simplify the expression and explain each step.
1. 4(3x + 2) -2
2. factor the expression completely 20b -16

please explain how to solve! will mark brainliest​

Answer:

6

Step-by-step explanation:

i had this same problem :)

Answers:

[tex]\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n} = 6[/tex]

Based on the limit comparison test, the series is convergent

========================================================

Explanation:

As n gets really large, the terms [tex]3^n[/tex] and [tex]3^n-2[/tex] are effectively the same. Taking the limit to infinity of the ratio leads to 1.

In other words,

[tex]\displaystyle \lim_{n \to \infty} \frac{3^n}{3^n-2} = \lim_{n \to \infty} \frac{3^n}{3^n} = 1[/tex]

That -2 doesn't really play a role when n gets very large.

This result is then multiplied by the 6 in the [tex]a_n[/tex] sequence, getting 6 as the final limit we want.

So,

[tex]L = \displaystyle \lim_{n \to \infty} \left(a_n \div b_n\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6}{3^n-2} \div \frac{1}{3^n}\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6}{3^n-2} \times \frac{3^n}{1}\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6*3^n}{3^n-2}\right)\\\\\\[/tex]

[tex]L = \displaystyle 6*\lim_{n \to \infty} \left(\frac{3^n}{3^n-2}\right)\\\\\\L = \displaystyle 6*\lim_{n \to \infty} \left(\frac{3^n}{3^n}\right)\\\\\\L = \displaystyle 6*\lim_{n \to \infty} (1)\\\\\\L = \displaystyle 6*1\\\\\\L = \displaystyle 6\\\\\\[/tex]

Since the limiting value is positive and not infinity, this means that both series [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] converge or they both diverge.

----------------------------

If we plug n = 2 into the [tex]b_n[/tex] sequence, we get

[tex]b_n = \frac{1}{3^n}\\\\b_2 = \frac{1}{3^2}\\\\b_2 = \frac{1}{9}[/tex]

The first term is a = 1/9

If we plugged n = 3, we would get [tex]b_3 = \frac{1}{27}[/tex]

This shows that the common ratio is r = 1/3

Because -1 < r < 1 is true, we know that the infinite geometric series converges. Therefore, [tex]\sum b_n[/tex] converges. We don't need to find the converging value.

Going back to the limit comparison test, we stated that both [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] either diverge together or converge together.

We've shown that the b series converges, so the 'a' series must converge as well.

Answer:

16.8  or 17 blue

50.4  or 50 brown

33.6  or 34 yellow

33.6  or 34 red

16.8  or 17 orange

16.8  or 17 green

Step-by-step explanation:

7 x 24 = 168 candies

blue = b

brown = w

yellow = y

red = r

orange = o

green = g

1b = 3w + 2y + 2r + 1o + 1g

1 +3 + 2 + 2 + 1 + 1 = 10

168/10 = 16.8

1(16.8) +3(16.8) + 2(16.8) + 2(16.8) + 1(16.8) + 1(16.8) =

16.8 blue

50.4 brown

33.6 yellow

33.6 red

16.8 orange

16.8 green

Answer:

100=9s+10

there are 10 students on each bus

Answer:

She had 16 feet of ribbon

Step-by-step explanation:

Answer:

16 ft of ribon

Step-by-step explanation:

divide 6 by 3 and get 2. there is 2 ft for every 8th of the ribbon so 2×8=16

hope it helped

x=1

combine like terms and simplify

Answer:

-2

Step-by-step explanation:

just had to answer it :)

The remainder from the given division is 0.

Given that, 24 divided by 4 is 6.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Here,

4|24|6

  24

______

    0

So, the remainder is 0.

Therefore, the remainder from the given division is 0.

To learn more about the division visit:

https://brainly.com/question/1575906.

#SPJ6

Answer:

As*Nc/Ns

Step-by-step explanation:

The square has Ns discrete points. The points are quite large and are close around each other

As = Area of square

Nc = number of points inside square

Ns = total number of points inside square

Ac = area of circle

Such that

Nc/Ns = Ac/As

We cross multiply

AcNs = NcAs

Dividing through by Ns will give:

Ac = NcAs/Na

Which Is also

= As *Nc/Na

I also added an attachment to help you!

Answer:

True

Step-by-step explanation:

In regression analysis, it tries to infer that there is a supposed relationship between two or more variables.

Now it has a couple of functions such as;

It allows us to directly estimate the parameters in linear functions only, although there are some other ways in which it would allow many non - linear functional forms to get estimated indirectly.

Regression also allows us to test and find out if there is a functional relationship between two or more variables. This is done by testing the hypothesis whether each of the slopes have a value of zero.

Thus, from the definitions given, we can see that regression is a basically a functional relationship between two or more variables, where one or more variables are used to predict a single variable of interest.

Thus, the given statement is true.

Answer:

the correct answer is 4

Answer:

C. R0, 270°

Step-by-step explanation:

R0, 270°:(x, y) → (y, –x)

Answer:

Step-by-step explanation:

the answer is c

Answer:

420

140 x 4 = 420

Step-by-step explanation:

Answer:

98.

Step-by-step explanation:

Answer:

0.98 would be the 98% as a decimal

Answer:

.

21

Step-by-step explanation:

Answer: 7y + 9

Step-by-step explanation: First you will distribute 3(2y + 3). This means we will multiply 3 to the numbers in the parenthesis. 3 x 2y = 6y and 3 x 3 = 9. This is 6y + 9.

Now we have the y left over so combine like terms 6y + y and that is 7y.

Answer:

7y + 9.

Step-by-step explanation:

1. Expand by distributing terms.

3(2y + 3) + y

2. Collect like terms.

(6y + y) + 9.

3. Simplify.

7y + 9.

Hope this helps.

Have a good night ma´am/sir.

Be safe!

Answer:

being happy j

Step-by-step explanation:

step by step explaination

Answer:

well for me it is both because i am only happy when everyone else around me is also happy

Step-by-step explanation:

Answer:B.

Step-by-step explanation:

-16 is the least. It is behind zero. 3 is near zero but it is still greater. 47 is way past zero.

Answer:

3460

Step-by-step explanation:

Answer:

lol

Step-by-step explanation:

imin middle school

Answer:

x = 2

Step-by-step explanation:

Since this is a 45-45-90 triangle, the 2 legs will be the same, meaning that y will also be [tex]\sqrt2[/tex].

We can then solve for x using the Pythagorean theorem:

[tex]\sqrt2^2+\sqrt2^2=x^2\\2+2=x^2\\4=x^2\\x=2[/tex]

Or, we could use a quicker approach: if the triangle is a 45-45-90 triangle, the hypotenuse will be [tex]\sqrt2[/tex] times the length of 1 leg. It essentially does the same thing; it's just faster so you could save time on tests.

Answer:

5 is the answer

Step-by-step explanation:

120/24=5

Answer:

A. 5

Step-by-step explanation:

The angle is 120 degrees because of certain rules which explanations I can't remember off the top of my head. To get 24z to equal 120 you plug in 5.

Answer:

7/8, 0.86, 0.9

Step-by-step explanation:

Convert 7/8 to a decimal:

7 / 8 = .875

Solve:

.875, .86, .9

Or:

7/8, 0.86, 0.9

Answer:

No value

Step-by-step explanation:

Y has zero solutions