Solve for x: 3(x + 1) = -2 (x-1) - 4

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:

word problems are pretty tricky

Step-by-step explanation:

y= punch

2*y > 4  Liters

y >2 Liters

Answer:2y>4

Step-by-step explanation:

Two times the amount of punch needed =2y. Because this amount must be greater than 4 liters, the inequality is given by 2y>4

Answer: Each towel costs $1.90

Step-by-step explanation:

$15.20 divided by 8 = $1.90

Answer:

13/18

Step-by-step explanation:

See attachment

Answer:

1.y=-2x+7

2. no

3.yes

Step-by-step explanation:

Answer:

FV= $5,325.8

Step-by-step explanation:

Giving the following information:

Mr. Clopu buys an 18-month CD that pays 4.34% simple interest for $5,000.

To calculate the future value, we need to use the following formula:

FV= (P*r*t) + P

P= $5,000

r= 0.0434/12= 0.00362

t= 18

FV= [(5,000*0.00362)*18] + 5,000

FV= $5,325.8

The value of the CD at the end of its term is $39,060

Given:

Time = 18 month

Principal = $5000

Interest rate = 434%

Future value = ?

Future value = Principal × Rate × Time

= 5,000 × 434% × 18

= 5000 × 434/100 × 18

= 5000 × 4.34 × 18

= 39,060

Therefore, the value of the CD at the end of its term is $39,060

Read more:

https://brainly.com/question/12164462

Answer:

This means that if you have that amount of those and you do whatever the rest of the question is.

Step-by-step explanation:

Answer:

120 different ways

Step-by-step explanation:

So Fundamental Counting Principle helps understand probability. So for this question, they are asking how many different ways there are.

To do that, we have to split into sets.

Set A: 4 Theme Parks

Set B: 6 Passes

Set C: 5 Food Options

Now we have to multiply the sets.

4 x 6 x 5 = 120

Therefore, the answer is 120 different ways.

Answer:

The two numbers are negative 1 and negative 9 which is -1 and -9

Answer:

    Step-by-step explanation:

D

Answer:

the answer is 2,3,and 5

Step-by-step explanation:

Answer:

2, 3, and 5

Step-by-step explanation:

Answer: 35 , 14

Step-by-step explanation:

[3(-2)^2-4 ]+[8 (3)-3]                     [8(3)-3] -[ 3(-1)^2-4]

35                                                      14

Answer:  A)    4x -8 = 128  

Step-by-step explanation:

We will represent the amount that the normal bus carries by   n= x  

We will represent  the amount that the large bus carries by  l = 2x  

We will also represent the amount that the small bus carries by  s = x-8  

Now add them to equal to 128.

x + 2x + x -8 = 128    

    4x -8 = 128  

Answer:

y equals 5x + 20

Answer:1.5

Step-by-step explanation:

Answer: 4/5

Step-by-step explanation:

Slope=rise/run

In this case we start at (-2,0)

We rise up 4 and run to the right 5 until we are at (3,4)

Answer:

1

Step-by-step explanation:

You could have just used a calculator tard lol

Answer:

1

Step-by-step explanation:

-7 +8=1 cause you have 1 positive left over

Answer:

y = -3x + 3

Step-by-step explanation:

Slope = -3

y-intercept = 3

Substitute values into slope intercept form :

y=mx + b

Where :

m= Slope

b = y-intercept

[tex]y = - 3x + 3[/tex]

Answer:

- 4

Step-by-step explanation:

Step 1:

4 ( 2 - w ) + w = 20           Equation

Step 2:

8 - 4w + w = 20       Multiply

Step 3:

8 - 3w = 20       Combine Like Terms

Step 4:

- 3w = 12     Subtract 8 on both sides

Answer:

w = - 4

Hope This Helps :)

Answer:

w = -4

Step-by-step explanation:

4(2 - W) + w = 20

Distribute:          

8 - 4w + w = 20

Subtract 8 from both sides:

-4w + w = 12

Simplify:

-3w = 12

Divide:

w = -4

Double check your work by substitution:

4(2 - W) + w = 20

4(2 - (-4)) + (-4) = 20

4(6) + (-4) = 20

24 + (-4)= 20

20 = 20

Since we know that 20 does equal 20, we can conclude that the final answer is:

w = -4

Answer:

I don’t think the question makes sense

Answer:

B- 44

Step-by-step explanation:

87.5 divided by 2 is 43.75. Since it's a square wall, the length and height are both the same, and since length times height is area, if you divide the area by two, you can get a length of one of the sides. Out of all the answers, 44 is the closest to 43.75.

hope this helped! -brooke :))

The relationship between strategy and written method in mathematics is that;

Strategies can be changed or modified whereas written methods cannot be changed or modified because they have standards upon which such methods are based.

A student wants to perform addition of 19 and 46.

He could add the number straight away by doing 19 + 46 = 65or he can

take away 1 from 46 to become 45 and add that 1 to 19 to become 20 and

then sum 45 and 20 together as 20 + 45 = 65.

So we can see that the two strategies used to add 19 and 46 gave the same result.

For example, we want to use partial products to multiply 13 x 52.

The solution would become (10 × 50) + (10 × 2) + (3 × 50) + (3 × 2) = 676.

In this method, there cannot be another way used as the standard for using partial products is written and fixed.

Read more at; https://brainly.com/question/18884089

Answer:1.7 x 10 ^ -5

Step-by-step explanation:

Answer:1.7 x 10-5

hope this helps

Answer: If 2 log x + 3 log y = 0, find y in terms of x.

sorry for my messy handwriting!!!

Step-by-step explanation:

9514 1404 393

Answer:

  If x-y is a natural number, then x and y are natural numbers.

Step-by-step explanation:

The converse of ...

  If P, then Q.

is ...

  If Q, then P.

__

Here, we have ...

  P = "x and y are natural numbers"

  Q = "x-y is a natural number"

So, the converse is ...

  If x-y is a natural number, then x and y are natural numbers.

_____

In this case, the converse is false.

Answer:

1.41

Step-by-step explanation:

Answer:

x = 5/(-4 z + y)

Step-by-step explanation:

Solve for x:

x y - 4 x z = 5

Hint: | Write the linear polynomial on the left-hand side in standard form.

Collect in terms of x:

x (-4 z + y) = 5

Hint: | Solve for x.

Divide both sides by -4 z + y:

Answer: x = 5/(-4 z + y)

the first thing we must do is define variables.

We have then:

n: number of cans that each student must bring.

We know that:

The teacher will bring 5 cans

There are 20 students in the class

At least 105 cans must be brought, but no more than 205 cans

Therefore the inequation of the problem is given by:

105 < 20n + 5 <205

Answer:

the possible numbers n of cans that each student should bring in is:               105 < 20n + 5 < 205

Answer:

3         8

18       48

22.5   60

27       72

Step-by-step explanation:

3:8 ratio

18/3=6

8*6=48

Answer:

48

60

72

Step-by-step explanation:

1. Find the number of times x or the first column numbers are multiplied to get y or the second column numbers.

2. Equation: 3*?=8, ? = 8/3

3. Multiply all of the other numbers by 8/3 to get the answers.

4. 3*8/3=8, 18*8/3=48, 22.5*8/3=60, 27*8/3=72.

Answers: 48, 60, 72

Answer:

17*21 = 357

Step-by-step explanation:

Firstly, set up your equation.

x*(x+4)=357

Multiply X by (x+4)

x^2+4x=357

You then subtract 357 from both sides

x^2+4x-357=0

Simplify using the quadratic formula shown, if you need assistance on solving this equation put it into a online calculator, or photomath as it shows the steps taken to solve it.

[tex]\frac{-4+\sqrt{4^2-4\cdot \:1\cdot \left(-357\right)}}{2\cdot \:1}\\[/tex]

Answer:-1.2 Degree Fahrenheit.

Step-by-step explanation:

Since,

The average daily changes,   total changes/number of days

Here,

The total changes = - 16.8° F ( - sign shows the decreasing )

And, the number of days = 14

Hence,

⇒ The average daily rate of change in the high temperature in degrees Fahrenheit is -1.2° F.

-16.8 / 14 = - 1.2 per day