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Salsk061 [2.6K]
3 years ago
10

Solve the system of linear equations by substitution x+4y =37 y = -x + 16

Mathematics
1 answer:
pantera1 [17]3 years ago
4 0
You plug -x+16 in for y in x+4y=37 to get x after you multiply x+4y=37 by -1.
-x-4(-x+16)=-37
-x+4x-64=-37
3x-64=-37
3x=27
x=9
Then you plug 9 into either equation to get y.
y=-x+16
y=-(9)+16
y=7

x=9 and y=7
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3 years ago
sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project
alukav5142 [94]

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min

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3 years ago
In 2018, the population will grow over 700,000.The population of a city in 2010 was 450,000 and was growing at a rate of 5% per
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The year is 2020.

Step-by-step explanation:

Let the number of years passed since 2010 to reach population more than 7000000 be 'x'.

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A population growth is an exponential growth and is modeled by the following function:

P=P_0(1+r)^x

Taking log on both sides, we get:

\log(P)=\log(P_0(1+r)^x)\\\log P=\log P_0+x\log (1+r)\\x\log (1+r)=\log P-\log P_0\\x\log(1+r)=\log(\frac{P}{P_0})\\x=\frac{\log(\frac{P}{P_0})}{\log(1+r)}

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x=\frac{\log(\frac{700,000}{450,000})}{\log(1+0.05)}\\x=\frac{0.192}{0.021}=9.13\approx 10

So, for x > 9.13, the population is over 700,000. Therefore, from the tenth year after 2010, the population will be over 700,000.

Therefore, the tenth year after 2010 is 2020.

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