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RUDIKE [14]
2 years ago
8

Find the x- and y-intercepts of the graph of the linear equation −4x+8y=−16.

Mathematics
1 answer:
Bogdan [553]2 years ago
8 0
Put it in slope form: y=mx+b
8y= 4x-16
Divide by 8
Y = 1/2x -2
1/2 is x intercept and -2 is y intercept
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A tank contains 100 gal of brine made by dissolving 80 Ib of salt in water. Pure water runs into the tank at the rate of 4 gal/m
ohaa [14]

Answer:

Step-by-step explanation:

Amount of brine = 100 gal

amount of salt = 80 lb

rate of water running = 4 gal / min

Let A be the amount of salt in lb in the tank at any time t.

(a) dA/dt = rate of salt in - rate of salt out

Rate of salt in = 0

rate of salt out = A x 4 / 100 = A / 25 lb/min

So, dA/dt = 0 - A/25 = - A/25 lb/min

\frac{dA}{A}=-\frac{1}{25}dt

\int \frac{dA}{A}=-\frac{1}{25}\int dt

A(t) = C e^{-0.04t}

When t = 0, A = 80 lb

So,

A(t) = 80 e^{-0.04t}

(b) Now, A = 40 lb

So,

40 = 80 e^{-0.04t}

0.5 = e^{-0.04t}

take log on both the sides

ln 0.5 = - 0.04 t

t = 17.3 minutes

8 0
3 years ago
3 consecutive even integers whose sum is 54
Andre45 [30]
N+n+2+n+4=54

3n+6=54

3n=48

n=16

16, 18, 20
4 0
3 years ago
Read 2 more answers
Mr.Fields ordered 3 tons of gravel for a drive way at a factory.how many pounds of gravel did he order?
soldi70 [24.7K]
Mr.Fields would have 6,000 pounds

4 0
3 years ago
If your starting salary is $40,000 and you  receive a 4.2% raise every year, how much  TOTAL money will you make in 15 years?
Oliga [24]
The first year, the amount is 40,000

the second year is 40000 + 4.2% of 40000, or 0.042 * 4000, so 40000+(0.042*4000)
common factoring that  we get 40000(1 + 0.042), or just 40000(1.042)

in short, the starting amount is 40000, and to get the next term's value you'd use the "common ratio" of 1.042, namely the multiplier of 1.042.

for the third year it'll be 40000(1.042) + (0.042 *40000(1.042) ), again, common factoring that

40000(1.042)(1 + 0.042) or 40000(1.042)(1.042) or 40000(1.042)²

therefore,

\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=40000\\
r=1.042\\
n=15
\end{cases}
\\\\\\
S_{15}=40000\left( \cfrac{1-1.042^{15}}{1-1.042} \right)\implies S_{15}\approx 40000\left( \cfrac{-0.8536}{-0.042} \right)
\\\\\\
S_{15}\approx 812951.42
5 0
3 years ago
Help me with this text please
saw5 [17]
I think the boxes must be filled with
1/3 and -1/5.
3 0
3 years ago
Read 2 more answers
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