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1 year ago

What is the rational expression in simplest form? State any restrictions on the variables.

Mathematics

1 answer:

allochka39001 [22]1 year ago

4 0

According to the question, the given rational expression can be simplified which is as shown below:

Rational expression = $\frac{12-4x}{x^{2} -9}=\frac{4(3-x)}{(x-3)(x+3)}$

For the simplification of the given expression, calculate the factors of the numerator as well as denominator terms and divide them from each other. In this change the sign of the expression before dividing with each other.

Rational expression = $\frac{-4}{(x+3)}$

The rational expression are also known as polynomial expression. The highest degree of these expression is two. And these expression uses concept of factor rule.

Therefore, the final expression is $\frac{-4}{(x+3)}$

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

To learn more about the polynomial expression from the given link:

<u>brainly.com/question/1280754</u>

#SPJ4

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A bacterial culture starts with 500 bacteria and doubles in size every half-hour.

tekilochka [14]

Answer:

a). 32000

b). $T_{t}=500\times 4^{t}$

c). 1259

Step-by-step explanation:

Growth of a bacteria is always exponential. Therefore, population of the bacteria is represented by the the geometric sequence.

Sum of the bacterial population after t hours will be represented by

$T_{n}=ar^{n}$

Where a = population at the start

r = ratio with the population is growing

n = time or duration of the growth in one hour

a). Population of 500 bacteria gets doubled after half an hour.

Or gets 4 times after an hour

This sequence will have a common ratio r = 4

and initial population a = 500

Therefore, population of the bacteria after 3 hours will be

$T_{3}=500\times 4^{3}$

$T_{3}=32000$

b). After t hours number of bacteria will be represented by

$T_{t}=500\times 4^{t}$

c). We have to calculate the population after 40 minutes.

That means duration 't' = 40 minutes of $\frac{2}{3}$ hours

By the formula,

$T_{\frac{2}{3}}=500\times 4^{\frac{2}{3}}$

$T_{\frac{2}{3}}=1259.92$ ≈ 1259

Therefore, number of bacteria after 40 minutes will be 1259.

8 0

3 years ago

Read 2 more answers

What does a flowchart contain of

icang [17]

A flowchart can also be defined as a diagrammatic representation of an algorithm, a step-by-step approach to solving a task. The flowchart shows the steps as boxes of various kinds, and their order by connecting the boxes with arrows. This diagrammatic representation illustrates a solution model to a given problem.

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4 years ago

How do I simply this, thanks!

stepan [7]

(-a^3b^2*-a^-2b^-3)^-2/2a^2b^-3 = a^4b^9/2a^8b^4 =b^5/2a^4 so your answer is b^5/2a^4

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3 years ago

During a visit to the tide pools, Brent observed 16 sea stars, 4 sea urchins, and 52 sea anemones. What is the ratio of sea anem

weeeeeb [17]

Answer:

16 to 52

Step-by-step explanation:

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2 years ago

The weights (to the nearest pound) of some boxes to be shipped are found to be:. Weight 65 68 69 70 71 72 90 95 frequency 1 2 5

Lena [83]

So the mean is 72.97

We need to subtract the mean from each value and square it.
(65-72.97)^2= 63.5209
(68-72.97)^2=24.7009
(69-72.97)^2=15.7609
(70-72.97)^2=8.8209
(71-72.97)^2= 3.8809
(72-72.97)^2=0.9409
(90-72.97)^2=290.0209
(95-72.97)^2=485.3209

Now we add up the new values ( also consider their frequency) and find their mean.
Add the values
63.5209+(2 •24.7009=49.4018)+(5•15.7609=78.8045)+(8•8.8209=70.5672)+(7•3.8809=27.1663)+(3•0.9409=2.8227)+(2•290.0209=580.0418)+(2•485.3209=970.6418)= 1,842.967
Divide by total numburs to find the mean
1,842.967/ 30=61.43223333

The standar deviation is the square root of the mean so is
Square root of 61.43223333=7.837871735
Round to the nearest tenth
Standard Deviation is 7.8

7 0

4 years ago