To find the equation of the axis of symmetry using factored form, we can use the multiply and conversion method which converts it into vertex form.
It can be multiplied and converted to vertex form.
Example: (x-3)(x+2) f(x)
f(x) = x^2 - x - 6
We can now combine the x terms to finish the square.
f(x) = (x^2 - x +1/4 ) - 6 - 1/4
f(x)= (x - 1/2)^2 -25/4
As a result, the vertex is (1/2, -25/4)
Any quadratic given in factored form can be solved this way.
If the parabola contains the equation y=f(x)=a(xr1)(xr2), the zeroes of f(x), i.e., r1 and r2, can be read off right away. The vertex then has coordinates (h,k), where k=f(h) is the result of inserting x=h through the function f(x), and h=(r1+r2)/2 is the average of the two zeroes.
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find the value of a and b when x=12.\frac{5x^2}{2}
Answer:
when x = 12, a = 360 and b = 16.8.
Step-by-step explanation:
Sally has 4 yards of a ribbon. How many 1/6 yard pieces can she cut?
Two angles are supplementary. The measure of one angle is 9° more than twice the measure of the other angle. What is the measure of the smaller angle?
If a = the measure of the smaller angle, we have:
[tex]\it a+2a+9^o=180^o\bigg|_{-9^o} \Rightarrow 3a=171^o\bigg|_{:3} \Rightarrow a=57^o[/tex]
A researcher fit a linear model to her data and calculated the correlation coefficient to be -0.29 which statement about the correlation among the data is true?
A given linear model shows negative correlation.
What is the correlation coefficient?The correlation coefficient describes how one variable moves in relation to another. A positive correlation indicates that the two move in the same direction, with a value of 1 denoting a perfect positive correlation. A value of -1 shows a perfect negative, or inverse, correlation, while zero means no linear correlation exists.
Given that, a researcher fit a linear model to her data and calculated the correlation coefficient to be -0.29.
Here, a linear model shows negative, or inverse, correlation.
Therefore, a given linear model shows negative correlation.
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A rent-to-own business has a game system advertised with a purchase price of $624.00. Calculate the APR if the finance terms are $21.99 per week for 52 weeks. Round the final answer to the nearest hundredth.
The APR if the finance terms are $21.99 per week for 52 weeks is 83.48%. Hence option 4 is correct.
What is APR and example?The annual percentage rate, or APR, is the interest rate that is charged on a loan balance that is still outstanding. The expected cost of the annual fees connected with a certain sort of borrowing is what the APR conceptually reflects.
APR is a commonly used formula by lenders that enables borrowers to compare various loan choices. The stated interest rate on a loan is typically insufficient on its own to help borrowers choose the best loan option.
A loan with a low stated interest rate could also have significant costs attached that should not be disregarded. The best alternative might be a loan with a smaller fee structure and a higher advertised interest rate. APR is calculated as (Periodic Interest Rate x 365 Days) x 100 i.e.
[tex]$\mathrm{APR=\left(\left(\frac{\frac{Fees+Interest}{Principal}}{n} \right) \times 365 \right) \times 100}[/tex]
where:
Interest = Total interest paid over life of the loan
Principal = Loan amount
n = Number of days in loan term
Fees = 0
Interest = 2Interest = $519.48
Principal = $624.00
n = 52 × 7 = 364 days
Plug the data in the formula:-
[tex]$\mathrm{APR=\left(\left(\frac{\frac{0+519.48}{624}}{364} \right) \times 365 \right) \times 100}[/tex]
APR = 83.48%
Thus, The APR if the finance terms are $21.99 per week for 52 weeks is 83.48%. Hence option 4 is correct.
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How do you convert a quadratic equation from factored form to vertex form?.
Expanding, which entails multiplying out the factors, allows an equation in factored form to be rewritten in standard quadratic form.
The steps we employ in doing so are as follows:
The formula should be y = ax2 + bx + c.Figure out -b / 2A. Here we get the vertex's x-coordinate. By simply substituting the value of -b / 2a into the equation for x and solving for y, you may determine the vertex's y-coordinate. This number represents the vertex's y-coordinate.Opposite of expanding is factoring an expression. Parenthesis or grouping symbols are removed from an expression when it is expanded. The Greatest Common Factor (GCF) from each phrase allows each extended statement to be factored.
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A parallelogram is a _____ polygon in which both pairs of opposite sides are parallel.
Answer:
Quadrilateral
Step-by-step explanation:
I remember learning this in math class. A parallelogram has two dimensions. Each of its four sides has two parallel pairs. The parallel sides have the same length.
Marcus bought 8.6 kg of sugar. He poured the sugar equally into 5 bottles. There was 0.35 kg of sugar left over. What was the mass of sugar in 1 bottle?
The mass of sugar in 1 bottle is 1.65kg.
What is the mass of sugar in one bottle?The equation that represents the information in the question is:
Total kg of sugar bought = total kg of the bottes + sugar left over
Total kg of sugar bought = (number of bottles x mass of sugar in one bottles + sugar leftover
8.6 = (5 x s) + 0.35
8.6 = 5s + 0.35
In order to determine the value of s, take the following steps:
Combine and add similar terms together:
8.6 - 0.35 = 5s
8.25 = 5s
Divide both sides of the equation by 5
s = 8.25 / 5
s = 1.65 kg
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someone help
f(-3x)
-3f(x)
f(3x)
3f(x)
The given expressions are the results of applying the function f to a value that is being multiplied by -3 or 3.
f(-3x) means that the function is applied to -3x, in this case the output is -3f(x)
f(3x) means that the function is applied to 3x, in this case the output is 3f(x)
It should be noted that the function f(x) could be any type of function and the output depends on the function's definition.
Answer: 3x^2
Step-by-step explanation:
e2023
How do you graph a linear inequality in slope intercept form?.
To graph a linear inequality in slope intercept form:
Put your inequality in slope intercept form by converting y to mx + b. Either the equal sign or the provided inequality symbol may be used.Map out the line. The line should be dotted if the inequality employs or >. The line should be solid if the inequality employs either or. Remember that you should plot the functions on a coordinate plane rather than a number line.Shade the area of the graph where the solutions are displayed. Choose the side to shade by using test points. Only one side of the line will have the shaded area.The solutions that make both inequalities true are all shown on the graph of an inequality system. When you are graphing inequalities, keep the following in mind: Form your inequality as y=mx+b, the slope intercept. Either the equal sign or the provided inequality symbol may be used.
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Alice carries out an experiment to record how quickly plants grow. One plant increases in height from 12.0 cm to 13.8 cm in one week. A second plant increases by the same percentage to 16.1 cm. What was the original height of the second plant
WILL GIVE BRAINLIEST
Answer:
14.0cm
Step-by-step explanation:
if 13.8 = 12.0
then 16.1 = ?
[tex] \frac{16.1}{13.8} \times 12.0cm = 14.0cm [/tex]
Answer:
14 cm
Step-by-step explanation:
1st plant:
13.8 - 12.0 = 1.8
1.8/12 = .15
.15 x 100 = 15% growth
2nd plant:
let x = original height
x + x(.15) = 16.1
1.15x = 16.1
x = 16.1 / 1.15 = 14.0 cm
In 1940, a coat cost $25.00. Thirty years later, the price increased by 310%. How much more did a coat sell for thirty years later?
Please answer and explain the answer I will mark brainlisest
Answer:
$77.5
Step-by-step explanation:
Has risen in price BY 310% To mean its price has added 310% from the old price:
Price new = Price old + (Price old × 310%).
To calculate the difference, we just need to calculate 310% of the old price (a percentage is a hundredth):
$25 × 310% = $25 × 3.1 = $77.5
Together, Kendra and Arnie checked out 12 books from the library. IF Kendra has more than one-third as many books as Arnie, at least how many books does Kendra have?
Answer:4
Step-by-step explanation:12/3=4
Which of the following describes the function x - 3?
O The degree of the function is even, so the ends of the graph continue in opposite directions. Because the leading coefficient is positive, the left side of
the graph continues down the coordinate plane and the right side continues upward.
O The degree : the function is even, so the ends of the graph continue in the same direction. Because the leading coefficient is negative, the left side of
the graph continues down the coordinate plane and the right side also continues downward.
O The degree of the function t even, so the ends of the graph continue in opposite directions. Because the leading coefficient is negative, the left side
of the graph continues up the coordinate plane and the right side continues downward.
O The degree of the function is even,
so the ends of the graph continue in the same direction. Because the leading coefficient is positive, the left side of
the graph continues up the coordinate plane and the right side also continues upward.
The leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.
What is function ?
function can be defined in such a way that it relates an input to the output.
Given function y = x-3
The degree of the function means the highest power of the variable
Here, the degree is 1, it is odd.
The leading coefficient is 1, which is positive.
By taking sample values of x, we get values of y with the graph as shown
From the graph, we can say that the degree of the function is odd, so the ends of the graph continue in opposite directions
Because the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.
The following describes the function x-3 that the degree of the function is odd, so the ends of the graph continue in opposite directions.
Hence, the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.
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which transformations were used to create congruent trapezoid W' X' Y' Z' from Trapezoid W XYZ
The translation and rotation of 180° about the origin. Then the correct option is A.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The translation does not change the shape and size of the geometry. But changes the location.
From the graph, the trapezoid W'X'Y'Z' is derived by the translation and rotation of 180° about the origin. Then the correct option is A.
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Can someone help me on this please?
Answer:
x > -1
10 ≤ d
k ≤ -24
Step-by-step explanation:
a)
First, we need to isolate the variable, for that we follow these steps13 + 4x > 9
Subtract 13 from both sides4x > -4
Divide both sides by 4x > -1
b)
We can solve this using the same method we used with finding x:99 - 5d ≤ 4d
Add 5d to both sides99 ≤ 9d
Divide both sides by 910 ≤ d
c)
Now onto the value of k:3k - 9 ≤ -6k - 225
Transfer like terms to the same side of the inequation3k + 6k ≤ 9 - 225
Add/subtract9k ≤ -216
Divide both sides by 9k ≤ -24
Why the ratio of sine of angle of incidence to the sine of angle of refraction is constant?.
Ratio of sine of angle of incidence to the sine of angle of refraction is constant by Snell’s law.
According to Snell's Law, the refractive index, or n, is a constant that represents the ratio of a wave's angle of incidence to angle of refraction as it passes through a boundary between two mediums.
₁n₂=n₂/n₁=sin θ₁/sin θ₂= v₁/v₂,
where n is the refractive index,
v is the speed in different medium and θ is the angle between the normal and the ray at the surface of boundary.
If we do an experiment and measure the angles of incidence and refraction, we will discover that a straight line passing through the origin results from plotting the sine of the angles of incidence and refraction.
This shows that the sine of the angle of incidence and the sine of the angle of refraction are directly related, and that the ratio of the two will result in a constant value that we refer to as the refractive index. The ratio of the sines of the angles corresponds to the proportion of the wave speeds through the medium.
Thus, we can say that refractive index is constant for a given pair of media.
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an isosceles triangle of sides 100cm, 60cm, and 60 cm has a base angle f, find f
Answer:
f = 53.13 degrees
Step-by-step explanation:
An isosceles triangle has two equal sides, so in this case the sides of length 60cm are equal. The base angle (f) is opposite the base of the triangle, which is the side of length 100cm.
To find the base angle, we can use the law of cosines.
c^2 = a^2 + b^2 - 2ab*cos(f)
where c is the hypotenuse (the side of length 100cm), a and b are the legs (the sides of length 60cm), and f is the base angle we are trying to find.
Substituting in the given values, we get:
100^2 = 60^2 + 60^2 - 2(60)(60)cos(f)
Simplifying this equation, we get:
10000 = 3600 - 3600cos(f)
so
cos(f) = (10000-3600)/3600 = 6400/3600 = (8/3)^2
then
f = cos^-1((8/3)^2)
Therefore, f = 53.13 degrees
Question 3(Multiple Choice Worth 2 points)
(Graphing Linear Equations LC)
Which of the following graphs has a slope of negative three halves and a y-intercept of 3?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
A graph which has a slope of negative three halves and a y-intercept of 3 include the following: C. graph of a line passing through the points 0 comma 3 and 2 comma 0.
What is the point-slope form?Mathematically, the point-slope form of any straight line can be calculated by using this expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided above, we have the following slope and data points on this line:
Points on x-axis = (0, 2).Points on y-axis = (3, 0).At data point (0, 3), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 3 = (0 - 3)/(2 - 0)(x - 0)
y - 3 = -3/2(x)
y = -3x/2 + 3
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Answer:
Step-by-step explanation:
A graph which has a slope of negative three halves and a y-intercept of 3 include the following: C. graph of a line passing through the points 0 comma 3 and 2 comma 0.
What is the point-slope form?
Mathematically, the point-slope form of any straight line can be calculated by using this expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.
x and y represents the data points.
From the information provided above, we have the following slope and data points on this line:
Points on x-axis = (0, 2).
Points on y-axis = (3, 0).
At data point (0, 3), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 3 = (0 - 3)/(2 - 0)(x - 0)
y - 3 = -3/2(x)
y = -3x/2 + 3
What is the solution to the system of equations y 2x 3. 5 and x 2y =- 14?.
The solution of the system of equations y = 2x - 3.5 and x - 2y = -14 is (7, 10.5).
In the given question, we have to solve the solution to the system of equations
y = 2x - 3.5..................(1)
x - 2y = -14...............(2)
Now putting the value of y from the equation 1 in the equation 2.
x - 2(2x - 3.5) = -14
Now simplifying the expression using the distributive property
x - 4x + 7 = -14
-3x + 7 = -14
Subtract 7 on both side, we get
-3x = -21
Divide by -3 on both side, we get
x = 7
Now putting the value of x in the equation 1,
y = 2(7) - 3.5
y = 14 - 3.5
y = 10.5
Hence, the solution to the system of equations y = 2x - 3.5 and x - 2y = -14 is (7, 10.5).
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The complete question is:
What is the solution to the system of equations y = 2x - 3.5 and x - 2y = -14?
cosA*1/tanA=cos^2A/sinA
Answer:
see explanation
Step-by-step explanation:
using the identity
• tan A = [tex]\frac{sinA}{cosA}[/tex]
consider left side
cos A × [tex]\frac{1}{tanA}[/tex]
= cos A × [tex]\frac{1}{\frac{sinA}{cosA} }[/tex]
= cos A × [tex]\frac{cosA}{sinA}[/tex]
= [tex]\frac{cos^2A}{sinA}[/tex]
= right side
Why is Avogadro's number a mole?.
The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³.
The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)
So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A
atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.
We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).
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The weights of adult male rhesus monkeys are normally distributed with
a mean of 17 pounds and a standard deviation of 3 pounds. What is the probability
that a randomly selected adult male rhesus monkey has a weight less than
14 pounds?
Answer:
15.87% (2 d.p.)
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
Mean μ = 17 poundsStandard deviation σ = 3 poundsTherefore, if the weights of adult male rhesus monkeys are normally distributed:
[tex]\boxed{X \sim\text{N}(17, 3^2)}[/tex]
where X is the weight of an adult male rhesus monkey.
To calculate the probability that a randomly selected adult male rhesus monkey has a weight less than 14 pounds, we need to find P(X < 14).
Calculator input for "normal cumulative distribution function (cdf)":
Lower bound: x = -100Upper bound: x = 14σ = 3μ = 17⇒ P (X < 14) = 0.158655253...
⇒ P (X < 14) = 15.8655253...%
⇒ P (X < 14) = 15.87%
Therefore, the probability that a randomly selected adult male rhesus monkey has a weight less than 14 pounds is approximately 15.87% (2 d.p.).
Given vector u = (1, 2) and v = (1, -4), determine the value of 4u + 3v. Click
and drag copies of the dotted vectors as many times as needed, lining them up head
to tail, in order to find the result graphically. You may have to negate the direction of
one of the vectors by pressing the link.
Let u and v be a vectors. Then u can be broken up into two components, r and s such that r is parallel to v and s is perpendicular to v.
How do you find vector U and V?The component of u perpendicular to v is referred to as s, while r is referred to as the projection of u onto v. Then, u v = u1v1 + u2v2 + + unvn is the dot product of u with v.
Keep in mind that u v is defined when u and v have the same number of components and that the dot product of two vectors is a scalar. Though the dot product is a union of two vectors, the outcome is not a vector, which is an intriguing observation.
In particular, u (v w) makes no sense if u, v, and w are vectors because v w is a scalar. Before confirming that the dot product has the desired geometric characteristics, we'll mention.
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When given vector u = (1, 2) and v = (1, -4), Then the value of 4u + 3v = ⟨7, -4⟩, graph in attachment.
How do you find vector U and V?The component of u perpendicular to v is referred to as s, while r is referred to as the projection of u onto v. Then, u v = u1v1 + u2v2 + + unvn is the dot product of u with v.
Keep in mind that u v is defined when u and v have the same number of components and that the dot product of two vectors is a scalar. Though the dot product is a union of two vectors, the outcome is not a vector, which is an intriguing observation.
Given u = (1, 2) and v = (1, -4),
4u + 3v = 4(1, 2) + 3(1, -4)
= (4, 8) + (3, -12)
= ⟨4 + 3, 8 + (-12)⟩
= ⟨7, -4⟩
Thus, 4u + 3v = ⟨7, -4⟩
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Use the figure.
5. Which of these arcs is the largest? (1 point)
A: NR
B: NRS
C:NST
D: NP
The measure of the arc NST will be the largest one. Then the correct option is C.
What is the arc length of the sector?Let r be the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be
Arc = (θ/2π) 2πr
If the central angle of the arc is maximum, then the measure of the arc will be maximum.
The measure of the angle ∠NST is maximum. Then the measure of the arc NST will be the largest one.
Thus, the correct option is C.
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13.
A sala ding of the figure shown is created using a vertical scale factor of 50% and a
ortzontal scale factor of 150%
Which
shows the correct scale drawing?
Answer:
of course it would be 45
Step-by-step explanation:
it right trusss
For what value of k is 3x² 2kx 27?.
For the roots to be real and equal, the value of k should be 9, -9.
The complete question is:
For what values of k are the roots of the quadratic equation 3x2 + 2kx + 27 = 0 real and equal?
For the roots of the equation to be real and equal, we first compare the given quadratic equation with standard form of quadratic equations, which is: [tex]ax^2+ bx+ c=0[/tex]
Thus, a = 3; b= 2k and c = 27
We know, for real and equal roots, Discriminant (D) = [tex]b^2 - 4ac[/tex] = 0
Therefore, we now substitute the values of a, b, and c in the above formula, we get
(2k)^2 - 4(3)(27) = 0
4k^2 - 324 = 0
4k^2 = 324
k^2 = 81
k= 9 or -9
Thus, the value of k is 9 or -9.
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Why is a right angle 90 degrees?.
A right angle is defined as an angle that measures exactly 90 degrees.
To prove this:
This definition of a right angle has been established by mathematical convention, and it is widely accepted and used in mathematics and geometry. The reason for this is that a right angle is the most convenient and natural angle to use as a standard unit of measure for angles.
One reason is that a right angle is easy to construct and measure. A right angle can be created by using a square or a set square, which are simple and inexpensive tools. Also, right angles are found in many natural and man-made objects, such as corners of walls and buildings, which makes them easy to recognize.
Another reason is that a right angle is a fundamental building block in Euclidean geometry, and it is used to define other geometric concepts such as parallel lines and perpendicular lines. The properties of a right angle make it a useful tool for solving geometric problems and for understanding the relationships between angles and shapes.
In summary, the 90 degrees definition of a right angle is a mathematical convention that is widely accepted due to its convenience, natural appearance in many objects, and its importance in Euclidean geometry.
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Can someone please help me with this math problem it is so confusing? The math problem is located in the picture, Thanks!
Domain:
Range:
The domain is the set of all x-values (or inputs) used by the function. In a graph like this, you want to see how the graph lines up with the x-axis.
As an interval, the domain is [-4,-1], as shown on the domain graph.
(Remember to write intervals from lesser-to-greater.)
The range is the set of all y-values (or outputs) used by the function. In a graph like this, you want to see how the graph lines up with the y-axis.
As an interval, the range is [-4,-2].
(Again, remember to write intervals from lesser-to-greater.)
two matrices are row equivalent if they have the same number of rows
Two matrices are row equivalent if they can be transformed into each other using elementary row operations.
Elementary row operations are operations such as the addition or subtraction of two rows, the multiplication or division of a row by a non-zero constant, or the interchange of two rows. Row equivalent matrices are equal in terms of row space, meaning any linear combination of the rows of one matrix will yield the same linear combination of the rows of the other matrix. An example of two row equivalent matrices is given below:
Matrix A =
[tex]\begin{bmatrix} 1 & 2 & 3 \\4 & 5 & 6 \end{bmatrix}[/tex]
Matrix B =
[tex]\begin{bmatrix} 1 & 2 & 3 \\2 & 3 & 4 \end{bmatrix}[/tex]
These matrices are row equivalent because adding the first row of Matrix A to the second row of Matrix B yields Matrix A. To show this mathematically, let row 1 of Matrix A be represented as r1, and row 2 of Matrix B be represented as r2. We can then say that r2 + r1 =
[tex]\begin{bmatrix} 1 & 2 & 3 \\6 & 8 & 10 \end{bmatrix}[/tex]
which is equal to Matrix A.
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