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

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

Mathematics
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You are given this, right? \(\dfrac{AB}{BC} = \dfrac{3}{4} \)

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right..
Now replace AB and BC with the lengths given in the figure. What do you get?
|dw:1433800191984:dw|
\(\dfrac{90}{10x-20} = \dfrac{3}{4}\) Ok?
oh okay
-20 is not the length of BC. The entire expression 10x - 20 is. See my equation above?
Now we solve that equation.
When you have a fraction equal to a fraction, you can cross multiply.
|dw:1433800210299:dw|
so x=14?????
|dw:1433800248981:dw|
x=14 right?
I just have a hard time making the equations.
Can you help me with a few more questions?
Now we cross multiply in our problem. \(3(10x - 20) = 4(90) \) \(30x - 60 = 360\) \(30x = 420\) \(x = 14\) You are correct.
yay! Thank you so much! Can you help me with a few more? I get confused when it comes to setting up the equations.
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.
Find the value of x. A. 7 B. 9 C. 11 D. 12
Do you know the triangle angle bisector theorem?
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.
I just don't know how to write an equation to solve.
That is a very cumbersome way to express this: |dw:1433800821218:dw|
Compare the above figure to your problem.
|dw:1433801007502:dw|
Here is the fugure from your problem with the letter "y" added.
The angle at the right was bisected. That means look at the segments on the opposite side. The segments are x and y. Ok?
I'm not really following....
wait! So it would be 9??? I think I'm understanding.
According tot he theorem, the segments are proportional to the adjacent sides, so you can write this: \(\dfrac{36}{x} = \dfrac{28}{y} \)
so it isn't 9?
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.
28x = 36(16 - x) 28x = 576 - 36x 64x = 576 x = 9
You are correct.
YAY!!! Thanks! can you help me with one more?
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
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 \(\dfrac{d}{5} = \dfrac{12}{15} = \dfrac{c}{10} \)
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
Do you understand what to do?
yes! Thank you very much for all your help!
You're welcome.

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