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3 years ago

Factor x^4+xy^3+x^3+y^3 completely showing work.

Mathematics

1 answer:

babymother [125]3 years ago

4 0

Answer:

Step-by-step explanation:

Hello, please consider the following.

$x^4+xy^3+x^3+y^3\\\\=x^3*x+x*y^3+x^3+y^3\\\\=x(x^3+y^3)+x^3+y^3\\\\\boxed{=(x+1)(x^3+y^3)}\\$

Thank you

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In 2016 the United States had a population of about 323 million people and was growing at 0.7 %. Use an explicit exponential mod

ElenaW [278]

Answer:

2047

Step-by-step explanation:

We are given that

Growing rate=0.7%

$\frac{dp}{dt}=\frac{0.7}{100}P$

$\int \frac{dP}{P}=0.007\int dt$

$lnP=0.007t+C$

Using the formula

$\int \frac{dx}{x}=ln x+C$

$P=e^{0.007t+C}=e^{0.007t}\cdot e^C=Ae^{0.007t}$

$e^C=A$

Initially when t=0,P=323 million

Substitute the values

$323 million=A$

$P=323e^{0.007t}$

Now, substitute P=400 million

$400=323e^{0.007t}$

$ln\frac{400}{323}=0.007t$

$ln(1.2384)=0.007t$

$t=\frac{ln(1.2384}{0.007}$

$t=30.5\approx 31 Years$

Year=2016+31=2047

Hence,In 2047 the U.S population will reach 400 million people.

5 0

3 years ago

Anne picked out 3 board games from her cabinet to take to a game night with her friends. She still has more than 10 board games

Tresset [83]

Answer:

x - 3 > 10

There were more than

board games in Anne's cabinet to start.

Step-by-step explanation:

The variable x represents how many board games were in Anne's cabinet to start. Since she has already picked out 3 board games to bring, the expression x–3 represents how many board games are still in the cabinet.

And, since Anne has more than 10 board games still in her cabinet, x–3 must be greater than 10.

This inequality shows the relationship.

x–3>10

Now, solve for x.

x–3

> 10

x–3+3

> 10+3 Add 3 to both sides

> 13 Simplify

So, there were more than 13 board games in Anne's cabinet to start.

8 0

3 years ago

Please answer and no explanation needed

rewona [7]

Wait isn’t it 30 or am I reading it wrong?

3 0

3 years ago

Solve for y.<br> 5(y+5)=-7(2y-1) + 7y

scZoUnD [109]

Answer: y=1.5

Step-by-step explanation: Isolate the variable by dividing each side by factors that don’t contain the variable.

4 0

4 years ago

Find the ratio of red marbles to total marbles. Write the ratio in simplest form.

DanielleElmas [232]

Answer:

3:5

Step-by-step explanation:

ratio is 4:6 so ratio equals 2:3

red marbles is 3/5

3 0

3 years ago