help

- anonymous

help

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- 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

- anonymous

@amistre64 @phi

- 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?

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## More answers

- anonymous

like the slope?

- phi

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

- anonymous

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

- 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 ?

- anonymous

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

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

- anonymous

ok

- phi

is that enough to answer the question ?

- anonymous

idk im not sure what to do next

- phi

look at your choices

- anonymous

so do i plug in 3 for plants

- phi

you can do that. what do you get ?

- anonymous

1.2 so its B because 2/5 = .4

- anonymous

am i right?

- 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

- anonymous

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

- 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)

- anonymous

oh okay

- phi

one more

- 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

- phi

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

- anonymous

y = hour and the tip is x?

- 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)

- anonymous

so i was wrong

- 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)

- phi

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

- anonymous

im not sure this one is really confusing

- 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

- phi

y will be the earnings

- phi

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

- anonymous

60$

- phi

and if you write it as an equation
y= 60

- phi

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

- anonymous

y = 5.25x + 60

- phi

pretty close.
even better.
and yes, bingo!

- anonymous

lol

- phi

now use x=4 to find how much she made

- anonymous

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

- anonymous

so its C

- phi

yes

- anonymous

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

- phi

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

- 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

- phi

yes

- 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

- phi

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

- anonymous

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

- 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)

- 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.

- anonymous

so the function f(x) has a large slope

- 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)

- phi

yes, 10 is bigger than 9

- anonymous

okay thnx

- phi

yw

- 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.

- anonymous

##### 1 Attachment

- phi

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

- 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*

- anonymous

now i think its D

- phi

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

- anonymous

ok

- phi

but no guarantees on that one.

- anonymous

ill check with someone else later but thnx

- 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

- phi

any thoughts?

- anonymous

the slope

- anonymous

so D

- phi

yes

- anonymous

thnx i got only 2 more

- 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

- anonymous

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

- phi

it might not be a line with this one.

- anonymous

oh ok

- 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

- anonymous

true

- phi

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

- anonymous

idk how to do that

- phi

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

- phi

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

- anonymous

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

- anonymous

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

- anonymous

r = 40? so A

- anonymous

@Nnesha

- phi

yes

- anonymous

i got one more plz

- 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.

- anonymous

##### 1 Attachment

- 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)

- anonymous

okay ill ask someone else thnx

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