Question

This function f can be used to represent the relationship between the number of gallons of water remaining, f(m), in a bathtub after m minutes of draining at a constant rate of 16 gallons per minute.

Part A

Complete the equation if W represents the amount of water, in gallons, in the bathtub before draining begins.

Select the options to the empty boxes to correctly complete the equation for the function.

f(m) = _________ ___________ __________

m W 16m 16W + - · ÷

This function f can be used to represent the relationship between the number of gallons of water remaining, f(m), in a bathtub after m minutes of draining at a constant rate of 16 gallons per minute.

Part B

The bathtub is completely drained after 5 minutes. When will f(m) = 0? How many gallons of water were in the bathtub before it started draining?

Select the options to the empty boxes to correctly complete the sentences

f(m) = 0 when _______.

The bathtub started with _______ gallons of water.

m ≥ 0 m ≥ 5 m ≤ 0 m ≤ 5 11 16 21 50 80 90 100

Answer 1

@Vocaloid

Answer 2

^That is how you tag someone

Answer 3

so the general format for a linear equation can be:

f(independent variable) = (rate of change)(independent variable) + initial value *** write this down somewhere where you'll remember it

Answer 4

our independent variable is m, and the rate of change is -16, and the initial value is W

substitute these into the equation I gave you and tell me what you get

Answer 5

m + w = -16

Answer 6

write this down

f(independent variable) = (rate of change)(independent variable) + initial value

replace "independent variable" with m
"rate of change" with -16
"initial value" with W

Answer 7

f(m) = -16(m) + W

Answer 8

good, or we can rewrite this as
f(m) = W - 16m

^ answer for part A

Answer 9

what about the second question ?

Answer 10

@Vocaloid

Answer 11

when the bathtub is drained f(m) = 0
m = 5 minutes

solve for W

f(m) = W - 16m

Answer 12

w = fm + 16m

Answer 13

ok, now substitute f(m) = 0 and m = 5

Answer 14

W = f(m) + 16m = ?

Answer 15

w = fm + 16m

Answer 16

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
ok, now substitute f(m) = 0 and m = 5
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 17

take these numbers and substitute them into the equation

please do not just repeat the same function again

Answer 18

5

Answer 19

f(m) = 0 and m = 5

this means you can take "0" and write "0" wherever f(m) shows up
this means you can take "5" and write "5" wherever m shows up

Answer 20

^ now use this logic to find:

W = f(m) + 16m

Answer 21

f(0) = and 5 = m

w = fm + 16m

Answer 22

Take this equation

W = f(m) + 16m

replace "f(m)" with 0
replace "m" with 5

then tell me what W equals.

Answer 23

w = 5

Answer 24

try one more time.

Answer 25

W = 0 + 165 right ?

Answer 26

w = 165

Answer 27

sorry made a typo

Answer 28

W = f(m) + 16m

when you see a number and a letter/variable together, it implies multiplication

Answer 29

so W = f(m) + 16*m

Answer 30

try solving it again

Answer 31

w = fm + 16m

Answer 32

@Vocaloid

Answer 33

please use the substitutions I have given you.

Answer 34

we have already stated that f(m) = 0 and m = 5

solve for W. W = f(m) + 16*m

Answer 35

replace m with 0 ?

Answer 36

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
we have already stated that f(m) = 0 and m = 5

solve for W. W = f(m) + 16*m
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 37

please read carefully.

Answer 38

w = fm + 16m

Answer 39

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
f(m) = 0 and m = 5

this means you can take "0" and write "0" wherever f(m) shows up
this means you can take "5" and write "5" wherever m shows up
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 40

^ using this information, calculate: W = f(m) + 16*m

please do ~NOT~ just repeat the same function again. Use this information to plug in for m and f(m)

Answer 41

W = f(0) + 165

w = 165

Answer 42

you're forgetting the multiplication

Answer 43

W = f(m) + 16*m


16*m means multiply 16 and m.

Answer 44

w=fm+16mx

Answer 45

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
f(m) = 0 and m = 5

this means you can take "0" and write "0" wherever f(m) shows up
this means you can take "5" and write "5" wherever m shows up
\(\color{#0cbb34}{\text{End of Quote}}\)
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 46

take this function

W = f(m) + 16*m

substitute for f(m) and m

then solve.

Answer 47

remember, * means multiply

Answer 48

= 0

Answer 49

try one more time.
remember:

f(m) = 0
m = 5

what is f(m) + 16*m?

Answer 50

16m

Answer 51

ok, but what is 16*m if m = 5?

Answer 52

80

Answer 53

good so your first blank is m ≥ 5 and your second blank is 80

I'll get back to you later, I really need a break.