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pooja195

  • one year ago

@mathmate

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  1. pooja195
    • one year ago
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    @mathmate

  2. mathmate
    • one year ago
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    We'll start with 6.8! Graphing linear ineq. in 2 variables!

  3. pooja195
    • one year ago
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    ok :)

  4. mathmate
    • one year ago
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    Are you familiar with plotting one linear equation, such as y=2x+3?

  5. pooja195
    • one year ago
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    yes

  6. mathmate
    • one year ago
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    In the slope-intercept form, y=ax+b, b is the y-intercept. Ok, good! Can you plot (draw) for me y=x+3

  7. mathmate
    • one year ago
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    You know that with a slope of 1, the line is at 45 deg. with the x-axis.

  8. pooja195
    • one year ago
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    |dw:1433470740581:dw|

  9. pooja195
    • one year ago
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    :/

  10. mathmate
    • one year ago
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    Beautiful! I expect much less in details, but that's nice!

  11. mathmate
    • one year ago
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    The line divides the x-y plane into two "half-planes". Each half plane represents the solution to the inequality of the form y\(\ge\)x+3 or y\(\le\)x+3.

  12. mathmate
    • one year ago
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    Can you shade for me the half plane representing y\(\ge\)x+3 ?

  13. pooja195
    • one year ago
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    |dw:1433471092615:dw|

  14. pooja195
    • one year ago
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    :/

  15. mathmate
    • one year ago
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    Very good! How do you decide which one to shade?

  16. pooja195
    • one year ago
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    its all solutions greater than y right?

  17. mathmate
    • one year ago
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    The book tells you to test a point, and see if the point is in the good region. If yes, you shade the region containing the point. If not, you shade the other region.

  18. mathmate
    • one year ago
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    For example, we can use (0,0) as a test point. (0,0) is below the line. We check if 0\(\ge\)0+3 is true. Since it is not true, (0,0) is not in the region, so it must be the "other" region, the one above the line.

  19. pooja195
    • one year ago
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    The teacher taught it a diffrent way :/

  20. pooja195
    • one year ago
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    But similar to that so its ok .-.

  21. mathmate
    • one year ago
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    |dw:1433471382597:dw|

  22. mathmate
    • one year ago
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    Can you tell me what he taught?

  23. pooja195
    • one year ago
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    he said if its greater than to shade up (postivie) If its less than shade down idk something like that >_<

  24. mathmate
    • one year ago
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    Yes, this is the better that I was going to show you!

  25. mathmate
    • one year ago
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    * better way

  26. mathmate
    • one year ago
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    Say if the inequality is y>x+3 check "y>", that means go towards the +(or plus) y-axis, so the upper half.

  27. mathmate
    • one year ago
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    If it was y<2x+3, then the "y<" tells you to take the half-plane towards the negative y-axis.

  28. mathmate
    • one year ago
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    Making sense?

  29. pooja195
    • one year ago
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    yep

  30. mathmate
    • one year ago
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    |dw:1433471680888:dw|

  31. mathmate
    • one year ago
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    Here are three examples, use your teacher's method to shade the correct half-plane. I forgot to write \(\le\) or \(\ge\) for the first two cases.

  32. pooja195
    • one year ago
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    |dw:1433471920376:dw|

  33. pooja195
    • one year ago
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    /.\

  34. mathmate
    • one year ago
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    The first (top-left) and the third (on the right) are correct. The second asks for y>-x/3-2, so the "y>" tells us to go for the + y-axis, so the region is above the line. Is that ok so far?

  35. pooja195
    • one year ago
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    yes

  36. mathmate
    • one year ago
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    |dw:1433472096086:dw|

  37. mathmate
    • one year ago
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    You're pretty good at it!

  38. mathmate
    • one year ago
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    Now if we have an inequality x+y\(\le\) 10 Can you draw the line, and the region represented by the inequality?

  39. mathmate
    • one year ago
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    When we have the general form of the equation, we can find the y-intercept by setting x=0, and solve for y. Similarly for the x-intercept (zero), we set y=0 and solve for x.

  40. mathmate
    • one year ago
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    x+y=5 would give an x-intercept of 5 and y-intercept of 5.

  41. mathmate
    • one year ago
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    |dw:1433472344866:dw|

  42. mathmate
    • one year ago
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    That's the kind of response that is sufficient.

  43. mathmate
    • one year ago
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    Both +x and +y are on the negative side, so the region is to the left, and downwards.

  44. mathmate
    • one year ago
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    It may look difficult because it is given in the general form. You can convert the general form to the point-slope form with which you are familiar, or use the intercepts I showed above.

  45. pooja195
    • one year ago
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    o.O im lost .0.

  46. mathmate
    • one year ago
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    Starting from where?

  47. pooja195
    • one year ago
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    nvm i understand >_<

  48. mathmate
    • one year ago
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    For x+y<=10 which is in general form, you can convert to y<=-x+10, would that be easier?

  49. mathmate
    • one year ago
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    One easy one to remember is x+y = K has both intercepts equal to K.|dw:1433472650720:dw|

  50. mathmate
    • one year ago
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    So are we good with 6.8?

  51. pooja195
    • one year ago
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    yes

  52. mathmate
    • one year ago
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    We'll do Chapter 7 then.

  53. pooja195
    • one year ago
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    :)

  54. mathmate
    • one year ago
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    System of linear equations and inequalities. ===========================

  55. mathmate
    • one year ago
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    A system of linear systems is simply a set of lines. With a system of two equations, there are two lines.

  56. mathmate
    • one year ago
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    |dw:1433473022450:dw|

  57. mathmate
    • one year ago
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    |dw:1433473082856:dw| represents the system of equations y=x+3 and x+y=8

  58. mathmate
    • one year ago
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    so far so good, you know where the lines are coming from (how they were drawn)?

  59. pooja195
    • one year ago
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    yep

  60. mathmate
    • one year ago
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    The intersection point (5.5, 5.5) represents the solution of the system, x=5.5, y=5.5. Right?

  61. mathmate
    • one year ago
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    * (2.5,5.5) |dw:1433473201267:dw|

  62. pooja195
    • one year ago
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    yeesss

  63. mathmate
    • one year ago
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    Now If we want to solve for the system of inequalities, y\(\le\)x+3 x+y\(\le\)8

  64. mathmate
    • one year ago
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    The boundaries of the required region are shown by the lines on the graph. Can you indicate the region (by "hatching" the region with parallel lines)?

  65. mathmate
    • one year ago
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    |dw:1433473435556:dw| The region which is hatched by both region is our solution set, as shown above.

  66. mathmate
    • one year ago
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    is that ok so far?

  67. pooja195
    • one year ago
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    yes

  68. mathmate
    • one year ago
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    ok, your turn to do something!

  69. mathmate
    • one year ago
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    Graph and show the solution set (region) of the following system of inequalities: y>-x+3 y<x+1

  70. mathmate
    • one year ago
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    Notice that ">" is represented by a dotted line, since the solution does not include the line.

  71. mathmate
    • one year ago
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    Also notice that y>-x+3 is the same as x+y>3 (use the two intercepts)

  72. pooja195
    • one year ago
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    |dw:1433473675355:dw|

  73. pooja195
    • one year ago
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    its messy this is why i didnt want to do graphs ;-;

  74. mathmate
    • one year ago
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    It's beautiful! However, it doesn't bother me if you don't use colours, and have no graduations.

  75. mathmate
    • one year ago
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    Now, remember that the > and < signs exclude the lines from the solution, so must be drawn with dotted lines!

  76. pooja195
    • one year ago
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    >:(

  77. mathmate
    • one year ago
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    |dw:1433474097592:dw|

  78. mathmate
    • one year ago
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    Can you show me how to have the fancy colours (but some other time!)?

  79. pooja195
    • one year ago
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    :)

  80. mathmate
    • one year ago
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    Now we need to hatch the region representing the solution. Use hatching (scribble some parallel lines).

  81. mathmate
    • one year ago
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    * the solution of the system of inequalities.

  82. mathmate
    • one year ago
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    |dw:1433474286903:dw|

  83. pooja195
    • one year ago
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    Got it.

  84. mathmate
    • one year ago
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    k, whenever you're ready, I'm waiting for you to draw/hatch the region of the solution set!

  85. pooja195
    • one year ago
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    So shading ? .-.

  86. mathmate
    • one year ago
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    yes, show by shading/hatching the solution set of the system of inequalities.

  87. mathmate
    • one year ago
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    similar to the example I did above.

  88. pooja195
    • one year ago
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    |dw:1433474544295:dw|

  89. pooja195
    • one year ago
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    O_O

  90. pooja195
    • one year ago
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    woah it screwed it up

  91. mathmate
    • one year ago
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    The solution set is which colour?

  92. mathmate
    • one year ago
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    No, I can understand, as long as you specify the colour.

  93. pooja195
    • one year ago
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    y>−x+3=pink y<x+1= mint

  94. mathmate
    • one year ago
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    For both of them to be true, the region is blue (intersection of pink and mint). So the blue region is the solution set. Is that ok?

  95. pooja195
    • one year ago
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    yes

  96. mathmate
    • one year ago
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    Here's another system of inequalities, but don't draw the graduations to safe yourself time! x\(\le\)4 y\(\ge\)2

  97. pooja195
    • one year ago
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    T_T

  98. mathmate
    • one year ago
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    |dw:1433474989120:dw|

  99. pooja195
    • one year ago
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    |dw:1433475046485:dw|

  100. pooja195
    • one year ago
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    >:(

  101. pooja195
    • one year ago
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    It keeps messing it up! >:(

  102. pooja195
    • one year ago
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    green= y pinkish=x

  103. mathmate
    • one year ago
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    That's ok, I can see that they are correct. So the solution set is......

  104. pooja195
    • one year ago
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    the pink

  105. mathmate
    • one year ago
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    the intersection of the two regions!

  106. mathmate
    • one year ago
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    We have two inequalities to be satisfied, so the region must satisfy BOTH regions. I will hatch it below.

  107. mathmate
    • one year ago
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    |dw:1433475274853:dw|

  108. mathmate
    • one year ago
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    still ok?

  109. pooja195
    • one year ago
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    yea

  110. mathmate
    • one year ago
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    :( not promising, he's crying!

  111. mathmate
    • one year ago
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    We only have one more topic to do.

  112. pooja195
    • one year ago
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    T_T

  113. mathmate
    • one year ago
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    an easy one. 7.5

  114. mathmate
    • one year ago
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    When we have a system of 2 linear equations, the system is represented by two straight lines, like this.

  115. mathmate
    • one year ago
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    |dw:1433475491469:dw|

  116. mathmate
    • one year ago
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    Are we good so far?

  117. pooja195
    • one year ago
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    i know this...

  118. mathmate
    • one year ago
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    Do you know what I am about to say? If yes, tell me!

  119. pooja195
    • one year ago
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    one line = many solutions two lines = one solution parell lines = no solution am i right?

  120. pooja195
    • one year ago
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    two lines interscting...

  121. mathmate
    • one year ago
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    You know the topic, but your list is not very precise. We are working with 2 lines. The intersection (or lack of it) can be described in three cases:

  122. mathmate
    • one year ago
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    Can you rename the three cases?

  123. mathmate
    • one year ago
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    1. non-parallel : _______ solutions 2. parallel and _________ : __________ solutions 3. parallel and __________ : __________ solutions.

  124. pooja195
    • one year ago
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    Now its more complicated -_-

  125. mathmate
    • one year ago
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    |dw:1433475774511:dw|

  126. pooja195
    • one year ago
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    Case 1 = one solution case 2 = no solution case 3 = infinte soltuions

  127. mathmate
    • one year ago
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    Exactly! 1. interscting, one solution eg. 2x+3y=4, 4x-2y=0 2. parallel and non-coincident: no solution eg. x+y=10, y=-x+7 3. parallel and coincident: infinite solutions. 2x+2y=4, y=-x+2

  128. mathmate
    • one year ago
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    I'll leave it to you to try some exercise on 7.5

  129. mathmate
    • one year ago
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    No, I'll give you two exercises now.

  130. mathmate
    • one year ago
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    Describe the no. of solutions of the following system: x+y=6 2x+2y=12

  131. pooja195
    • one year ago
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    you know me so well xD

  132. mathmate
    • one year ago
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    can you elaborate please?

  133. pooja195
    • one year ago
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    nawh its ok :P

  134. pooja195
    • one year ago
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    -2(x+y=6) -2x-2y=-12 2x+2y=12 0=0 Infinte solutions.

  135. mathmate
    • one year ago
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    Very well. now, how many solutions does the following system have: 2x+y=3 y=-2x-6

  136. pooja195
    • one year ago
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    2x-2x-6+6=3+6 0x=9 0=9 no solution

  137. pooja195
    • one year ago
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    *soltuons

  138. mathmate
    • one year ago
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    Exactly!

  139. pooja195
    • one year ago
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    :)

  140. mathmate
    • one year ago
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    We're done for 6.8 and 7, how's that?

  141. pooja195
    • one year ago
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    :) good

  142. pooja195
    • one year ago
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    @mathmate

  143. mathmate
    • one year ago
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    ok, Chapter 8?

  144. pooja195
    • one year ago
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    yh

  145. mathmate
    • one year ago
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    gimme a minute to find the page!

  146. mathmate
    • one year ago
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    Ok, in chapter 8, we're doing exponents!

  147. mathmate
    • one year ago
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    First we need to know the laws of exponents, how to multiply, divide, raise powers, and take roots.

  148. mathmate
    • one year ago
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    Then an application would be to convert numbers to and from scientific notations.

  149. mathmate
    • one year ago
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    Finally, there will be a few problems related to decay and growth, e.g. number of rabbits after a certain time, etc.

  150. pooja195
    • one year ago
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    ok :)

  151. mathmate
    • one year ago
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    P. 440 gives some vocabularies.

  152. mathmate
    • one year ago
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    |dw:1433538712158:dw| can you name A and B?

  153. pooja195
    • one year ago
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    A=base

  154. mathmate
    • one year ago
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    Good!

  155. pooja195
    • one year ago
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    B= expoenet

  156. mathmate
    • one year ago
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    Also good!

  157. mathmate
    • one year ago
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    Now calculate: (answer in exponential form)|dw:1433538857123:dw|

  158. pooja195
    • one year ago
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    7^5

  159. mathmate
    • one year ago
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    Excellent! Can you now write the question AND answer in exponential form?

  160. mathmate
    • one year ago
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    don't bother with LaTex. We both understand regular text.

  161. mathmate
    • one year ago
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    I gtg, but answer is 7^2 \(\times\)7^3 = 7^5

  162. pooja195
    • one year ago
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    7^5=16807

  163. pooja195
    • one year ago
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    -.- nvm

  164. pooja195
    • one year ago
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    ok :)

  165. pooja195
    • one year ago
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    i see my mistake .-.

  166. mathmate
    • one year ago
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    I'd like it in exponential form! so in general 7^2*7^3 = 7*(2+3) =7^5

  167. mathmate
    • one year ago
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    or in general x^a * x^b = x^(a+b) this is one of the laws of exponents! sorry gtg

  168. pooja195
    • one year ago
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    its ok :0 bai

  169. mathmate
    • one year ago
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    @pooja195

  170. mathmate
    • one year ago
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    So, what is \(x^3y^2 \times xy^3\). Express answer in exponential form.

  171. pooja195
    • one year ago
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    x^4y^5

  172. mathmate
    • one year ago
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    Good, how about \(\large \frac{x^2y^3}{xy}\)

  173. pooja195
    • one year ago
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    x^1y^2

  174. mathmate
    • one year ago
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    good! Now express x^3y^2\(\div\)(x^4y^4) in positive exponents.

  175. pooja195
    • one year ago
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    1/xy^2

  176. mathmate
    • one year ago
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    Good, I think you mean 1/(xy^2)

  177. mathmate
    • one year ago
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    Power of a power property: example: (a^2)^3 = a^(2*3) = a^6

  178. pooja195
    • one year ago
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    ^right

  179. mathmate
    • one year ago
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    Simplify (2x^2)^3

  180. mathmate
    • one year ago
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    Hint: Product of powers: (a^x b^y)^z = a^(xz)*b^(yz)

  181. pooja195
    • one year ago
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    8x^6

  182. mathmate
    • one year ago
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    \(\large (a^x b^y)^z = a^{xz}*b^{yz}\)

  183. mathmate
    • one year ago
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    Wow, you're good! Am I too slow?

  184. pooja195
    • one year ago
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    kinda :P

  185. mathmate
    • one year ago
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    please let me know whenever this happens!

  186. mathmate
    • one year ago
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    Now simplify ((-3)^3)^3

  187. pooja195
    • one year ago
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    (−3)^9=−19683

  188. mathmate
    • one year ago
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    That's a calculator answer! I need the answer in exponential form, if possible!

  189. mathmate
    • one year ago
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    (-3)^9 is almost good!

  190. mathmate
    • one year ago
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    I mean it's good, but not simplified enough!

  191. pooja195
    • one year ago
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    o.O i used the calc im allowed to use on the finals .-. this is what i got what more simplifed can it be? o.O

  192. mathmate
    • one year ago
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    you can simplify it as (-3)^9=(-1)^9*3^9 = -3^9

  193. pooja195
    • one year ago
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    -_-

  194. mathmate
    • one year ago
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    That's alright. I am demanding!

  195. pooja195
    • one year ago
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    -_-

  196. mathmate
    • one year ago
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    We have two circles of radii r and 2r. Find the ratio of the area of the big circle to the small circle.

  197. pooja195
    • one year ago
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    i havent learned this

  198. mathmate
    • one year ago
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    Have you learned A=pi r^2 ?

  199. pooja195
    • one year ago
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    We havent done much with that i know that stuff from last year though (formula) idk that nor have we learned it THIS year

  200. mathmate
    • one year ago
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    ok, I'll solve this: A1/A2 = pi (2r)^2 /(pi r^2) =(2r)^2/r^2 =4r^2/r^2 =4

  201. pooja195
    • one year ago
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    hmm ok....

  202. mathmate
    • one year ago
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    Simplify (-5)^4 * (-5)^4

  203. pooja195
    • one year ago
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    in exponetional form?

  204. mathmate
    • one year ago
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    Yep! Pretend you have no calculator!

  205. pooja195
    • one year ago
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    5^8

  206. mathmate
    • one year ago
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    Perfect, you got rid of the negative signs because the final power is even! Very good!!

  207. mathmate
    • one year ago
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    Simplify (5y^2)^3 * (y^3)^2

  208. pooja195
    • one year ago
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    125y^12

  209. mathmate
    • one year ago
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    Excellent, did you calculate 125=5^3 in your head?

  210. pooja195
    • one year ago
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    yes 5*5=25*5=125

  211. mathmate
    • one year ago
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    How about 25*16

  212. pooja195
    • one year ago
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    400 ;-; how many more of these?

  213. mathmate
    • one year ago
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    Just to see if you are used to using your head. My conclusion is that you are! lol

  214. mathmate
    • one year ago
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    25*16 is the same as counting how much money you have when you have 16 quarters.

  215. mathmate
    • one year ago
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    What is (1/2)n^3 when n=-2?

  216. pooja195
    • one year ago
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    -4

  217. mathmate
    • one year ago
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    Good, still too slow?

  218. mathmate
    • one year ago
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    Recall: x^0=1, and x^1=x

  219. mathmate
    • one year ago
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    What is (3pi)^0

  220. pooja195
    • one year ago
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    1

  221. mathmate
    • one year ago
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    Excellent!

  222. mathmate
    • one year ago
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    Rewrite 3x^(-2)/(y^3z^(-1)) with positive exponents!

  223. mathmate
    • one year ago
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    |dw:1433557420958:dw| What is 'a' on the graph (the y-intercept)

  224. pooja195
    • one year ago
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    \[\huge\frac{3z}{x^2y^3}\] We did not learning graphing exponetionall functions

  225. mathmate
    • one year ago
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    Good for the positive exponents, actually, very good! Are you sure about not having done graphics for exponential functions?

  226. mathmate
    • one year ago
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    what about things like solve 4^x=4096

  227. pooja195
    • one year ago
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    x=6

  228. mathmate
    • one year ago
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    Calculator or in your head?

  229. pooja195
    • one year ago
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    -.- paper.

  230. pooja195
    • one year ago
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    pencil

  231. mathmate
    • one year ago
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    Excellent! :)

  232. mathmate
    • one year ago
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    |dw:1433558060131:dw|

  233. pooja195
    • one year ago
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    we havent learned this

  234. mathmate
    • one year ago
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    You see that when a<0, the graph flips about the y-axis.

  235. mathmate
    • one year ago
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    ik, but just a quick overview, please bear with me!

  236. pooja195
    • one year ago
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    no ;-;

  237. mathmate
    • one year ago
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    ok then.

  238. mathmate
    • one year ago
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    Have you done graphing calculator?

  239. pooja195
    • one year ago
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    huh?

  240. mathmate
    • one year ago
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    8.3 is for using the graphing calculator!

  241. mathmate
    • one year ago
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    Does everybody in school have one? Like the Ti-83 or ti-83+

  242. pooja195
    • one year ago
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    yea

  243. mathmate
    • one year ago
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    So you have one too?

  244. pooja195
    • one year ago
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    ye

  245. mathmate
    • one year ago
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    Do you know how to graph on the calculator?

  246. pooja195
    • one year ago
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    no becuse we have never had to

  247. mathmate
    • one year ago
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    That's good! I am not for it either. It doesn't do much.

  248. mathmate
    • one year ago
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    It's much easier to teach students how to use the graphics calculator than graphing with pencil and paper.

  249. mathmate
    • one year ago
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    Guess your teacher does neither! :(

  250. pooja195
    • one year ago
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    we graph with paper n pencil ;;

  251. mathmate
    • one year ago
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    But...you just said you didn't graph exponential functions?

  252. pooja195
    • one year ago
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    Not this im talking about the slope stuff lel this we ahve never done

  253. mathmate
    • one year ago
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    ok, so you graphed straight lines! Still it's very good that the teacher asked you to graph on pencil and paper.

  254. mathmate
    • one year ago
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    ok, "the average weight w (in pounds) of an Atlantic cod can be modelled by w=1.21(1.42)t where t is the age of the fish(in years).

  255. mathmate
    • one year ago
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    Find the ratio of the weight of a 5-year old cod to the weight of a 2-year-old cod.

  256. pooja195
    • one year ago
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    5:2