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KaylaClemens15

  • 3 years ago

1.A local bank has a debit card that gives a $3 reward each month you use your card for $50 or more in purchaces. Write an equation relating rewards earned,y, to total monthly purchaces, x. Give the domain of this function. 2. A local credit union has a debit card that rewards 3% of your total monthly purchases. Write an equation relating rewards earned,y, to total monthly purchases, x. Give domain of this function.

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  1. anonymous
    • 3 years ago
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    the second one is easiest i think you get 3% of your monthly purchases, so if you call your monthly purchases \(x\) then you get \(y=0.03x\)

  2. anonymous
    • 3 years ago
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    it has no lower limit, so i would say the domain is \((0,\infty)\) or "positive numbers"

  3. KaylaClemens15
    • 3 years ago
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    Honestly, any input would be appreciated. I'm totally clueless!

  4. anonymous
    • 3 years ago
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    this is not quite accurate, since you cannot spend say \(\pi\) dollars so maybe the domain is positive integers

  5. anonymous
    • 3 years ago
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    how fancy is this math class?

  6. anonymous
    • 3 years ago
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    maybe you can get away with saying "positive numbers"

  7. KaylaClemens15
    • 3 years ago
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    It's just Algebra 1

  8. anonymous
    • 3 years ago
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    okay so you probably don't have to be so picky for the second one you can use \(y=0.03x\) and say the domain is positive numbers

  9. anonymous
    • 3 years ago
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    for the first one, it is really \[y= \left\{\begin{array}{rcc} 0 & \text{if} & x <50\\ 3& \text{if} & x \geq50 \end{array} \right. \]

  10. anonymous
    • 3 years ago
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    but that might be too fancy as well, so maybe you can just say \(y=3\) if \(x\geq50\) or maybe even just say \(y=3\) and the domain is \(x\geq 50\)

  11. KaylaClemens15
    • 3 years ago
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    Okay, thank you so much!! I've been stuck on math problems all night. I still have 3 more to go :(

  12. anonymous
    • 3 years ago
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    are they hard?

  13. anonymous
    • 3 years ago
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    go ahead and post, i will look, or just ask here

  14. KaylaClemens15
    • 3 years ago
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    I'll type it here, if that's alright

  15. anonymous
    • 3 years ago
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    go ahead, i will answer if i can

  16. KaylaClemens15
    • 3 years ago
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    1. Abigail orders a large 2 topping pizza for $14 and a medium 1 topping pizza for $10. If all coats of a medium pizza are 80% of a similar large pizza, find rhe price of a large plain cheese and the cost of each large pizza topping.

  17. KaylaClemens15
    • 3 years ago
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    costs*

  18. anonymous
    • 3 years ago
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    whoa this is going to take a second not too long though

  19. KaylaClemens15
    • 3 years ago
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    You don't have to do it if you don't want to! I understand.

  20. anonymous
    • 3 years ago
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    oh no we can definitely do this for sure

  21. KaylaClemens15
    • 3 years ago
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    Alrighty, thank you so much.

  22. anonymous
    • 3 years ago
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    we can call the price of the topping \(y\) and the price of the large plain pizza \(x\) so the price of the medium plain pizza is \(0.8x\)

  23. KaylaClemens15
    • 3 years ago
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    Okay

  24. anonymous
    • 3 years ago
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    then the first part tells you \[x+2y=14\] and the second part say \[.8x+y=10\]

  25. KaylaClemens15
    • 3 years ago
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    Right

  26. anonymous
    • 3 years ago
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    now before we solve this, i can make a good guess, which is that \(x=10\) and \(y=2\)

  27. anonymous
    • 3 years ago
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    because \(10+2\times 2=14\) and \(0.8x\times 10+2=8+2=10\)

  28. anonymous
    • 3 years ago
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    i am assuming of course that the toppings for the large and small pizza are the same if they are not the same you cannot solve the problem

  29. KaylaClemens15
    • 3 years ago
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    Yeah

  30. anonymous
    • 3 years ago
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    in any case to solve \[x+2y=14\]\[.8x+y=10\] multiply the second equation by -2 and add you get \[x+2y=14\] \[-1.6x-2y=-20\] \[-.6x=-6\] \[x=-6\div -.6=60\div 6=10\]

  31. anonymous
    • 3 years ago
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    so it is right large pizza is $10, medium is $8, toppings are $2

  32. anonymous
    • 3 years ago
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    so far so good?

  33. KaylaClemens15
    • 3 years ago
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    Thank you so much! You make the problems seem so much easier. I might actually get some sleep tonight for school tomorrow!

  34. anonymous
    • 3 years ago
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    yw any more or are you done?

  35. KaylaClemens15
    • 3 years ago
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    I have one more.

  36. KaylaClemens15
    • 3 years ago
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    It's the hardest one

  37. anonymous
    • 3 years ago
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    k

  38. anonymous
    • 3 years ago
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    ready?

  39. KaylaClemens15
    • 3 years ago
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    Nathan wants to go to a hockey game with friends. Tickets are $18, but students can get discounted tickets for $12. They want to spend no more than $80, including $8 for parking. The vehicle they will take can only hold 7 people. Write and graph (it's a regualr coordinate graph) a system of foir inequalities modeling their possible ticket purchases. Let x= number of student tickets and y= number of regular tickets

  40. anonymous
    • 3 years ago
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    one thing we know is that \(x+y\leq 7\)

  41. anonymous
    • 3 years ago
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    because at most 7 people can go

  42. anonymous
    • 3 years ago
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    we also know that they are going to pay $8 for parking, leaving \(80-8=\$72\) for tickets and so \(12x+18y\leq 72\)

  43. anonymous
    • 3 years ago
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    i think the other two inequalities are the easy ones, both \(x\geq 0\) and \(y\geq 0\) which just means you are in quadrant 1

  44. anonymous
    • 3 years ago
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    can you graph \(x+y=7\)?

  45. KaylaClemens15
    • 3 years ago
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    Uh, no :/

  46. anonymous
    • 3 years ago
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    |dw:1363921714846:dw|

  47. anonymous
    • 3 years ago
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    if \(x=0\) you get \(y=7\) so \((0,7)\) is on the graph, and similarly \((7,0)\) is on the graph plot the points, connect the dots

  48. anonymous
    • 3 years ago
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    you got it from the picture?

  49. KaylaClemens15
    • 3 years ago
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    I can't see your drawing because I'm on my phone, I can't access a computer.

  50. KaylaClemens15
    • 3 years ago
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    I know how to graph points, so I should be fine

  51. anonymous
    • 3 years ago
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    ooh ok

  52. KaylaClemens15
    • 3 years ago
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    Whatt do I do next?

  53. anonymous
    • 3 years ago
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    the line \(12x+18y=72\) contains the points \((0,4)\) and \((6,0)\) so plot those points as well and connect the dots

  54. anonymous
    • 3 years ago
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    then shade everything in quadrant 1, and below those two lines

  55. anonymous
    • 3 years ago
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    i obviously cannot draw it here for you to see, but that is what you have to do

  56. KaylaClemens15
    • 3 years ago
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    Yes, I understand

  57. anonymous
    • 3 years ago
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    then i guess you are done any point that is shaded in the picture is possible

  58. KaylaClemens15
    • 3 years ago
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    Ok, sweet. Thank you very much for all your time and help. Have a nice night! :)

  59. anonymous
    • 3 years ago
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    you too

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