Step-by-step explanation:
4(2x-7)+4>-88
4(2x-7)>-92 Subtract 4 from both sides
8x-27>-92 Distributive property
8x>-65 Add 4 to both sides
-8x<65 I call this the negative switch, but it is called something else
x<-8.125
BRIDGES The lower arch of the Sydney Harbor Bridge can be modeled by g(x) = - 0.0018 * (x - 251.5) ^ 2 + 118 where in the distance from one base of the arch and g(x) is the height of the arch. Select all of the transformations that occur in g(x) as it relates to the graph of f(x) = x ^ 2
The transformations to the graph of the quadratic function are given as follows:
The graph stretches vertically because of the multiplication by 3.The graph is translated left because x -> x + 7.The graph is translated down because y -> y - 6.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.Additionally, when the function is multiplied by |a| > 1, it is said that the function is vertically stretched by a factor of a.
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Find the mean of the following data set. 42, 45, 58, 63 1. 42 2. 47 3. 52
Answer:
52
Step-by-step explanation:
42, 45, 58, 63
The mean is the sum divided by the number of terms
(42+ 45+ 58+ 63)/4
208/4
52
Answer:
Step-by-step explanation:
42 + 45 + 58 +631 + 422 + 473 + 52 = 1723
then divide by 7 to get 246.142857
hope this helps :)
Can anyone help me with this math question please I will give brainlist!!
Answer:
b. (6, 4)
Step-by-step explanation:
i hope this helps :)
Answer:
B. (6,4)
Step-by-step explanation:
The point is inside the triangle.
Solve this system of equations algebraically:
y – 10 = 11x + x2
y – 12x = 30
The first solution is (–4, –18).
The second solution is (
,
).
Answer:
(-4,-18) and (5,90)
Step-by-step explanation:
I'll assume the first equation is supposed to be y – 10 = 11x + x^2
This is a parabola. The second equation is a straight line:
y – 12x = 30
We want to find the points at which these lines intersect. They will intersect for any (x,y) that
Let's rearrange the second equation to isolate y:
y – 12x = 30
y = 30 + 12x
Now we can take the this value of y and substitute it into the first equation:
y – 10 = 11x + x^2
(30 + 12x) – 10 = 11x + x^2
20 + 12x = 11x + x^2
0 = x^2 -x -20
We can factor this into (x+4)(x-5)
That means x can be either -4 or 5.
Find the value of y using these values of x in both original equations:
For x = -4
y – 10 = 11x + x^2
y = 11x + x^2 + 10
y = 11(-4)+(-4)^2 +10
y = -44 + 16 + 10
y = -18 The point both lines meet is at (-4, -18) which was already given in the problem.
For x = 5
y – 10 = 11x + x^2
y = 11x + x^2 + 10
y = 11(5) + (5)^2 + 10
y = 55 + 25 + 10
y = 90
The second point both lines meet is (5,90).
We should use both solutions in the second equation to verify these values, but I'll graph them, instead. See the attached graph to prove these points are correct.
how to determine if a binomial is a factor of a polynomial
A binomial is a factor of a polynomial has been determined by using the
polynomial division method.
To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:
Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.
Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.
Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.
Repeat the division process with the new polynomial obtained from the subtraction step.
Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.
If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.
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find the inverse of the linear transformation y1 = x1 7x2 y2 = 3x1 20x2
Linear transformations are defined as mathematical functions that map a vector space to another vector space. An inverse of a linear transformation is a transformation that will take the output of the first transformation and get back to the original input.
A linear transformation is invertible if and only if its matrix representation is invertible. The matrix representation of the linear transformation can be represented as below:\(\begin{pmatrix} 1 & 7\\ 3 & 20 \end{pmatrix}\)The inverse of the above matrix can be found using the formula\( A^{-1} = \frac{1}{det(A)}adj(A)\)Where det(A) is the determinant of the matrix A, and adj(A) is the adjugate of A.
The determinant of A is calculated as\( det(A) = \begin{vmatrix} 1 & 7\\ 3 & 20 \end{vmatrix} = 20 - 21 = -1\)The adjugate of A is calculated as\(adj(A) = \begin{pmatrix} 20 & -7\\ -3 & 1 \end{pmatrix}\)Therefore, the inverse of the linear transformation can be calculated as\(A^{-1} = \frac{1}{-1}\begin{pmatrix} 20 & -7\\ -3 & 1 \end{pmatrix} = \begin{pmatrix} -20 & 7\\ 3 & -1 \end{pmatrix}\)Thus, the inverse of the linear transformation y1 = x1 + 7x2 and y2 = 3x1 + 20x2 is given by y1 = -20x1 + 7x2 and y2 = 3x1 - x2.
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In a survey of 2,600 people who owned a certain type of car, 1,170 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
45%
Step-by-step explanation:
To find the percent you need to divide 1,170 by 2,600.
. a simple undirected graph has 10 edges. 2 of the vertices are of degree 4, and the rest of the vertices are of degree 3. how many vertices are in this graph?
There are 4 vertices with degree 3, and 2 vertices with degree 4. So, there are a total of 6 vertices in this graph.
In a simple undirected graph with 10 edges, 2 vertices have a degree of 4 and the rest have a degree of 3. To determine the number of vertices in this graph, use the formula:
Sum of degrees = 2 * number of edges
Let x be the number of vertices with degree 3. Then:
(2 * 4) + (3 * x) = 2 * 10
8 + 3x = 20
3x = 12
x = 4
We also know that two of the vertices have a degree of 4, which means that together they contribute 8 to the sum of all vertex degrees. This leaves us with 20 - 8 = 12 degrees left to distribute among the other vertices. Since the remaining vertices all have a degree of 3, we can set up the equation 3x = 12, where x is the number of remaining vertices. Solving for x, we get x = 4. Therefore, the graph has a total of 6 vertices - two with a degree of 4 and four with a degree of 3.
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help pleasee asap! im super confused
Answer:
x = 4
Step-by-step explanation:
A midpoint divides the segment into two equal parts. Each is half the length of the whole.
XY = (1/2)XZ
5x+4 = (1/2)(8x +16)
5x +4 = 4x +8
x = 4 . . . . . . . . . subtract 4x+4 from both sides
_____
Check
5x+4 = 5(4)+4 = 24
8x+16 = 8(4) +16 = 48
So, XY is half of XZ.
Evaluate
14/75
×
15/22
Give your answer as a fraction in its simplest form.
Answer:
\( \frac{14}{75 } \times \frac{15}{22} = \frac{7}{55} \)
Step-by-step explanation:
\(75 \div 15 = 5 \: 14 \div 2 = 7 \: 22 \div 2 = 11\)
The value of the fraction is given by the equation A = 7 / 55
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first fraction be represented as p = 14/75
Let the second fraction be represented as q = 15/22
Now , A = p x q
Substituting the values in the equation , we get
A = ( 14/75 ) x ( 15/22 )
A = 210 / 1650
A = 42 / 330
A = 14 / 110
A = 7/55
Therefore , the value of A is 7/55
Hence , the fraction is A = 7/55
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Parker invests money in an account paying a simple interest of
1.1% per year. If he invests $110 and no money will be added or
removed from the investment, how much will he have in one
year, in dollars and cents?
Answer:
111.21
Step-by-step explanation:
Took the test
all working out must be shown.
(a) Solve the differential equation (4 marks) -xy, given that when x=0, y=50. You may assume y>0. (b) For what values of x is y decreasing? (2 marks)
(a) To solve the differential equation -xy, we can use separation of variables. By integrating both sides and applying the initial condition when x=0, y=50, we can find the particular solution.
(b) The value of x for which y is decreasing can be determined by analyzing the sign of the derivative of y with respect to x.
(a) Given the differential equation -xy, we can use separation of variables to solve it. Rearranging the equation, we have dy/y = -xdx. Integrating both sides, we get ∫(1/y)dy = -∫xdx. This simplifies to ln|y| = -\(x^{2}\)/2 + C, where C is the constant of integration. Exponentiating both sides, we have |y| = e^(-\(x^{2}\)/2 + C) = e^C * e^(-\(x^{2}\)/2). Since y > 0, we can drop the absolute value and write the solution as y = Ce^(-\(x^{2}\)2). To find the particular solution, we use the initial condition y(0) = 50. Substituting the values, we have 50 = Ce^(-0^2/2) = Ce^0 = C. Therefore, the particular solution to the differential equation is y = 50e^(-\(x^{2}\)/2).
(b) To determine the values of x for which y is decreasing, we analyze the sign of the derivative of y with respect to x. Taking the derivative of y = 50e^(-\(x^{2}\)/2), we get dy/dx = -x * 50e^(-\(x^{2}\)/2). Since e^(-\(x^{2}\)2) is always positive, the sign of dy/dx is determined by -x. For y to be decreasing, dy/dx must be negative. Therefore, -x < 0, which implies that x > 0. Thus, for positive values of x, y is decreasing.
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write the equation of a line parallel to 2x+3y=12 that passes through the point (-3,4)
Answer:
\(y = \frac{-2}{3}x + 2\)
Step-by-step explanation:
The first step is convert the given equation in a dependent and independent equation.
\(2x + 3y = 12\)
\(3y = 12 - 2x\)
\(y = 4 - \frac{2}{3}x\)
\(x\) is the independent variable and \(y\) the dependent variable.
Since both lines are parallel the slope of both equations are the same
\(y = \frac{-2}{3}x + b\)
Now for find the unknow \(b\) replace the \(x\) and \(y\) fo the given point.
\(4 = (\frac{2}{3})3 + b\)
\(4 = 2 + b\)
\(4 - 2 = b\)
\(2 = b\)
So the final equation is equal to
\(y = \frac{-2}{3}x + 2\)
Hedi Earns 3% commission on the jewelry she sells each week last week she sold $730 worth of jewelry how much commission did she make
730*0.03=21.9
She makes $21.90
Graph the line.
y=-5x+4
15 points
Answer:
go up 4 on the y axis and then go up five and to the left 1. Also go to desmos and it will answer all out your graphing question.
Step-by-step explanation:
Brainliest pls
step by step explanation pls?
Answer:
x = 34
Step-by-step explanation:
x/3 - 7/3 = 9
Combine like terms
(x-7)/3 = 9
Multiply each side by 3
(x-7)/3 * 3 = 9*3
x-7 = 27
Add 7 to each side
x-7+7 = 27+7
x = 34
PLEASE HELP ANSWER THIS THNAK YOU
Answer:
112 cm (red, 4)
Step-by-step explanation:
length = b
width = a
b = 7a
42 = b - a
42 = 7a - a
42 = 6a
a = 7 => b = 7a b = 7*7 = 49
Perimeter = 2*(a+b)
= 2*(7+49)
= 2*(56)
= 112 cm
(Use Solving Systems by Graphing to find a solution for this question)
One cellphone provider DU charges AED10 per month plus an activation fee of AED20. A second cellphone provider ETISALAT charges AED11 per month plus an activation fee of AED15. For what number of months is the cost of either cellphone provider the same?
Answer:
5 months
Step-by-step explanation:
One cellphone provider charges AED10 per month plus an activation fee of AED20.
If I used the services of this cellphone provider for x months, total charges for the services,
y = 10x + 20 --------(1)
Similarly, charges for the second cellphone provider for x months of uses will be,
y = 11x + 15 -------(2)
Input-output table for equation (1)
x 1 2 3 4 5
y 30 40 50 60 70
Input output table for equation (2)
x 1 2 3 4 5
y 26 37 48 59 70
From these tables, we find (5, 70) is a common point for both.
It reveals that after the uses of 5 months charges for both the cellphone providers will be same (y = $70)
Help me, please! Love math but there are some things that fumble my brain. Look at the picture below and follow directions. Please provide a reasonable answer.
Answer:
In 2007 it was 450 and 2011 it was 300
Step-by-step explanation:
So the change was 300 I think this correct
There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 blues?
Answer:
Step-by-step explanation:
Total marbles = 5 + 6 + 2 = 13
P( getting blue ball from first draw) = 5/13
The marble is not replaced. So, Now total marbles will be 12 & number blue marbles will be 4
P( getting blue ball from second draw) = 4/12 = 1/3
P(getting two blues) = \(\frac{5}{13}*\frac{1}{3}\\\)
= 5/39
a + 3 + 2a = - 1 + 3a + 4 solve for A
Answer:
A=0
Step-by-step explanation:
a + 3 + 2a = - 1 + 3a + 4
a+2a-3a=-1+4-3
3a-3a=0.
0=0
Determine the
percent of the population for the following given that mu = 100 and
sigma = 15 Draw a picture and record the values, showing your
work
C. X ≥ 124.75
We can use the standard normal distribution table or calculate the z-score and find the corresponding area under the curve. The percentage of the population for X ≥ 124.75 is approximately 3.86%.
To find the percentage of the population for X ≥ 124.75, we need to calculate the z-score, which represents the number of standard deviations an observation is from the mean. The formula for the z-score is:
z = (X - μ) / σ
In this case, X is 124.75, μ is 100, and σ is 15. Plugging in these values, we get:
z = (124.75 - 100) / 15 = 1.65
Using the standard normal distribution table or a calculator, we can find the area under the curve to the right of the z-score of 1.65. The area represents the percentage of the population for X ≥ 124.75.
From the standard normal distribution table, we find that the area to the right of the z-score 1.65 is approximately 0.0495. Multiplying this by 100, we get 4.95%.
However, since we are interested in X ≥ 124.75, we need to consider the area to the left of the z-score of 1.65 and subtract it from 1. This gives us:
1 - 0.0495 = 0.9505
Multiplying 0.9505 by 100, we find that the percentage of the population for X ≥ 124.75 is approximately 95.05%. Therefore, the percentage of the population for X ≥ 124.75 is approximately 3.86%.
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please help, i have no clue what i’m doing in trigonometry lol
does anyone else like despise egdenuity math with like their whole heart because you want to try to understand it and you think you do until it confuses the hell out of out and you just want to scream your head off ??!
like me personally i love math when im not home schooled and i am actually in my classes everyday with my friends and when we all mess around but still manage to get our work done but online i hate it so much like theres no point its just to confusing for me XD
Overall, learning math online can be a challenge, but with the right strategies and resources, it can be easier to understand and enjoy.
What is mathematics?Mathematics is the study of numbers, shapes, and patterns. It is used to describe, explain, and predict physical and abstract phenomena. Mathematics is an important tool in many fields of study, including natural and social sciences, engineering, medicine, finance, and business. It is also a valuable tool for problem-solving and decision-making in everyday life. Mathematics involves both deductive and inductive reasoning, and is characterized by its use of abstraction, formalism, and logical reasoning. Mathematics is a universal language and its applications are found in a variety of disciplines.
I understand how frustrating it can be to try to learn math online. It can be difficult to understand and remember concepts when we are not in a classroom setting with our peers and teachers. Additionally, not being able to ask questions and get help from our peers or teachers in real-time can make it even more difficult to understand and learn math.
Overall, learning math online can be a challenge, but with the right strategies and resources, it can be easier to understand and enjoy.
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Is the relation a function? If it is a function, state the domain and range. If not, circle or
highlight the part that causes it to not be a function.
Answer:
Please check the explanation.
Step-by-step explanation:
Writing this relation in set notation using curly braces:
{(1, 3), (2, 5), (3, -1), (4, 0), (5, 6)}
The relation clearly indicates that each input is related to exactly one output. In other words, there is no repetition of 'x' values.
Hence, this relation is a function.
We know that the domain is the set of all x values.
Thus, the domain is: {1, 2, 3, 4, 5}
We know that the domain is the set of all y values.
Thus, the range is: {-1, 0, 3, 5, 6}
SALES Cars and trucks are the most popular vehicles. Last year, the number of cars sold was 39,000 more than three times the number of trucks sold. There were 216,000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year.
Given :
Miki has 104 nickels and 88 dimes. She wants to divide her coins into groups where each group has the same number of nickels and the same number of dimes.
There were 216,000 cars sold last year.
To Find :
Equation that can be used to find the number of trucks, t, sold last year.
Solution :
Let , number of truck sold is t and number of car sold is c.
It is given that the number of cars sold was 39,000 more than three times the number of trucks sold.
So ,
\(c=3t+39000\\\\t=\dfrac{c-39000}{3}\)
Putting value of c = 216000 in above equation , we get :
\(t=\dfrac{c-39000}{3}\\\\t=\dfrac{216000-39000}{3}\\\\t=59000\)
Hence , this is the required solution .
An equation is formed of two equal expressions. An equation that can be used to find the number of trucks, t is 216,000 = 39,000 + 3t.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that in the Last year, the number of cars sold was 39,000 more than three times the number of trucks sold. Therefore, we can write,
Number of cars sold = 39,000 + 3 times the number of trucks sold
Number of cars sold = 39,000 + 3t
where t represents the number of trucks sold.
Given that number of cars sold is 216,000. Therefore, the equation can be solved for t as shown below.
216,000 = 39,000 + 3t
216,000 - 39,000 = 3t
3t = 177,000
t = 177,000 / 3
t = 59,000
Hence, an equation that can be used to find the number of trucks, t is 216,000 = 39,000 + 3t.
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Solve for b
a) 2b x 3 = 6 c) 6 + 7b = 41
b) 32 - 3b = 2 d) 100/ 5b = 2
a) The solution for b in the equation 2b × 3 = 6 is b = 1.
b) The solution for b in the equation 32 - 3b = 2 is b = 10.
c) The solution for b in the equation 6 + 7b = 41 is b = 5.
d) The solution for b in the equation 100/5b = 2 is b = 10.
a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.
2b × 3 = 6
(2b × 3) / 2 = 6 / 2
3b = 3
b = 3/3
b = 1
Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.
c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.
6 + 7b - 6 = 41 - 6
7b = 35
b = 35/7
b = 5
Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.
b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.
32 - 3b - 32 = 2 - 32
-3b = -30
b = (-30)/(-3)
b = 10
Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.
d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.
(100/5b) × 5b = 2 × 5b
100 = 10b
b = 100/10
b = 10.
Therefore, the solution for b in the equation 100/5b = 2 is b = 10.
In summary, the solutions for b in the given equations are:
a) b = 1
c) b = 5
b) b = 10
d) b = 10
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The Delhi metro track is 240 \text{ km}240 km240, start text, space, k, m, end text long today. Two years ago, it was 200 \text{ km}200 km200, start text, space, k, m, end text long.
By what percentage did the metro track increase in the last two years?
The Delhi metro track increased by 20% in the last two years.
The Delhi metro track increased from 200 km to 240 km in the last two years. To calculate the percentage increase, we need to find the difference between the new and old lengths, divide it by the old length, and then multiply by 100.
The difference in length is 240 km - 200 km = 40 km.
The percentage increase, we divide the difference by the old length: 40 km ÷ 200 km = 0.2.
Finally, we multiply by 100 to get the percentage: 0.2 × 100 = 20%.
Therefore, the Delhi metro track increased by 20% in the last two years.
Another way to calculate the percentage increase is by using the formula:
Percentage increase = (new value - old value) ÷ old value × 100.
In this case, the new value is 240 km and the old value is 200 km.
So, the percentage increase = (240 km - 200 km) ÷ 200 km × 100 = 40 km ÷ 200 km × 100 = 0.2 × 100 = 20%.
Therefore, the Delhi metro track increased by 20% in the last two years.
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Guido tiene la cuarta parte de la edad de su padre Andrés y el triple de la edad de su hermano David. ¿Qué edad tiene cada uno, si sus edades suman 48 años?
Answer:
Guido tiene 9 años, Andrés tiene 36 años y David tiene 3 años.
Step-by-step explanation:
Con la información proporcionada, sabes que la edad de los tres suma 48, lo que se puede expresar como:
x+y+z=48, donde:
x es la edad de Guido
y es la edad de Andrés
z es la edad de David
Además, de acuerdo al enunciado puedes decir que la edad del papá Andrés es cuatro veces la edad de Guido y que la edad de David es la tercera parte de la edad de Guido y puedes escribir las siguientes ecuaciones:
y=4x
z=x/3
Ahora puedes reemplazar estas dos ecuaciones en la primera y despejar x:
x+4x+x/3=48
5x+x/3=48
16x/3=48
16x=48*3
16x=144
x=144/16
x=9
Después, puedes reemplazar el valor de x en y=4x para encontrar el valor de y:
y=4x
y=4*(9)
y=36
Finalmente, debes reemplazar el valor de x en z=x/3 para encontrar el valor de z:
z=x/3
z=9/3
z=3
De acuerdo a esto, Guido tiene 9 años, Andrés tiene 36 años y David tiene 3 años.
Resolve ax/a+x into an infinite series. Write the first 5 terms. Consider x as the variable. Then, use summation notation to create a formula for the infinite series
The infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.
The infinite series for ax/a+x can be represented as a geometric series. The first five terms can be expressed as:
\(Term 1: ax/(a+x)\\Term 2: (ax)^2/(a+x)^2\\Term 3: (ax)^3/(a+x)^3\\Term 4: (ax)^4/(a+x)^4\\Term 5: (ax)^5/(a+x)^5\)
The infinite series can be expressed using summation notation as:
\(∑_(n=1)^∞ (ax)^n / (a+x)^n\)
Using the formula for a geometric series, the sum of the infinite series can be calculated as:
\(S = ax/(a+x) * 1/(1-ax/(a+x)) \\ = ax/(a+x) * (a+x)/(a-ax) \\ = ax/(a-ax) \\ = a/a-x\)
Therefore, the infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.
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