All categories

2 years ago

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

Mathematics

2 answers:

iogann1982 [59]2 years ago

6 0

The answer is the first choice - see picture for solution:

kolezko [41]2 years ago

4 0

Answer:

Option 1.

Step-by-step explanation:

According to rational root theorem, all the potential rational roots of a function f(x) is defined as

$roots=\dfrac{p}{q}$

where, p is a factor of constant term and q is the factor of leading coefficient.

The given function is

$f(x)=9x^4-2x^2-3x+4$

Here, leading coefficient is 9 and factors of 9 are ±1, ±3, ±9.

Constant term is 4 and factors of 4 are ±1, ±2, ±4.

All the potential rational roots of f(x) are

$\pm \dfrac{1}{9},\pm \dfrac{2}{9},\pm \dfrac{4}{9},\pm \dfrac{1}{3},\pm \dfrac{2}{3},\pm \dfrac{4}{3},\pm 1,\pm 2,\pm 4$

Therefore, option 1 is correct.

You might be interested in

Prof. okamoto selects 3 different students to report on 3 different current events. if there are 27 students in the class, in ho

kenny6666 [7]

Consider this option:
C³₂₇=27!/(3!*24!)=25*13*9=2925 ways to select 3 students.

8 0

2 years ago

In a completely randomized experimental design involving three assembly methods, 30 employees were randomly selected and 10 were

AnnZ [28]

Answer:

$F = \frac{MSR}{MSE} =\frac{45.89}{6.27}=7.32$

So then the best option is:

a. 7.32

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

If we assume that we have $3$ groups and on each group from $j=1,\dots,10$ we have $10$ individuals on each group we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between=Treatment}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

And we have this property

$SST=SS_{between}+SS_{within}$

Where SST represent the total sum of squares.

The degrees of freedom for the numerator on this case is given by $df_{num}=k-1=3-1=2$ where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by $df_{den}=df_{between}=N-K=30-3=27$ .

And the total degrees of freedom would be $df=N-1=30 -1 =29$

From the info given we know that $MSR=\frac{SSR}{2}=45.89$

And $MSE=\frac{SSE}{27}=6.27$

From definition the F statisitc is defined as:

$F = \frac{MSR}{MSE} =\frac{45.89}{6.27}=7.32$

So then the best option is:

a. 7.32

3 0

2 years ago

Prachi was 5 kilometers east of her home when she began driving farther east at 70 kilometers per hour. Let f(n) be Prachi's dis

Yanka [14]

Answer:

Prachi was 5 kilometers east of her home when she began driving farther east at 70 kilometers per hour.

Let f(n) be Prachi's distance from her home at the beginning of the nth hour of her drive.

f is an arithmetic sequence.

Write an explicit formula for the sequence.

f(n) = 70n + 5

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (–5, 1)? Check all that ap

Bond [772]

So the right options are:

$y=-\frac{2}{5}x-1$

$2x+5y = -5$

$y-1=-\frac{2}{5}(x+5)$

Further explanation:

Given equation of line is:

2x+5y=10

We have to convert it into point-slope form

$2x+5y=10\\5y=-2x+10\\Dividing\ both\ sides\ by\ 5\\y=-\frac{2}{5}x+\frac{10}{5}\\y=-\frac{2}{5}x+2$

The co-efficient of x is the slope of the line

So,

$m= -\frac{2}{5}$

As the required line is parallel to given line, it will also have same slope.

Let m1 be the slope of required line

Then the line will be:

$y=m_1x+b$

Putting the value of slope

$y=\frac{2}{5}x+b$

Putting (-5,1) in the equation to find the value of b

$1=-\frac{2}{5}(-5)+b\\1=2+b\\b=1-2\\b=-1$

Putting the values of slope and b in equation

$y=-\frac{2}{5}x-1$

Multiplying the whole equation by 5 will give us:

5y = -2x-5

2x+5y = -5

Another form of equation of line is Point-slope form

$y-y_1=m(x-x_1)$

Putting the values of slope and point in the equation, we get

$y-1=-\frac{2}{5}(x+5)$

So the right options are:

$y=-\frac{2}{5}x-1$

$2x+5y = -5$

$y-1=-\frac{2}{5}(x+5)$

Keywords: Point-Slope form, Parallel lines

Learn more about point slope form at:

#LearnwithBrainly

4 0

1 year ago

Read 2 more answers

A printer ink cartridge that can print 550 pages has already printed 127 pages. Which solution represents the correct equation a

babunello [35]

P + 127 = 550 P = 423

6 0

2 years ago

Read 2 more answers