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I have 5 questions i really need help with!!! Please help me! attached in comments

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- anonymous

- mathstudent55

1. Use the formula in the figure to find x
|dw:1436809516866:dw|

- anonymous

so 8+15=6+x?

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## More answers

- mathstudent55

|dw:1436809633896:dw|

- mathstudent55

Almost, but keep in mind that two variables written together mean multiplication, not addition.

- mathstudent55

8 * 15 = 6 * x

- anonymous

so 8x15= 120 and 120/6=20 correct?

- mathstudent55

Exactly.
1 down, 4 to go.

- mathstudent55

|dw:1436809837663:dw|

- anonymous

Yay :)

- mathstudent55

Let's do 2 now.

- mathstudent55

Here is the rule for problem 2.
|dw:1436809889123:dw|

- mathstudent55

One external segment times its entire secant equals the other external segment times its entire secant.

- anonymous

So (10*6)10=(8*x)8

- mathstudent55

|dw:1436810128136:dw|

- mathstudent55

No.
Here you DO need some additions.

- anonymous

16*10=(8+x)8

- 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

We need to solve this for x:
10(16) = 8(8 + x)

- anonymous

160=64+8x?

- mathstudent55

yes

- anonymous

96=8x because 160-64=96?

- mathstudent55

yes

- anonymous

so the answer is x=12

- mathstudent55

correct

- mathstudent55

Ready for problem 3?

- anonymous

yes :)

- mathstudent55

|dw:1436810571796:dw|

- 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

|dw:1436810702662:dw|

- anonymous

So 2x= 36?

- 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

|dw:1436810831719:dw|

- anonymous

x

- mathstudent55

Good.
What is the length of the entire secant?
|dw:1436810876026:dw|

- anonymous

x(2x)
the entire secant is x+x which

- anonymous

3x=36

- anonymous

x=12?

- 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

There is a big difference between adding x to 2x which is 3x, and multiplying x by 2x which is 2x^2.

- mathstudent55

The equation then is:
\(x(x + x) = 6^2\)
\(x(2x) = 36\)
\(2x^2 = 36\)
Now divide both sides by 2.

- anonymous

x^2= 6

- mathstudent55

???
What is 36/2 = ???

- anonymous

oh! 18! I was thinking square root it

- mathstudent55

\(2x^2 = 36\)
\(\dfrac{2x^2}{2} = \dfrac{36}{2} \)

- mathstudent55

Good. Now we have this. Now take square root of both sides.
\(x^2 = 18\)

- anonymous

3 rad 2?

- mathstudent55

Yes! Correct.

- mathstudent55

|dw:1436811486694:dw|

- anonymous

Thank you soo much. Im afraid i have to go But you helped me a lot!

- anonymous

I need to take my final!

- 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

You're welcome.

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