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ehidna [41]
2 years ago
9

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9x4 – 2x2 – 3x + 4?

Mathematics
1 answer:
maria [59]2 years ago
6 0

Answer:

  (a)  ±1/9, ±2/9, ±1/3, ±4/9, ±2/3, ±1, ±4/3, ±2, ±4

Step-by-step explanation:

The leading coefficient is 9; the constant is 4. The rational roots will be ...

  ±(divisor of 4)/(divisor of 9)

The divisors of 4 are 1, 2, 4. The divisors of 9 are 1, 3, 9. Then the rational roots can be any of ...

  ±1/9, ±2/9, ±1/3, ±4/9, ±2/3, ±1, ±4/3, ±2, ±4

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The table shows various values of a linear function f (x).
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The value of  f –1(13) is 4

<h3>How to determine the inverse value?</h3>

The table of values is given as:

x –4 0 2 5 9 13

f (x) –11 1 7 16 28 40

A linear function is represented as:

y = mx + b

Where b represents the y-intercept and m represents the slope

From the graph, when x = 0, y = 1.

This means that b = 1

So, we have

y = mx + 1

Also from the graph, when x = 2, y = 7.

So, we have:

7 = 2m + 1

Subtract 1 from both sides

7 - 1 = 2m + 1 - 1

Evaluate the difference

6 = 2m

Rewrite the above equation as:

2m = 6

Divide both sides of the equation by 2

m = 3

Substitute m = 3 in y = mx + 1

y = 3x + 1

The notation  f –1(13) implies that y = 13

So, we have

13 = 3x + 1

Subtract by 1

3x = 12

Divide by 3

x = 4

Hence, the value of  f –1(13) is 4

Read more about linear functions at:

brainly.com/question/4025726

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4 0
2 years ago
Which of the following correctly uses absolute value to show the distance between -70 and 13?
Svet_ta [14]
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Find the slope of the line that passes through (2, 3) and (4, 4).
GuDViN [60]
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3 0
3 years ago
Read 2 more answers
What percent of 75 is 40
9966 [12]

The answer is: " 53 \frac{1}{3} % " .

__________________________________________

→ " 53 \frac{1}{3} % " of 75 is "40" .

__________________________________________

Explanation:

To solve:

\frac{x}{100} * 75 = 40 ;

→ Rewrite as:

\frac{x}{100} * \frac{75}{1} = 40 ;

→ The "100" cancels to "4" ; and the "75" cancels to "3" ;

→ {since: "{100 ÷ 25 = 4}" ; and since: "{75 ÷ 25 = 3"} ;

→ So; we rewrite the problem as:

→ \frac{x}{4} * \frac{3}{1} = 40 ;

→ which is:

\frac{x}{4} * 3 = 40 ;

→ Divide each side of the equation by "3" ;

\frac{x}{4} * 3 ÷ 3 = 40 ÷ 3 ;

to get:

→ \frac{x}{4} = \frac{40}{3} ;

Now, cross-multiply:

→ 3x = (4)*(40) ;

→ 3x = 160 ;

Divide each side of the equation by "3" ;

to isolate "x" on one side of the equation; & to solve for "x" ;

→ 3x / 3 = 160 / 3 ;

to get:

→ x = 53 \frac{1}{3} .

______________________________

6 0
4 years ago
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