The SVD for the inverse of matrix A can be obtained by taking the inverse of the singular values of A and transposing the matrices U and V.
Let A be an [tex]nxn[/tex] invertible matrix with SVD given by A = UΣ [tex]V^t[/tex] where U and V are orthogonal matrices and Σ is a diagonal matrix with positive singular values on the diagonal. Since A is invertible, rank(A) = n, and thus all the singular values of A are non-zero. The inverse of A can be obtained by using the formula A^-1 = VΣ^-1U^T, where Σ^-1 is obtained by taking the reciprocal of the non-zero singular values of A.
To obtain the SVD for A^-1, we first note that the transpose of a product of matrices is equal to the product of the transposes in reverse order. Therefore, we have A^-1 = (VΣ^-1U^T)^T = UΣ^-1V^T. We can then express Σ^-1 as a diagonal matrix with the reciprocal of the non-zero singular values of A on the diagonal. Thus, the SVD for A^-1 is given by A^-1 = UΣ^-1V^T, where U and V are the same orthogonal matrices as in the SVD of A, and Σ^-1 is a diagonal matrix with the reciprocal of the non-zero singular values of A on the diagonal.
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Two sides of a triangle each measure 8 inches. Maria says the triangle must be isosceles. Is maria correct? explain.
Maria is not correct. Just because two sides of a triangle measure 8 inches, it does not mean that the triangle is isosceles.
An isosceles triangle is a triangle in which two sides are congruent, meaning they have the same length. However, just because two sides of a triangle have the same length, it does not necessarily mean that the triangle is isosceles.
There could be a third side with a different length. Therefore, it is a possibility that the third side of the triangle is not 8 inches, hence the triangle is not isosceles.
To confirm if a triangle is isosceles, we must measure all three sides and if two sides are congruent then it's an isosceles triangle.
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x+y=3
x^2+y^2=17
Solve the simultaneous equations
The possible solution set for the system is (- 1, 4) and (4, - 1).
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the equations as -
x + y = 3
x² + y² = 17
Refer to the graph of the function attached. The points of intersection represents the possible solution set.
Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).
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If f(x) is divided by x-2 what is the remainder?
Answer: By the Remainder Theorem, the remainder when f(x) is divided by x-2 is f(2)
Step-by-step explanation:
Is the absolute value of a complex number real?
The absolute value of a complex number is real.
The absolute value of a complex number is also known as its magnitude. It is a non-negative scalar quantity that represents the distance of the complex number from the origin in the complex plane.
The absolute value of a complex number is represented by the symbol "|z|" where z is the complex number.
The absolute value of a complex number is always a real number. For example, the absolute value of the complex number 4 + 3i is 5 (the distance of this point from the origin), which is a real number.
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What is an equation of the line, in point-slope form, that passes through the given point and has the given slope? point: (9,3); slope: 4/9
A. y-9=4/9(x+3)
B. y-9=4/9(x-3)
C. y+3=4/9(x-9)
D. y-3=4/9(x-9)
The equation of the line passing through point (9, 3) and having a slope of 4/9 is y - 3 = (4/9)(x - 9)
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The standard linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
The equation of a line passing through the point (x₁, y₁) and having a slope of m is given as:
y - y₁ = m(x - x₁)
Given that a line passes through point (9, 3) and have a slope of 4/9, the equation is:
y - 3 = (4/9)(x - 9)
The equation of the line is y - 3 = (4/9)(x - 9)
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How do you multiply integers in 7th grade?
To begin, determine the absolute value of each integer. After that, multiply or compute the product of the absolute numbers. Finally, identify the final answer's sign. According to the rule, if the signs of the two numbers vary, the final result will be negative.
What is integer?Determine the absolute value of each number first. After that, multiply or compute the absolute number product. Finally, determine the sign of the final answer. If the signs of the two numbers differ, the final result will be negative, according to the rule. A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts. The set of whole numbers and their inverses is known as the integers. The set of integers does not include fractions or decimals.
Here,
Determine the absolute value of each number first. After that, multiply or compute the absolute number product. Finally, determine the sign of the final answer. If the signs of the two numbers differ, the final result will be negative, according to the rule.
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Can someone help me please? thank you.
What are the 4 steps to solving equations?
An equation can be solved in four steps.
1. Find the equation's terms and coefficients.
2. To isolate the variable, using inverse techniques.
3. Re-enter the value into the first equation to verify your conclusion.
4. Consider the issue in light of the remedy.
Finding an equation's terms and coefficients is the first step in solving it. Any constants, variables, and coefficients must be located, and their relationships must be understood.Once the terms are known, it is feasible to isolate the variable and perform inverse operations to solve for the unknown, such as addition, subtraction, multiplication, and division.
It is crucial to check the solution after solving the issue by inputting the original formula once more. The answer is accurate if the equation still holds true. Understanding the answer requires consideration of the problem's context. This necessitates figuring out the response's applicability and how to apply it to the bigger issue.
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Joseph has a loyalty card good for a 20% discount at his local pharmacy. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $42.05? Round to the nearest cent.
The total cost of good will equals to $33.64 after considering the 20% discount he had at the pharmacy.
What is a loyalty card?A loyalty card is an identity card issued by a retailer to its customers as a form of consumer incentive scheme in which credits are accumulated for future discounts with each transaction.
Now, we will have to calculate the total cost of all the items he wants to buy after considering the 20% discount.
First, we will calculate the discounted amount:
= 20% * $42.05
= $8.41
Second, we will calculate the new amount of cost:
= $42.05 - $8.41
= $33.64
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Is it possible to draw a triangle has set of sides 9cm 7cm and 17cm give the reason?
It is not possible to construct a triangle whose sides are 9 cm 7 cm and 17 cm because the sum of two sides(9 cm and 7 cm) are smaller than third sides(17 cm).
In the given question, we have to check that it is possible to construct a triangle whose sides are 9 cm 7 cm and 17 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.
To check this we firstly add the 9 and 7
9 + 7 < 17
16 < 17
Now we add 17 and 7
17 + 7 > 9
24 > 9
Now we add 9 and 17
9 + 17 > 7
26 > 7
It is not possible to construct a triangle whose sides are 9 cm 7 cm and 17 cm because the sum of two sides(9 cm and 7 cm) are smaller than third sides(17 cm).
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The length of a rectangle is 12 inches the width is 2 inches
Answer:
The area is 24 inches, the perimeter is 30 inches.
Step-by-step explanation:
Find the standard form equation of a circle given a center of (7, 14) and a point on the circle of (4, 15).
This is the standard form equation of the circle is [tex](x - 7)^{2}[/tex] + [tex](y - 14)^{2}[/tex] = 10
What is the standard form of equation?The standard form equation of a circle is [tex](x - h)^{2}[/tex] + [tex](y - k)^{2}[/tex] = [tex]r^{2}[/tex], where (h, k) is the center of the circle and r is the radius.
Given the center of the circle as (7, 14) and a point on the circle as (4, 15), we can use the distance formula to find the radius:
r = [tex]\sqrt{(4 - 7)^{2} + (15 - 14)^{2} }[/tex] = [tex]\sqrt{(-3)^{2} + (1)^{2} }[/tex]= [tex]\sqrt{9 + 1}[/tex] = [tex]\sqrt{10}[/tex]
So the standard form equation of the circle is:
[tex](x - 7)^{2}[/tex] + [tex](y - 14)^{2}[/tex] = [tex]\sqrt{(10)^{2} }[/tex]
Which can be written as:
[tex](x - 7)^{2}[/tex] + [tex](y - 14)^{2}[/tex] = 10
So the standard form equation of the circle is [tex](x - 7)^{2}[/tex] + [tex](y - 14)^{2}[/tex] = 10
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How do you enlarge a triangle with scale factor 1 2?
Every coordinate point of the original triangle is multiplied by the scale factor 1/2 if the scale factor is 1/2. multiplying by half after a scale factor of two.
What is Scale Factor?The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.
K is the scaling factor for x in the equation y = Kx. This expression can also be visualised in terms of proportionality:
y ∝ x
K can therefore be regarded as a proportionality constant in this context.
Basic Proportionality Theorem also aids in a better understanding of the scale factor.
Shapes in various dimensions can be scaled using the Scale Factor. In geometry, we study many geometrical forms that exist in both two- and three-dimensions. The scale factor is a way to compare figures with similar appearances but differing scales or measurements. Consider two circles that resemble one another but may have different radii.
The scaling factor indicates how much a figure has increased or decreased from its initial value. With the use of the scale factor, any original shape can be drawn in an enlarged or shrunk form.
Formula of Scale Factor
Dimensions of Original Shape x scale Factor = Dimension of new shape
Scale factor = Dimension of New Shape/Dimension of Original Shape
What is Dilation?The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger. The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image. Dilation comes in two varieties:
Increase in an object's size is referred to as expansion.Contraction is the reduction of an object's size.How to enlarge a triangle with scale factor ?The scale factor (or ratio) and the centre of the dilation are included in a dilation's description.A fixed point in the plane serves as the centre of dilation.The image is an enlargement if the scale factor is greater than 1. (a stretch). The image is a decrease if the scale factor is between 0 and 1. (a shrink). The figure and the image are consistent if the scale factor is 1.To know more about Scale Factor,Refer to:
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Every coordinate point of the original triangle is multiplied by the scale factor 1/2 if the scale factor is 1/2. multiplying by half after a scale factor of two.
What is Scale Factor?The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.K is the scaling factor for x in the equation y = Kx. This expression can also be visualised in terms of proportionality:y ∝ xK can therefore be regarded as a proportionality constant in this context.Basic Proportionality Theorem also aids in a better understanding of the scale factor.Shapes in various dimensions can be scaled using the Scale Factor. In geometry, we study many geometrical forms that exist in both two- and three-dimensions. The scale factor is a way to compare figures with similar appearances but differing scales or measurements. Consider two circles that resemble one another but may have different radii.The scaling factor indicates how much a figure has increased or decreased from its initial value. With the use of the scale factor, any original shape can be drawn in an enlarged or shrunk form.Formula of Scale Factor
Dimensions of Original Shape x scale Factor = Dimension of new shape
Scale factor = Dimension of New Shape/Dimension of Original Shape
What is Dilation?The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger. The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image. Dilation comes in two varieties:Increase in an object's size is referred to as expansion.Contraction is the reduction of an object's size.How to enlarge a triangle with scale factor ?The scale factor (or ratio) and the center of the dilation are included in a dilation's description.A fixed point in the plane serves as the center of dilation.The image is an enlargement if the scale factor is greater than 1. (a stretch).The image is a decrease if the scale factor is between 0 and 1. (a shrink).The figure and the image are consistent if the scale factor is 1.To know more about Scale Factor visit:
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Let g(x) = 2x and h(x) = x^2 + 4. Evaluate (h ∘ g)(−5).
Answer:
(h ￮ g)(- 5) = 104
Step-by-step explanation:
evaluate g(- 5) , then substitute the value obtained into h(x)
g(- 5) = 2(- 5) = - 10 , then
h(- 10) = (- 10)² + 4 = 100 + 4 = 104
Kevin drew a scale drawing of a house. The scale he used was 1 millimeter : 4 meters. If the actual length of the living room is 8 meters, how long is the living room in the drawing?
If the actual length of the living room is 8 meters, according to the scale drawing living room in the sketching should be 2 millimeters
What is the scale drawing?Scale drawings are images that depict objects at a scale different from their actual size. Depending on the size of the object being represented and how the sketching will be used, they can depict objects at either a bigger or smaller scale than full size. The scale gives the proportion of a distance at full size to the distance that, at the scale in use, would have the same length.
Scale drawings are used to illustrate objects when sketching them at their true scale would not be practical or beneficial. This could be because depicting the object as its whole would be difficult or difficult to fit on a single sheet of paper.
since 4meter = 1mm
then 8meter = 2mm
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What is table of numbers?
A table of numbers is a collection of numbers arranged in a specific format, usually in rows and columns.
Write the uses of table of numbers.The numbers in the table can represent various types of data, such as measurements, counts, or statistical values. Tables of numbers can be used to organize, compare, and analyze data in a clear and easy-to-read format. They are often used in fields such as math, statistics, and data analysis. Tables can be created using spreadsheet software, or they can be created manually using a pen and paper. The table can be used to represent a function, a data set, a matrix or a multiplication table, etc
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Complete question is: What is table of numbers?
Solve this problem using 45-45-90
The right angled triangle's side measures 19, its hypotenuse is approximately 8100.25.
what is triangle ?Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners.
given
Let's say we don't know the triangle's hypotenuse and that angle A is approximately 33.56.
Cos and Cos-1 are available. Make sure it is set to degrees.
Cos(33.56)=6750/h
h=8100.25
The right angled triangle's side measures 19, its hypotenuse is approximately 8100.25.
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what is -3(-x-4) + 12x
Answer:
15x + 12
Step-by-step explanation:
-3(-x-4) + 12x
3x + 12 +12x
15x + 12
We can't simplify anymore, so the answer is 15x + 12
Asher is painting a wall on a storage shed. He knows one can of paint covers an area of 24 square feet. Asher uses a meter stick to measure the wall, as shown. What is the fewest number of cans of paint Asher needs to paint the wall?
Therefore , the solution of the given pentagon is the wall has a square footage of 80.7293. Asher requires four cans in total.
A pentagon is what?A polygon with five sides and five angles is called a pentagon. Penta and Gonia, two words that each denote five angles, are the components of the word "pentagon." The shape is created when the sides of such a pentagon come together at their ends.
Here,
Given that a storage shed's wall has a pentagonal shape.
A pentagon's surface can be separated into two shapes. The first shape is a rectangle, while the second is a triangle.
The rectangular shape measures 1+1+1 = 3 meters in length.
(1 + 1) = 2 metres is the width.
3 x 2 = 6 square meters make up the space of the rectangle.
Three meters make up the triangle's base.
The triangle measures 1 meter in height.
The triangle's area is 1/2 base, 1/2 height, or 1/2 x 3-1, or 3/2 square meters.
The pentagon's total area is 7.5 square meters, or 6 + 3/2 square meters.
10.7639 square feet are equal to 1 square meter.
(7.5 x 10.7639) square feet are equal to 7.5 square meters.
= 80.7293 square meters
24 square feet are covered by one can of paint.
He requires 80.7293/24 = 3.36 square feet in order to cover it.
Therefore, he requires a minimum of 4 cans oil paint.
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It takes approximately 3.7*10^4 hours for the light in Proxima Centauri, the next closest star to our son, to reach us from there. The speed of light is 6.71 *10^8 miles per hour. What is the distance from there to earth? Given distance = rate x time. Express your answer in scientific notation.
The distance from here to earth is 2.48 x 10^13 miles.
What is the distance?Scientific notation is used compress larger numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 3 x 10² is equivalent to 300.
Distance is the product of rate and time.
Distance = rate x time.
( 3.7*10^4) x (6.71*10^8)
(3.7 x 6.7) x 10^[4 + 8]
24.827 x 10^12
2.48 x 10^13 miles
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10. Find a third number so that the three numbers form a right triangle:
i) 9,41, _
ii) 13,85, _
Help me! Thank you!
Bing chilling
Equation of constant proportionality is y = kx or y = k/x,
she pay for 40 party favours is 3.125
What is Constant of Proportionality?If the ratio of one variable to the other is constant, then the two variables have a proportional relationship, If x and y have a proportional relationship, the constant of proportionality is the ratio of y to x. Sometimes, we also represent it as x is to y.the rate of change also know as the constant of proportionality (k = y/x) which is the constant ratio between two proportional quantities y/x denoted by the symbol k which may be a positive rational number. The x value is directly proportional to the y value such as in the equation y = kx.We use constant of proportionality in mathematics to determine the nature of proportionality, whether it is direct proportion or indirect proportion. The constant of proportionality helps in solving the equations involving ratios and proportions.To learn more about Constant of Proportionality refers to:
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A rectangle playground has a width of 540 feet and
Let I be the flux of G = (9e^y, 3x^2 ex^3 , 0) through the upper hemisphere S of the unit sphere.
(a) Find a vector field A of the form (0, 0,...) such that curl(A) = G.
(b) Calculate the circulation of A around 88.
(c) Compute the flux of G through S (a)
A= _____ +(C1,C2,C3)
(b) integrate A .ds =
(c) I =
Answer:
check Here.
Step-by-step explanation:
(a) A can be found by solving the equation curl(A) = G, which means that the curl of A in the x, y, and z directions must equal the corresponding components of G. To find A, we can use the vector identity curl(A) = del x A - del y A + del z A.
From this, we get:
del y A = 9e^y
del x A = -3x^2 ex^3
del z A = 0
So A = (f(z), g(x, y), h(x, y, z)) where f, g, h are arbitrary differentiable functions.
(b) Circulation of A around C is given by the line integral of A . ds, where C is a closed curve and ds is an infinitesimal element of C. Since we are given a specific curve 88, we need to know the parametric representation of the curve to calculate the circulation.
(c) The flux of G through S is given by the surface integral of G . dS, where dS is an infinitesimal element of the surface S. Since we are given the upper hemisphere of the unit sphere as S, we can use spherical coordinates to parametrize the surface and then use the divergence theorem to calculate the flux.
Note that the specific values of A, the circulation, and the flux are dependent on the choice of f, g, h and the representation of 88, and dS.
Help please for this geo
Using the indirect measurement, the height of pole is obtained to be 21 ft.
What is indirect measurement?
Using various measurements to determine the required measurement is known as indirect measurement.
Height of the fire hydrant, hf = 3ft
Height of the shadow of the fire hydrant, h'f = 4 ft
Height of the pole, hp = x
Height of the shadow of the pole, h'p = 28 ft
Both the shadows are casted at the same time, i.e. 4 pm.
So, use the method of indirect measurement -
hf/h'f = hp/h'p
3/4 = x/28
x = (3 × 28)/4
x = 84/4
x = 21
Therefore, the height of pole hp = 21 ft.
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Expand 3(t - 2). (Simplify your answer.)
Answer: it’s 3t - 6
But here’s how I got that
Step-by-step explanation:
Imma need some help here
Answer:
no it is not a solution
Step-by-step explanation:
to determine if (- 5, 4 ) is a solution to the system, substitute the x- coordinate x = - 5 into the right side of both equations and if the value obtained is equal to the y- coordinate y = 4 then it is a solution.
Note that this must be true for both equations
y = 3(- 5) + 19 = - 15 + 19 = 4 ← True
y = - 2(- 5) - 7 = 10 - 7 = 3 ≠ 4 ← False
thus (- 5, 4 ) is not a solution to the system of equations.
plssss i’ll give points?
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A line intersects the point and is perpendicular to y=(x / 4)-2. (4,-1). y=15-4 x is the equation for this perpendicular line.
What is the perpendicular line of the equation?In order to determine the equation for the line perpendicular to the line [tex]$y=\frac{x}{4}-2$[/tex]passing through the point (4,-1)
The slope-intercept version of the equation for the line is [tex]$y=\frac{x}{4}-2$[/tex].
Inversely, the perpendicular line has a negative slope of m=-4.
Consequently, the perpendicular line's equation is y=-4 x+a.
Using the notion that the line should pass through the specified location, we can use the formula [tex]-1=(-4) \cdot(4)+a[/tex] to determine a.
Thus, a=15. The line's equation is therefore y=15-4 x.
Lines that cross at a straight angle (90 degrees) are said to be perpendicular. Many perpendicular lines can be seen in the actual world. Examples include the edges of a set square, a clock's arms during particular times of day, the corners of a blackboard, a window, and the Red Cross emblem.
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the perimiter of a rectangle is 30 inches. if its length is three times its width, find the dimensions
The answer is l = 3.75 and l = 11.25.
Given the length l and width w of a rectangle, its perimeter is:
P=2(l+w)
This formula can be used to form an equation as we already know the value of P.
So, Let the width be w. The length will be 3w. As the perimeter is 30 inches, the width can be found as follows.
2(w+3w)=30
4w=15
w=3.75
Thus, the width is 3.75 inches. The length will be 3*3.75=11.25 inches.
Steps:
Step 1: Let the width of the rectangle be w. Step 2: Since the length is 3 times the width, the length of the rectangle is 3w. Step 3: The perimeter of the rectangle is 30 inches. Step 4: We can write the formula for the perimeter of the rectangle as 2w + 2(3w) = 30. Step 5: Solve for w, then we get w = 3.75Step 6: therefore l = 3w = 3.75 * 3 = 11.25.To know about the Parameters of Rectangle:
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Which of the following is commutative for rational numbers Class 8?subtraction and divisionmultiplication and divisionaddition and subtractionaddition and multiplication
subtraction addition is commutative for rational numbers Class 8
LHS means left-hand side of the equation and RHS means right-hand side of the equation
3c(-5) = (-5)3c
The LHS of the above expression can also be written as 3 * c * (-1) * 5
The RHS of the above expression can also be written as (-1) * 5 * 3 * c
Since, this expression involved multiplication, it will definitely represent a multiplicative property. Since the order of the numbers that are being multiplied has been changed between LHS and RHS, and it is yielding the same result, it indicates that this is the commutative property of multiplication. This property states that a group of numbers can be multiplied in any order. Hence, the answer is C.
8+3.4=3.4+8
In the above, the order of the numbers being added has been changed across RHS and LHS, but is yielding the same result, it is representing the commutative property of addition. This property states that a group of numbers can be added in any order. Hence, the correct answer is C.
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