means look at the segments on the opposite side. The segments are x and y. Ok?

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1I'm not really following....

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1wait! So it would be 9??? I think I'm understanding.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1According tot he theorem, the segments are proportional to the adjacent sides, so you can write this: \(\dfrac{36}{x} = \dfrac{28}{y} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now 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.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.128x = 36(16  x) 28x = 576  36x 64x = 576 x = 9

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You are correct.

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1YAY!!! Thanks! can you help me with one more?

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1last 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

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Ok, 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 \(\dfrac{d}{5} = \dfrac{12}{15} = \dfrac{c}{10} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Use the left two fractions as a proportion and solve for d. Then use the right two fractions as a proportion and solve for c

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Do you understand what to do?

jaylelile
 one year ago
Best ResponseYou've already chosen the best response.1yes! Thank you very much for all your help!
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