Question

help

Answer 1

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

Answer 2

@amistre64 @phi

Answer 3

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?

Answer 4

like the slope?

Answer 5

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

Answer 6

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

Answer 7

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 ?

Answer 8

yup.

\[6 = \frac{ 2 }{ 5 }(15) + b\] then \[6 = 6 + b \] to get \[0=b\] so \[b = 0\]

Answer 9

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:
\[ F= \frac{2}{5} P\]

Answer 10

ok

Answer 11

is that enough to answer the question ?

Answer 12

idk im not sure what to do next

Answer 13

look at your choices

Answer 14

so do i plug in 3 for plants

Answer 15

you can do that. what do you get ?

Answer 16

1.2 so its B because 2/5 = .4

Answer 17

am i right?

Answer 18

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

Answer 19

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

Answer 20

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)

Answer 21

oh okay

Answer 22

one more

Answer 23

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

Answer 24

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

Answer 25

y = hour and the tip is x?

Answer 26

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)

Answer 27

so i was wrong

Answer 28

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)

Answer 29

ok, can you write what you think y and x stand for ?

Answer 30

im not sure this one is really confusing

Answer 31

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

Answer 32

y will be the earnings

Answer 33

if she got no tips, how much are her earnings? Based on what they tell you.

Answer 34

60$

Answer 35

and if you write it as an equation
y= 60

Answer 36

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

Answer 37

y = 5.25x + 60

Answer 38

pretty close.
even better.

and yes, bingo!

Answer 39

lol

Answer 40

now use x=4 to find how much she made

Answer 41

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

Answer 42

so its C

Answer 43

yes

Answer 44

What is the slope of the line that passes through (2, 5) and (−1, 5)?

−3
0 <-- my choice
Undefined
3

Answer 45

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

Answer 46

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

Answer 47

yes

Answer 48

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

Answer 49

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

Answer 50

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

Answer 51

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)

Answer 52

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.

Answer 53

so the function f(x) has a large slope

Answer 54

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)

Answer 55

yes, 10 is bigger than 9

Answer 56

okay thnx

Answer 57

yw

Answer 58

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.

Answer 59

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

Answer 60

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*

Answer 61

now i think its D

Answer 62

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

Answer 63

ok

Answer 64

but no guarantees on that one.

Answer 65

ill check with someone else later but thnx

Answer 66

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

Answer 67

any thoughts?

Answer 68

the slope

Answer 69

so D

Answer 70

yes

Answer 71

thnx i got only 2 more

Answer 72

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

Answer 73

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

Answer 74

it might not be a line with this one.

Answer 75

oh ok

Answer 76

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

Answer 77

true

Answer 78

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

Answer 79

idk how to do that

Answer 80

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

Answer 81

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

Answer 82

\[10 = \frac{ k }{ 20 } \] \[20 * 10 = k \] \[k = 200\]

Answer 83

\[r = \frac{ 200 }{ w }\]

Answer 84

r = 40? so A

Answer 85

@Nnesha

Answer 86

yes

Answer 87

i got one more plz

Answer 88

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.

Answer 89

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)

Answer 90

okay ill ask someone else thnx