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Destinyyyy

  • one year ago

Need help and a memory refresher on 8 problems.. Please do not give me answers. I want to remember how to solve them. This is my midterm review.

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  1. Destinyyyy
    • one year ago
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    11. Perform the indicated operations and write in standard form. (-10 + square root -9) ^2

  2. Destinyyyy
    • one year ago
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    16. Solve the problem. A rain gutter is made from sheets of aluminum that are 24 inches wide. The edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 58 square inches. There are two solutions to this problem. Round to the nearest tenth of an inch.

  3. Destinyyyy
    • one year ago
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    21. Solve the linear inequality. Other than not solution sign, use interval notation to express the solution set and graph the solution set on a number line. x-1 over 16 >/ x-4 over 20 + 1 over 80

  4. Destinyyyy
    • one year ago
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    @jim_thompson5910 @welshfella @Nnesha

  5. Destinyyyy
    • one year ago
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    Please help me finish. I still have a chapter test and midterm to do for another class. Im majorly behind since the system keeps glitching.

  6. Destinyyyy
    • one year ago
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    @IrishBoy123

  7. jim_thompson5910
    • one year ago
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    Hopefully in your lesson somewhere you learned that \[\Large i = \sqrt{-1}\] ? or no?

  8. Destinyyyy
    • one year ago
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    Yes I did last term.

  9. jim_thompson5910
    • one year ago
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    ok great

  10. jim_thompson5910
    • one year ago
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    what we can do is rewrite -9 as -1*9 and simplify like this \[\Large \sqrt{-9} = \sqrt{-1*9}\] \[\Large \sqrt{-9} = \sqrt{-1}*\sqrt{9}\] \[\Large \sqrt{-9} = i*3\] \[\Large \sqrt{-9} = 3i\] make sense?

  11. Destinyyyy
    • one year ago
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    Yes!

  12. jim_thompson5910
    • one year ago
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    \[\Large \left(-10+\sqrt{-9}\right)^2\] turns into \[\Large \left(-10+3i\right)^2\]

  13. Destinyyyy
    • one year ago
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    Yep I have that.

  14. jim_thompson5910
    • one year ago
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    Next you'll use the box method or FOIL or the distributive property to expand out \[\Large \left(-10+3i\right)^2\]

  15. jim_thompson5910
    • one year ago
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    personally I like the box method but you can choose which one you want to do

  16. Destinyyyy
    • one year ago
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    So.. (-10+3i)(-10+3i)

  17. jim_thompson5910
    • one year ago
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    yes

  18. jim_thompson5910
    • one year ago
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    keep going

  19. Destinyyyy
    • one year ago
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    I got.. 100-51i

  20. jim_thompson5910
    • one year ago
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    incorrect

  21. Destinyyyy
    • one year ago
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    Yeah...

  22. Destinyyyy
    • one year ago
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    Not sure where im going wrong.. (-10+3i)(-10+3i) 100-30i-30i+9i 100-60i+9i 100-51i

  23. jim_thompson5910
    • one year ago
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    3i times 3i = 9i^2 not just 9i

  24. jim_thompson5910
    • one year ago
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    since i = sqrt(-1), squaring both sides gives i^2 = -1

  25. Destinyyyy
    • one year ago
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    Omg -.-

  26. Destinyyyy
    • one year ago
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    91-60i

  27. jim_thompson5910
    • one year ago
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    perfect

  28. Destinyyyy
    • one year ago
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    Okay. For number 16. Solve the problem. A rain gutter is made from sheets of aluminum that are 24 inches wide. The edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 58 square inches. There are two solutions to this problem. Round to the nearest tenth of an inch. I got to -20+- square root 296 all over -4

  29. Destinyyyy
    • one year ago
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    the square root 296 can turn into 2 square root 74

  30. Destinyyyy
    • one year ago
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    -20 +- 2 square root 74 all over -4 Then I can -20 and -4 --> 5

  31. Destinyyyy
    • one year ago
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    I'm kinda stuck there.

  32. jim_thompson5910
    • one year ago
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    I'm not sure how you got that. What quadratic equation did you get to?

  33. Destinyyyy
    • one year ago
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    Um.. -2x^2 +20x -13=0 -20+- square root (20)^2 -4(-2)(-13) all over 2(-2) Some girl earlier said to- 2x+y=20 y=20-2x x*y=13 x*(20-2x)=13

  34. Destinyyyy
    • one year ago
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    Im really not sure. I followed what she said. And I responded saying I was stuck and she didnt reply.

  35. jim_thompson5910
    • one year ago
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    ok let's start with a 24 inch line |dw:1444423527504:dw|

  36. jim_thompson5910
    • one year ago
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    we will bend this line into a partial rectangle like this |dw:1444423553539:dw| I can't do animations on here but hopefully you can picture what is going on

  37. Destinyyyy
    • one year ago
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    I can.

  38. jim_thompson5910
    • one year ago
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    after the bending is done, we have this left over |dw:1444423623561:dw|

  39. jim_thompson5910
    • one year ago
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    if we make x = depth, then we have this |dw:1444423774023:dw|

  40. jim_thompson5910
    • one year ago
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    what is the length of the bottom side?

  41. Destinyyyy
    • one year ago
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    What do you mean? As in y?

  42. jim_thompson5910
    • one year ago
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    hint: |dw:1444423922673:dw|

  43. jim_thompson5910
    • one year ago
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    replace the question marks with some expression in terms of x

  44. Destinyyyy
    • one year ago
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    I understand what your saying but I keep thinking Y. Unless its 58?

  45. jim_thompson5910
    • one year ago
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    |dw:1444424117414:dw|

  46. Destinyyyy
    • one year ago
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    Or is it still 24 even though the edges have been bent.

  47. Destinyyyy
    • one year ago
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    Oh..

  48. jim_thompson5910
    • one year ago
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    there are 2 xs being subtracted off, so that's how I got 24-2x

  49. jim_thompson5910
    • one year ago
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    |dw:1444424187334:dw|

  50. Destinyyyy
    • one year ago
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    Yes I understand now.

  51. jim_thompson5910
    • one year ago
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    Area = Length * Width 58 = (24 - 2x) * x 58 = 24x - 2x^2 -2x^2 + 24x - 58 = 0 solve for x using the quadratic formula

  52. Destinyyyy
    • one year ago
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    Okay. Im at.. -24 +- 4 square root 65 over -4

  53. jim_thompson5910
    • one year ago
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    you made an error somewhere

  54. Destinyyyy
    • one year ago
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    -24 +- square root 576 +464 over -4

  55. jim_thompson5910
    • one year ago
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    it should be -464 not +464

  56. jim_thompson5910
    • one year ago
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    b^2 - 4ac (24)^2 - 4*(-2)*(-58) 576 - 464

  57. Destinyyyy
    • one year ago
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    Oops I put a + in front of the 4...

  58. Destinyyyy
    • one year ago
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    Now I have.. 6+- -1 square root 7

  59. jim_thompson5910
    • one year ago
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    good, \[\Large x = 6 \pm \sqrt{7}\]

  60. Destinyyyy
    • one year ago
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    Answer-> 3.4 and 8.6

  61. jim_thompson5910
    • one year ago
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    both are correct

  62. Destinyyyy
    • one year ago
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    Okay thank you.. 6 left.. 21. Solve the linear inequality. Other than not solution sign, use interval notation to express the solution set and graph the solution set on a number line. x-1 over 16 >/ x-4 over 20 + 1 over 80

  63. jim_thompson5910
    • one year ago
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    This? \[\Large \frac{x-1}{16} \ge \frac{x-4}{20} + \frac{1}{80}\]

  64. Destinyyyy
    • one year ago
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    I know the answer is -10.. Its the only option.. My first attempt I canceled out the fractions by using 4... Yes thats it.

  65. jim_thompson5910
    • one year ago
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    I would use 80 instead

  66. Destinyyyy
    • one year ago
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    True..

  67. jim_thompson5910
    • one year ago
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    Multiply every term by the LCD 80 to clear out the fractions \[\Large \frac{x-1}{16} \ge \frac{x-4}{20} + \frac{1}{80}\] \[\Large 80*\frac{x-1}{16} \ge 80*\frac{x-4}{20} + 80*\frac{1}{80}\] \[\Large 5(x-1) \ge 4(x-4) + 1\]

  68. Destinyyyy
    • one year ago
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    Yep.. Should of figured that out :/ ... x</ -10

  69. jim_thompson5910
    • one year ago
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    correct

  70. Destinyyyy
    • one year ago
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    Its [-10, infinity) correct?

  71. jim_thompson5910
    • one year ago
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    yes, sorry I misread your first inequality it should be \(\Large x \ge -10\) which turns into `[-10, infinity)`

  72. Destinyyyy
    • one year ago
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    Okay. Sorry typed the wrong one.

  73. Destinyyyy
    • one year ago
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    Next problem.. 24. Determine whether the equation defines y as a function of x. xy + 5y = 1

  74. Destinyyyy
    • one year ago
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    I don't remember doing any problems like this. And I couldn't find any examples from my notes.

  75. jim_thompson5910
    • one year ago
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    We solve for y to get xy + 5y = 1 y(x + 5) = 1 y = 1/(x + 5) which is definitely a function. You can graph to verify that it passes the vertical line test. Any given input (x) produces EXACTLY ONE output (y)

  76. Destinyyyy
    • one year ago
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    Okay!

  77. Destinyyyy
    • one year ago
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    26. Evaluate the function at the given value of the independent variable and simplify. f(x) = 3x2 - 4x + 4; f(x - 1)

  78. Destinyyyy
    • one year ago
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    I'm not sure on this one either.. I was thinking plug (x-1) in for the x's but im not sure. If you want me to post in a new question I can.

  79. jim_thompson5910
    • one year ago
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    You're right. Replace each x with x-1 and simplify \[\Large f(x) = 3x^2 - 4x + 4\] \[\Large f(\color{red}{x}) = 3(\color{red}{x})^2 - 4(\color{red}{x}) + 4\] \[\Large f(\color{red}{x-1}) = 3(\color{red}{x-1})^2 - 4(\color{red}{x-1}) + 4\] now simplify the right hand side

  80. jim_thompson5910
    • one year ago
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    ` If you want me to post in a new question I can. ` yes please. It's getting laggy with all of these questions. It's a good idea to have one question per post to avoid clutter and lag

  81. Destinyyyy
    • one year ago
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    Okay Ill do it now..

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