## anonymous one year ago I have 5 questions i really need help with!!! Please help me! attached in comments

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1. anonymous

2. mathstudent55

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

3. anonymous

so 8+15=6+x?

4. mathstudent55

|dw:1436809633896:dw|

5. mathstudent55

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

6. mathstudent55

8 * 15 = 6 * x

7. anonymous

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

8. mathstudent55

Exactly. 1 down, 4 to go.

9. mathstudent55

|dw:1436809837663:dw|

10. anonymous

Yay :)

11. mathstudent55

Let's do 2 now.

12. mathstudent55

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

13. mathstudent55

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

14. anonymous

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

15. mathstudent55

|dw:1436810128136:dw|

16. mathstudent55

No. Here you DO need some additions.

17. anonymous

16*10=(8+x)8

18. 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.

19. mathstudent55

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

20. anonymous

160=64+8x?

21. mathstudent55

yes

22. anonymous

96=8x because 160-64=96?

23. mathstudent55

yes

24. anonymous

so the answer is x=12

25. mathstudent55

correct

26. mathstudent55

Ready for problem 3?

27. anonymous

yes :)

28. mathstudent55

|dw:1436810571796:dw|

29. mathstudent55

Use the same idea for the secant as before: the external segment times the entire secant. For the tangent, just square its length.

30. mathstudent55

|dw:1436810702662:dw|

31. anonymous

So 2x= 36?

32. 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?

33. mathstudent55

|dw:1436810831719:dw|

34. anonymous

x

35. mathstudent55

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

36. anonymous

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

37. anonymous

3x=36

38. anonymous

x=12?

39. 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

40. mathstudent55

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

41. mathstudent55

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

42. anonymous

x^2= 6

43. mathstudent55

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

44. anonymous

oh! 18! I was thinking square root it

45. mathstudent55

$$2x^2 = 36$$ $$\dfrac{2x^2}{2} = \dfrac{36}{2}$$

46. mathstudent55

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

47. anonymous

48. mathstudent55

Yes! Correct.

49. mathstudent55

|dw:1436811486694:dw|

50. anonymous

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

51. anonymous

I need to take my final!

52. 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.

53. mathstudent55

You're welcome.