Jack owes a total of $24.00 to 6 different friends. If Jack owes each friend an equal amount, which answer choice represents the change in Jack's money when he pays one friend?

Exact value:  [tex]c = \frac{-11+\sqrt{165}}{22}[/tex]

Approximate value:    c = 0.08387

Round the approximate value however you need to

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Work Shown:

Let x = 1+c

[tex]\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\[/tex]

We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.

Each new term is found by multiplying the previous term by 1/x.

Assuming -1 < r < 1 is true, the infinite geometric sum is

[tex]S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\[/tex]

Plug in S = 11 and solve for x

[tex]S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\[/tex]

Use the quadratic formula to find the two solutions

[tex]x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\[/tex]

Using these x values, we find that the corresponding r values are

r = 1/x = 1/(1.08387) = 0.92262

r = 1/x = 1/(-0.08387) = -11.92321

The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387

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Using the solution that corresponds to x = 1.08387, we find the value of c is

[tex]x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\[/tex]

Answer:

1: y = 3/2 + 1/2

Step-by-step explanation:

y1 -y2/x1 - x2

8-2 / 5-1

6/4 = 3/2

y-2=3/2(x-1)

y-2=3/2x - 3/2

y-2 +2= 3/2x - 3/2 +2

y=3/2x + 1/2

Answer:

3.2 hours

Step-by-step explanation:

Answer: Indep. is: $3 and the dependent is $1

Step-by-step explanation:

Every item is $3, but if you add more then you also add $1

Answer:

C.1/12

Step-by-step explanation:

Divide 5/12 by 5 since he cut it into 5 equal pieces

Answer:

10 days

Step-by-step explanation:

4ft-2ft= so the snail moves 2ft every 24hrs

20ft÷2ft= takes the snail 10 days

Answer:

Defining Variables:

Let the number of days the snail takes to climb = x days

Total distance climbed in x days = x*4

Total distance slipped in x days = 2*x

Solving for the number of days:

Since the total distance the snail climbs is 20ft (depth of well)

The total distance climbed - total distance slipped = 20

replacing the variables

4x - 2x = 20

2x = 20

x = 10

Therefore, it will take the snail 10 days to reach the top

Answer:

The constant of proportionality is the ratio between two directly proportional quantities

Step-by-step explanation:

Two quantities are directly proportional when they increase and decrease at the same rate.

Answer:The constant of proportionality is the constant value of the ratio of two proportional quantities x and y, typically the equation is Y=KX.

Step-by-step explanation:

Answer:

The slope is 2. As x increase y is increase and as x decrease y decrease

Answer:

Step-by-step explanation:10,000square you have to multiply them my all squares to get the answer

Answer:

5/12

Step-by-step explanation:

Isn't this just a ratio?

Answer:

27

Step-by-step explanation:

The area of the triangle is 30.9 square units.

We have,

From the figure,

Height = Distance between (-2, 6) and (-2, 0).

Base = Distance between (-2, 0) and (7, -5).

To find the distance between two points in a Cartesian coordinate system, use the distance formula:

Distance = [tex]\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]

Height:

Distance = √((-2 - (-2))² + (0 - 6)²)

Distance = √(0² + (-6)²)

Distance = √(0 + 36)

Distance = √36

Distance = 6

Base:

Distance = √((7 - (-2))² + (-5 - 0)²)

Distance = √((7 + 2)² + (-5)²)

Distance = √(9² + (-5)²)

Distance = √(81 + 25)

Distance = √106

Distance ≈ 10.3

Now,

The area of the triangle.

= 1/2 x base x height

= 1/2 x 10.3 x 6

= 10.3 x 3

= 30.9 square units

Thus,

The area of the triangle is 30.9 square units.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ4

Answer:

Bro this has no solution

Answer: 4(x−5)

Step-by-step explanation: I think this is right. If it’s not Im sorry. But if it is hope this helps!

Answer:c

Step-by-step explanation:

The measures of the angles in triangle ABC are; m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°

It follows that the right angle is between the two shorter sides;

On this note, the angle, m∠A is opposite side BC;

Therefore, from sine formula;

m∠A ≈ 73.7°

And from sum of angles in a triangle;

m∠A ≈ 16.3°

Read more on right triangle;

https://brainly.com/question/2437195

Answer:

true

Step-by-step explanation:

Because it is

Answer: 8 SUVs to 57 total

Step-by-step explanation: You add 34 + 15 + 8 which gives you 57 Then you see there are 8 SUVs. So the answer is 8 to 57.

Sorry. I kinda got ahead of myself and excited. Guess mistakes happen. I was right the first time. I'm just so tired right now

Answer:

12x - 12

Step-by-step explanation:

-2(x  + 6)

open the parenthesis

-2 * x + -2 * 6

-2x - 12

-2x - 12

Answer:

ok

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

-3x+7=28

     -7=28

           -7

-3x/21

x=-7

Answer:

The couch is 867 and the coffee table is 289

Step-by-step explanation:

The question states that the couch is 3 times the cost of the coffee table. This means this includes the cost of the couch and the coffee table. So I would do 1156= x+3x, which equals 1156=4x. X is the cost of the coffee table. 3x is the cost of the couch. I'd divide 1156 by 4 and get 289. Now you take 289 and plug it in the equation, 1156=x+3x. X would equal to 289, and 3x would equal to 867.

Answer:  It is irrational.

Step-by-step explanation:

√18 is an irational number. Multiplying most rational numbers by an irrational number results in an irrational number.

Answer:

look at attached image, hope this helps! :)

Not enough information is given to answer this question. If there was 100% water at the beginning of the hike and now there is 80% it would be 20% but without the information, you cant know.

Answer:6.03*10^3

Step-by-step explanation:

(3.1 *10^2)(2*10^3)

2*10^3=20*10^2

(3.1*10^2)(20*10^2)

(60.3*10^2)=

6.03*10^3

Answer:                        

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

hope it helps

please mark as Brainliest

Answer:

x = 2

Step-by-step explanation:

For me it's easier to work with decimals than fractions, so I converted 3/4 to .75

.75(x + 18) = 15

.75x + 13.5 = 15  

That was just distributing the .75 but here is where it gets a bit confusing.

.75x + 13.5 = 15

       -13.5     -13.5

.75x = 1.5

Divide both sides by .75 to isolate the variable.

x = 2

Hope that helps and have a great day!