jaylelile
  • jaylelile
AB:BC is 3:4. Solve for x. A.11 B.14 C.120 D.140
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
jaylelile
  • jaylelile
1 Attachment
mathstudent55
  • mathstudent55
You are given this, right? \(\dfrac{AB}{BC} = \dfrac{3}{4} \)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

jaylelile
  • jaylelile
right..
mathstudent55
  • mathstudent55
Now replace AB and BC with the lengths given in the figure. What do you get?
jaylelile
  • jaylelile
|dw:1433800191984:dw|
mathstudent55
  • mathstudent55
\(\dfrac{90}{10x-20} = \dfrac{3}{4}\) Ok?
jaylelile
  • jaylelile
oh okay
mathstudent55
  • mathstudent55
-20 is not the length of BC. The entire expression 10x - 20 is. See my equation above?
mathstudent55
  • mathstudent55
Now we solve that equation.
mathstudent55
  • mathstudent55
When you have a fraction equal to a fraction, you can cross multiply.
mathstudent55
  • mathstudent55
|dw:1433800210299:dw|
jaylelile
  • jaylelile
so x=14?????
mathstudent55
  • mathstudent55
|dw:1433800248981:dw|
jaylelile
  • jaylelile
x=14 right?
jaylelile
  • jaylelile
I just have a hard time making the equations.
jaylelile
  • jaylelile
Can you help me with a few more questions?
mathstudent55
  • mathstudent55
Now we cross multiply in our problem. \(3(10x - 20) = 4(90) \) \(30x - 60 = 360\) \(30x = 420\) \(x = 14\) You are correct.
jaylelile
  • jaylelile
yay! Thank you so much! Can you help me with a few more? I get confused when it comes to setting up the equations.
mathstudent55
  • mathstudent55
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.
jaylelile
  • jaylelile
Find the value of x. A. 7 B. 9 C. 11 D. 12
mathstudent55
  • mathstudent55
Do you know the triangle angle bisector theorem?
mathstudent55
  • mathstudent55
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.
jaylelile
  • jaylelile
I just don't know how to write an equation to solve.
mathstudent55
  • mathstudent55
That is a very cumbersome way to express this: |dw:1433800821218:dw|
mathstudent55
  • mathstudent55
Compare the above figure to your problem.
mathstudent55
  • mathstudent55
|dw:1433801007502:dw|
mathstudent55
  • mathstudent55
Here is the fugure from your problem with the letter "y" added.
mathstudent55
  • mathstudent55
The angle at the right was bisected. That means look at the segments on the opposite side. The segments are x and y. Ok?
jaylelile
  • jaylelile
I'm not really following....
jaylelile
  • jaylelile
wait! So it would be 9??? I think I'm understanding.
mathstudent55
  • mathstudent55
According tot he theorem, the segments are proportional to the adjacent sides, so you can write this: \(\dfrac{36}{x} = \dfrac{28}{y} \)
jaylelile
  • jaylelile
so it isn't 9?
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
28x = 36(16 - x) 28x = 576 - 36x 64x = 576 x = 9
mathstudent55
  • mathstudent55
You are correct.
jaylelile
  • jaylelile
YAY!!! Thanks! can you help me with one more?
jaylelile
  • jaylelile
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
mathstudent55
  • mathstudent55
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 \(\dfrac{d}{5} = \dfrac{12}{15} = \dfrac{c}{10} \)
mathstudent55
  • mathstudent55
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
mathstudent55
  • mathstudent55
Do you understand what to do?
jaylelile
  • jaylelile
yes! Thank you very much for all your help!
mathstudent55
  • mathstudent55
You're welcome.

Looking for something else?

Not the answer you are looking for? Search for more explanations.