## anonymous 3 years ago Help!? PLEASE! Screenshot attached! 2 questions! 1 question answered! ONE TO GO!

1. anonymous

5 people means 3.6 seconds so y people will be t seconds we can show it this way : |dw:1350566474324:dw|

2. anonymous

now cross multiply and get the connection between y (number of people) and t (seconds)

3. anonymous

and hey .. how are you ? :)

4. anonymous

$t=.72p$

5. anonymous

|dw:1350566721091:dw|

6. anonymous

if you multiply one side by 100 you should multiply the other by 100 too

7. anonymous

we need to isolate t from the equation that i gave you

8. anonymous

no .. it's final answer is correct but i want you to be able to get it by yourself

9. anonymous

there is no 75 in decart's answer :|

10. anonymous

$\frac{ 5 }{ y } = \frac{ 3.6 }{ t }$ multiply both sides by $y \times t$ we get: $5t = 3.6y$ now divide both sides of the equation by 5 we get: $t = \frac{ 3.6 }{ 5 } \times y$ which is the same as $t=0.72y$

11. anonymous

yes sorry i was washing dishes lol

12. anonymous

division of two fractions is like multiplying the first by the reciprocal of the second

13. anonymous

$\frac{ a }{ b } \div \frac{ c }{ d } = \frac{ a }{ b } \times \frac{ d }{ c }$

14. anonymous

so you can rewrite the problem as .. ?

15. anonymous

no i just gave an example

16. anonymous

you have to multiply the first fraction by the reciprocal of the second..

17. anonymous

|dw:1350568226013:dw|

18. anonymous

yes .. and changed the division to multiplication this his how you divide two fractions..

19. anonymous

$\frac{ (x^2-x-6)(x^2+5x+4) }{ (x^2-2x-3)(x^2+x-12) }$

20. anonymous

this is now what you have to simplify "so, do I multiply x^2 + x - 12 by x^2 + 5x + 4 now? " no.. why you say that ?

21. anonymous

$\frac{ a }{ b } \neq a * b$

22. anonymous

we changed the division to multiplication because we divided FRACTION BY FRACTION

23. anonymous

no it's not right

24. anonymous

$\frac{ 5 }{ 3 } * \frac{ 4 }{ 2 } = ?$

25. anonymous

26. anonymous

right you just multiplied 5 with 4 and divided by the multiplication of 3 with 2

27. anonymous

|dw:1350569102823:dw|

28. anonymous

so same here .. after we changed the division into multiplication it's just multiplication of two fractions

29. anonymous

you tell me .. how do we multiply those two fractions ?

30. anonymous

i wont get mad why would i :| look : $\frac{ x^2-x-6 }{ x^2-2x-3 } \times \frac{ x^2+5x+4 }{ x^2+x-12 } = \frac{ (x^2-x-6)(x^2+5x+4) }{ (x^2-2x-3)(x^2+x-12) }$

31. anonymous

i dont know why you multiply numerator by denominator

32. anonymous

this is what you get after the multiplication of the two fractions now we better factor every term than open the brackes like x^2-x-6 = x^2-3x+2x-6 = x(x-3)+2(x-3) = (x+2)(x-3)

33. anonymous

yes look : whenever there is multiplication of two fractions you multiply numerator by numerator and denom by denom.. whenever there is division of two fractions you keep the first fraction as it is you change the division into multiplication but then for the second fraction you flip numerator and denominator and then you have multiplication of two fractions..

34. anonymous

yes as i wrote up there

35. anonymous

I'll just to butt in for a bit, the general flow of fraction division goes like this: 1. Turn the division into a multiplication by inverting the second fraction 2. Factorise as much as possible and eliminate common terms. 3. Solve by multiplying the numerator by the numerator and denominator by denominator. Yes I wrote the same thing as cool sorry :/.

36. anonymous

now it's better to factor every term than open the brackets .. so factoring x^2-x-6 gives = x^2-3x+2x-6 = x(x-3)+2(x-3) = (x+2)(x-3)

37. anonymous

can you factor the rest of the terms ?

38. anonymous

yes.. i just showed the way

39. anonymous

you see my last expression is (x+2)(x-3)

40. anonymous

now factor the rest of the terms .. what do you get ?

41. anonymous

so are you factoring the rest ?

42. anonymous

good so how the expression looks like ?

43. anonymous

after you change every term by it's factored form

44. anonymous

you have to replace every term by it's factored from like replaceing " x^2 - x- 6" by " (x+2)(x-3) " in the last expression

45. anonymous

very good

46. anonymous

now you can eliminate some of them..

47. anonymous

if you have the same thing in the numerator and in the denominator you can eliminate it ..

48. anonymous

and one more ..

49. anonymous

|dw:1350571449666:dw|

50. anonymous

so what is left .. $\frac{ x+2 }{ x-3 }$

51. anonymous

yes

52. anonymous

yw :)

53. anonymous

i hope the next question of this kind will be easier for you now that you know the steps

54. anonymous