To approximate the integral I = ∫x ln(x+1)dx using a power series, we can first use integration by parts to obtain:
I = x(ln(x+1) - 1) + ∫(1 - 1/(x+1))dx
Next, we can use the geometric series expansion to write 1/(x+1) as:
1/(x+1) = ∑(-1)^n x^n for |x| < 1
Substituting this into the integral above and integrating term by term, we get:
I = x(ln(x+1) - 1) - ∑(-1)^n (x^(n+1))/(n+1) + C
where C is the constant of integration.
To obtain an error of less than 0.0001, we need to find a value of n such that the absolute value of the (n+1)th term is less than 0.0001. We can use the ratio test to find this value:
|(x^(n+2))/(n+2)|/|(x^(n+1))/(n+1)| = |x|/(n+2)
For the ratio to be less than 0.0001, we need:
|x|/(n+2) < 0.0001
Choosing x = 0.5, we get:
0.5/(n+2) < 0.0001
Solving for n, we get n > 4980.
Therefore, we can approximate the integral I to within an error of 0.0001 by using the power series:
I ≈ x(ln(x+1) - 1) - ∑(-1)^n (x^(n+1))/(n+1)
with n = 4981.
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Greg is a contractor and need to fix the top of the chimney on his client's house before
winter comes. In order to get reach the chimney, he needs to place a 24 foot ladder 13
feet above the ground. How far from the base of the house should Greg place the
ladder? Round your answer to the nearest tenth.
Therefore , the solution of the given problem of trigonometry comes out to be base distance is 20.174 foot.
What is the meaning of trigonometry?Trigonometry is a branch of mathematics that examines the relationship between the square line segment and The field first appeared inside the Seventeenth century, most likely beginning in the third century BC, as a result of the fusion of astronomy and mathematics studies. Numerous geometric equations and potential uses in calculations are covered by precise mathematical techniques. Trigonometry is the study of the six basic trigonometric operations. They go by many different names and abbreviations, such as sine, divergence, tangential, secant, etc (csc). In trigonometry, triangle characteristics are investigated, particularly those of right triangles. But to master geometry, one must be fully conversant with the properties of every polygon.
Here,
Greg has ladder of 24 foot
thus,
to find the : how much distance ladder should be placed.
We use trigonometry ratios:
=> h²= p²+ b²
=> 24² = 13² + b²
=> √576 - 169 = b
=>20.174 = b
Therefore , the solution of the given problem of trigonometry comes out to be base distance is 20.174 foot.
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Can someone help me? Picture attached
Answer:
6
5^2 + square root 11^2 = 36
square root 36= 5
Please help me I have until tomorrow.
Answer:
number 6, y=-6 number 7 x=2 and
Step-by-step explanation:
and number 10, 4 - 6 / -3 + 5, 4 - 6/2, - 2 / 2, Solution: -1
a store clerk makes a display with 36 bags each bag has 48 beads how many beads are in the display
What is the exponential form of root 2?
The Exponential Form of the number root 2 , is represented as [tex](2)^{\frac{1}{2} }[/tex] , because the term "root" means the exponent is [tex]\frac{1}{2}[/tex] .
The Root of a number x ; is defined as another number, which when multiplied by itself by given number of times is equal to x .
The Square Root of a "number x" is ; denoted by symbol "[tex]\sqrt{x}[/tex]" .
we have to express the number root 2 in exponential form ;
So, we write root 2 as ⇒ [tex]\sqrt{2}[/tex] ;
we know that the square root of any number x , in exponential form is written as [tex]x^{\frac{1}{2} }[/tex] ;
So , the exponential form of root 2 is [tex](2)^{\frac{1}{2} }[/tex] .
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Based on the above graph, which of the four occupations listed is expected to add the greatest number of jobs from 2006 to 2016?
a.
Registered nurses
b.
Postsecondary teachers
c.
Waiters and waitresses
d.
Computer systems analysts
Registered nurses is expected to add the greatest number of jobs from 2006 to 2016.
Hence, Option A is correct
What do you mean by graph Growth Rate?
A graph displaying the evolution of a nation's population may serve as an illustration of a growth curve. In statistics, growth curves are frequently used to identify trends in the growth over time of a quantity, whether it be linear, exponential, or cubic.If k0 and a>0, the decay is represented by the function y=f(x)=aekx. The function is a decreasing function, meaning that as x rises, y falls. Range: The range of the graph is always positive real numbers if a>0, and the graph is always above the x axis.By subtracting the current number from the prior value, you may get the growth rate. To obtain a percentage representation of the growth rate, divide this difference by the prior amount and multiply the result by 100.To know more about growth rate of a graph here
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Answer:
a
Step-by-step explanation:
How to find endpoint with midpoint and one endpoint formula?
To find the endpoint with the midpoint and one endpoint formula, use the following steps:
Step 1: Identify the midpoint of the line segment. The midpoint is the point that is exactly halfway between the two endpoints.
Step 2: Identify one endpoint of the line segment. This is the point that you already know.
Step 3: Use the midpoint and one endpoint to find the other endpoint. To do this, add or subtract the difference between the x-coordinates of the midpoint and one endpoint from the x-coordinate of the midpoint to find the x-coordinate of the other endpoint. Then, add or subtract the difference between the y-coordinates of the midpoint and one endpoint from the y-coordinate of the midpoint to find the y-coordinate of the other endpoint.
Step 4: Write the coordinates of the other endpoint. The point (x,y) represents the other endpoint of the line segment.
Note: The x-coordinate of the other endpoint is the x-coordinate of the midpoint + or - the difference of x-coordinate of the midpoint and one endpoint, and the y-coordinate of the other endpoint is the y-coordinate of the midpoint + or - the difference of y-coordinate of the midpoint and one endpoint.
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Solve 4x + 2 = 12 for x using the change of base formula log base b of y equals log y over log b.a. −1.442114 b. −0.207519 c. 2.55789 d. 3.79248
x using the change of base formula will be B) -0.207519.
What is logarithm ?
Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8
Have given ,
4x + 2 = 12
equation. We can do this by subtracting 2 from both sides:
4x = 10
Next, we divide both sides by 4:
x = 2.5
So, the solution is x = 2.5
x using the change of base formula will be B) -0.207519.
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What is the full table of 5?
A "full table of 5" refers to a multiplication table that includes all of the products of the number 5 multiplied by the integers from 1 to some maximum value.
Write the complete table of 5.Here is an example of a full table of 5:
5 x 1 = 5
5 x 2 = 10
5 x 3 = 15
5 x 4 = 20
5 x 5 = 25
5 x 6 = 30
5 x 7 = 35
5 x 8 = 40
5 x 9 = 45
5 x 10 = 50
In this example, the maximum value for the multiplier is 10, but a full table of 5 can continue with any number of rows. This table is useful for memorizing the multiplication facts of 5, and also to see the pattern of the multiples of 5.
It's worth to mention that if you are looking for a way to calculate the products you could use a loop or a function that takes the maximum value of the multipliers as an input and prints the full table of 5.
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reflection across y = -x
X(-4,-3), M(-3,-2), (-1,-5)
Reflection across the y = -x line is equivalent to a rotation of 180 degrees about the origin.
The coordinates of X(-4,-3) after reflecting across the y = -x line would be (3, 4)
The coordinates of M(-3,-2) after reflecting across the y = -x line would be (2, 3)
The coordinates of (-1,-5) after reflecting across the y = -x line would be (5,1)
So, after reflecting across the y = -x line, the coordinates of the points are flipped along the line x = y and they are moved to the opposite quadrant.
What is 0.55 hectometers expressed in decimeters?a.550 dmb.5.5 dmc.55 dmd.0.00055 dmwhat is 0.55 hectometers expressed in decimeters? a.550 dmb.5.5 dmc.55 dmd.0.00055 dm brainly
The value of 0.55 hectometers expressed in decimeters is 550 decimeters. The result is obtained by using the concept of unit ladder system.
How the unit ladder method works?The common length units are kilometers to milimeter. The conversion can be described in a unit ladder system as follows.
km (kilometers)
hm (hectometers)
dam (decameters)
m (meters)
dm (decimeters)
cm (centimeters)
mm (millimeters)
Every time the length unit goes down, it is multiplied by ten. Every time the length unit goes up, it is divided by ten.
We have 0.55 hectometers. Express that value in decimeters!
From hectometers to decimeters, it goes down 3 times. So,
0.55 hectometers = 0.55 × 10 × 10 × 10 decimeters
0.55 hectometers = 0.55 × 1000 decimeters
0.55 hectometers = 550 decimeters
Hence, 0.55 hectometers is equal to 550 decimeters.
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3. Choose any two complex numbers z, and z2 and show that the following statements are true for
those numbers. Then prove that the statements are true for any z₁ = a + bi and z₂ = c + di.
a. Z₁ + Z₁ and Z₂ + Z₂ are both real numbers.
b. Z₁-Z₁ and 22-Z₂ are both pure imaginary numbers.
c. Z₁ + Z₂ = Z₁ + Z₂
d. Z₁ Z₂ = Z₁ Z2
4. For what complex number z does z=z? Justify your conclusion.
The following statements are true for all the numbers. The proof is shown as follows.
What is an imaginary number?A real number is multiplied by an imaginary unit, I whose feature i2 = 1 defines it as an imaginary number. Bi is an imaginary number, while b2 is its square. For instance, the square of the fictitious integer 5i is 25. Zero is regarded as both real and fictitious by definition.
We know z₁ = a + bi and zbar= a-bi
z1+z1bar=2a that is purely real. Similarly with z2 +z2bar
z1-z1bar=-2bi that is purely imaginary. Similarly with z2-z2bar
Again
z1bar+z2bar= a-bi+c-di
z1+z2(whole bar)=a+c-(b+d)i
Hence Z₁ + Z₂ = Z₁ + Z₂
Similarly
z1bar.z2bar=z1.z2(whole bar)
Hence proved
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some one answer thiss y+3=-2(x-3)
Answer: y = -2x+3.
Step-by-step explanation:
To answer this question, you must first use the FOIL method.
now the equation is this
y+3=-2x+6, since a negative * a negative is equal to a positive.
subtract 6 from both sides.
y-3=-2x
add three to both sides
y=-2x + 3
Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript one-fourth x?
8 Superscript three-fourths x
RootIndex 7 StartRoot 8 EndRoot Superscript x
RootIndex 12 StartRoot 8 EndRoot Superscript x
8 Superscript StartFraction 3 Over 4 x EndFraction
The equivalent expression is RootIndex 12 StartRoot 8 EndRoot Superscript x. Option C
What is an equivalent expression?An equivalent expression can be described as an expression that has the same solution as the original expression.
The equivalent always have a different arrangement of variables, terms and factors but the solution is the same with the initial expression.
From the information given, we have that;
3Root 8 Superscript one-fourth x
This is represented as;
[tex]\sqrt[3]{8}^\frac{1}{4} ^x[/tex]
Now, take the cube root of 8, we have;
[tex]8^\frac{1}{3} * \frac{1}{4}^x[/tex]
Multiply the exponents, we get;
[tex]8^\frac{1}{12}^x[/tex]
Now, represent in root for, we have;
[tex]\sqrt[12]{8} ^x[/tex]
Hence, the correct option is C
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Answer:
C
Step-by-step explanation:
;)
What are the domain and range of this function?
The correct option regarding the domain and the range of the quadratic function y = (x + 3)² - 5 is given as follows:
B. Domain all real values, Range [-5, infinity.]
How to obtain the domain and the range of the function?The function for this problem is defined as follows:
y = (x + 3)² - 5.
Which is a concave up quadratic function with vertex at (-3,-5).
The quadratic function has no restrictions regarding the input, hence the domain is composed by all real values.
The minimum value of the function is of -5 at the vertex, hence the range is all values that are -5 or greater.
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Why is area of a circle π r 2?
Area of circle equals Area of produced rectangle equals 1/2 π(2r) r.
Since r is the circle's radius and is equal to 22/7 or 3.14, the area of the circle is equal to πr².
What is circle ?All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The following is a list of a circle's attributes:
A closed 2D form that isn't a polygon is a circle. It has one face that curves.If two circles have the same radius, they are said to be congruent.Equal chords are always located equally from the circle's center.The center of the circle is the perpendicular bisector of a chord.The line joining the points of two overlapping circles will be perpendicular to the line joining the points of the circles' centers.The tangents drawn at the diameter's endpoints are perpendicular to one another.Look closely at the above illustration; if we divide the circle into smaller pieces and arrange them in a particular order, a parallelogram will result. The circle progressively becomes the shape of a rectangle as it is split into smaller and smaller segments. The likelihood that it will have the above-illustrated rectangle form increases with the number of parts it has.
A rectangle's area equals its length times its width.
The ratio of a circle's radius to a rectangle's width (r)
When we compare a rectangle's length to a circle's circumference, we can see that the length is equal to half the diameter of the circle.
Area of circle equals Area of produced rectangle equals 1/2 π(2r) r.
Since r is the circle's radius and is equal to 22/7 or 3.14, the area of the circle is equal to πr².
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The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball. 2 4. 7
Baseball 1. 6. 5
Soccer 7. 4. 4
Football. 8. 15. 10
Explain what the ratio 5:73 represents.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 5:73 represents the ratio of 7th grade football players to total athletes.
The ratio 5:73 represents the ratio of total athletes to 7th grade football players.
The ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
Use the graph below to fill in the blank with the correct number: (1 point)
f(−2) = _______
The solution would be 2.The point's y value at x = -2 provides a clue as to how f(-2) would behave.
What do you mean By graph Intercept function?
The set of ordered pairs where f(x)=y is displayed as the graph of a function in mathematics. These pairs are the Cartesian coordinates of points in two-dimensional space and, in the typical case where x and f(x) are real numbers, they form a subset of this plane.See if any vertical lines that were drawn intersect the curve more than once by carefully examining the graph. The graph does not represent a function if there is any such line. The graph does represent a function if no vertical line can cross the curve more than once.To know more about relations of a function here
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Dani had $200 in her savings account. When she turned 18, the bank began charging her a $5.00/month fee. Write a function in terms of a for the balance of her savings account if she doesn't notice the monthly fee.
Complete the following. Use standard slope-intercept form.
The function in terms of balance of the savings account is B(a) = 200 - 5a.
What are equations?A formula known as an equation uses the equals sign to express how two expressions are equal. The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfil the equality are known as the equation's solutions.
Let the number of months be represented as a.
The fee that would be deducted ever month can thus be represented as 5a.
The initial deposit in the bank is $200, and if we include the deduction the equation is as follows:
B(a) = 200 - 5a
Hence the function in terms of balance of the savings account is B(a) = 200 - 5a.
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Helpppppp Lots of points ASAP
1. The value of the m∠2 is 67°.
2. The third length in the triangle is 10 cm.
3. It should be noted that this is a rotation.
What is an equation?An equation is a expression that shows the relationship between numbers and variables.1)
In the triangle:m∠1 + 21 + 46 = 180° (sum of angles in a triangle)
m∠1 = 113°m∠1 + m∠2 = 180 (angle in a staight line)1
113 + m∠2 = 180
m∠2 = 180 - 113
= 67°
2. Let x represent the third length:
x + 12 + 13 = 35 (perimeter)
x = 35 - 25
x = 10
3. It should be noted that the diagram illustrated is a a rotation.
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Which set of ordered pairs does not represent a function?
○ {(−1, -3), (3, 7), (−4, 7), (−2, —2)}
O {(2, 4), (7, 9), (-6, 8), (-5,4)}
O {(9,-2), (9,5), (-9, 1), (3,0)}
O {(-4,-8), (-2, 7), (-5, -6), (3, 7)}
Submit Answer
There is no function in the first set of ordered pairs. It is not a function because the X value of 7 repeats.
what is function ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
Only the first set of ordered pairs is a function; the second, third, and fourth do not represent functions.
This is due to the need that each x value have a unique y value. So you note that, with the exception of the first set of ordered pairs, all sets of ordered pairs have two distinct x-values that share a same y-value, which is not possible.
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What is the greatest common factor of the polynomial below?
20x^3-14x
—————————————-
A. 2x^2
B. 6x^2
C. 6x
D. 2x
The greatest common factor of the polynomial 20x^3-14x is D. 2x.
What is greatest common factor?The concept that will be sued here is common factor. A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. The largest factor that splits both numbers is said to be the greatest common factor. List the prime factors of each integer before calculating the greatest common factor.
For instance, the numbers 12, 20, and 24 share the components 2 and 4. The GCF of 12, 20, and 24 is 4 because it is the largest.
The common factor that ca be gotten from 20x² : are: 1, 2, 4, 5, 10, 20, x
The common factor that ca be gotten from 14x are : 1, 2, 7, 14, x
Then greatest common factor of the polynomial is 2x.
Hence, 2x(10x² - 7)
Therefore, option D is correct.
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What are prime factors
Answer:
1.) A prime factor is any prime number that can be multiplied to give the original number.
For example, the prime factor of 24 is:
1, 2, 3, 4, 6, 8, 12, and 24.
2.) A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.
Step-by-step explanation:
You're welcome.
Amelia ordered pancakes, a side of bacon, and orange juice. She also says that she will take care of the tax. How much does she owe?
Answer:
45 cents
Step-by-step explanation:
Let's suppose that the strength in newton of usual men can be
found by f = 500 ln(w + 1), where w is the man's weight in
pounds. Find the strength of a man who is 200 pounds. Round
your answer to the nearest tenth.
newton
So the strength of a man who is 200 pounds is approximately 2649.2 newton, rounded to the nearest tenth.
What is weight?Weight is a measure of the force exerted on an object due to gravity. It is measured in units of force such as pounds, kilograms, or newtons. The weight of an object is equal to the force of gravity acting on it and is equal to the mass of the object multiplied by the acceleration due to gravity.
What is newton?Newton (N) is the unit of force in the International System of Units (SI). It is named after Sir Isaac Newton, the famous English physicist, mathematician, and astronomer. It is defined as the force that is required to accelerate an object with a mass of one kilogram at a rate of one meter per second squared.
f = 500 ln(200 + 1)
f = 500 ln(201)
then we can calculate the value of ln(201) using a calculator, and the result is 5.298317366548036
then we can substitute the result into the original equation and get
f = 500 * 5.298317366548036 = 2649.15868
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How do you dilate a triangle by 2 3?
A dilation is a transformation that changes the size of an object by a scale factor. To dilate a triangle by a scale factor of 2/3, you will need to follow these steps:
Identify the center of dilation: The center of dilation is a fixed point around which the dilation takes place. This point is usually denoted by the letter "C".Identify the vertices of the triangle: The vertices of the triangle are the points that determine the shape and position of the triangle.Calculate the new coordinates of the vertices: To dilate a triangle by a scale factor of 2/3, you need to multiply the coordinates of each vertex by the scale factor. For example, if the coordinates of a vertex are (x, y), the new coordinates will be (2/3x, 2/3y).Plot the new coordinates: Once you have calculated the new coordinates of the vertices, you can plot them on the coordinate plane to create the dilated triangle.Connect the new points to form the new triangle: Connect the new points with lines to form the new triangleNote that the center of dilation C and the dilation factor are the same for all points on the triangle, also if the dilation factor is less than 1, the image is smaller than the original and if the dilation factor is greater than 1, the image is larger than the original.
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The complete question is -
How do you dilate a triangle by a scale factor of 2/3?
-3(2x-1)≤x-18 pls solve w/ explanation and steps
Do sides 5 cm 12cm and 13cm form a right-angled triangle give reason?
Answer:
No they do not
Step-by-step explanation:
Sides 5 cm and 12cm can form a right angled triangle because 5 + 12 = 17 which is a greater number than 13 meaning it cannot
What is i^33 simplified?
i³³ simplified is i.
What is the Complex Number?
A complex number is a number in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
When raising a complex number to a power, we can use the property [tex](a + bi)^n = a^n + (na^{(n-1)})bi + (n(n-1)/2!)a^{(n-2)(bi)^2} + .... + (n(n-1)...21)(a*bi)^n[/tex]
It is also possible to simplify the powers of complex numbers using De Moivre's Theorem:
[tex](a + bi)^n = a^n + (na^{(n-1)})bi + (n(n-1)/2!)a^{(n-2)(bi)^2} + .... + (n(n-1)...21)(a*bi)^n[/tex]
Where [tex](a + bi)^n = r^n * (cos(n\theta) + i*sin(n\theta))[/tex]
Where r is the magnitude, θ is the argument, and n is an integer.
For example, if we raise i to the power of 3, we can use De Moivre's Theorem:
i³ = (cos(90) + isin(90))³ = cos(270) + isin(270) = -i
So, i³ = -i
When raising complex numbers to powers, the magnitude will be raised to the power of n while the argument will be multiplied by n.
i² = -1, so i³³ can be written as (i²)¹⁶ * i = (-1)¹⁶ * i = i
Therefore, i³³ simplified is i.
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Which of the following pairs of triangles can be proven similar through SSS similarity?
Answer:
C
Step-by-step explanation:
There are 3 pairs of corresponding sides with proportional lengths.
The ratios of the lengths of corresponding sides are equal AB/XY = BC/YZ = AC/XZ, then ΔABC and ΔXYZ proven similar through SSS .
To prove two triangles similar using the SSS (Side-Side-Side) similarity criterion, all three pairs of corresponding sides of the two triangles must be proportional .
The SSS similarity criterion states that if the ratio of the lengths of corresponding sides in two triangles is equal, then the triangles are similar.
Given that we have a list of triangles, to compare the ratios of their corresponding sides to see if any pairs satisfy the SSS similarity criterion.
The three pairs of corresponding sides in the triangles are denoted as follows:
Side A: Sides that are corresponding in length between the two triangles.
Side B: Sides that are corresponding in length between the two triangles.
Side C: Sides that are corresponding in length between the two triangles.
Since the specific list of triangles is not provided, I cannot give you the exact pairs that proven similar through SSS similarity. However, I provide with an example:
Example:
Consider two triangles, ΔABC and ΔXYZ, where the corresponding sides are as follows:
ΔABC: AB, BC, and AC
ΔXYZ: XY, YZ, and XZ
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