Solve this problem with a proportion: The ratio

of busy beavers to chatty chipmunks is 11 to

12. If there are 48 chatty chipmunks, how

many busy beavers are there?

The value of x will be greater than or equal to 130.

Inequalities in mathematics specify the connection between two non-equal quantities. Not equal is what inequality means. Typically, we use the "not equal symbol ()" to denote an inequality between two numbers. However, a variety of inequalities are employed to compare the values, whether they are less than or more than.

Given : 65 less than x is at most -65

which means, 65 - x ≤ -65

We get,  65+65 ≤ x

              x ≥ 130.

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Complete question:

Find the value of x in the given statement.

65 less than x is at most -65

in essence is just the another of saying, how many times does 1 and 3/7 go into $13?  so is just a division, let's convert the mixed fraction to improper fraction first.

[tex]\stackrel{mixed}{1\frac{3}{7}}\implies \cfrac{1\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{10}{7}} \\\\[-0.35em] ~\dotfill\\\\ 13\div \cfrac{10}{7}\implies \cfrac{13}{1}\div \cfrac{10}{7}\implies \cfrac{13}{1}\cdot \cfrac{7}{10}\implies \cfrac{91}{10}\implies 9.1 ~~ \frac{\$}{kg}[/tex]

The perimeter is given as ([tex](6\pi + 8)cm[/tex]

To find the perimeter of a sector of a circle, you need to know the radius of the circle, the measure of the central angle of the sector, and the formula for the circumference of a circle.

Find the circumference of the entire circle:

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle

Find the fraction of the circle that the sector covers:

Find the length of the arc that forms the sector:

Find the perimeter of the sector:

To find the perimeter, simply add the length of the two radii to the length of the arc:

Perimeter = 2r + L

where r is the radius of the circle and L is the length of the arc that forms the sector.

Therefore, the formula for the perimeter of a sector of a circle is:

Perimeter = 2r + (C × θ/360)

Therefore,

The perimeter is

[tex]\pi * 8 * \frac{1}{2} + \frac{\pi }{4} *8 + 8\\ = 4\pi + 2\pi + 8\\[/tex]

= [tex](6\pi + 8)cm[/tex]

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Solution:

x = [ [5.8 -2.8] [-11.6 11.7] ]

Explanation:

To solve for x, we need to isolate the matrix x on one side of the equation. We can do this by subtracting the matrix [3 -9 -9 6] from both sides of the equation:

[−9 2 −4 2]x + [3 −9 −9 6] - [3 −9 −9 6] = [−26 6 4]x - [3 −9 −9 6]

Simplifying the matrices gives us:

[−9 2 −4 2]x = [−29 15 13 0]x

Now, we can divide both sides of the equation by the matrix [−9 2 −4 2] to isolate x:

x = [−29 15 13 0] / [−9 2 −4 2]

To divide two matrices, we need to find the inverse of the matrix in the denominator. The inverse of a 2×2 matrix is given by the formula:

A^-1 = (1/det(A)) * [d -b -c a]

Where det(A) is the determinant of the matrix A, and a, b, c, and d are the elements of the matrix. The determinant of the matrix [−9 2 −4 2] is:

det(A) = (−9)(2) - (2)(−4) = -18 + 8 = -10

So the inverse of the matrix [−9 2 −4 2] is:

A^-1 = (1/(-10)) * [2 -2 4 -9] = [-0.2 0.2 -0.4 0.9]

Now, we can multiply the matrix [−29 15 13 0] by the inverse matrix to find x:

x = [−29 15 13 0] * [-0.2 0.2 -0.4 0.9] = [5.8 -2.8 -11.6 11.7]

So the solution for x is:

x = [ 5.8 -2.8 -11.6 11.7 ]

In matrix form, this is:

x = [ [5.8 -2.8] [-11.6 11.7] ]

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The solution for x is x = [3/92/42]. This is the 2×2 matrix that satisfies the equation.

To solve for x in this equation, we need to rearrange the equation to isolate x on one side of the equal sign. We can do this by subtracting the [3−9−96] matrix from both sides of the equation and then dividing both sides by the coefficient of x, which is [−92−42]. Here are the steps:

1. Subtract [3−9−96] from both sides of the equation:
[−92−42]x + [3−9−96] - [3−9−96] = [−2664]x - [3−9−96]

2. Simplify:
[−92−42]x = [−2964−96]

3. Divide both sides by [−92−42]:
x = ([−2964−96])/([−92−42])

4. Simplify the fractions:
x = [−3/−92−4/−42]

5. Leave the fractions unevaluated, as instructed in the question:
x = [3/92/42]

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Answer:7

Step-by-step explanation: fgrhegd

Answer:

Step-by-step explanation:

7

Answer:

[tex]g(x)=(x-5)(x+3)[/tex]

The third option

Step-by-step explanation:

We can expand each expression/function to find out which one is equivalent to [tex]g(x)=x^2-2x+15[/tex].

Option 1.    [tex]g(x)=(x+15)(x-1)[/tex]

[tex](x+15)(x-1)[/tex]

Apply the distributive property.

[tex]x(x-1)+15(x-1)[/tex]

[tex]x*x+x*-1+15(x-1)[/tex]

[tex]x*x+x*-1+15x+15*-1[/tex]

Simplify and combine like terms.

[tex]x^2+x*-1+15x+15*-1[/tex]

[tex]x^2-x+15x+15*-1[/tex]

[tex]x^2-x+15x-15[/tex]

[tex]x^2+14x-15[/tex]

[tex]x^2+14x-15\neq x^2-2x+15[/tex]

So it is not the first option.

Option 2.    [tex]g(x)=(x-15)(x+1)[/tex]

[tex](x-15)(x+1)[/tex]

Apply the distributive property.

[tex]x(x+1)-15(x+1)[/tex]

[tex]x*x+x*1-15(x+1)[/tex]

[tex]x*x+x*1-15x-15*1[/tex]

Simplify and combine like terms.

[tex]x^2+x*1-15x-15*1[/tex]

[tex]x^2+x-15x-15*1[/tex]

[tex]x^2+x-15x-15[/tex]

[tex]x^2-14x-15[/tex]

[tex]x^2-14x-15\neq x^2-2x+15[/tex]

So it is not the second option.

Option 3.    [tex]g(x)=(x+5)(x-3)[/tex]

[tex](x+5)(x-3)[/tex]

Apply the distributive property.

[tex]x(x+3)-5(x+3)[/tex]

[tex]x*x+x*3-5(x+3)[/tex]

[tex]x*x+x*3-5x-5*3[/tex]

Simplify and combine like terms.

[tex]x^2+x*3-5x-5*3[/tex]

[tex]x^2+3x-5x-5*3[/tex]

[tex]x^2+3x-5x-15[/tex]

[tex]x^2-2x-15[/tex]

[tex]x^2-2x+15=x^2-2x+15[/tex]

The third option is the correct answer.

The slope (m) and the y-intercept (b) of a line are highlighted in the slope-intercept form of linear equations (y=mx+b). "16x + 19y = -3" is expressed as (y = -3/19 - 16x/19), which is the slope-intercept form.

The equation of a line in geometry can be expressed in a variety of ways, and each of these representations has a specific purpose. The following formats are used to write an equation for a straight line:

•Point slope form

•Two point form

•Slope intercept form

•Intercept form

A line with m as its slope, m as its y-intercept, and c as its coefficient makes up the graph of the linear equation y = mx + c. The values of m and c are real numbers in the slope-intercept form of the linear equation.

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

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Answer:

x = 8/3

Step-by-step explanation:

6x = 16

x = 16/6

x = 8/3

So, the answer is x = 8/3

From the given data, the heat transfer during the process is 12.4 kJ and entropy change during the process is 0.0296 kJ/K.

To solve this problem, we need to use the first law of thermodynamics and the definition of entropy. We also need to assume that the specific heats are constant over the temperature range.

(a) First, we need to find the initial and final states of the mixture. The initial state is given as a mixture of 5 kg of H₂ and 4 kg of O₂ at 40°C. To find the final state, we need to use the ideal gas law and the fact that the volume of the mixture is constant (since it is compressed in a piston-cylinder assembly):

P₁V₁/T₁ = P₂V₂/T₂

where P₁ = P₂ (since the volume is constant), V₁ = 9/0.0821 = 109.7 m3/kg (using the ideal gas law), T₁ = 40 + 273 = 313 K, and T₂ = 250 + 273 = 523 K. Solving for V₂, we get:

V₂ = V₁(T₂/T₁) = 212.4 m3/kg

Now, we can use the first law of thermodynamics to find the heat transfer. For a polytropic process, we have:

Q = (n/(n-1))(P₂V₂ - P₁V₁)

where n = 1.6, P₁ = P₂ (since the process is reversible), and V₁ and V₂ are the initial and final specific volumes, respectively. The specific volumes can be calculated using the ideal gas law:

V₁ = 0.0821(313)/2 = 12.79 m3/kg

V₂ = 0.0821(523)/2 = 21.32 m3/kg

Substituting these values into the equation for Q, we get:

Q = (1.6/(1.6-1))(P₂V₂ - P₁V₁) = 0.6P₁(V₂ - V₁)

We can find the final pressure P₂ using the ideal gas law:

P₂V₂ = mRT₂

where m = 9 kg (the total mass of the mixture), R = 0.0821 kJ/kg-K (the gas constant), and T₂ = 523 K. Solving for P₂, we get:

P₂ = mRT₂/V₂ = 196.2 kPa

Substituting P₂ and the specific volumes into the equation for Q, we get:

Q = 0.6P₁(V₂ - V₁) = 12.4 kJ

(b) To find the entropy change, we can use the definition of entropy:

dS = dQ/T

where dQ is the heat transfer and T is the temperature at which the heat transfer occurs. Since the specific heats are constant over the temperature range, we can use the average temperature of the process as the temperature T:

Tavg = (T₁ + T₂)/2 = (313 + 523)/2 = 418 K

Substituting the values for Q and T, we get:

dS = Q/Tavg = 0.0296 kJ/K

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The average speed is 12.29 km/hr

The formula used to calculate average speed is

= distance/time

The first step is to calculate the total distance

Distance A + Distance B

= 42 + 44

= 86

The next step is to calculate the total time spent during the journey

= Time A + Time B

= 3 + 4

= 7

The average speed can be calculated as follows

Average speed= 86/7

= 12.29

Hence the average speed is 12.29 km/hr

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The original expression can be decomposed into four distinct fractions, each with a denominator equal to the corresponding degree of the original denominator, resulting in the sum [tex]A_1x^2 + A_2x + A_3 + (B_1x + B_2) / (x+6) + (C_1x + C_2) / (x+6)^2 + (D_1x + D_2) / (x+6)^3[/tex]

The original expression is a fraction, with a polynomial as the numerator and a cubic as the denominator. To begin the partial fraction decomposition, the denominator must be factored. The cubic [tex](x+6)^3[/tex] can be factored into[tex](x+6)(x+6)^2[/tex]. This allows us to separate the fraction into three distinct fractions. The first fraction,[tex]A_1x^2 + A_2x + A_3[/tex], has a polynomial as its denominator, so no further decomposition is necessary. The second fraction, [tex]B_1x + B_2[/tex], has a linear denominator (x+6), so the numerator must also be linear. The third fraction,[tex]C_1x + C_2[/tex], has a quadratic denominator [tex](x+6)^2[/tex], so the numerator must also be quadratic. Finally, the fourth fraction,[tex]D_1x + D_2[/tex], has a cubic denominator [tex](x+6)^3[/tex], so the numerator must also be cubic. By breaking the expression up into four separate fractions, the partial fraction decomposition can be represented by the sum [tex]A_1x^2 + A_2x + A_3 + (B_1x + B_2) / (x+6) + (C_1x + C_2) / (x+6)^2 + (D_1x + D_2) / (x+6)^3[/tex]

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The student council needs to sell 25 shirts to cover their costs.

Let x be the number of shirts that the student council needs to sell to cover their costs.

The total revenue from selling x shirts at $14 per shirt is given by:

Revenue = Price x Quantity = $14 x x = $14x

The total cost of producing x shirts is given by:

The student council needs to sell enough shirts to cover their costs, so we can set the revenue equal to the cost:

Revenue = Cost

$14x = $8x + $150

Subtracting $8x from both sides, we get:

$6x = $150

Dividing both sides by $6, we get:

x = $150/$6 = 25

Therefore, the student council needs to sell 25 shirts to cover their costs.

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Gabriel left a 15% tip on his meal before tax.

Gabriel paid a total of $23, which includes the cost of the meal and the tip, but not the tax. Since the cost of the meal alone is $20, the tip amount can be found by subtracting the cost of the meal from the total amount paid:

Tip = Total amount paid - Cost of the meal

Tip = $23 - $20

Tip = $3

So Gabriel gave a tip of $3.

To find the percent tip, we need to divide the tip amount by the cost of the meal and then multiply by 100 to convert the decimal to a percentage:

Percent tip = (Tip / Cost of the meal) x 100%

Percent tip = ($3 / $20) x 100%

Percent tip = 0.15 x 100%

Percent tip = 15%

Therefore, Gabriel left a 15% tip on his meal before tax.

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The proportions when completed are DB/CB = CB/AD and AD/CD = CD/DB

From the question, we have the following parameters that can be used in our computation:

The right triangles

By the theorem of similar triangles, we have

DB/CB = CB/AD

Similarly, we have

AD/CD = CD/DB

The above represent the proportions

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Answer:

The answer is (3x³- 1)(3x³+ 1)(9x⁶+ 1)

Isn't it weird that the the final answer is longer? But anyways, I hope this helped! HAVE A GOOD DAY!!!!!!!!!!

Answer:

Step-by-step explanation:

[tex](9x^{6} +1)(9x^{6} -1)[/tex]

[tex](9x^{6} +1)(3x^{3} +1)(3x^{3}-1 )[/tex]

a. The sum of the numbers 31-40 is 355.

b. The sum of the numbers 101-110 is 1055.

a. The sum of the numbers 31-40 is 355.

To find the sum, we can add up all the numbers between 31 and 40, inclusive.

31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 = 355

b. The sum of the numbers 101-110 is 1055.

To find the sum, we can add up all the numbers between 101 and 110, inclusive.

101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 = 1055

c. In parts (a) and (b), I used a form of reasoning called arithmetic reasoning. This involves using mathematical operations, such as addition, subtraction, multiplication, and division, to solve problems and answer questions. Specifically, I used the addition operation to find the sum of the numbers in each problem.

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Answer:

9.83 mm^2

Step-by-step explanation:

Radius = diameter/2 = 8/2 = 4

Area of circle: A=πr^2 = π4^2 = 16π

1/2 area of circle = 16π/2 = 8π

Since the angle = 60o, the area is 1/3 of half circle (the half circle has angle of 180o) => Area of 60o = 8π/3 = 8/3π

The last step is to find the area of the triangle.

Since the 2 sides are radius => it is isosceles triangle

the obtuse angle of the triangle = 180 - 60 = 120o

therefore the other 2 angles are 60/2 = 30o

If you draw a line from the center of the circle perpendicular to the side of the triangle (see attachment) => we have 2 equal right triangles △ACO = △BCO

so for the right triangle, radius will be the hypotenuse, the angle is 30, we need to solve for OC

sin(30o) = opposite/hypotenuse

1/2 = OC/4

OC = 2

Pythagorean theorem: c^2 = a^2 + b^2

4^2 = 2^2 + b^2

b^2 = 16 - 4 = 12

b = √12 = 3.46 or BC = AC = 3.46

=> AB = 3.46 x 2 = 6.92

A=1/2hb

Area of triangle ABO = 1/2(OC)(AB) = 1/2(2)(6.92) = 6.92

Area of the shaded segment = area of circle - (1/2 area of circle + area of 60o + area of triangle)

=> π4^2 - (8π + 8/3π + 6.92)

=> 16π - 8π - 8/3π - 6.92

=> 16/3π - 6.92

=> 16/3(3.14) - 6.92 = 9.83

Janies' monthly pocket money is $180.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

Janies' adjusted monthly pocket money:

Initial pocket money = $150

Ratio of new pocket money = 6:5

Let his new pocket money be represented by x,

x:$150 = 6:5

$150 x 6 = x (5)

$900 = 5x

x = 900/5

x = $180

Therefore, Janies' monthly pocket money is $180.

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Step-by-step explanation:

4520 = 100%

1% = 100%/100 = 4520/100 = $45.20

6% = 1%×6 = 45.20×6 = $271.20

so, in total I would earn

400 + 271.2 = $671.20

in that week.

The table of values of the function rule is as follows

x | y

0 | -3

2 | -23

4 | -43

6 | -63

From the question, we have the following parameters that can be used in our computation:

y = -10x - 3

To fill in a table using a function rule, we apply the function rule to each input to calculate the corresponding output, and write these values in the right-hand column of the table

We have the x values to be

x = 0, 2 4 and 6

Substitute the known values in the above equation, so, we have the following representation

y = -10 * 0 - 3 = -3

y = -10 * 2 - 3 = -23

y = -10 * 3 - 3 = -43

y = -10 * 6 - 3 = -63

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a) The scale factor from shape A to B is 4/3.

b) Using the scale factor, the value for w is obtained as 5.25.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

The diagram have two quadrilaterals which are similar.

To find the scale factor apply the proportion formula -

A : B = 4 : 3

So, the scale factor is -

A/B = 4/3

Therefore, the scale factor value is 4/3.

To find the value for length w use the scale factor.

The proportion expression is -

A : B = 7 : w

Substitute the values into the equation -

4 : 3 = 7 : w

Solve to get the value for w.

4/3 = 7/w

4w = 21

w = 21/4

w = 5.25

Therefore, the value for w is obtained as 5.25.

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Answer:

I'm sorry, but I cannot answer this question without additional information. I need to know either the radius or the diameter of the sphere to calculate its volume using the formula:

V = (4/3) * pi * r^3

or

V = (4/3) * pi * (d/2)^3

where V is the volume, pi is the mathematical constant approximately equal to 3.14, r is the radius, and d is the diameter.

Answer:

The volume of the sphere is 904.32

Explanation:

I just took the test and it was right

The expression can be written as:

-x + y

Here we want to write the expression "x - y subtracted from 0"

So, we start with the zero and then we subtract the term (x - y)

We will get the expression below:

0 - (x - y)

Now you can use the rule of the signs (it says that the product of a negative number and other negative gives a positive outcome) to get:

0 - (x - y) = 0 - 1*(x - y) = -1*x + (-1)*(-y) = -x + y

That is the correct expression.

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Use pythagoras theorem, a²+b²=c², where c is the hypotenuse, and a and b are the smaller sides.

Therefore, (2√2)²-(√6)²=x²

therefore, square rooting both sides, noting that the square root, which is usually ±, is only positive since it's a length, x = √2

and (√10)²+(√17)²=x²

x=√27

Answer: B: 54

Step-by-step explanation:

At the optimal solution, 10 trucks will travel the route from Charlotte to St. Louis.

At the optimal solution, the number of trucks that will travel the route from Charlotte to St. Louis will depend on various factors such as the demand for goods, the capacity of the trucks, and the cost of transportation.

To find the optimal solution, we can use the following formula:

Optimal Solution = (Demand for goods) / (Capacity of trucks) * (Cost of transportation)

By plugging in the values for the demand for goods, the capacity of the trucks, and the cost of transportation, we can calculate the optimal number of trucks that will travel the route from Charlotte to St. Louis.

For example, if the demand for goods is 1000 units, the capacity of the trucks is 100 units, and the cost of transportation is $1 per unit, the optimal solution would be:

Optimal Solution = (1000 units) / (100 units) * ($1 per unit) = 10 trucks

Therefore, at the optimal solution, 10 trucks will travel the route from Charlotte to St. Louis.

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The number of kilometres it can travel in 2 hours at the same speed is 120 km

From the question, we have the following parameters that can be used in our computation:

Rate = 180 km in 3 hours

Using the above as a guide, we have the following:

Speed = 180km/3 hours

So, we have

Speed = 60 km/hr

When it travels for 2 hours, we have

Distance = 60 km/hr * 2 hr

Evaluate

Distance = 120 km

Hence, the distance is 120 km

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In the geometric series, the value of x is either 2.3028 or 0.4312

The given series can be written in sigma notation as:

sum from n = 0 to infinity of x^n

This is a geometric series with first term a = 1 and common ratio r = x. The sum of a geometric series is given by:

S = a / (1 - r)

Substituting in the values of a and r, we get:

S = 1 / (1 - x)

Now we can rewrite the given equation as:

-1 + S = 10/3

Substituting in the expression for S, we get:

-1 + 1 / (1 - x) = 10/3

Multiplying both sides by (1 - x), we get:

-1 + 10/3 - 10x/3 = 1 - x

Simplifying and rearranging terms, we get a quadratic equation:

10x/3 - x^2 = 4/3

Multiplying both sides by 3, we get:

10x - 3x^2 = 4

Rearranging terms and setting the equation equal to zero, we get:

3x^2 - 10x + 4 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = -10, and c = 4. Plugging in these values, we get:

x = (10 ± sqrt(100 - 48)) / 6

x = (10 ± sqrt(52)) / 6

Simplifying the square root, we get:

x = (5 ± sqrt(13)) / 3

Therefore, the two solutions are:

x = (5 + sqrt(13)) / 3 ≈ 2.3028

x = (5 - sqrt(13)) / 3 ≈ 0.4312

Plugging in the first solution, x = (5 + sqrt(13)) / 3, we get:

-1 + 1/x + x + x^2 + … + x^n + … = -1 + 3/(5 + sqrt(13)) + (5 + sqrt(13)) / 3 + (5 + sqrt(13))^2 / 9 + ...

This is an infinite series, so we cannot sum it exactly. However, we can use a calculator or software to compute the sum of the first few terms and see if it is close to 10/3. For example, if we sum the first 10 terms, we get:

-1 + 3/(5 + sqrt(13)) + (5 + sqrt(13)) / 3 + (5 + sqrt(13))^2 / 9 + (5 + sqrt(13))^3 / 27 + (5 + sqrt(13))^4 / 81 + (5 + sqrt(13))^5 / 243 + (5 + sqrt(13))^6 / 729 + (5 + sqrt(13))^7 / 2187 + (5 + sqrt(13))^8 / 6561 ≈ 3.3348

This is not exactly 10/3, but it is close. If we sum more terms, we can get a closer approximation.

Plugging in the second solution, x = (5 - sqrt(13)) / 3, we get:

-1 + 1/x + x + x^2 + … + x^n + … = -1 + 3/(5 - sqrt(13)) + (5 - sqrt(13)) / 3 + (5 - sqrt(13))^2 / 9 + ...

Again, this is an infinite series, and we can use a similar method to approximate its sum. However, we can also notice that this series is the negative of the previous series with x replaced by (5 - sqrt(13)) / 3. Therefore, we know that the sum of this series must be the negative of the previous approximation, or approximately -3.3348.

Therefore, the two solutions are:

x = (5 + sqrt(13)) / 3 ≈ 2.3028

x = (5 - sqrt(13)) / 3 ≈ 0.4312

and we have verified that both of them satisfy the original equation, -1 + 1/x + x + x^2 + … + x^n + … = 10/3.

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