Find the first four terms of the sequence given by the following.<br> an = 42-8(n-1), n=1, 2, 3....

What is the numerator of the simplified sum?

sashaice [31]

Answer:

4x + 6

Step-by-step explanation:

$\frac{x}{x² + 3x + 2} + \frac{3}{x + 1}$

To determine what the numerator would be, after simplifying both fractions, take the following steps:

Step 1: Factorise the denominator of the first fraction, x² + 3x + 2.

Thus,

x² + 2x + x + 2

(x² + 2x) + (x + 2)

x(x + 2) +1(x + 2)

(x + 1)(x + 2)

We would now have the following as our new fractions to add together and simplify:

$\frac{x}{(x + 1)(x + 2)} + \frac{3}{x + 1}$

Step 2: find the highest common factor of the denominator of both fractions.

Highest common factor of (x + 1)(x + 2) and (x + 1) = (x + 1)(x + 2)

Step 3: To add both fractions, divide the highest common factor gotten in step 2 by each denominator, and then multiply the result by the numerator of each fraction.

Thus,

$\frac{x}{(x + 1)(x + 2)} + \frac{3}{x + 1}$

$\frac{x + 3(x + 2)}{(x + 1)(x + 2)}$

$\frac{x + 3x + 6)}{(x + 1)(x + 2)}$

$\frac{4x + 6)}{(x + 1)(x + 2)}$

Therefore, the numerator of the simplified form sum of both fractions = 4x + 6

8 0

3 years ago

What are the coordinates of B if the midpoint of line segment AB is (2,-5) and the coordinates of point A is (4,4)?

Vlad1618 [11]

Answer:

i think it will be 20 unit diatance .

6 0

3 years ago

Jenna has a piece of paper that is 84 square inches in area. it is 10 1/2 inches long. what is the length of the piece of paper

Ronch [10]

I hope this helps you

6 0

3 years ago

26. Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics

hjlf

The test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

<h3>What are null hypotheses and alternative hypotheses?</h3>

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics course.

Then they are given a post-test once the professor has concluded lecturing on the material.

Pre-test and post-test scores for 4 students in an elementary statistics class are given below.

Then we have

$\mu _d = \mu _{post} - \mu _{pre}$

Then the null hypotheses and alternative hypotheses will be

H₀: $\mu _d = 0$

Hₐ: $\mu _d > 0$

Then the test statistic will be

$\rm \overline{x} _d = \dfrac{\Sigma x_d}{n} = \dfrac{15+12+10+1}{4}\\\\\overline{x} _d = 9.5$

Then

$\rm S_d = 6.02$

The test statistic value is given by

$\rm t = \dfrac{\overline{x} _d }{\dfrac{S_d}{\sqrtn}} \\\\t = \dfrac{9.5}{\dfrac{6.02}{\sqrt4}}\\\\t = 3.16$

Since this is a right-tailed test, so the critical value is given by

$\rm t_{n-1}(\alpha ) = t_3 (0.05) = 2.353$

Since the test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

Hence, we can conclude that $\mu _d > 0$ that is test scores have improved.

More about the null hypotheses and alternative hypotheses link is given below.

brainly.com/question/9504281

#SPJ1

7 0

2 years ago

ツ---Graph y=-x^2-2. Identify the vertex of the graph.Tell whether it is a minimum or maximum.---ツ

balandron [24]

Hey!

Hope this Helps...

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Below, I added what the graph of (x^2)-2 looks like...