## anonymous one year ago help

1. anonymous

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

@amistre64 @phi

3. phi

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

like the slope?

5. phi

the first step is find the slope which is change in y divided by change in x

6. anonymous

$\frac{ 8 - 6 }{ 20 -15 } = \frac{ 2 }{ 5 }$

7. phi

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

yup. $6 = \frac{ 2 }{ 5 }(15) + b$ then $6 = 6 + b$ to get $0=b$ so $b = 0$

9. phi

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

ok

11. phi

is that enough to answer the question ?

12. anonymous

idk im not sure what to do next

13. phi

14. anonymous

so do i plug in 3 for plants

15. phi

you can do that. what do you get ?

16. anonymous

1.2 so its B because 2/5 = .4

17. anonymous

am i right?

18. phi

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

thnk you so much i have more can you help w/?

20. phi

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

oh okay

22. phi

one more

23. anonymous

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

any thought on what x and y represent in this problem ?

25. anonymous

y = hour and the tip is x?

26. phi

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

so i was wrong

28. phi

next, what in the problem goes with "number of hours". we read this $5.25 in tips per hour. that means to figure out how much in tips we need to know how many hours she worked (she get 5.25 for each hour) 29. phi ok, can you write what you think y and x stand for ? 30. anonymous im not sure this one is really confusing 31. phi we want to write down an equation that lets us calculate how much she made we would write y = something and y is what we are trying to calculate 32. phi y will be the earnings 33. phi if she got no tips, how much are her earnings? Based on what they tell you. 34. anonymous 60$

35. phi

and if you write it as an equation y= 60

36. phi

now add in how much she makes in tips. can you do that ?

37. anonymous

y = 5.25x + 60

38. phi

pretty close. even better. and yes, bingo!

39. anonymous

lol

40. phi

now use x=4 to find how much she made

41. anonymous

y = 5.25(4) + 60 so y = 21 + 60 equals y = 81

42. anonymous

so its C

43. phi

yes

44. anonymous

What is the slope of the line that passes through (2, 5) and (−1, 5)? −3 0 <-- my choice Undefined 3

45. phi

yes (5-5)/(-1-2) = 0/(-3) = 0

46. anonymous

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

yes

48. anonymous

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

can you find the slope for g(x) (think of g(x) as "y") ?

50. anonymous

$\frac{ 30 - 12 }{ 6 -4 } = \frac{ 18 }{ 2 } = 9$

51. phi

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

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

so the function f(x) has a large slope

54. phi

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

yes, 10 is bigger than 9

56. anonymous

okay thnx

57. phi

yw

58. anonymous

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

60. phi

what is the change in y divided by change in x for g(x) ?

61. phi

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

now i think its D

63. phi

it might be, but I would go with with g(x) slope is larger than f(x)

64. anonymous

ok

65. phi

but no guarantees on that one.

66. anonymous

ill check with someone else later but thnx

67. anonymous

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

any thoughts?

69. anonymous

the slope

70. anonymous

so D

71. phi

yes

72. anonymous

thnx i got only 2 more

73. anonymous

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

this is similar to the one with the plants and it was like.4

75. phi

it might not be a line with this one.

76. anonymous

oh ok

77. phi

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

true

79. phi

but it sounds like "inverse variation" in other words $y = \frac{k}{x}$

80. anonymous

idk how to do that

81. phi

use an (x,y) pair to "solve for k" or in this case $r = \frac{k}{w}$ use a (w,r) pair

82. phi

in other words, use (20,10) i.e. w=20, r=10 in that equation and simplify to find k

83. anonymous

$10 = \frac{ k }{ 20 }$ $20 * 10 = k$ $k = 200$

84. anonymous

$r = \frac{ 200 }{ w }$

85. anonymous

r = 40? so A

86. anonymous

@Nnesha

87. phi

yes

88. anonymous

i got one more plz

89. anonymous

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

91. phi

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

okay ill ask someone else thnx