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Ksju [112]
3 years ago
15

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x^5

– 2x^4 + 9x^3 – x^2 + 12?
Mathematics
1 answer:
Reil [10]3 years ago
5 0

Answer:

The correct option is A.

Step-by-step explanation:

The question is:

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?

A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12

B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x

C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3

D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48

<u>Solution:</u>

The function given to us is:

3x5 – 2x4 + 9x3 – x2 + 12

Find the factors of 12 and consider it as 'p'

The factors of 12 are:

p = +/- 1 , +/-2 , +/-3 , +/- 4 , +/-6

Now find the factors of 3 and consider it as 'q'

The factors of 3 are:

q = +/- 1 , +/- 3

We know that we write rational terms in p/q form.

Therefore the Rational roots are given by p/q

+/- 1 , +/-2 , +/-3 , +/- 4 , +/-6 , +/- 1/3 , +/- 2/3 , +/- 4/3

Now we will solve the first function given in part A.

f(x) = 3x^5 – 2x^4 - 9x^3 + x^2 - 12

Again find the factors of 12 and consider it as 'p'

The factors are:

p = +/- 1 , +/-2 , +/-3 , +/- 4 , +/-6

Now find the factors of 3 and consider it as 'q' .

q = +/- 1 , +/- 3

Rational root are given by p/q

+/- 1 , +/-2 , +/-3 , +/- 4 , +/-6 , +/- 1/3 , +/- 2/3 , +/- 4/3

Therefore the rational roots of the given function matches the rational roots of the given equation.

Hence the correct option is A.

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Answer:

81.39% increase.

Step-by-step explanation:

Given: There is change in number from 43 to 78.

First lets find the amount of change or difference in number.

Difference in number= 78-43= 35

∴ Difference in number show that there is an increase of 35 number.

Now, finding the percent change in the number.

Percent= \frac{Difference\ in\ number}{base\ number} \times 100

⇒ Percent change in number= \frac{35}{43} \times 100= 81.39\%

∴ 81.39% increase in the number.

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3 years ago
What is m in the simultaneous equation <br> M -n=1<br><br> M+n=3
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In this set of data, at what percentile is 10? At what percentile is 18? 10, 10, 10, 12, 14, 16, 16, 18, 18, 18​
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Step-by-step explanation:

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3 years ago
(06.01) In the below system, solve for y in the first equation. x + 3y = 6 2x − y = 10 one thirdx + 2 negative one thirdx + 6 −x
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we have that

x + 3y = 6 -------> first equation

2x − y = 10


x + 3y = 6-----> substract x both sides

-x+x+3y=6-x

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y=(6-x) /3

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5 0
3 years ago
Please help
Alenkasestr [34]

Answer:

Domain: {-4, -2, 1, 2, 4}

Range: {-4, -2, -1, 1, 4}

The relation is a function.

Step-by-step explanation:

A <u>relation</u> is any set of ordered pairs, which can be thought of as (input, output).

A function is a <em>relation</em> in which no two ordered pairs have the same first component and different second components.

Remember that a function can only take on <u>one output for each input</u>. We cannot plug in a value and get out two values.

The Vertical Line Test allows us to know whether or not a graph is actually a function.  If a vertical line intersects the graph in all places <u><em>at exactly one point</em></u>, then the relation is a function.

I did the Vertical Line Test on your given graph. As you can see from the attached screenshot, each vertical line crosses the graph only once. Therefore, the given relation is a function.

The <u><em>domain</em></u> of the given relation is the set of x-values, while the <em><u>range</u></em> is the set of y-values. You'll have to list the ordered pairs in order to determine the domain and range of the given relation.

Relation:  {(-4, -1), (-2, 1), (1, -2), (2, 4), (4, -4)}.

Domain: {-4, -2, 1, 2, 4}

Range: {-4, -2, -1, 1, 4}

Please mark my answers as the Brainliest if you find my explanations helpful :)

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