mikewwe13:

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

8 months ago
Ultrilliam:

@Vocaloid

8 months ago
Ultrilliam:

^That is how you tag someone

8 months ago
Vocaloid:

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

8 months ago
Vocaloid:

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

8 months ago
mikewwe13:

m + w = -16

8 months ago
Vocaloid:

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

8 months ago
mikewwe13:

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

8 months ago
Vocaloid:

good, or we can rewrite this as f(m) = W - 16m ^ answer for part A

8 months ago
mikewwe13:

what about the second question ?

8 months ago
mikewwe13:

@Vocaloid

8 months ago
Vocaloid:

when the bathtub is drained f(m) = 0 m = 5 minutes solve for W f(m) = W - 16m

8 months ago
mikewwe13:

w = fm + 16m

8 months ago
Vocaloid:

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

8 months ago
Vocaloid:

W = f(m) + 16m = ?

8 months ago
mikewwe13:

w = fm + 16m

8 months ago
Vocaloid:

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

8 months ago
Vocaloid:

take these numbers and substitute them into the equation please do not just repeat the same function again

8 months ago
mikewwe13:

5

8 months ago
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

8 months ago
Vocaloid:

^ now use this logic to find: W = f(m) + 16m

8 months ago
mikewwe13:

f(0) = and 5 = m w = fm + 16m

8 months ago
Vocaloid:

Take this equation W = f(m) + 16m replace "f(m)" with 0 replace "m" with 5 then tell me what W equals.

8 months ago
mikewwe13:

w = 5

8 months ago
Vocaloid:

try one more time.

8 months ago
mikewwe13:

W = 0 + 165 right ?

8 months ago
mikewwe13:

w = 165

8 months ago
Vocaloid:

sorry made a typo

8 months ago
Vocaloid:

W = f(m) + 16m when you see a number and a letter/variable together, it implies multiplication

8 months ago
Vocaloid:

so W = f(m) + 16*m

8 months ago
Vocaloid:

try solving it again

8 months ago
mikewwe13:

w = fm + 16m

8 months ago
mikewwe13:

@Vocaloid

8 months ago
Vocaloid:

please use the substitutions I have given you.

8 months ago
Vocaloid:

we have already stated that f(m) = 0 and m = 5 solve for W. W = f(m) + 16*m

8 months ago
mikewwe13:

replace m with 0 ?

8 months ago
Vocaloid:

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid we have already stated that f(m) = 0 and m = 5 solve for W. W = f(m) + 16*m \(\color{#0cbb34}{\text{End of Quote}}\)

8 months ago
Vocaloid:

please read carefully.

8 months ago
mikewwe13:

w = fm + 16m

8 months ago
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 \(\color{#0cbb34}{\text{End of Quote}}\)

8 months ago
Vocaloid:

^ 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)

8 months ago
mikewwe13:

W = f(0) + 165 w = 165

8 months ago
Vocaloid:

you're forgetting the multiplication

8 months ago
Vocaloid:

W = f(m) + 16*m 16*m means multiply 16 and m.

8 months ago
mikewwe13:

w=fm+16mx

8 months ago
Vocaloid:

\(\color{#0cbb34}{\text{Originally Posted by}}\) @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 \(\color{#0cbb34}{\text{End of Quote}}\) \(\color{#0cbb34}{\text{End of Quote}}\)

8 months ago
Vocaloid:

take this function W = f(m) + 16*m substitute for f(m) and m then solve.

8 months ago
Vocaloid:

remember, * means multiply

8 months ago
mikewwe13:

= 0

8 months ago
Vocaloid:

try one more time. remember: f(m) = 0 m = 5 what is f(m) + 16*m?

8 months ago
mikewwe13:

16m

8 months ago
Vocaloid:

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

8 months ago
mikewwe13:

80

8 months ago
Vocaloid:

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.

8 months ago