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3 years ago

Why is 5.621313 a rational number?

Mathematics

2 answers:

julsineya [31]3 years ago

6 0

It is a rational number because it can be made into a fraction

liberstina [14]3 years ago

3 0

yes

pLS MARK ME AS BRAINLIEST :)

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What does not represent an integer

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Fractions and decimals

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3 years ago

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Solve for c. Solve for x. Solve for c. Solve for x. Solve for x.

Mariana [72]

Answer:

1) The option $c=9-a+b$ is correct.

2) The option x=-2 or x=-3 is correct.

3) The option $c=9-a+b$ is correct.

4) The option $x=\frac{11}{3}$ is correct.

5) The option x=-2 or x=-3 is correct.

Step-by-step explanation:

1) Given equation is $\sqrt{a-b+c}=3$

Now to solve the equation for c:

$\sqrt{a-b+c}=3$

Squaring on both sides we get

$(\sqrt{a-b+c})^2=3^2$

$a-b+c=9$

$c=9-a+b$

Therefore the option $c=9-a+b$ is correct.

2) Given equation is $\sqrt{3x+10}=x+4$

Now to solve the equation for x:

$\sqrt{3x+10}=x+4$

Squaring on both sides we get

$(\sqrt{3x+10})^2=(x+4)^2$

$3x+10=x^2+8x+16$

$x^2+8x+16-3x-10=0$

$x^2+5x+6=0$ which is a quadratic equation in x.

We can solve it by finding factors

$x^2+5x+6=(x+2)(x+3)$

$(x+2)(x+3)=0$

x+2=0 or x+3=0

Therefore x=-2 or x=-3

Therefore the option x=-2 or x=-3 is correct.

3) Given equation is $\sqrt{a-b+c}=3$

Now to solve the equation for c:

$\sqrt{a-b+c}=3$

Squaring on both sides we get

$(\sqrt{a-b+c})^2=3^2$

$a-b+c=9$

$c=9-a+b$

Therefore the option $c=9-a+b$ is correct.

4) Given equation is $\sqrt{x+3}=2\sqrt{x-2}$

Now to solve the equation for x:

$\sqrt{x+3}=2\sqrt{x-2}$

Squaring on both sides we get

$(\sqrt{x+3})^2=(2\sqrt{x-2})^2$

$x+3=2^2(x-2)$

$x+3=4(x-2)$

$x+3=4x-8$

$4x-8-x-3=0$

$3x-11=0$

$x=\frac{11}{3}$

Therefore the option $x=\frac{11}{3}$ is correct.

5) Given equation is $\sqrt{3x+10}=x+4$

Now to solve the equation for x:

$\sqrt{3x+10}=x+4$

Squaring on both sides we get

$(\sqrt{3x+10})^2=(x+4)^2$

$3x+10=x^2+8x+16$

$x^2+8x+16-3x-10=0$

$x^2+5x+6=0$ which is a quadratic equation in x.

We can solve it by finding factors

$x^2+5x+6=(x+2)(x+3)$

$(x+2)(x+3)=0$

x+2=0 or x+3=0

Therefore x=-2 or x=-3

Therefore the option x=-2 or x=-3 is correct.

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3 years ago

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Solve for the function X(s) in the Laplace domain by taking the Laplace transform of the following differential equations with g

Sedaia [141]

Answer:

X(s) = 2/[s³(s + 9)]

Step-by-step explanation:

Here is the complete question

Solve for the function X(s) in the Laplace domain by taking the Laplace transform of the following differential equations with given initial conditions.

dx/dt + 9x = 16t² x(0) = 0 and dx(0)/dt = 5

Solution

dx/dt + 9x = 16t²

Taking the Laplace transform of the differential equation, we have

L{dx/dt + 9x} = L{16t²}

L{dx/dt} + L{9x} = L{16t²}

L{dx/dt} + 9L{x} = 16L{t²}

sL{x} - x(0) + 9L{x} = 16L{t²}

L{x} = X(s)

L{t²} = 2!/s³

Substituting X(s) and L{t²} into the equation above, we have

sX(s) - x(0) + 9X(s) = 2!/s³

Substituting x(0) = 0 into the equation above, we have

sX(s) - x(0) + 9X(s) = 2!/s³

sX(s) - 0 + 9X(s) = 2!/s³

sX(s) + 9X(s) = 2!/s³

Factorizing X(s), we have

(s + 9)X(s) = 2!/s³

X(s) = 2/[s³(s + 9)]

So X(s) in the Laplace domain is

X(s) = 2/[s³(s + 9)]

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3 years ago

Which statements are true for the image below? Check all that apply.

Arlecino [84]

Answer:

its 1,3,4,and 7

Step-by-step explanation:

i just did it

so A,C,D,and G

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4 years ago

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The ratio of pens to pencils in the box is 84 to 112. Which statement describes this relationship?

Oksi-84 [34.3K]

Answer:

For every 84 pens there are 112 pencils in the box.

Step-by-step explanation:

We are given the following information in the question.

We are given a ratio of pens to pencil is 84 to 112.

Ratio is a relationship between two numbers that helps us to know how first number is related to the second number.

This can be written as: 84 : 112

This can be read as: For every 84 pens there are 112 pencils in the box.

Simplifying the fraction we have:

$\displaystyle\frac{84}{112} = \frac{21}{28}$

This ration can be written as 21 : 28 which means for every 21 pens in a box there are 28 pencils in the box.

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3 years ago

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