Simplify the complex fraction: 4/(x+3)/(1/x+3) A. 12x+4/x^2+3x. B. 4x/3x+9. C. 4x/3x^2+10x+3. D. None of these

Answers

Answer 1

Answer: The answer is C. 4x/3x^2+10x+3

$( (4)/(x+3))/( (1)/(x) +3) = ( (4)/(x+3))/( (1)/(x)+ (3x)/(x)) =( (4)/(x+3))/( (1+3x)/(x) ) = (4)/(x+3)* (x)/(1+3x)= (4x)/((x+3)(1+3x)) = (4x)/(x+3 x^(2) +3+9x)$ $= (4x)/(3 x^(2) +10x+3)$

Answer 2

Answer:

Answer:

The correct option is C.

Step-by-step explanation:

The given expression is

$((4)/(x+3))/(((1)/(x)+3))$

$((4)/(x+3))/(((1)/(x)+3))=((4)/(x+3))/((1+3x)/(x))$

The complex faction can be simplified as

$(((a)/(b)))/(((c)/(d)))=(a)/(b)* (d)/(c)$

$((4)/(x+3))/(((1)/(x)+3))=(4)/(x+3)* (x)/(1+3x)$

$((4)/(x+3))/(((1)/(x)+3))=(4x)/((x+3)(1+3x))$

$((4)/(x+3))/(((1)/(x)+3))=(4x)/(x(1+3x)+3(1+3x))$

$((4)/(x+3))/(((1)/(x)+3))=(4x)/(x+3x^2+3+9x)$

$((4)/(x+3))/(((1)/(x)+3))=(4x)/(3x^2+10x+3)$

Therefore the correct option is C.

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On a certain day, the company took 92 people on whale watching trips. There were 40 children aged 12 and under, of which some children were under three years. If x represents the number of children under three years, which equation can be used to find the value of x, where C represents the total amount of money collected from tickets that day? (92 − x)36 + (92 − 40) ⋅ 48 = C
(40 + x)36 + (92 − (40 + x)) ⋅ 48 = C
(92 + x)36 + (92 − (40 + x)) ⋅ 48 = C
(40 − x)36 + (92 − 40) ⋅ 48 = C

Answers

If x represents the number of children under three years, which equation can be used to find the value of x, where C represents the total amount of money collected from tickets that day is (40 + x)36 + (92 − (40 + x)) ⋅ 48 = C

Answer:

(40 + x)36 + (92 − (40 + x)) ⋅ 48 = C

Step-by-step explanation:

Log8(2-5x)=log8(-4x+3)

Answers

2 - 5x > 0 and -4x + 3> 0

log8(2-5x)=log8(-4x+3) <=> 2 - 5x = - 4x + 3 <=> -5x + 4x = 3 - 2 <=> -x = 1 <=> x = -1;

2 - 5(-1) = 7 > 0 and -4(-1) + 3 = 7 > 0 ;

the solution is -1;

Pllsss I needddd helpp

Answers

I can’t see, make it clear

Use the Laplace transform to solve the given initial value problem. y' + 6y = e^4t ; y(0)=2 ...?

Answers

Performing laplace transform of the equation.

sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)

Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)

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Final answer:

The Laplace transform method is applied to solve the differential equation y' + 6y = e^4t with the initial condition y(0)=2. After transforming, simplifying, and solving for Y(s), we use inverse Laplace transform to find the solution y(t) in the time domain.

Explanation:

Laplace transform is a powerful tool in the field of mathematics used for solving differential equations. To solve the given initial value problem y' + 6y = e^4t ; y(0)=2, we can start by taking the Laplace transform of both sides of the equation.

The Laplace transform of y' is sY(s) - y(0) and the Laplace transform of y is Y(s). Therefore, the Laplace transform of y' + 6y gives sY(s) - y(0) + 6Y(s). Given that y(0)=2, this simplifies to sY(s) + 6Y(s) - 2.

On the right-hand side, the Laplace transform of e^4t is 1/(s-4). Thus, we have the equation sY(s) + 6Y(s) - 2 = 1/(s-4).

By solving for Y(s), we can find the inverse Laplace transform to get the solution y(t) in the time domain.

Learn more about Laplace Transform here:

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Use the following number line to determine if the expressions are true or false.

Answers

Answer:

${ \tt{a < b→true}} \n { \bf{reason :because \: - 1 \: is \: less \: than \: 4.5 }}\n \n { \tt{ |a| > b →false}} \n { \bf{reason :1 \: is \: not \: greater \: than \: 4.5 }}\n \n { \tt{a < |b| →true}}$

Answer:

true

false

true

Step-by-step explanation:

If x = −3, which number line shows the value of |x|?

Answers

The value of the absolute expression |x| at x = - 3 will be 3.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ |x|

If x = - 3, then the value of the expression will be given as,

⇒ |-3|

The value of the absolute function is always positive. Then the value of the expression is given as,

⇒ |-3|

⇒ 3

The value of the absolute expression |x| at x = - 3 will be 3.

More about the Algebra link is given below.

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Answer: