The table shows the distance Penelope is from the park as she walks to soccer practice. Assume the relationship between the two quantities is linear.

Time (min), x Distance (m), y

5 1,930
10 1,380
15 830
20 280

The 5th interval is called perfect

Interval notation is a method to represent an interval on a number line.

The 5th interval is called perfect

Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.

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The scale factor of the two rectangles is 1.5

According to Euclidean Plane Geometry, a rectangle is a quadrilateral with equal opposed sides and four right angles. In other words, a rectangle is a parallelogram with a right angle of 90 degrees or an equiangular quadrilateral (i.e., 360°/4 = 90°). A rectangle is referred to as a square if its four sides are all the same length.

The ratio of the matching side lengths of two comparable figures is known as the scale factor. We know that the ratio of the respective side lengths of the two rectangles equals equivalent to r since Rectangle A and Rectangle B are similar to one another by the scale factor r.

We can set up the following ratio to determine the scale factor if the lengths of rectangles A and B are 1.5r+2.25 units and 3 units, respectively.

(1.5r+2.25) / 3 = r

Solving for r, we get:

r = (1.5r + 2.25) / 3

multiply both sides of the equation by 3

3r = 1.5r + 2.25

Subtract 1.5r from both sides

1.5r = 2.25

divide both sides by 1.5

r = 2.25/1.5

r = 1.5

Therefore, the scale factor of the two rectangles is 1.5.

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a) 7 examples are:

[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]

b) Fabric Larry will have left after using [tex]2\frac{2}{3}[/tex] yard out of [tex]5\frac{5}{6}[/tex] yard to make a bag for his computer is: [tex]3\frac{3}{6} yard[/tex]

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

7 examples of mathematical expression are:

[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]

For the second part of the question:

Larry had 5 3/6 yards of fabric. He used 2 2/3 yards to make a bag for his computer. Write an expression that will show how much of the fabric Larry will have left.

The mathematical expression that represents the amount of fabric Larry has left is:

5 3/6 - 2 2/3 = 2 7/18

You can simplify this further:

2 7/18 = 2 1/6

The amount of fabric Larry will have left is 2 1/6 yards.

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Answer:

The least common denominator is 8, you need to multiply the 3 by 2.

Answer:

8

Step-by-step explanation:

Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility test for three.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

add all number

9+9+0 = 18

and 18/3 = 6

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On solving the provided question, we can say that in this triangle 2x-6 = 3 => 2x = 9 => x = 9/2 and 2z = 4 => z = 2

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

in this triangle

2x-6 = 3

2x = 9

x = 9/2

2z = 4

z = 2

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Therefore , the solution of the given problem of ratio comes out to be

lim C(p) as p->19 = 152900.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Here,

a) To find the cost of removing 90% of the impurities, we can substitute 90 for p in the equation:

C(p) = 8100p / (100-p)

C(90) = 8100(90) / (100-90)

C(90) = 729000

So the cost of removing 90% of the impurities is Rs. 729000.

b) To find the limit of C(p) as p approaches 19, we can substitute 19 for p in the equation:

lim C(p) as p->19 = 8100(19) / (100-19)

lim C(p) as p->19 = 152900

The value of the limit of C(p) as p approaches 19 means that as the percentage of impurities approaches 19, the cost of purification approaches Rs. 152900.

c) It is not possible to purify completely as the percentage of impurities approaches 100. It's because as the percentage of impurities becomes closer to 100, the denominator of the fraction becomes smaller, thus the value of the cost of purification becomes larger, and it is impossible to pay an infinite amount of money.

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The correct answer of expression 's+3' is (c) Teresa wasn't sure how far she would swim during the first class. She would swim 3 laps during the second class. She used the sign "+" instead of "x" or any other notation.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression is (Number/variable, Math Operator, Number/variable)

The answer here should be Option C, as she used the sign "+" instead of "x" or any other notation. She wanted to add something.

And as it is very clear that she wanted to write the information about two classes, so that makes the second term for second class and first term for first class.

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The complete Question is:

Teresa wrote this expression (s+3) to describe the total distance she was going to swim during two swim classes. Which situation could be described by this expression?

A. Teresa wasn't sure how far she would swim during the first class. She would swim 3 fewer laps during the second class.

B. Teresa wasn't sure how far she would swim during the first class. She would swim the same distance for 3 classes.

C. Teresa wasn't sure how far she would swim during the first class. She would swim 3 laps during the second class.

D. Teresa wasn't sure how far she would swim during the first class. She would swim 3 times farther during the second class.

The the wind speed of a tornado with Beaufort number 9 is 51.3 miles per hour.

What is speed?

Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in meters per second (m/s) in this example because the distance is measured in meters (m) and the time is measured in seconds (s).

Given:

The Beaufort Scale measures the intensity of tornadoes. For a tornado

with Beaufort number B, the formula [tex]v = 1.9B^\frac{3}{2}[/tex] may be used to

estimate the tornado's wind speed in miles per hour.

We have to estimate the wind speed of a tornado with Beaufort number 9.

Plug B = 9 in the formula [tex]v = 1.9B^\frac{3}{2}[/tex]

⇒

[tex]v = 1.9(9)^\frac{3}{2} \\v = 1.9(27)\\v = 51.3[/tex]

Hence, the the wind speed of a tornado with Beaufort number 9 is

51.3 miles per hour.

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After simplifying each expression, we get (2+5a - 10 b), (8a² - 15ca +2c),

(11- 2a+b) and (a+ b) respectively.

The word simplify means to write an expression, equation or problems

in the simplest form so as to easy to evaluate it. we simplify an expression by removing the parenthesis and collecting like terms.

exercise 1.

given, A = 7 - 4a + 7a - 3b -5 -7b +2a

We collect the like term and get

A= 7 - 5 -4a +7a +2a -3b- 7b

A = 2 + 5a -10b

next, given B = 4a × 2a -5c - c +8c -3c × 5a

             B = 8a² -6c +8c - 15ca

        B = 8a² -15ca +2c

exercise 2.

given, A = 7 + [(2- a) -( 2+a) +9] + (b-5)

at first, we remove the parenthesis and get

A= 7 + [2-a - 2 -a+ 9] +b- 5

A = 7 + 9- 2a +b- 5

after collecting the like term

A = 11- 2a + b

given, B = 15 - [(7-b) - 9- (a-17)]

  B = 15 - [7- b- 9 - a+17]

 B = 15 - [15 - b -a]

after removing the parenthesis

B = b +a

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The secret calculator app is used to protect confidential Photos, Videos, Documents, Passwords, Notes, Contacts and To Dos.

The term calculator is referred as a device that performs arithmetic operations on numbers and it does the basic calculators can do only addition, subtraction, multiplication and division mathematical calculations.

Here we need to find definition and the usage of secret calculator app.

As per the definition of calculator here we know that the app is used to acts like a photo vault to store all password protected files, and can only be viewed inside the app.

As the user who is unaware of this app you will never expect a simple calculator looking app is used to hide files.

Here if you want to access this you will need the password to open the photos from your child.

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So x = 2.1 is the only possible value of x that makes the equation true.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

The equation is given as follows:

-3x + 6.3 = 0

To find the value of x, we need to isolate x on one side of the equation. We can do this by adding 3x to both sides:

-3x + 3x + 6.3 = 0 + 3x

6.3 = 3x

Now we can divide both sides by 3:

x = 6.3/3

x = 2.1

So x = 2.1 is the only possible value of x that makes the equation true.

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Answer:

x = 16/9

Step-by-step explanation:

9x -16 = 0

9x = 16

x = 16/9

Let's check

9(16/9) -16 = 0

144/9 - 16 = 0

16 - 16 = 0

0 = 0

So, x = 16/9 is correct!

Answer:

Step-by-step explanation:

9x = 16

x = 16/9

Answer:(-2,-2)

Step-by-step explanation:

The radical has a value of 0 when x = -2. At that point, the function value is ...

 f(-2) = √(-(-2)-2) -2 = √(0) -2

 f(-2) = -2

Answer:

-8 [tex]\leq[/tex] -8

Step-by-step explanation:

-8[tex]\leq[/tex]2-10

-8[tex]\leq[/tex]-8

Answer:

-8

Step-by-step explanation:

-8≤2-10
2-10 = -8
-8≤-8

Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

In the given question, we have to find what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

As we know that,

(1) Negative Slope: A line with a negative slope is one that is moving from left to right in a downward direction. The rise to run ratio of the line, in other words, is negative.

(2) Decreasing Function: For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

(3) Constant Slope: Small slopes correspond to low speeds, negative slopes to high speeds, and constant slopes (straight lines) to steady speeds.

Hence, Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

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The length of the straw is 3.74 inches.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

In rectangular box,

Length (l) = 2 inches

Width (w) = 1 inches

Height (h) = 3 inches

Here, The straw is said to fit into the box diagonally from the bottom.

So, the length (s) of the straw is calculated as:

⇒ s = √ l² + w² + h²

⇒ s = √ 2² + 1² + 3²

⇒ s = √ 4 + 1 + 9

⇒ s = √ 14

⇒ s = 3.74 inches

Thus, The length of straw = 3.74 inches

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The length of the straw will be 3.7416  inches long in radical form.

If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula : X²=l²+b²+h²

Here,

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 3 inch , b= 2 inch , h= 1 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

X²=14

X=√14

i.e. X=3.7416

We get, X= 3.7416 (in radical form)

Hence, the length of the straw will be  5.91607 inches.

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The simplified ratio that compares 5 meters to 100 centimeters is 5: 1 .Option A

Ratio is simply described as the non equal comparison of two numbers, variables, or events.

It shows how many times a number or variable contains another.

The comparison is also based on size.

From the information given, we have;

5 meter to 100 centimeters

It is important to note that;

100 centimeters = 1 meters

Also, 1 meter= 100 centimeters

5 meters = x centimeters

cross multiply

x = 100(5)

Multiply the values

x = 500 centimeters

Then,

5 meters = 1 meter

Hence, the ratio is 5:1

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The answer to 7^2 is 49. This means that 7 is multiplied by itself two times. To solve the given problem following steps should be followed :

Step 1: To calculate the value of 7 power 2, we need to use the exponentiation operator (^).

Step 2: The operator is written as 7^2, which is read as "seven to the power of two".

Step 3: We can calculate the value of 7 power 2 by multiplying 7 by itself 2 times.

Step 4: 7 × 7 = 49

Therefore, 7 power 2 = 49.

An expression known as "power" is defined as the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.

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The probabilities are given as follows:

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

Hence the probability of one senior having the birthday on the same day as the graduation is of:

P(X = 1) = 68 x 1/365 x (364/365)^67 = 0.1550.

The probability of more than one is given as follows:

P(X > 1) = 1 - P(X <= 1).

In which:

P(X <= 1) = P(X = 0) + P(X = 1)

Hence:

Finally:

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The speed of the Bike is 5 meters per second

Speed is a scalar quantity that describes how fast an object is moving . It is defined as the distance an object travels divided by the time it takes to travel that distance. The units of speed are typically meters per second (m/s) or kilometers per hour (km/h).

To find out how fast you are traveling on your bike, you can use the formula:

Speed = [tex]\frac{Distance}{Time}[/tex]

In this case, the distance is 340 meters and the time is 68 seconds. So, you can plug these values into the formula and get:

Speed = 340 meters / 68 seconds

Speed =  [tex]\frac{340 meters}{68 seconds}[/tex]  =   5 meters per second

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Answer:

y = 2x + 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 10) ← 2 points on the line

m = [tex]\frac{10-0}{0-(-5)}[/tex] = [tex]\frac{10}{0+5}[/tex] = [tex]\frac{10}{5}[/tex] = 2

the line crosses the y- axis at (0, 10 ) ⇒ c = 10

y = 2x + 10 ← equation of line

Answer:

70⁰

Step-by-step explanation:

We need to use the knowledge of trigonometry to find the indicated angle. Given the information in relation to the angle we have the opposite and the hypotenuse.

we therefore use Sine in this calculations

Sin ? = opposite/ hypotenuse

= 16/17

= 0.9412

to get the angle we get the sine inverse

Sine inverse of 0.9412 = 70.25⁰

= 70⁰

Answer:

? ≈ 70°

Step-by-step explanation:

using the sine ratio in the right triangle

sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{16}{17}[/tex] , then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{16}{17}[/tex] ) ≈ 70° ( to the nearest degree )

A rectangle is a four-sided geometric shape where opposite sides are parallel and congruent. The diagonals of a rectangle are two lines that connect the opposite corners of the rectangle, and they bisect each other at 90 degrees.

Briefly defined, what is rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Given the sides of rectangle WXYZ are WY = 14x + 10 and XZ = 11x + 22. We can find the length of the diagonals using the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the diagonal of the rectangle) is equal to the sum of the squares of the other two sides (the sides of rectangle)

Diagonal WX: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)

Diagonal YZ: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)

So, the lengths of the diagonals of rectangle WXYZ are √(317x^2 + 940x + 584) units.

Note that the diagonals of a rectangle are congruent and the value of x is not a known, the diagonal of rectangle is the value of the square root of the expression.

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Answer: 66

Step-by-step explanation:

I skipped it to see the answer hope this helps

Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.

Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k

y = a(x-h)^2 + k

Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get

7 = a(-2 - h)^2 + k

It passing through (1, 10), we can substitute the values of x and y in the equation and get

10 = a(1 - h)^2 + k

It passing through (2,27), we can substitute the values of x and y in the equation and get

27 = a(2 - h)^2 + k

Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k

Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.

Step-by-step explanation:

Answer:

x=2, y=4. (2, 4).

Step-by-step explanation:

3x-3y=-6 implies 3(x-y)=3(-2), so x-y=-2.

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

x-y=-2

3x+y=10

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

4x=8

x=8/4=2

2-y=-2

y=2-(-2)=2+2=4

2x2+4x5=0 is a quadratic equation that can be solved. 2 x 2 + 4 x - 5 = 0. To find the answers, start with the quadratic formula.

Using the quadratic formula, determine the roots of the quadratic equations 2x2-3x-5= 0. The equation's roots must be located. As a result, the equation's roots are 5/2 and -1. Which equation with 2 as a root must be identified. As a result, 2 is not a root of x2-4x + 5= 0.

Since 2 is not a root, x2 + 3x-12= 0 cannot be solved. Thus, 2 is the root of the equation 2x2-7x + 6= 0. The roots of the quadratic equation ax2 + bx + c= 0 are real and equivalent if the discriminant is equal to zero (b2-4ac=0), a, b, and c are real values, and a0. The roots in this situation arex= -b/2a.

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Area of the convex polygon whose vertices are the centroids of these 7 triangles is 184.

What is a convex polygon?

A polygon that forms the edge of a convex set is said to be convex polygon. This indicates that the union of the interior and the boundary of the polygon has the line segment connecting two points of the polygon.

Given,

 AB = CD = EF = GH = 10

 BC = DE = FG = HA = 11

 Triangles of side length 6,8,10 is cut from corners 23×27 rectangle.

Using the above information, we marked the position of A,B,C,D,E,F,G,H and J, taking the upper left corner of rectangle as origin.

The centroid of a triangle can be found using the formula,

 Centroid = [tex](\frac{x_{1} + x_{2}+x_{3}}{3} , \frac{y_{1} +y_{2}+y_{3}}{3})[/tex]

For ΔJAB,

[tex]C_{1}[/tex] = (8/3 , -35/6)

For ΔJBC,

[tex]C_{2}[/tex] = ( 9 , -23/6)

For ΔJCD,

[tex]C_{3}[/tex] = ( 46/3, -35/6)

For ΔJDE,

[tex]C_{4}[/tex] = ( 18 , -23/2)

Area of convex polygon = [tex]\frac{1}{2} [x_{1} y_{2} + x_{2}y_{3}+.........+x_{n}y_{1}] - [y_{1}x_{2}+y_{2}x_{3}+......+y_{n}x_{1}][/tex]

From figure we find the area of C₁C₂C₃C₄C₈, where C₈ = (8/3 , -23/2)

Area =

[tex]\frac{1}{2} [8/3 (-23/6 )+ 9(-35/6)+46/3(-23/2)+18(-23/2)+8/3(-35/6)] - [(-35/9)9+(-23/6)46/3+(-35/6)18+(-23/2)8/3+(-23/2)8/3][/tex]

= 184 / 2

Therefore total area of convex polygon = 2 × 184/2 = 184 sq. units

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Answer:

Refer to the attached image.

Step-by-step explanation:

this is a question of set of equations and solution is as follows,

Williamston Daily newspaper started printing newspaper.

Three years ago they had 5900 subscribers.

every month there is an increase of 66 new subscribers.

n is the number of months the paper has been printed.

so, the linear model will be  

B= early subscriber + number of month × increments

B= 5900 + n × 66

B= 66 n + 5900

Example - subscribers after 3 months,

n = 3

= 66 x 3 +5900

= 198 + 5900

= 6000

set of equations

A system of equations is a set or collection of equations that you deal with all together at once. Linear equations are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.

Linear equations

Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.

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