Which of the following is a solution of the equation 2x y 10 *?

The nature of roots of quadratic equation x²-2x-1 are real and distinct.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is x²-2x-1=0.

Nature of Roots depending upon Discriminant

If the discriminant is equal to zero (b² – 4ac = 0), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax² + bx + c = 0, are real and equal.

a=1, b=-2 and c=-1

b² – 4ac =4-4(1)(-1)

=4+4=8>0

b² – 4ac>0

So roots are real and distinct.

Hence, the nature of roots of quadratic equation x²-2x-1 are real and distinct.

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The reverse of multiplying whole numbers is dividing whole numbers. It is a method used to determine the number of times a number (divisor) can be found in another number (dividend).

All natural numbers and 0 are included in a group of numbers known as whole numbers. They belong to the category of real numbers, which excludes fractions, decimals, and negative numbers. Numbers used for counting are also regarded as whole numbers.

Whole numbers are all natural numbers other than zero (0). We are aware that when we talk about natural numbers, we are referring to a group of counting numbers beginning with 1 and continuing through to 9 and beyond. A collection of numbers without fractions, decimals, or even negative integers are known as whole numbers. It is made up of zero and a collection of positive numbers.

The reverse of multiplying whole numbers is dividing whole numbers. It is a method used to determine the number of times a number (divisor) can be found in another number (dividend).

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9/2 x +48 is an equation to represent the real ashton’s hip between these variables.

To write this type of fraction = 4 + 1/2 - The integer 4 in the expression is the amount of feet of rope that was cut.

Thus to know the number of 1/2 foot pieces produced, let this number be x. Thus, we have 1/2 of x pieces = 2

 x/2 = 4; x = 2x4 = 8

Thus, it has 8 pieces of 1/2 foot long piece each of rope.

9/2 x +48 is an equation to represent the real ashton’s hip between these variables.

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Given,

[tex]\longrightarrow\rm{64^x=\dfrac{1}{256^y}}[/tex]

We have to find out the value of 3x + 4y.

Multiplying both sides by [tex]\rm{256^y}[/tex] we get,

[tex]\longrightarrow\rm{64^x\cdot256^y=1}[/tex]

Then we will write 64 and 256 as powers of 4 as,

[tex]\rm{64=4^3}[/tex]

[tex]256=4^4[/tex]

Then,

[tex]\longrightarrow\rm{(4^3)^x\cdot(4^4)^y=1}[/tex]

[tex]\longrightarrow\rm{4^{3x}\cdot4^{4y}=1\quad\quad[\because(a^m)^n=a^{mn}]}[/tex]

[tex]\longrightarrow\rm{4^{3x+4y}=1\quad\quad[\because a^m\cdot a^n=a^{m+n}]}[/tex]

Now we will take log to the base 4.

[tex]\longrightarrow\rm{\log_4(4^{3x+4y})=\log_4(1)}[/tex]

[tex]\small\text{$\longrightarrow\rm{(3x+4y)\log_4(4)=\log_4(1)\quad\quad[\because\log_b(a^m)=m\cdot\log_b(a)]}$}[/tex]

We have,

[tex]\rm{\log_4(4)=1}[/tex]

[tex]\log_4(1)=0[/tex]

Then,

[tex]\longrightarrow\rm{(3x+4y)(1)=0}[/tex]

[tex]\longrightarrow\rm{\underline{\underline{3x+4y=0}}}[/tex]

Hence 0 is the answer.

Answer:

3510 marbles

Step-by-step explanation:

45 x 6 = 270

270 x 13 = 3510

Hope this helps :)

Answer:3510

Step-by-step explanation:

:)

To determine the properties of the roots of the quadratic equation (of the form ax^2 + bx +c=0), we need to compute the discriminant (b^2 - 4 a c). If the discriminant is greater than 0, the roots are unequal and real. If the discriminant is zero, the roots are equally real.

In algebra, the quadratic equation (from the Latin quadratus 'square') is rewritten in standard form as ax² + bx +c = 0

where x represents an unknown value, a, b, and c represent known numbers and a ≠ 0. (If a = 0 and b ≠ 0, the equation is linear rather than quadratic.) The numbers a, b, and c are the coefficients of the equation, the quadratic coefficient, the linear coefficient, and the constant or free period and called.

For the quadratic equation ax²+ bx+ c=0, a ≠ 0 , we found that the roots of that equation are given by

[tex]\alpha = \frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]  and [tex]\beta = \frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

The term inside the square root is called the discriminant. Discriminants can be used to analyze the types of solutions to quadratic equations without actually solving the equations. Method is as follows.

           D = b²-4ac > 0

If an equation has two distinct real solutions, i.e. α and β are real.

     α - β = [tex](\frac{-b+\sqrt{D} }{2a} ) -( \frac{-b - \sqrt{D} }{2a})[/tex]

             = [tex]\frac{-b +\sqrt{ D } +b + \sqrt{D} }{2a}[/tex] = 2√D/2a= √D/a

i.e., α-β ≠0

⇒ α ≠ β

i. For perfect squares, the roots are real, rational, and unique.

ii. If not a perfect square, the root is real, irrational, and unique.

if D = b²- 4ac =0, the equation has a real solution, i.e. a double root. Also, the α = β = -b/2a

If D= b²- 4ac < 0, then equation has only non-real solutions.

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The slope of the line y = 3 is equal to 0.

The inclination of the supplied line with respect to the x-axis is known as the slope of any line.

The findings indicate that y = 3.

As well known,

the equation for a straight line is y = mx + c.

Where 'c' is the y-axis intercept and 'm' is the slope on the y-axis.

We obtain m = 0 and c = 3 by comparing equation (1) with the standard equation of the straight line.

The formula for a horizontal line is y = 3. Since the y coordinate has not changed, the slope is zero.

The slope of the line y = 3 is therefore equal to 0.

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The tulip border should be half the size of the garden, which is 108m.

A rectangle is a closed 2-D shape with four sides, four corners, and four right angles (90°). The opposing sides of a rectangle are equal and parallel. A rectangle has two dimensions: length and width, as it is a two-dimensional structure.

A rectangle is a type of quadrilateral with four 90-degree-distance vertices and parallel sides that are equal to one another. It is also referred to as an equiangular quadrilateral because of this. A rectangle can also be referred to as a parallelogram since its opposing sides are equal and parallel.

A quadrilateral with four equal and right-angled angles is a rectangle. A square also has all equal sides in addition to all equal angles.

Tulip border area = (1/2) (area of garden)

                             = (1/2) (18 x 12)

                             = (1/2) (216)

                             =  108

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The end behavior of the graph of the polynomial function y = 10x^9 + 4x is asymptotic to negative infinity as x approaches negative infinity, and asymptotic to positive infinity as x approaches positive infinity.

The end behavior of a polynomial function is determined by the degree of the polynomial. The polynomial function y = 10x^9 + 4x is a degree 9 polynomial, so it will exhibit an asymptotic behavior in which the graph approaches either positive or negative infinity as x approaches either positive or negative infinity. In this case, the graph will approach negative infinity as x approaches negative infinity, and it will approach positive infinity as x approaches positive infinity. This behavior is due to the fact that the highest degree term (10x^9) will dominate the behavior of the graph as x gets very large in either the positive or negative direction. The lower degree terms (4x) will have a smaller effect on the end behavior of the graph.

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Base area can be determined using the same method as the square's area, which is side side or base edge².

A square pyramid consists of three parts. Apex refers to the pyramid's highest point. The base is the square at the bottom. Faces are the three triangle sides.

A square pyramid consists of three parts.

Square Pyramid Base Area

Due to the square base of the square pyramid, its base area can be determined using the same method as the square's area, which is side side or base edge².

Example: Assume that a square pyramid's base edge is given as seven units. Thus, BA = 7 x 7 = 49 square units is the size of the square pyramid's base.

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The book should be sold at Rs.181.49 to receive a 5% profit.

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is one of the ways to represent a dimensionless relationship between two numbers; other methods include ratios, fractions, and decimals. Percentages are often denoted by the symbol "%" written after the number.

Given here, CP for Sajan = 180

and SP for Sajan = (1+20%)

                            = 1.2 × 180

                            = 216

CP for Niranjan = 216 and SP = 0.8 × 216

                                              = 172.8

CP for Niranjan = 172.8

therefore to sell it at 5% profit we get  SP for Niranjan = 172.8 × 1.05

                                                                                          = 181.49

Hence selling price for Niranjan is equal to Rs.181.49                  

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Answer:

B

Step-by-step explanation:

prime number ( 1 ≤ x ≤ 30 )

= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

for answer choice A: 3-2 = 1

C: 5-2 = 3

D: 11-2 = 9

The potential rational roots must be factors of -6/15. These factors are ±1, ±2, ±3, ±6, and ±10.

The rational root theorem states that all rational roots of a polynomial equation must be factors of the constant term divided by factors of the leading coefficient.

In the case of the polynomial f(x)=15x^11-6x^8, the constant term is -6 and the leading coefficient is 15. This means that all potential rational roots must be factors of -6/15. These factors are ±1, ±2, ±3, ±6, and ±10. Therefore, the potential rational roots of f(x)=15x^11-6x^8 are ±1, ±2, ±3, ±6, and ±10.

The rational root theorem is an important tool for solving polynomial equations. It allows us to quickly determine all the potential rational roots of a polynomial equation, which can then be used to solve the equation. In the case of f(x)=15x^11-6x^8, the potential rational roots can be used to determine the factorization of the polynomial. For example, if we were to factorize f(x) using the potential rational roots ±1, ±2, ±3, ±6, and ±10, we would get[tex](x+1)(x-1)(x+2)(x-2)(x+3)(x-3)(x+6)(x-6)(x+10)(x-10)[/tex]. This factorization can then be used to solve the equation.

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Answer:

A) [tex]{2s + 5t = 49.50\\\\s = 2t[/tex]

B) Keegan paid $5.50 for each t-shirt and $11 for each short.

Step-by-step explanation:

A)

⭐ What is a system of equations?

We are asked to create a system of equations for Keegan's situation.

Let s = the price for every short

Let t = the price for every t-shirt

So, if Keegan buys 2 shorts and 5 t-shirts, his cost will be $49.50.

As an equation, this situation would be:

[tex]2s + 5t = 49.50[/tex]

It's given that the cost of 1 short is twice the cost of 1 t-shirt.

As an equation, this situation would be:

[tex]s = 2t[/tex]

B)

⭐How can we solve a system of equations?

For this problem, the best way to solve this system of equations is through substitution. I will demonstrate how to use substitution for this problem.

Using the equations [tex]2s + 5t = 49.50[/tex] and [tex]s = 2t[/tex], we will literally substitute a variable from one equation into another equation to solve for the other variable.

Given that [tex]s = 2t[/tex]:

[tex]2s + 5t = 49.50[/tex]

[tex]2(2t) + 5t = 49.50[/tex]

[tex]4t + 5t = 49.50[/tex]

[tex]9t = 49.50[/tex]

[tex]t = 5.50[/tex]

∴ It costs Keegan $5.50 for one t-shirt.

Now, we can substitute the value of t into the same equation to solve for the value of s.

Given that [tex]t = 5.50[/tex]:

[tex]2s + 5(5.50) = 49.50[/tex]

[tex]2s + 27.5 = 49.50[/tex]

[tex]2s = 22[/tex]

[tex]s = 11[/tex]

∴ It costs Keegan $11 for one short.

The number of kids in the class teenagers wearing leggings is 3.

In such a fraction, the value above the horizontal line is referred to as the numerator.

In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.

As per the given,

Number of kids = 36

Fraction of kids are teenagers = 1/4 of 36

(1/4)36 = 9 kids

Fraction of teenagers wear leggings = 1/3 of 9

(1/3)9 = 3 kids

Hence "There are three students in the class who are teenagers and wearing leggings".

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Answer:

820 teens

Step-by-step explanation:

20 percent is also 1/5 so 4100*1/5 is 4100/5 so it is 820

Answer:

PA = PB

Step-by-step explanation:

The radius OA = OB

so triangles OPA is congruent to OPB because OA = OB, OP is the same side, angle OPA = angle OPB = 90o

therefore PA = PB

The horizontal asymptote of F(x)=3x^2/x^2-4 is y=0, meaning the graph approaches this line as x goes towards infinity. The vertical asymptote is x=2, which is a double root of the denominator; this means the graph approaches a line parallel to the x-axis as x approaches 2.

The horizontal asymptote of F(x)=3x^2/x^2-4 is y=0. This means that as x goes towards infinity, the graph approaches a line parallel to the y-axis. The vertical asymptote is x=2, which is a double root of the denominator; this means the graph approaches a line parallel to the x-axis as x approaches 2. In other words, the graph has a vertical line at x=2 where the graph approaches, but never reaches, a horizontal line. The fact that the vertical asymptote is a double root of the denominator means that the graph will approach two lines, one on either side of the asymptote, as x approaches 2. It is important to note that the vertical asymptote is not the same as the y-intercept, which will be located at the point where the graph intersects the y-axis.

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Answer:

10

Step-by-step explanation:

If no base is written, the common logarithm is implied.

Answer:

the value of x will depend on the base of the logarithm.

Step-by-step explanation:

The base of a logarithm is the number that is used as a factor in the exponential equation that defines the logarithm. For example, in the logarithmic equation log10(x) = 100, the base is 10.

In the equation log(x) = 100, the base of the logarithm is not given. In order to solve for x, we need to know the base of the logarithm. Without this information, we cannot find the value of x.

For example, if the base of the logarithm is 10, we can rewrite the equation as log10(x) = 100, and then use the following property of logarithms to solve for x:

log10(x) = 100

10^(log10(x)) = 10^100

x = 10^100

On the other hand, if the base of the logarithm is 2, we can rewrite the equation as log2(x) = 100, and then use the following property of logarithms to solve for x:

log2(x) = 100

2^(log2(x)) = 2^100

x = 2^100

Answer:

Step-by-step explanation:

Joscelyn,  we know that [tex]x^{2}[/tex] = 49 means ,

x = [tex]\sqrt{49}[/tex]

7 * 7 = 49

x = 7

for b)   it looks like the question is

-64 = [tex]b^{2}[/tex]

teacher don't like to tell anyone that you can have a negative under the square root sign.  Because it means you have to understand imaginary numbers.  :/

[tex]\sqrt{-64}[/tex] = b

another way to write the negative sign is  [tex]i^{2}[/tex]

[tex]\sqrt{64i^{2} }[/tex] = b

use properties of square roots

[tex]\sqrt{64}[/tex]*[tex]\sqrt{i^{2} }[/tex] = b

8i = b

written well,  this looks like

0 + 8i = b

if the questions doesn't have the negative sign

then it's just

8 = b

The value of x = +7, -7 and the value of b = -4

Given an equation :

x² = 49,

b³ = -64

x * x = 49 ( 7 * 7 = 49 and -7 * -7 = 49 )

b * b * b = -64 ( (-4) * (-4) * (-4) )

On solving

x = +7, -7 and b = -4

An equation is a condition on a variable while an expression is simply a polynomial in one or more variables.

An equation contains an equal sign while an expression does not contain an equal sign. An expression contains operators, constants, and variables in it.

answer x = +7, -7 and b = -4

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The rational root theorem states that it is a representation to determine the rational zeros or the solution of the given polynomial function.

As given in the question,

Therefore, the rational root theorem helps us to find rational solution or zeros of the of any polynomial function.

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Answer:

Below

Step-by-step explanation:

Replace the '8' with any number

here is one

y = 7 x + 4

Answer:

28 1/5

Step-by-step explanation:

​ 6 38/45+2 5/9 ​

6 38/45 = 308/45

2 5/9 = 23/9

The common factor is 45

308/45 + 115/45 = 423/15 = 141/5

141/5 = 28 1/5

Answer:

9[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

6 [tex]\frac{38}{45}[/tex] + 2[tex]\frac{5}{9}[/tex]  Use a common denominator of 45 so that you can add together

6 [tex]\frac{38}{45}[/tex] + 2[tex]\frac{25}{45}[/tex]  Multiply the top and bottom of the second fraction by 5

8 [tex]\frac{63}{45}[/tex]

8 + [tex]\frac{45}{45}[/tex] + [tex]\frac{18}{45}[/tex]  I broke up [tex]\frac{63}{45}[/tex] because I know that [tex]\frac{45}{45}[/tex] is another name for 1

8 + 1 + [tex]\frac{18}{45}[/tex]

9 [tex]\frac{18}{45}[/tex]  Divide the numerator and the denominator by 9 to simplify

9[tex]\frac{2}{5}[/tex]

Answer:

1) x = 10

m<LOH = 55

m<GOH = 85

m< KOG = 40

2) x = 3

m<CQR = 22

m<BQC = 53

m< AQB = 33

m< PQA = 72

3) x = 45

m<TYZ = 41

m<XYT = 49

m< SYX = 90

m< XYZ = 90

4) x = 7

m < KJL = 30

m< NJK = 50

m< MJL = 56

Step-by-step explanation:

1)

Straight line = 180°

So

4x + 15 + 9x - 15 + 4x = 180

17x + 10 = 180

x = (180-10)/17

x = 10

m<LOH = 40

m<GOH = 85

m< KOG = 55

2)

Straight line = 180°

So

7x + 1 + 56 - x + x + 30 + 24x = 180

31x + 87 = 180

x = (180 - 87) / 31

x = 3

m<CQR = 72

m<BQC = 33

m< AQB = 53

m< PQA = 22

3)

Straight line = 180°

So

2x + x + 4 + x - 4 = 180

4x = 180

x = 45

m<TYZ = 41

m<XYT = 49

m< SYX = 90

m< XYZ = 90

4)

Straight line = 180°

So

2(3x + 4) + 11x - 3 + 8x = 180

6x + 8 + 19x -3 = 180

25x + 5 = 180

x = (180 -5) / 25

x = 7

m < KJL = 30

m< NJK = 50

m< MJL = 56

I hope my answer helps you.

The factors of 3[tex]x^{2}[/tex] -4x -4 is (3x+2)(x-2)

Let's start by putting empty brackets.

()

We know that 3[tex]x^{2}[/tex] is 3x*x

Each of these can be inserted into a particular bracket.

(3x)(x)

The factors of -4 are then examined. How many different methods are there to multiply two numbers to reach -4?

1 × -4 = -4

2 × -2 = -4

Choosing which pair to utilize and  where to place each is now the challenging part. You might need to try each one separately at first, but with practice this will become simpler. I'll begin with the right couple, which are +2 and -2.

(3x + 2)(x - 2)

We can enlarge it once again to confirm whether this is accurate. Do not forget to multiply each value in the second bracket by each value in the first bracket

so, 3x *x = 3[tex]x^{2}[/tex]

3x *  -2 = -6x

Then

2 * x =2x

2 * -2 = -4

All of these together gives us 3[tex]x^{2}[/tex] - 6x +2x -4 which is 3[tex]x^{2}[/tex] - 4x -4

If we had reversed the factors by putting (3x−2)(x+2), it would have given us 3[tex]x^{2}[/tex] - 4x -4, which is close but not exactly what we are looking for.

If the alternative set of components, 1 and -4, had been employed, we would have had ( 3 x + 1 ) ( x- 4 ), which would be 3[tex]x^{2}[/tex]- 11x -4

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A discontinuity is a point at which a function is not continuous. This means that there is a break or gap in the function at that point, which can be caused by a variety of factors such as a sudden change in the value of the function, a division by zero, or an undefined value.

A function can have a "hole" if it is not defined at a certain input value. For example, consider the following function:

f(x) = 1/x

This function has a hole at x=0 because it is not defined at that value. If you try to evaluate the function at x=0, you will get an error or an undefined result.

A hole is a missing or incomplete part of a function. For example, a function may have a hole at a certain point if the function is not defined at that point, or if there is a gap in the graph of the function at that point.

So, while a discontinuity is a break or gap in a function, a hole is a missing or incomplete part of the function. These two concepts are related, but they are not the same thing.

To determine whether a function has a hole, you can consider the domain of the function, which is the set of all input values for which the function is defined. If there are any values in the domain for which the function is not defined, then the function has a hole at those values.

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f(x) = 1/x

Because it is not defined at x=0, this function has a gap there. You will encounter an error or an undefined outcome if you attempt to evaluate the function at x=0.

A hole is a component of a function that is absent or inadequate. For instance, if a function is not defined at a particular point or if there is a gap in the function's graph at that location, the function may have a hole there.

Therefore, a hole is a missing or unfinished portion of the function, whereas a discontinuity is a break or gap in the function. Although these two ideas are distinct from one another, they are linked.

Answer:

3 hot dogs, 4 buns

Step-by-step explanation:

You can figure this out

Answer: 3 packages of hot dogs, and 4 packages of buns

Step-by-step explanation:

8 x 3 =24

6 x 4 =24

same amount of hot dogs as there are buns

Answer:

Reflecting triangle ABC over line m

Step-by-step explanation:

By reflecting triangle ABC over line m angle A and angle C overlap, proving they are the same angle, which is true because side AB and BC are equal in length.

2149450.133 is the formula for the anticipated student population in 2026.

A population is a distinct group of people, animals, or other objects that can be identified for the purposes of data collection and analysis by at least one common trait. The majority of the time, data is collected from samples in order to learn more about huge populations. the entire population being investigated. Example: At a football game, you ask 100 people chosen at random what their primary occupation is. 100 persons make up your sample, but everyone present at the match is the population.

Given:

Population in 2020: 284

Population growth annually is 4%.

Year predicted is 2026.

Let n = the difference in population between the forecasted year and 2020 (2026 minus 2020 = 6).

The equation:

Estimated population is equal to the sum of the population in 2020 and the annual growth rate.

= 284 + (284 × 4%)ⁿ

= 284 + (284 × 0.04)⁶

= 284 + (11.36)⁶

= 284 +2149166.133

=2149450.133

Therefore, the estimated population of the students in 2026 is 2149450.133.

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The nature of roots of the equation 4x² -4x -19 = 0 is : The roots are real.

Given quadratic equation to us is 4x² -4x -19 = 0.

With respect to Standard form ax² +bx +c = 0 , Discriminant of the quadratic equation is given by b² - 4ac . Here's a table for Nature of Roots .

SI. NO.          CONDITION                    NATURE OF ROOTS

   1               Discriminant > 1                   Real roots

    2              Discriminant = 1                   Equal roots

    3              Discriminant < 1                   Complex roots

Hence here , with respect to Standard form ,

• a = 4 , • b = -4 & •c = -19 .

⇒ Discriminant = b² - 4ac

⇒ Discriminant = (-4)² - 4 (4) (-19)

⇒ Discriminant = 16 + 304

⇒ Discriminant = 320

Hence since Discriminant is Greater than 0 , hence the nature of roots of the quadratic equation is real.

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