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2 years ago

Complete factorization of x^3+4x^2-20x-48

Mathematics

1 answer:

miskamm [114]2 years ago

5 0

Answer:

(x + 6) • (x + 2) • (x - 4)

Step-by-step explanation:

STEP

Equation at the end of step 1

(((x3) + 22x2) - 20x) - 48

STEP

Checking for a perfect cube

2.1 x3+4x2-20x-48 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3+4x2-20x-48

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: x3-48

Group 2: 4x2-20x

Pull out from each group separately :

Group 1: (x3-48) • (1)

Group 2: (x-5) • (4x)

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Evaluate the expression below if m = 350.<br><br> 3.5m =

Lena [83]

Answer:

1,225

Step-by-step explanation:

3.5×350=1225

its saying m is 350 and the question is asking 3.5 times 350

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2 years ago

Refer to the figure to the right.

Gemiola [76]

Answer:

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1 year ago

In a long division exercise the divisor is 8x5−4x. What is the degree of the remainder for which the division process can be st

labwork [276]

Answer:

The degree of the remainder should be 4 for the division process to be stopped

Step-by-step explanation:

From the question, we have the degree of the divisor as 5

So, for the division process to be stopped, the degree of the remainder should be one less than the degree of the divisor

Once the degree of the remainder is less than the degree of the divisor, we have no option that to stop and not proceed further with the division

So in the case of the particular question, the degree of the remainder should be of degree 4

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2 years ago

Suppose a local manufacturing company claims their production line has a variance of less than 9.0. A quality control engineer d

Alexxx [7]

Answer:

$\chi^2 =\frac{35-1}{9} 2.12^2 =16.979$

$p_v =P(\chi^2$

If we compare the p value and the significance level provided we see that $p_v$ so on this case we have enough evidence in order to reject the null hypothesis at the significance level provided. And that means that the population variance is significantly lower than 9

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

$n=35$ represent the sample size

$\alpha=0.01$ represent the confidence level

$s =2.12$ represent the sample deviation obtained

$\sigma_0 =3$ represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance specification is lower than 9 and the deviation lower than 3, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 \geq 9$

Alternative hypothesis: $\sigma^2$

Calculate the statistic

For this test we can use the following statistic:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

$\chi^2 =\frac{35-1}{9} 2.12^2 =16.979$

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case df= n-1= 35-1=34. And since is a left tailed test the p value would be given by:

$p_v =P(\chi^2$

In order to find the p value we can use the following code in excel:

"=CHISQ.DIST(16.979,34,TRUE)"

Conclusion

6 0

3 years ago

Find the coordinates of the midpoint of the segment whose endpoints are H(10, 1) and K(4, 7).

Oliga [24]

The formula of a midpoint of a segment AB:

$A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\M_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)$