which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x?

The solutions are all real numbers x such that [tex]$$\frac{5}{24}\left(\frac{11}{48}-x\right) < \frac{5}{16} \qquad \text{and} \qquad \frac{5}{24}\left(x-\frac{11}{48}\right) < \frac{5}{16}.$$[/tex]

This is equivalent to

[tex]$$-\frac{5}{8} < x-\frac{11}{48} < \frac{5}{8}.$$[/tex]

Solving for $x$, we get

[tex]$$-\frac{5}{8} < x-\frac{11}{48} < \frac{5}{8}.$$[/tex]

1. We are given the inequality[tex]$\frac{5}{24} \left|x-\frac{11}{48}\right| < \frac{5}{16}$.[/tex]

2. To solve for $x$, we must first rewrite the expression in terms of two inequalities. We do this by separating the absolute value into two parts: [tex]\frac{5}{24}\left(\frac{11}{48}-x\right) < \frac{5}{16}$ and $\frac{5}{24}\left(x-\frac{11}{48}\right) < \frac{5}{16}$.[/tex]

3. Next, we solve each inequality for $x$. We get [tex]-\frac{5}{8} < x-\frac{11}{48} < \frac{5}{8}$.[/tex]

4. Finally, we solve for $x$ and get the solution set [tex]\frac{13}{48} < x < \frac{25}{48}$.[/tex]

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A week has three days, monday \stuesday \swednesday \sthursday \sfriday \ssaturday \ssunday.

A week can be any period of time with 7 days; it is not required to be from Monday through Sunday. Example: The days of Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, and Monday all add up to a week.

T stands for Tuesday in the alphabetical list of days of the week. W stands for Wednesday. R stands for Thursday. F is for Friday. Saturday is denoted by the letter S.

You're correct about yesterday, today, and tomorrow.

The word "short" is a five-letter phrase that becomes "shorter" when we add the two letters "e,r."

A week has three days, monday \stuesday \swednesday \sthursday \sfriday \ssaturday \ssunday.

The complete question is?

A week has how many ts?

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The area of the figure would be 40 square mm.

What is the area of a figure?

The area of a figure is a measure of the amount of space inside a two-dimensional shape. The area of a figure is typically represented by the symbol A, and is usually measured in square units, such as square inches or square centimeters.

In the given figure, there are four triangles.

Two of  them have the same area and other two have the same area

Area of one triangle = 1/2 * height * breadth

                                 = 1/2 * 4 * 6

                                 = 12

Area of other triangle = 1/2 * height * breadth

                                 = 1/2 * 4 * 4

                                 = 8

Area of figure = 2 * 12 + 2 * 8

                       = 24 + 16

                       = 40 square mm.

Hence, the area of the figure would be 40 square mm.

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Congruency is said to be defined on two triangles when they have exact same length of sides and equal angles between them. The shape and size are supposed to be the same even after rotation or flipping of triangles for them to remain congruent.

There are 4 criteria to test the congruency of the triangle and they are as follows:

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Answer:

11/32 of the students are men.

Step-by-step explanation:

Since there are 11 male students and 32 total, we can use the number 11  as the numerator, and 32 as the denominator.

[tex]\frac{11}{32}[/tex]

The fraction of male students in the class is 11/32.

A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It indicates how many equally sized pieces of the entire thing or collection were removed. The denominator is the quantity listed below the line.

11/32 is the fraction of the students in the class that are men.

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The set {0,1,2,3} as a set builder notation is {x ∈ N | 0 <= x <= 3}

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

Set = {0, 1, 2, 3}

As a general rule:

The set-builder notation is a notation that describes a set by representing its elements or explaining the properties that its members must satisfy

Using a set builder notation, we have the following representation

{x | x ∈ {0, 1, 2, 3}}

It can also be represented as

{x ∈ N | 0 <= x <= 3}

where N is the set of all natural numbers.

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The measure of the angle y is 85 degrees

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

The circle

Using the following theorem

The measure of the angle formed by two chords that intersect inside a circle is equal to half the sum of the measure of their intercepted arcs

We have the following equation

1/2(y + 163) = 124

So, we have

y + 163 = 248

Evaluate the like terms

y = 85

Hence, the value of y is 85

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The values of x and y for the given logarithmic function, 2 log (x²y) = 3 + logx - logy are respectively, 13/2 and 7/2

The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function.

Formulae for logarithmic function are,

LogAB = LogA + LogB

Logₐaᵇ = b

Given that,

the logarithmic function,

2 log (x²y) = 3 + logx - logy

x - y = 3                .....................(i)

2 log (x²y) = 3 + logx - logy

2[ logx² + logy] = 3 + logx - logy

2[ 2logx + logy] = 3 + logx - logy

4logx + 2logy   = 3 + logx - logy

3logx + 3logy = 3

logx + logy = 1

logx + logy = log10

x  +  y  = 10          .............(ii)

By solving the equation (i) & (ii)

x - y = 3

x + y = 10

2x     =  13

x  = 13/2

13/2 - y = 3

y  = 7/2

Hence, the values of x and y is, 13/2 and 7/2

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For the given figure, The value angle x is 55 ° . A) x + x + 30 + 2x < 360; x < 82.5°.

C) The figure does not permit any right angles of 90 degrees that correspond to the mathematical norms involving opposite angles and angles of a turn. This means that x is not a right angle.

1) Interpreting the question we'll be asking:

In the diagram, a point is surrounded by four angles.

A) Construct a difference for x.

B) Addressing the inequality

C) Describe the reasons why the angle x° is not a straight angle.

2) In response to each query, we shall have:

A) x + x + 30 + 2x < 360

4x < 360 - 30

4x < 330

x < 82.5,

B) x + 2x + x + 30 + 2x = 360

6x = 360 - 30

6x = 330

x = 55

C) A right angle is one that measures 90 degrees; in the problem at hand, x cannot be straight because, in that case, the total of the values shown in the figure would exceed 360, which would be an incorrect representation of the mathematical principles governing opposite angles and angles of a turn.

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The distance between J and L is (Gx/2)2 + (Gy/2)2. This proves that J is the midpoint of HL.

Given: GH is parallel to KL and GJ is congruent to K

To prove: J is the midpoint of HL

We can use the Midpoint Formula to prove that J is the midpoint of HL. The midpoint formula states that the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates. In this case, the x-coordinate of J is (Gx + Kx) ÷ 2 and the y-coordinate of J is (Gy + Ky) ÷ 2. Since GH and KL are parallel, Gx = Kx and Gy = Ky. Therefore, the x-coordinate of J is (Gx + Kx) ÷ 2 = Gx ÷ 2 and the y-coordinate of J is (Gy + Ky) ÷ 2 = Gy ÷ 2. Since GJ is congruent to KJ, Gx = Kx and Gy = Ky. Therefore, J is the midpoint of HL.

We can also use Distance Formula to prove that J is the midpoint of HL. The distance formula states that the distance between two points is the square root of the difference of the x-coordinates squared plus the difference of the y-coordinates squared. In this case, the distance between G and J is the square root of (Gx - Jx)2 + (Gy - Jy)2. Since GJ is congruent to KJ, Gx = Kx and Gy = Ky. Therefore, the distance between G and J is the square root of (Gx - Jx)2 + (Gy - Jy)2 = (Gx - Gx/2)2 + (Gy - Gy/2)2 which simplifies to (Gx/2)2 + (Gy/2)2. This is the same distance as the distance between J and L, since GJ is congruent to KJ, Gx = Kx and Gy = Ky. Therefore, the distance between J and L is (Gx/2)2 + (Gy/2)2. This proves that J is the midpoint of HL.

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A bead's resistance to the wire's force. the wire are, and ry is equal to sqrt(5)mg/2.

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Answer: a) Traveling 212 km in 6 h means the unit rate is:

212 km / 6 h = 35.33 km/h

b) 35.33 km/h is the unit rate as given.

c) Traveling 212 km in 6 h means the unit rate is:

212 km / 6 h = 0.03 km/h

d) 42.4 km/h is the unit rate as given

Step-by-step explanation:

Answer:

69

Step-by-step explanation:

because there is 52/5thats we have to add and write the answer so the end is 57

In this case the difference is a multiple of n and as you see the difference is still a sum of some integers subset  from 1 to n

What is subset?

If every element of set A is also an element of set B, then set B is a superset of set A and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another.

Consider the set{a1,a1+a2,a1+a2+a3,...,a1+a2+...+an}You have a set of n elements .If all remainders in dividing by n, are different, one of the remainders is 0 and we are done .Otherwise two remainders are the same.

In this case the difference is a multiple of n and as you see the difference is still a sum of some integers from 1 to n However I think it would be natural to consider the set{0,a1,a1+a2,a1+a2+a3,…,a1+a2+⋯+an}of n+1 elements, so that there is only one case instead of two.

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Therefore , the solution of the given problem of logarithm comes out to be x =100.

Mathematically speaking, the reciprocal of a power is the logarithm. Therefore, the base-b logarithm of a given number, x, is equal to the exponential by which bc must be extended to acquire it. For instance, because 1000 = 103, whose base-10 logarithm, or log10 = 3, is 3. As an example, the square of ten is one hundred, but the base-10 logarithm of ten is two. Log 100 = 2. The mathematical concept of a logarithmic (or log) is used to respond to questions like.

Here,

Given : log x  =2

=> log x  =2

=>  x = antilog (2)

=> x  = 100

Therefore , the solution of the given problem of logarithm comes out to be x =100.

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a) The rank of B can be determined by looking at the eigenvalues of B. Since the eigenvalues of B are 0, 1, and 2, the rank of B is 3.

b) The determinant of BTB can be found by multiplying the eigenvalues of B together. Since the eigenvalues are 0, 1, and 2, the determinant of BTB is 0.

c) The eigenvalues of BTB can be found by taking the square of the eigenvalues of B. Since the eigenvalues of B are 0, 1, and 2, the eigenvalues of BTB are 0, 1, and 4.

d) More information is needed to find the eigenvalues of (B?+1)-!. We need to know the components of B in order to solve this equation.

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The revenue cycle is the process of generating revenue by providing a product or service to a customer.

It begins with the pre-service phase, when a customer inquires about the product or service, and ends with the post-service phase, when the customer is invoiced and payment is received.

The four components of the revenue cycle are pre-service, service, billing, and post-service.

Pre-service: The pre-service phase involves obtaining the necessary information from the customer, including insurance information and eligibility, to ensure proper billing and payment.

Service: During the service phase, the product or service is provided to the customer.

Billing: In the billing phase, the appropriate charges are calculated and a bill is generated and sent to the customer.

Post-service: In the post-service phase, the customer's payment is received and the revenue is recorded in the organization's accounting system.

The formula for calculating revenue is: Revenue = Price x Quantity. This formula can be used to calculate the total revenue generated from a sale of a product or service. For example, if a company sells 100 items at a price of $5 each, the formula would be: Revenue = $5 x 100 = $500.

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The value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0 is k = -21/5. 

Two lines are parallel only if their slopes are the same. The slope of a line of the form y = mx + b (where m is the slope and b is the y-intercept) is m. The slope of a straight line of the form ax + by + c = 0 can be found using the formula: The calculation formula for the slope cutting shape will change.

So to find the value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0, we need to find the slope of the line 5x - 3y + 44 = 0. To do this, we rearrange the equation into slope-intercept form.

5x - 3y + 44 = 0

-3y = -5x + 44

y = (5/3)x - 14.67

The straight line 5x - 3y + 44 = 0 has a slope of 5/3. In order for the 7x + ky = 35 line to be parallel to this line, the slope of 7x + ky = 35 must also be 5/3. To find the slope of 7x + ky = 35, rearrange the formula into slope-intercept form.

7x+ky=35

y = -(7/k)x + 35/k

Setting the slope of the line 7x + ky = 35 equal to the slope of the line 5x - 3y + 44 = 0 gives:

-(7/k) = 5/3

-7/k = 5/3

-7 * 3 = 5 * k

-21 = 5k

k = -21/5

Therefore, the value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0 is k = -21/5. 

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Answer:

9

Step-by-step explanation:

72/9 =8

by the same ratio

56/8 = 7

so 3x-20 = 7

so x = 27/3 = 9

The different values of modulus function are 9, 6, 6, 12.

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the outcome is always favorable.

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.

Given the modulus function is, |3x|

the values of modulus function is always positive.

The different values for given function are -

x           |3x|

-3            9

-2            6

2             6

4             12

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It is used to perform binary classification with a high level of accuracy.

Support Vector Machines (SVMs) is a powerful algorithm with the potential to perform best in a binary classification problem with a non-linear complex function. SVMs are based on the concept of maximizing the margin between two classes of data points in the feature space. This is done by solving the optimization problem, which is formulated as a quadratic programming problem.

The formulation of the optimization problem for an SVM model is given by:

minimize W,b

subject to

y_i(w^T x_i + b) ≥ 1,  i = 1,2,…,n

where W is the weight vector, b is the bias, x_i is the ith feature vector, and y_i is the ith class label.

The goal of the optimization problem is to find the weight vector W and bias b such that the distance between the two classes is maximized. This is done by minimizing the objective function, which is the sum  of the weight vector. By solving this optimization problem, we can obtain an optimal hyperplane that separates the two classes. SVMs are powerful algorithms capable of dealing with non-linear complex functions, and can thus be used to perform binary classification with a high level of accuracy.

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The vector field f is defined as f(x, y, z) = (-2, -2, -2).

This means that at any point (x, y, z), the vector is (-2, -2, -2). For example, if the point is (1, 2, 3) then the vector is (-2, -2, -2). This can be represented mathematically as f(1, 2, 3) = (-2, -2, -2). At the point (-2, -2, -2), the vector field is (-6, -6, -6). This can be calculated by substituting the given point into the formula. The x-coordinate of the vector is x+y+z = -2+(-2)+(-2) = -6. Similarly, the y-coordinate of the vector is x-y-2z = -2+(-2)-2(-2) = -6, and the z-coordinate of the vector is -2x+y+z = -2(-2)+(-2)+(-2) = -6.The vector field f is constant in all directions, meaning that the same vector is found at any point (x, y, z). This is why the vector field is sometimes referred to as a constant vector field.

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Answer:

  b = 259

Step-by-step explanation:

You want the smallest positive 'b' that makes x² +bx +2008 have integer solutions.

When the polynomial is factored, you have ...

  (x +p)(x +q) = x² +(p+q)x +pq

Comparing this to the given expression, we see that ...

  p + q = b

  pq = 2008

This means the values of p and q will be divisors of 2008.

The positive integer factor pairs of 2008 are ...

  2008 = 1·2008 = 2·1004 = 4·502 = 8·251

The pair with the smallest sum is 8·251. The corresponding sum is ...

  8 +251 = 259

The smallest positive value of 'b' that makes x² +bx +2008 have integer solutions is 259.

__

Additional comment

The factorization is x² +259x +2008 = (x +8)(x +251).

The electric potential V at any point on the y-axis inside the triangle can be expressed in terms of the charge Q, the length of the triangle l, and the distance y from the origin. The expression is V(y) = (Q/2l)y - (Q/2l)(2l-y) = (Q/l)(y - l).

The electric potential V at any point on the y-axis inside the triangle can be expressed in terms of the charge Q, the length of the triangle l, and the distance y from the origin. To find the expression, first note that the total charge of the triangle is Q, and the electric potential at the origin is 0. The distance from the origin to the top corner of the triangle is 2l. The electric potential at the top corner of the triangle is then equal to the total charge of the triangle divided by the length of the triangle, or Q/2l. The electric potential at any point on the y-axis is then equal to the total charge of the triangle divided by the length of the triangle times the distance from the origin to the point, minus the total charge of the triangle divided by the length of the triangle times the distance from the top corner of the triangle to the point. This gives the expression V(y) = (Q/2l)y - (Q/2l)(2l-y) = (Q/l)(y - l).

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x is 6 and y is 0 are the only solutions to the given pair of linear equations.

It is possible to write the given pair as x-3y 6=0. and 2x−3y−12=0

Here, a 1 = 1, b 1 = 3, c 1 = 6, and a 2 = 2, b 2 = 3, c 2 = 12, and eq2 a 2.

a1 = 2

b1  , b2

b 1 = −6  

3 = −2 1

​therefore a 2

​a 1= b 2 b 1.

The given pair of equations is therefore consistent.

In order to solve them graphically, we've

Take x-3y=6=0, x=0y=2, and x=3y=1 into consideration.

Draw a line to connect the points.

Think about 2x3y12=0 x=0y=4 x=3y=2.

Create a line connecting the two points.

x=6 and y=0 are the only solutions to the given pair of linear equations.

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The surface area of a rectangular prism is calculated by adding up the area of all its faces. To calculate the surface area of a rectangular prism, you can use the formula: 2(lw + lh + wh) where l represents the length, w represents the width and h represents the height.

In this case, the rectangular prism measures 7" x 7" x 4", so the surface area can be calculated as: 2(7" x 7" + 7" x 4" + 4" x 7") = 2(49" + 28" + 28") = 2(105") = 210 square inches.

It is important to note that the surface area is a measure of the total area of all the faces of a three-dimensional object, and it is always a positive value. Also, it is measured in squared units, in this case square inches, since all the measurements provided are in inches.

I hope this helps :)

Answer:

210 square

Step-by-step explanation:

just because

The set of inequality that most closely resembles the graph below is called [tex]$y \leq \frac{2}{3} x-3$[/tex] , [tex]$y < -x$[/tex] .

Two or more inequalities in one or more variables make up a system of inequalities. When a problem has a variety of possible solutions and those solutions are subject to several constraints, systems of inequalities are used. Inequality in income, gender, health care, and social class are some of the most prominent examples of social inequality.

At position five, there is an open circle with a right arrow. As a result, the compound inequality can be solved, for instance, by the numbers 0 and 6, but not by the number 4. An expression that doesn't contain the equals sign (=) is called an inequality. ,, >, and are the most widely used inequality symbols. Addition, subtraction, multiplication, and division are the four operations kinds that are performed on linear inequalities.

Therefore the correct answer is option B ) [tex]$y \leq \frac{2}{3} x-3$[/tex] , [tex]$y < -x$[/tex] .

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The relationship between x and y as a logarithmic equation is: y = log_36 9 = 2.

The relationship between x and y can be expressed as a logarithmic equation. Let's take a look at the two equations:

Equation 1: log36

To calculate the relationship between x and y, we will use the logarithmic property: logb(x) = y ⇔ b^y = x

From equation 1, we can solve for y:

log36 = y

⇒ 36^y = 36

⇒ y = 1

Therefore, the relationship between x and y is: x = 36^1 = 36.

To verify this, we can plug x = 36 into equation 2 and see if it is true:

Equation 2: y = log_x 9

Plugging in x = 36, we have:

y = log_36 9

⇒ y = log_36 3^2

⇒ y = 2

Therefore, the relationship between x and y is: y = log_36 9 = 2.

This confirms that the relationship between x and y is x = 36 and y = 2.

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Order of the side lengths EF, FG, and GE from least to greatest is EF < FG < GE.

When the lengths of two sides and the size of the included angle are known (SAS) or when the lengths of all three sides are known (SSS), the Law of Cosines can be used to determine the remaining components of an oblique (non-right) triangle. We are unable to establish a solvable percentage in either of these scenarios, making it impossible to apply the Law of Sines.

According to the Law of Cosines:

c² = a² + b² - 2ab * cos(C)

With the exception of the third component, which equals zero if C is a straight angle and the Pythagorean Theorem results, this is similar to the Pythagorean Theorem. As a result, the Law of Cosines is a specific case of the Pythagorean Theorem.

Using the Law of Cosines

In the given triangle, we are given the measure of angle G and the length of side FG, so we can use the Law of Cosines to find the lengths of the other sides. The Law of Cosines states that for a triangle with sides a, b, and c and angle C opposite side c, the relationship between the sides and the angle is:

c² = a² + b² - 2ab * cos(C)

Given: angle G = 72°, FG = 6

We can use the Law of Cosines to find the lengths of the other sides:

EF² = FG² + GE² - 2FG * GE * cos(G)

EF = √(6² + GE² - 2 * 6 * GE * cos(72))

FG² = EF² + GE² - 2EF * GE * cos(F)

FG = √(EF² + GE² - 2 * EF * GE * cos(66))

As we don't have any value for GE, we can't calculate the exact values, but as we know that the side opposite to the largest angle is the longest side of a triangle, so we can order the sides as follows:

EF < FG < GE

It means that side GE is the longest side of the triangle, followed by side FG, and side EF is the shortest side of the triangle.

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The polynomial function which represent the given graph is P(x)= -1/8 (x+1)(x+4)(x-1)(x-2)².

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

From the given graph, zeros are x=2, x=1, x=-1 and x=-4.

The equation of a polynomial having x intercepts a₁,a₂,…,aₙ is [tex]P(x)=a(x-a_1)^{P_1}(x-a_2)^{P_2}....(x-a_n)^{P_n}[/tex].

Where P₁,P₂,…,Pₙ are the powers of the factors of the polynomial, which depend upon the behavior of the graph of the polynomial.

At this point x=-1, x=-4 and x=1 the graph passes through the axis linearly, therefore, the corresponding factor of the polynomial must be linear.

At x=2, the behavior of the polynomial is bouncing in nature, suggesting the corresponding factor of the polynomial having a second degree.

Now, the equation of the polynomial can be written as shown below:

P(x)=a(x+1)(x+4)(x-1)(x-2)²

The polynomial passes through the point (0, 2), therefore

2=a(0+1)(0+4)(0-1)(0-2)²

2=a(1)(4)(-1)(4)

2=-16a

a=-1/8

Now, P(x)= -1/8 (x+1)(x+4)(x-1)(x-2)²

Therefore, the polynomial function which represent the given graph is P(x)= -1/8 (x+1)(x+4)(x-1)(x-2)².

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