## anonymous one year ago Tom wants to hang a mirror in his room. The mirror and frame must have an area of 14 square feet. The mirror is 3 feet wide and 4 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? Square with an inner frame with height of 3ft on the left frame and width of 4ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x. 4x2 + 14x − 2 = 0 3x2 + 10x − 14 = 0 2x2 + 12x − 14 = 0 x2 + 7x − 14 = 0

1. Vocaloid

well, let's draw a picture of a 3*4 mirror with a frame that is x inches thick |dw:1440372180188:dw|

2. Vocaloid

now, let's see if we can write an expression, using x, for the width and length of the whole thing (mirror + frame)

3. anonymous

So the answer would be C right?

4. Vocaloid

hm, not C, let's keep going |dw:1440372299021:dw| any ideas?

5. Vocaloid

can you tell me what the length and width are in terms of x?

6. anonymous

\[x^3\]

7. Vocaloid

uh, not quite... let's just look at the length first, ok? do you see how the length of the whole thing is just the length of the mirror + x on each side?

8. Vocaloid

|dw:1440372540133:dw|

9. anonymous

4x?

10. Vocaloid

almost but not quite... length of the mirror + width of the frame on each side = ?

11. anonymous

0?

12. Vocaloid

|dw:1440372618481:dw| maybe just look at it from one dimension?

13. Vocaloid

the length of the mirror is 4 and the width of the frame is x, so the total length is...?

14. anonymous

4x^2?

15. Vocaloid

nope, not quite... |dw:1440372717991:dw|

16. anonymous

Idk.

17. Vocaloid

pretend that it's a straight line... add together length of mirror + width of frame = ?

18. anonymous

19. Vocaloid

the answer isn't C.... hm, maybe I can break it down another way... let's just go back to our mirror, without the frame for now|dw:1440372900669:dw|

20. Vocaloid

the length is 4, agreed?

21. anonymous

144?

22. Vocaloid

let's just forget about the frame for a sec and just look at the mirror... the mirror is 4 feet long, agreed?|dw:1440372976654:dw|

23. Plasmataco

... Y u so genius @Vocaloid

24. anonymous

yes

25. Vocaloid

ok, now let's put the frame around it now|dw:1440373034973:dw|

26. Vocaloid

can you tell me what this length is now? (we don't know what x is yet, but we can write an expression using x)|dw:1440373076022:dw|

27. Vocaloid

just add: width of frame + length of mirror + width of frame = ?

28. Vocaloid

29. anonymous

30. Vocaloid

31. Vocaloid

|dw:1440373181795:dw|

32. Plasmataco

Lul

33. anonymous

-.-

34. Vocaloid

the length is 4 + x + x, agreed?

35. Plasmataco

U sound like my mom when I do calculus. :3

36. anonymous

Yes

37. Vocaloid

alright, now can you find the width?|dw:1440373262344:dw|

38. anonymous

3*4*x?

39. Vocaloid

not quite.... just like before, we add width of mirror + width of frame + width of frame = ?

40. Vocaloid

|dw:1440373318819:dw|

41. anonymous

3+2x

42. Vocaloid

fantastic! so our length is 4 + 2x our width is 3 + 2x our area (stated in the problem is 14) so, do you think you can take it from here?

43. anonymous

So its B?

44. Vocaloid

area = (width)*(length) 14 = (4 + 2x)(3 + 2x) simplify that and you will get your answer....

45. Vocaloid

start by doing FOIL on the right side

46. anonymous

Is it A?

47. Vocaloid

start by doing FOIL on the right side, please..... (4 + 2x)(3 + 2x) = ??

48. Plasmataco

@Vocaloid I believe she is correct

49. Vocaloid

I already know the answer, I want her/him to learn so she/he can do this in the future without my guidance

50. anonymous

I am a girl...

51. Vocaloid

right, I figured as much, just making sure so, start by doing FOIL on the right side... (4 + 2x)(3 + 2x) = ?

52. anonymous

@Vocaloid Am i correct there is no way it can be D. And i already asked about B and C. So only possible can be is A? Am i correct?

53. Vocaloid

the point is to get the correct answer by actually doing the math, not by guessing... the answer is either A or B, I'll give you that

54. anonymous

You said it wasn't b...

55. Vocaloid

do you understand FOIL?

56. anonymous

Earlier

57. anonymous

Yes. I am just in a big hurry

58. Plasmataco

Lol... U sound real stressed

59. anonymous

VERY

60. anonymous

2x*2x+2x*3+4*2x+3*4-12

61. Vocaloid

almost... (2x + 3)(2x + 4) = (2x)(2x) + (4)(2x) + (3)(2x) + (3)(4)

62. Vocaloid

there's no -12 at the end but other than that, you're on the right track... now start combining like terms

63. anonymous

@Vocaloid I am in a bigggg hurrrryyy

64. anonymous

My school starts tomorrow and i almost finsihed

65. Vocaloid

your deadline =/= my problem (2x)(2x) + (4)(2x) + (3)(2x) + (3)(4) 4x^2 + 8x + 6x + 12 = 4x^2 + 8x + 6x + 12 now we set that equal to 14...

66. anonymous

I am tring to get this done

67. Vocaloid

4x^2 + 8x + 6x + 12 = 14

68. anonymous

there is 40 more questions i have to do

69. anonymous

70. Vocaloid

right

71. anonymous

Thank you.