anonymous
  • anonymous
I have 5 questions i really need help with!!! Please help me! attached in comments
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathstudent55
  • mathstudent55
1. Use the formula in the figure to find x |dw:1436809516866:dw|
anonymous
  • anonymous
so 8+15=6+x?

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mathstudent55
  • mathstudent55
|dw:1436809633896:dw|
mathstudent55
  • mathstudent55
Almost, but keep in mind that two variables written together mean multiplication, not addition.
mathstudent55
  • mathstudent55
8 * 15 = 6 * x
anonymous
  • anonymous
so 8x15= 120 and 120/6=20 correct?
mathstudent55
  • mathstudent55
Exactly. 1 down, 4 to go.
mathstudent55
  • mathstudent55
|dw:1436809837663:dw|
anonymous
  • anonymous
Yay :)
mathstudent55
  • mathstudent55
Let's do 2 now.
mathstudent55
  • mathstudent55
Here is the rule for problem 2. |dw:1436809889123:dw|
mathstudent55
  • mathstudent55
One external segment times its entire secant equals the other external segment times its entire secant.
anonymous
  • anonymous
So (10*6)10=(8*x)8
mathstudent55
  • mathstudent55
|dw:1436810128136:dw|
mathstudent55
  • mathstudent55
No. Here you DO need some additions.
anonymous
  • anonymous
16*10=(8+x)8
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
We need to solve this for x: 10(16) = 8(8 + x)
anonymous
  • anonymous
160=64+8x?
mathstudent55
  • mathstudent55
yes
anonymous
  • anonymous
96=8x because 160-64=96?
mathstudent55
  • mathstudent55
yes
anonymous
  • anonymous
so the answer is x=12
mathstudent55
  • mathstudent55
correct
mathstudent55
  • mathstudent55
Ready for problem 3?
anonymous
  • anonymous
yes :)
mathstudent55
  • mathstudent55
|dw:1436810571796:dw|
mathstudent55
  • mathstudent55
Use the same idea for the secant as before: the external segment times the entire secant. For the tangent, just square its length.
mathstudent55
  • mathstudent55
|dw:1436810702662:dw|
anonymous
  • anonymous
So 2x= 36?
mathstudent55
  • mathstudent55
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?
mathstudent55
  • mathstudent55
|dw:1436810831719:dw|
anonymous
  • anonymous
x
mathstudent55
  • mathstudent55
Good. What is the length of the entire secant? |dw:1436810876026:dw|
anonymous
  • anonymous
x(2x) the entire secant is x+x which
anonymous
  • anonymous
3x=36
anonymous
  • anonymous
x=12?
mathstudent55
  • mathstudent55
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
mathstudent55
  • mathstudent55
There is a big difference between adding x to 2x which is 3x, and multiplying x by 2x which is 2x^2.
mathstudent55
  • mathstudent55
The equation then is: \(x(x + x) = 6^2\) \(x(2x) = 36\) \(2x^2 = 36\) Now divide both sides by 2.
anonymous
  • anonymous
x^2= 6
mathstudent55
  • mathstudent55
??? What is 36/2 = ???
anonymous
  • anonymous
oh! 18! I was thinking square root it
mathstudent55
  • mathstudent55
\(2x^2 = 36\) \(\dfrac{2x^2}{2} = \dfrac{36}{2} \)
mathstudent55
  • mathstudent55
Good. Now we have this. Now take square root of both sides. \(x^2 = 18\)
anonymous
  • anonymous
3 rad 2?
mathstudent55
  • mathstudent55
Yes! Correct.
mathstudent55
  • mathstudent55
|dw:1436811486694:dw|
anonymous
  • anonymous
Thank you soo much. Im afraid i have to go But you helped me a lot!
anonymous
  • anonymous
I need to take my final!
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
You're welcome.

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