## anonymous one year ago Which of the following is a solution of x2 + 4x + 6? −2 + i times the square root of 2 2 + i times the square root of 2 −2 + three i times the square root of 2 −2 + three i times the square root of 2

1. anonymous

you have a choice you can use the quadratic formula or you can complete the square you pick

2. anonymous

actually there is a third choice, namely to cheat

3. anonymous

how do i do that, any of it ?

4. anonymous

do you know the quadratic formula?

5. anonymous

i need a refresher.

6. anonymous

the solutions to $ax^2+bx+c=0$ are $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ in your case $$a=1,b=4,c=6$$ but also in your case completing the square is easier

7. anonymous

lets solve $x^2+4x+6=0$ by completing the square ready?

8. anonymous

sorry i was working it out xD

9. anonymous

10. anonymous

so far I got |dw:1438546685018:dw|

11. anonymous

$4^2-4\times 6=-8$

12. anonymous

$x=\frac{-4\pm\sqrt{-8}}{2}$

13. anonymous

then $\sqrt{-8}=\sqrt{4\times 2\times (-1)}=\sqrt{4}\sqrt{2}\sqrt{-1}=2\sqrt{2}i$

14. anonymous

giving you $\frac{-4\pm2\sqrt{2}i}{2}$ divide each term by $$2$$ and get $-2\pm\sqrt{2}i$

15. anonymous

it would have been easier to complete the square there would have been no denominator

16. anonymous

is that supposed to be the answer ?

17. anonymous

lol yes it is "supposed to be" but in fact they wrote $-2\pm i\sqrt{2}$

18. anonymous

xD are you able to help me out with more ?

19. anonymous

sure

20. anonymous

Solve x2 + 4x + 1 = 0. x equals the quantity of 4 plus or minus square root 12 all over 2 x equals negative 4 plus or minus square root 3 x equals negative 2 plus or minus square root 3 x equals the quantity of 4 plus or minus square root 13 all over 2

21. anonymous

lets complete the square for this one, unless you want to use the formula again

22. anonymous

in fact i will just write down the steps for completing the square without skipping any so you can try one on your own

23. anonymous

$x^2+4x=1=0$ subtract 1 from both sides get $x^2+4x=-1$

24. anonymous

alright

25. anonymous

then half of 4 is 2, and 2 squared is 4 go right to $(x+2)^2=-1+4$ or $(x+2)^2=3$

26. anonymous

take the square root of both sides, don't forget the $$\pm$$ get $x+2=\pm\sqrt3$

27. anonymous

subtract 2 from both sides to solve for x, get $x=-2\pm\sqrt3$ done

28. anonymous

looks like option C in your choices

29. anonymous

xD I thought I wa supposed to do it lol

30. anonymous

Solve 6 over x minus 4 equals 4 over x for x and determine if the solution is extraneous or not. x = -8, extraneous x = -8, non-extraneous x = 8, extraneous x = 8, non-extraneous what about this one xD

31. anonymous

this is not a quadratic i guess

32. anonymous

$\frac{x}{x-4}=\frac{4}{x}$ right?

33. anonymous

no that is not right $\frac{6}{x-4}=\frac{4}{x}$ hows that?

34. anonymous

the x in the numerator is a 6

35. anonymous

as the math teacher say "cross multiply" and get $6x=4(x-4)$ which is a linear equation can you solve that one?

36. anonymous

yea let me try xD

37. anonymous

i will wait

38. anonymous

x=-8?

39. anonymous

yes

40. anonymous

would it be extraneous?

41. anonymous

how do i tell if its extraneous or non-extraneous?

42. anonymous

if it does not make the denominator zero, then it is not extraneous or put another way, if it does make the denominator zero, then it is extraneous

43. anonymous

in this case it does not, so it is not extraneous

44. anonymous

oh now i get it

45. anonymous

$\frac{6}{x-4}=\frac{4}{x}$ sustitute $$x=-8$$ get $\frac{6}{-8-4}=\frac{4}{-8}$ or $-2=-2$ a perfectly good solution

46. anonymous

well actually $-\frac{1}{2}=-\frac{1}{2}$ but you get the idea

47. anonymous

you up for some more xD? Or you tired out?

48. anonymous

49. anonymous

What is the axis of symmetry for f(x) = 2x2 + 8x + 8? x = −2 x = −4 x = 4 x = 2

50. anonymous

oops axis of symmetry of $$y=ax^2+bx+c$$ is $-\frac{b}{2a}$

51. anonymous

in your case $$a=2,b=8$$

52. anonymous

let me know when you get $x=-2$

53. anonymous

what is c?

54. anonymous

nothing?

55. anonymous

c in your case is 8 but it does not figure in to the axis of symmetry it is just $x=-\frac{b}{2a}$

56. anonymous

so 2?

57. anonymous

58. anonymous

oh so x=-2?

59. anonymous

$x=-\frac{8}{2\times 2}\\ x=-2$

60. anonymous

What is the standard form equation of the line shown below? −3x + 2y = 5 3x − 2y = −5 y − 4 = three halves(x − 1) y = three halvesx + five halves

61. anonymous

you need the slope first you know how to find it?

62. anonymous

y=mx+b?

63. anonymous

that is the "slope intercept" form not standard form but in any case you need $$m$$ (the slope) first

64. anonymous

what is the standard form again ?

65. anonymous

standard form will be one of your first two choices $ax+by=c$

66. anonymous

im not understanding how i would use it

67. anonymous

in fact we don't have to do any work at all for this one since only choice B is in standard form just pick that one and move on

68. anonymous

Simplify open parentheses x to the 2 fifths power close parentheses to the 5 sixths power. x to the 37 over 30 power x to the 13 over 30 power x to the 10 elevenths power x to the 1 third power

69. anonymous

i really appreciate you helping me <3

70. anonymous

$\huge (b^m)^n=b^{m\times n}$ is what you need for this one, i.e.multiply the exponents

71. anonymous

yw

72. anonymous

so what would the b be?

73. anonymous

multiply $\frac{2}{5}\times \frac{5}{6}$

74. anonymous

in this case $$b$$ is $$2$$

75. anonymous

do i cross multiply?

76. anonymous

$\huge (2^{\frac{2}{5}})^{\frac{5}{6}}$ $\huge 2^{\frac{2}{5}\times \frac{5}{6}}$ hell no

77. anonymous

multiply just means multiply

78. anonymous

so$\frac{ 10 }{ 30 }$

79. anonymous

$\frac{2}{5}\times \frac{5}{6}$ we can cancel stuff too

80. anonymous

the five

81. anonymous

$\frac{2}{\cancel{5}}\times \frac{\cancel{5}}{6}=\frac{2}{6}$ is a start

82. anonymous

then you can cancel the 2 as well

83. anonymous

or you could cancel here $\frac{1\cancel{0}}{3\cancel{0}}=\frac{1}{3}$

84. anonymous

either way you get $$\frac{1}{3}$$ and also you do NOT cross multiply

85. anonymous

ok gotcha cx makes more sense now

86. anonymous

whew final answer $\huge 2^{\frac{1}{3}}$

87. anonymous

What is the simplified form of the quantity 12 z-squared minus 7z minus 12 over the quantity 3 z-squared plus 2z minus 8 ? 4z plus 3 over z plus 2 4z minus 3 over z plus 2 4z plus 3 over z minus 2 4z minus 3 over z minus 2

88. anonymous

lol

89. anonymous

wait wouldnt it be x1/3

90. anonymous

$\frac{12z^2-7z-12}{3z^2+2z-8}$ factor and cancel

91. anonymous

hold on let me go back and look

92. anonymous

yeah sorry $\huge x^{\frac{1}{3}}$ the base was x, not 2

93. anonymous

ahh gotcha

94. anonymous

for the last one you have to factor and cancel i suck at factoring, but i am good at cheating http://www.wolframalpha.com/input/?i= \frac{12z^2-7z-12}{3z^2%2B2z-8}

95. anonymous

i dont understand how to use that xD

96. anonymous

this will work better http://www.wolframalpha.com/input/?i=%2812z^2-7z-12%29%2F%283z^2%2B2z-8%29 apparently it is $\frac{4z+3}{z+2}$

97. anonymous

A?

98. anonymous

click on the link to the second one and see how i wrote it in wolfram

99. anonymous

yeah A

100. anonymous

questions are all over the map must be an on line course ...

101. anonymous

What is the simplified form of the seventh root of x times the seventh root of x times the seventh root of x times the seventh root of x? this one would be $\sqrt[7]{4x}$ right?

102. anonymous

no

103. anonymous

yea it is XD

104. anonymous

and oh i thought it was

105. anonymous

one answer is $x^{\frac{4}{7}}$

106. anonymous

another is $\sqrt[7]{x^4}$

107. anonymous

the power is four, not the coefficient

108. anonymous

$x\times x\times x\times x=x^4$not $$4x$$

109. anonymous

4 times the seventh root of x x to the four-sevenths power the seventh root of 4x x to the seven fourths power

110. anonymous

111. anonymous

$\huge \sqrt[7]{x^4}=x^{\frac{4}{7}}$

112. anonymous

make that a B

113. anonymous

Which of the following represents the zeros of f(x) = 6x3 + 25x2 - 24x + 5? -5, one third, one half 5, -one third, one half 5, one third, - one half 5, one third, one half

114. anonymous

cheat like crazy for this one

115. anonymous
116. anonymous

$\{-5,\frac{1}{2},\frac{1}{3}\}$

117. anonymous

so A?

118. anonymous

otherwise you have to figure out that it factors as $(3 x-1) (2 x-1) (x+5)$

119. anonymous

yeah A

120. anonymous

Use the graph below for this question: What is the average rate of change from x = −1 to x = −2?

121. anonymous

$5-7=-2$

122. anonymous

although the question is confusing since it says "from -1 to -2" which is backwards

123. anonymous

maybe they want you to say 2, i am not clear on that the question is ill posed

124. anonymous

not uncommon for an on line class btw

125. anonymous

sorry i was talking to my brother

126. anonymous

i gotta run now good luck with the rest keep posting in a new thread, i am sure you will get lots of answers

127. anonymous

thank you so much!!!

128. anonymous

yw any time!