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  1. anonymous
    • one year ago
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    The number of fish (F) in a fish tank increases when the number of plants (P) increases. Write the correct equation for this scenario, and solve for the number of fish when the number of plants is 3. Plants Fish 15 6 20 8 F = P; F = 3 F = .4P; F = 1.2 F = 90 over P; F = 30 F = 90 over P; F = 270

  2. anonymous
    • one year ago
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    @amistre64 @phi

  3. phi
    • one year ago
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    you could think of Plants as x and Fish as y then you have the two points (15,6) and (20,8) do you know how to find the equation of a line through 2 points?

  4. anonymous
    • one year ago
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    like the slope?

  5. phi
    • one year ago
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    the first step is find the slope which is change in y divided by change in x

  6. anonymous
    • one year ago
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    \[\frac{ 8 - 6 }{ 20 -15 } = \frac{ 2 }{ 5 } \]

  7. phi
    • one year ago
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    yes. now write down the equation y = m x + b you found m is 2/5 so you know \[ y = \frac{2}{5} x + b \] replace y and x with the values from one of the points for example, use (15,6) i.e. let x=15 and y=6 then find b can you do that ?

  8. anonymous
    • one year ago
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    yup. \[6 = \frac{ 2 }{ 5 }(15) + b\] then \[6 = 6 + b \] to get \[0=b\] so \[b = 0\]

  9. phi
    • one year ago
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    yes, so the equation becomes \[ y = \frac{2}{5} x \] (adding b=0 is not necessary) or, renaming x and y back to plants and fishes i.e. use P and F: \[ F= \frac{2}{5} P\]

  10. anonymous
    • one year ago
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    ok

  11. phi
    • one year ago
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    is that enough to answer the question ?

  12. anonymous
    • one year ago
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    idk im not sure what to do next

  13. phi
    • one year ago
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    look at your choices

  14. anonymous
    • one year ago
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    so do i plug in 3 for plants

  15. phi
    • one year ago
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    you can do that. what do you get ?

  16. anonymous
    • one year ago
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    1.2 so its B because 2/5 = .4

  17. anonymous
    • one year ago
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    am i right?

  18. phi
    • one year ago
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    yes, and notice that 2/5 is the same a 0.4 so we could write the equation as y = 0.4 x or F= 0.4 P

  19. anonymous
    • one year ago
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    thnk you so much i have more can you help w/?

  20. phi
    • one year ago
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    notice that once you realize that 2/5 is 0.4 then F= 0.4 P means only choice B works. (all the other choices have the wrong equation)

  21. anonymous
    • one year ago
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    oh okay

  22. phi
    • one year ago
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    one more

  23. anonymous
    • one year ago
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    Rae earns $60 for playing music on Saturday nights at the local coffee house. She makes an average of $5.25 in tips per hour. Write the function of Rae's earnings, and solve for how much she would make after 4 hours. y = 5.25x + 60; $65.25 y = 60x + 5.25; $85.75 y = 5.25x + 60; $81.00 y = 60x + 5.25; $185.25

  24. phi
    • one year ago
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    any thought on what x and y represent in this problem ?

  25. anonymous
    • one year ago
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    y = hour and the tip is x?

  26. phi
    • one year ago
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    look at this sentence: how much she would make after 4 hours ? what do they want us to calculate? I would say "how much she makes" i.e. earnings. what do we "use" to figure out the earnings? the number of hours so you should think y (I want to know this ) equals stuff with an x (put in x and do some arithmetic)

  27. anonymous
    • one year ago
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    so i was wrong

  28. phi
    • one year ago
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    next, what in the problem goes with "number of hours". we read this $5.25 in tips per hour. that means to figure out how much in tips we need to know how many hours she worked (she get 5.25 for each hour)

  29. phi
    • one year ago
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    ok, can you write what you think y and x stand for ?

  30. anonymous
    • one year ago
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    im not sure this one is really confusing

  31. phi
    • one year ago
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    we want to write down an equation that lets us calculate how much she made we would write y = something and y is what we are trying to calculate

  32. phi
    • one year ago
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    y will be the earnings

  33. phi
    • one year ago
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    if she got no tips, how much are her earnings? Based on what they tell you.

  34. anonymous
    • one year ago
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    60$

  35. phi
    • one year ago
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    and if you write it as an equation y= 60

  36. phi
    • one year ago
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    now add in how much she makes in tips. can you do that ?

  37. anonymous
    • one year ago
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    y = 5.25x + 60

  38. phi
    • one year ago
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    pretty close. even better. and yes, bingo!

  39. anonymous
    • one year ago
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    lol

  40. phi
    • one year ago
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    now use x=4 to find how much she made

  41. anonymous
    • one year ago
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    y = 5.25(4) + 60 so y = 21 + 60 equals y = 81

  42. anonymous
    • one year ago
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    so its C

  43. phi
    • one year ago
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    yes

  44. anonymous
    • one year ago
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    What is the slope of the line that passes through (2, 5) and (−1, 5)? −3 0 <-- my choice Undefined 3

  45. phi
    • one year ago
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    yes (5-5)/(-1-2) = 0/(-3) = 0

  46. anonymous
    • one year ago
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    The function for the cost of materials to make a muffin is f(x) = Three fourths x + 3, where x is the number of muffins. The function for the selling price of those muffins is g(f(x)), where g(x) = 3x + 4. Find the selling price of 20 muffins. 18 49 51 58 <--- my choice

  47. phi
    • one year ago
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    yes

  48. anonymous
    • one year ago
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    Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x) Dawn writes 800 pages in 80 days. x g(x) 2 −6 4 12 6 30 The function f(x) has a larger slope. The function g(x) has a larger slope. They both have the same slope. The relationship between slopes cannot be determined. idk this one

  49. phi
    • one year ago
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    can you find the slope for g(x) (think of g(x) as "y") ?

  50. anonymous
    • one year ago
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    \[\frac{ 30 - 12 }{ 6 -4 } = \frac{ 18 }{ 2 } = 9\]

  51. phi
    • one year ago
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    and if we want to be sure, check another (x,y) pair (in case they are being tricky) (12- -6) / (4-2) = 18/2 = 9 good , we get the same slope (which means g(x) is a straight line)

  52. phi
    • one year ago
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    the 800 pages in 80 days means 800/80 = 10 pages per day when you see a "rate" (or the "per" word) , you can think of that as a slope.

  53. anonymous
    • one year ago
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    so the function f(x) has a large slope

  54. phi
    • one year ago
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    for example, if you remember the "tip" problem, you were told 5.25 per hour (the per was a clue that the 5.25 is a slope that multiplies x)

  55. phi
    • one year ago
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    yes, 10 is bigger than 9

  56. anonymous
    • one year ago
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    okay thnx

  57. phi
    • one year ago
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    yw

  58. anonymous
    • one year ago
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    Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x) = 2x + 3 The function g(x) going through 1 on the x axis and 1, 4 The function f(x) has a larger slope. <--- my choice The function g(x) has a larger slope. They both have the same slope. The relationship between slopes cannot be determined.

  59. anonymous
    • one year ago
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  60. phi
    • one year ago
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    what is the change in y divided by change in x for g(x) ?

  61. phi
    • one year ago
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    notice the change in x is 0 and we get change in y divided by 0 which technically is not defined, but we can think of as approaching infinity I hope they are not being tricky... but I would say the slope of g(x) is *very large*

  62. anonymous
    • one year ago
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    now i think its D

  63. phi
    • one year ago
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    it might be, but I would go with with g(x) slope is larger than f(x)

  64. anonymous
    • one year ago
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    ok

  65. phi
    • one year ago
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    but no guarantees on that one.

  66. anonymous
    • one year ago
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    ill check with someone else later but thnx

  67. anonymous
    • one year ago
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    jorge was tracking the decreasing temperature in the morning. At 7 a.m., it was 65 degrees Fahrenheit. At 9 a.m., it was 55 degrees Fahrenheit. If Jorge made the function f(x) = −5x + 100, what would the −5 represent? The temperature at midnight The length of time he recorded for The total change in degrees The rate at which the temperature was decreasing

  68. phi
    • one year ago
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    any thoughts?

  69. anonymous
    • one year ago
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    the slope

  70. anonymous
    • one year ago
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    so D

  71. phi
    • one year ago
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    yes

  72. anonymous
    • one year ago
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    thnx i got only 2 more

  73. anonymous
    • one year ago
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    The number of roses (r) in a garden increases when the number of weeds (w) decreases. Write the correct equation for this scenario, and solve for the number of roses when there are 5 weeds. Weeds Roses 10 20 20 10 r = 200 over w; r = 40 r = 200 over w; r = 1000 r = 2w; r = 10 r = 2w; r = 2.5

  74. anonymous
    • one year ago
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    this is similar to the one with the plants and it was like.4

  75. phi
    • one year ago
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    it might not be a line with this one.

  76. anonymous
    • one year ago
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    oh ok

  77. phi
    • one year ago
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    if we assume a straight line through the two points (10,20) and (20,10) we get y= -x +30 or r = - w + 30 and none of your choices have that equation

  78. anonymous
    • one year ago
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    true

  79. phi
    • one year ago
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    but it sounds like "inverse variation" in other words \[ y = \frac{k}{x} \]

  80. anonymous
    • one year ago
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    idk how to do that

  81. phi
    • one year ago
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    use an (x,y) pair to "solve for k" or in this case \[ r = \frac{k}{w} \] use a (w,r) pair

  82. phi
    • one year ago
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    in other words, use (20,10) i.e. w=20, r=10 in that equation and simplify to find k

  83. anonymous
    • one year ago
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    \[10 = \frac{ k }{ 20 } \] \[20 * 10 = k \] \[k = 200\]

  84. anonymous
    • one year ago
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    \[r = \frac{ 200 }{ w }\]

  85. anonymous
    • one year ago
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    r = 40? so A

  86. anonymous
    • one year ago
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    @Nnesha

  87. phi
    • one year ago
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    yes

  88. anonymous
    • one year ago
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    i got one more plz

  89. anonymous
    • one year ago
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    Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts? graph going through 3, 2 and 3, 4 x g(x) 2 1 4 3 6 5 The function f(x) has a higher y-intercept. The function g(x) has a higher y-intercept. They both have the same y-intercept. The relationship between y-intercepts cannot be determined.

  90. anonymous
    • one year ago
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  91. phi
    • one year ago
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    f(x) is a vertical line and does not have a y-intercept. so cannot be determined. (maybe you should choose cannot be determined for the other question about a vertical line)

  92. anonymous
    • one year ago
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    okay ill ask someone else thnx

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