## anonymous one year ago What is the simplified form of x plus 1 over x squared plus x minus 6 ÷ x squared plus 5x plus 4 over x plus 4 ? 1 over the quantity x plus 3 times the quantity x plus 4 1 over the quantity x plus 3 times the quantity x minus 2 1 over the quantity x plus 4 times the quantity x minus 2 1 over the quantity x plus 3 times the quantity x plus 1

1. anonymous

@satellite73

2. anonymous

$\frac{ x + 1 }{ x^2 + x -6 } \div \frac{ x^2 + 5x + 4 }{ x + 4 }$ @satellite73

3. anonymous

@satellite73

4. anonymous
5. anonymous

you go that right?

6. anonymous

nice use of the equation tool btw

7. anonymous

i can show you another trick in using wolfram

8. anonymous

okay and heres the question

9. anonymous

simplify (12z^2 - 25z + 12)/ (3z^2 + 2z - 8)

10. anonymous

using the link i got (4z - 3)/(x + 2)

11. anonymous

ok i so take what you wrote, copy and paste it directly in to wolfram

12. anonymous

yeah i did that and got (4z - 3)/(x + 2)

13. anonymous

yeah i get that too, but of course with a z

14. anonymous

i could also show you how to do it without wolfram, it is "factor and cancel"

15. anonymous

oh yeah typo lol sorry okay i think it'll be better without wolframe alpha in case my teacher asks

16. anonymous

ok then here is the deal do you know how to factor?

17. anonymous

sometimes but not really it'll be helpful if you showed me though

18. anonymous

i don't actually, believe it or not if i wanted to factor i would cheat

19. anonymous

what i mean is that i have no good way to show you how

20. anonymous

i usually use a site for factoring

21. anonymous

that works, of course wolfram will do that too

22. anonymous

so in case the teacher asks, you can say something like this ;

23. anonymous

$(12z^2 - 25z + 12)=(4 z-3) (3 z-4)$ and $(3z^2 + 2z - 8)= (3 z-4) (z+2)$

24. anonymous

so $\frac{12z^2+25z+12}{3z^2+2z-8}=\frac{4z-3)(3z-4)}{(3z-4)(z+2)}$

25. anonymous

oh and then you cross out (3z - 4)?

26. anonymous

there is a common factor top and bottom of $$3z-4$$ which cancels, you get $\frac{(4z-3)(3z-4)}{(3z-4)(z+2)}=\frac{4z-3}{z+2}$

27. anonymous

exactly what you said

28. anonymous

that is the idea of all of these factor and cancel

29. anonymous

okay cool i get it now

30. anonymous

as to how to factor, you are pretty much on your own, but you can use wolfram to do it for sure

31. anonymous

okay thnx

32. anonymous

and you can use wolfram to give the final answer too, but once you have it factored it is easy to cancel

33. anonymous

ill also ask someone else on os

34. anonymous

want to try another one ?

35. anonymous

yeah

36. anonymous

ok i get a cup of coffee, you post

37. anonymous

ok What polynomial identity should be used to prove that 21 = 25 - 4?

38. anonymous

wow do you have any choices? $$21=25-4$$ is simple arithmetic

39. anonymous

What polynomial identity should be used to prove that 21 = 25 - 4? Difference of Cubes Difference of Squares Square of Binomial Sum of Cubes

40. anonymous

ooh ok

41. anonymous

25 and 4 are two squares

42. anonymous

then B?

43. anonymous

$25=5^2$ and $2^2$ so yeah B

44. anonymous

what a dumb retricequestion next?

45. anonymous

thnx

46. anonymous

given the parent function of f(x) = x3, what change will occur when the function is changed to f(x - 3)? Shift to the right 3 units Shift to the left 3 units Shift up 3 units Shift down 3 units

47. anonymous

when you subtract inside the function it move is 3 units to the RIGHT

48. anonymous

thnx

49. anonymous

ased on the table of values below, find the slope between points where x = 1 and where x = 4. x y 1 8 3 6 4 −1

50. anonymous

what is the corresponding y value when x = 1?

51. anonymous

ok ok

52. anonymous

8

53. anonymous

$\frac{-1-8}{4-1}$ is whatyou have to compuote

54. anonymous

i get $\frac{-9}{3}=-3$

55. anonymous

thnx

56. anonymous

yw

57. anonymous

how many more?

58. anonymous

a couple Which of the following expressions is the conjugate of a complex number with 2 as the real part and 3i as the imaginary part? 2 + 3i 2 − 3i 3i + 2 3i − 2

59. anonymous

the conjugate of $$a+bi$$ is $$a-bi$$

60. anonymous

so b?

61. anonymous

the conjugate of $$2+3i$$ is $$2-3i$$ that was an easy one

62. anonymous

yeah b

63. anonymous

okay thnx

64. anonymous

yw next?

65. anonymous

Two car washers, Michelle and Nancy, are working on your car. Michelle can complete the work in 6 hours, while Nancy can complete the work in 3 hours. How many hours does the car washing take if they work together? 3 2 six eighths four thirds

66. anonymous

we go right to the answer (otherwise it take like forever) but remember this simple trick $\frac{6\times 3}{6+3}$

67. anonymous

got that ?

68. anonymous

so 18/9 = 2

69. anonymous

yes

70. anonymous

Bob and Susie wash cars for extra money over the summer. Bob's income is determined by f(x) = 6x + 13, where x is the number of hours. Susie's income is g(x) = 4x + 18. If Bob and Susie were to combine their efforts, their income would be h(x) = f(x) + g(x). Assume Bob works 3 hours. Create the function h(x) and indicate if Bob will make more money working alone or by teaming with Susie. h(x) = 2x + 5, work alone h(x) = 2x + 5, team with Susie h(x) = 10x + 31, team with Susie h(x) = 10x + 31, work alone

71. anonymous

see the trick? it is easy

72. anonymous

yup

73. anonymous

$g(x) = 4x + 18$ $h(x)=6x+13$ $g(x)+h(x)=4x+18+6x+13$

74. anonymous

combine like terms,what do you get?

75. anonymous

10x + 31

76. anonymous

ok good so C or D

77. anonymous

yup but i think its with team work so C?

78. anonymous

not sure if bob works 3 hours alone he makes $f(3)=6\times 3+13=18+13=31$

79. anonymous

oh so D

80. anonymous

don't jump the gun

81. anonymous

if they both work 3 hours they make a total of \pg(3)=10\times 3+31=61\]

82. anonymous

oh

83. anonymous

$h(3)=10\times 3+31=61$\]

84. anonymous

if he has to split it, then yes he is better off working alone

85. anonymous

so is its C then?

86. anonymous

i think D not really clear, but i think D

87. anonymous

ok

88. anonymous

next?

89. anonymous

What is the equation of the quadratic graph with a focus of (3, 6) and a directrix of y = 4?

90. anonymous

this takes a second

91. anonymous

k

92. anonymous

half way between 6 and 4 is 5, so the vertex is $$(3,5)$$

93. anonymous

therefore it will look like $4p(y-5)=(x-3)^2$ we need $$p$$

94. anonymous

the distance between 4 and 5 is 1, so p = 1 and one answer is $4(y-5)=(x-3)^2$ now sure what your answer choices look like

95. anonymous

f(x) = one fourth (x − 3)2 + 1 f(x) = one fourth (x − 3)2 + 5 f(x) = −one fourth (x − 2)2 + 5 f(x) = −one fourth (x − 2)2

96. anonymous

$4(y-5)=(x-3)^2\\ y-5=\frac{1}{4}(x-3)^2\\ y=\frac{1}{4}(x-3)^2+5$

97. anonymous

thnx Which of the following is a solution of x2 + 2x + 8? 4 + i times the square root of 7 −1 + i times the square root of 7 2 + i times the square root of 7 −4 + i times the square root of 7

98. anonymous

x^2 + 2x +8

99. anonymous

you want do step by step? or wolfram it?

100. anonymous

step by step so i can learn

101. anonymous

ok a) subtract 8 from both sides, what do you get?

102. anonymous

if that is not clear say so i will tell you

103. anonymous

oh note that you are starting with $x^2+2x+8=0$

104. anonymous

x^2 + 2x = 8

105. anonymous

i meaN -8

106. anonymous

ok good

107. anonymous

SO X^2 + 2X = -8

108. anonymous

$x^2+2x=8$ now what is half of 2?`

109. anonymous

oops $x^2+2x=-8$ what is half of two?

110. anonymous

1

111. anonymous

so x^2 + x = -8/2?

112. anonymous

no slow

113. anonymous

oh sorry

114. anonymous

half of 2 is 1, so we go right to $(x+1)^2=-8+1^2$ or $(x+1)^2=-7$

115. anonymous

ok

116. anonymous

take the square root, get $x+1=\pm\sqrt{-7}$ or $x+1=\pm\sqrt{7}i$

117. anonymous

subtract 1, get $x=-1\pm\sqrt{7}i$

118. anonymous

thnx

119. anonymous

What are the possible numbers of positive, negative, and complex zeros of f(x) = -3x4 - 5x3 - x2 - 8x + 4? Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0 Positive: 1; negative: 3 or 1; complex: 2 or 0 Positive: 3 or 1; negative: 1; complex: 2 or 0 Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0

120. anonymous

ok we do this, then i gotta split

121. anonymous

$f f(x) = -3x^4 - 5x^3 - x^2 - 8x + 4$

122. anonymous

it is a polynomial of degree 4, so it has 4 zeros for sure

123. anonymous

there is one change in sign of the coefficients, which is a fancy way of saying that the go "minus, minus, minus, minus , PLUS" only once change in sign therefore there is one positive zero there cannot be no positive zeros because you count down by twos

124. anonymous

$f(x) = -3x^4 - 5x^3 - x^2 - 8x + 4$ $f(-x) = -3x^4 + 5x^3 - x^2 + 8x + 4$

125. anonymous

here there are 3 changes in sign from -3 to +5, from +5 to -1 and from -1 tp +8 so there are either 3 negative zeros, or one negative zero

126. anonymous

possibilities therefore are 1 positive, 3 negative (total of 4) or 1 positive, 1 negative 2 complex (total of 4)

127. anonymous

now i really have to bolt ask your sister how to do the rest good luck!

128. anonymous

thnx and ok bye

129. anonymous

bye !