Answers
The solutions of the system are x = 1, y = 2 and z = -1.
And we solve the system with the help of Jordan-canonical form.
What is matrix?A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.
Given:
A system of equations,
x + y - 2z = 5
-x + 2y + z = 2
2x + 3y - z = 9
In the matrix form;
[tex]\left[\begin{array}{ccc}1&1&-2\\-1&2&1\\2&3&-1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}5\\2\\9\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}1&1&-2\\0&0&-10/3\\0&1&3\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}5\\10/3\\-1\end{array}\right][/tex]
That means,
x = 1, y = 2 and z = -1.
Therefore, the solutions of the system are x = 1, y = 2 and z = -1.
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Related Questions
What is the nature of roots of 2x² 4x +3?.
Answers
D) The quadratic equation's roots, 2x2 4x + 3 = 0, are imaginary in nature.
How may a quadratic problem be solved in four different ways?The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.
Given a quadratic equation, it is 2x 2 + 4x + 3= 0.
∴ a=2,b=4,c=3
As a result, the discriminant of this equation is given by D=b 2 4ac.
∴D=(4) \s2 \s −4(2)(3) (3)
∴D=16−24
∴D=−8<0
The equation's roots are therefore fictitious.
An easy quadratic equation is what?The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. An example of a quadratic equation is x2 + 2x + 1.
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Full Question = The nature of the roots of the quadratic equation 2x ^2 + 4x + 3= 0 are
A. Real & Distinct
B. Real & Equal
C. No Real Roots
D. Imaginary
There are nine different type of bacteria on the Petri dih. What percent of the bacteria on the Petri dih i of type 3
Answers
The number of bacteria of type 3 that will be found on the Petri dish will be 36.84%.
The percentage of bacteria of type 3 on the Petri dish can be calculated using the percentage formula:
P = (Final value - Initial value) / Initial value multiplied by 100.In this case, the final value is the number of bacteria of type 3 in the Petri dish, which is 7. The initial value is the total number of bacteria in the Petri dish, which is the sum of all the bacteria of all types, which is:
1 + 2 + 1 + 7 + 4 + 1 + 1 + 1 + 1 = 19Hence:
P = (7 - 0) / 19 x 100 P = 7 / 19 x 100 P = 36.84%.Therefore, 36.84% of the bacteria in the Petri dish are of type 3.
This question should be provided as:
There are nine different types of bacteria on the Petri dish. A drawing shows some colonies of bacteria on the Petri dish. The number of bacteria in different colonies is as follows:
Colony bacteria
1 2
2 1
3 7
4 4
5 1
6 1
7 1
8 1
9 1
What percent of the bacteria on the Petri dish is of type 3?
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What does sum limit mean?.
Answers
The value L that a function f(x) approaches when its input value x approaches a predetermined value c is referred to as the function's limit.
The limit of f(x) as x approaches c does not exist if, at the value c, there is no single value L that the function f(x) can be considered to approach.
The behavior of the function as it approaches c from both the right and the left must be examined in order to ascertain whether this is true of the function (that is, from x values that are larger and smaller than c, respectively).
A fundamental idea in calculus is the concept of limits. Limits help one to comprehend the connection that a function creates between its variables.
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What is the total area, in square centimeters, of the shaded sections of the trapezoid below?
Answers
The shaded areas therefore cover a total area of 86.84 cm2.
What is the total area?Let's calculate the whole trapezoid's area. You multiply by the height after adding the top and bottom sides and dividing the result by two.
To get the length of the top side, we sum the values that make up that side.
6.4+5.2+9.6=21.2
The underside is 5.2.
The top and bottom sides are added.
21.2+5.2=26.4
We multiply by 2.
26.4/2=13.2
We increase by the height, which is 6.2 as we can see.
13.2×9.1=120.12
Next, we locate the rectangle's unlit portion.
6.4×5.2 = 33.28
To get the total area of the two shaded triangles, we deduct this from the trapezoid's overall area.
120.12 - 33.28 = 86.84
The shaded areas therefore cover a total area of 86.84 cm2.
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Solve the system by substitution.
y=2x+3
3x+2y=6
Answers
Answer:
(0, 3 )
Step-by-step explanation:
y = 2x + 3 → (1)
3x + 2y = 6 → (2)
substitute y = 2x + 3 into (2)
3x + 2(2x + 3) = 6 ← distribute parenthesis and simplify left side
3x + 4x + 6 = 6
7x + 6 = 6 ( subtract 6 from both sides )
7x = 0 , then
x = 0
substitute x = 0 into (1) for y
y = 2(0) + 3 = 0 + 3 = 3
solution is (0, 3 )
In gym cla tudent were aked to form ix equal group. If there were 18 tudent in each group, then how many total tudent were there?
Answers
If there were 18 students in each group and they were asked to form six equal groups, then there would be a total of 108 students.
i.e. (18 students x 6 groups = 108 students)
When a group of students are asked to form a certain number of equal groups, the total number of students can be determined by multiplying the number of students in each group by the number of groups.
In this case, the students were asked to form six equal groups and there were 18 students in each group.
To find the total number of students, we simply multiply 18 by 6.
18 x 6 = 108Therefore, there were 108 students in total.
This is because when you have x number of groups and y number of students in each group, the total number of students is xy.
In this case x=6 and y=18, so the total number of students is 6*18 = 108.
Question:
"In gym class, students were asked to form ix equal group. If there were 18 students in each group, then how many total students were there?"
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List the first five multiples of the denominator in each fraction in order of least to greatest. Fraction Multiples 2/5 3/2
Answers
The first five multiplies of the denominator in each fraction in order of least to greatest are given below.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
There are two fractions,
2/5 and 3/2.
The first five multiplies of the denominator of 2/5:
5 x 1 = 5
5 x 2 = 10
5 x 3 = 15
5 x 4 = 20
5 x 5 = 25
The first five multiplies of the denominator of 3/2:
2x 1 = 2
2x 2 = 4
2x 3 = 6
2x 4 = 8
2x 5 = 10
Therefore, the first five multiplies of denominator are given above.
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When the standard deviation is 4 The variance is equal to?.
Answers
The standard deviation is 4 The variance is equal to 16.
In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.
Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.
The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.
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An investor bought a share of a stock at the beginning of 2015. At the beginning of 2017, the share was worth $1050. From the beginning of 2015 to the beginning of 2017 the value of the share halved each year, but from the beginning of 2017 to the beginning of 2019, the value of the share increased by 1.5 times each year. The investor sold the share at the beginning of 2019. Find and interpret the difference between what the investor paid for the share and what the investor sold the share for.
Answers
$656.25 is the difference between the investor paid for the share and the investor sold the share.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that At the beginning of 2017, the share was worth $1050.
From the beginning of 2015 to the beginning of 2017 the value of the share halved each year.
In 2017 it is 1050.
In 2016 , it is 2100
In 2015, it is 4200
Beginning of 2017 to the beginning of 2019, the value of the share increased by 1.5 times each year.
In 2017, 1050×1.5=1575
In 2018, 1575×1.5=2362.5
In 2019, 2362.5×1.5=3543.75
The investor paid for share is 4200 and the investor sold is 3543.75.
Difference =4200-3543.75
=656.25
Hence, $656.25 is the difference between the investor paid for the share and the investor sold the share.
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Leslie surveyed 80 students in her grade and found that 47 students had a dog with those students 17 of them also had a cat there were 24 students at a cap and no dog there were nine students that did not have a cat or dog move values to create a to table that shows the data from Leslie survey
Answers
Leslie's survey found that 58.75% of students had a dog, 21.25% had a cat, and 11.25% had neither.
This can be visualized in the following table:
Dog | Cat | Neither
47 | 17 | 24
9 | 0 | 0
Leslie's survey results showed that out of the 80 students surveyed, 47 of them had a dog, 17 of them had both a dog and a cat, 24 of them had a cat but no dog, and 9 of them had neither a dog nor a cat.
This shows that a higher percentage of students surveyed had a dog (58.75%) than a cat (21.25%). Furthermore, a higher percentage of students surveyed had either a dog or a cat (79%) than those that had neither (11.25%).
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URGENT PLS ANSWER ASAP THANKS!!
Answers
Answer:
A
Step-by-step explanation:
Angle A=Angle X
AB=XY
AC=XL
Explanation
Notice the tick marks on the triangles, they indicate the congruent or like sides. So we have 1 tick mark side and the 90 degree angle indicator and the 2 tick mark side. This is Side Angle Side congruency. The second triangle was reflected so it is a mirror image. The tick marks are your true indicators. I attached a picture.
What is the degree of the polynomial 3x2y3 4xy x6 y5?.
Answers
The degree of the polynomial p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵ is 6.
A degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 2x^3 + 4x^2 - 5x + 7, the degree is 3 (the highest power of x is x^3). A polynomial of degree 0 is a constant polynomial and a polynomial of degree 1 is a linear polynomial.
To find the degree of a polynomial, you can do the following:
→ Write the polynomial in standard form, with the terms arranged in descending order of exponents.
→ Take the exponent of the term with the highest exponent. This exponent is the degree of the polynomial.
Given,
p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵
Here,
Degree of polynomial is 6
As, 6 is highest of all the exponent given in p(x)
Hence, the degree of the polynomial p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵ is 6.
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R^2-59R-82r^2+60 is equivalent to
Answers
Answer: 83r^2 - 59 + 60
Step-by-step explanation:
R^2 - 59R - 82r^2 + 60
= 83r^2 - 59 + 60
The formula to determine the period of one
swing of a simple pendulum is
L
T = 2√, where L is the length of the
string and g is the acceleration due to
gravity. Solve the formula to solve for g in
terms of T, T and L.
Answers
Answer:
To solve for g in terms of T, L, we can manipulate the formula T = 2π √(L/g) as follows:
First, we divide both sides by 2π:
T/2π = √(L/g)
Then, we square both sides:
(T/2π)² = (L/g)
Then, we multiply both sides by g^2 :
(T^2/4π^2) = L
Finally, we divide both sides by L:
(T^2/4π^2 * L) = g
So the formula for g in terms of T, L is g = (T^2/4π^2 * L)
Please note that this formula is only valid for simple pendulum and not for any complex pendulum, and also the result is in terms of acceleration due to gravity g.
In 1970 a dress cost $40.00. Ten years later, the price increased by 77%. How much more did it sell for ten years later?
please help and explain the answer I will mark brainlisest
Answers
Answer:
70.80
Step-by-step explanation:
40.00 increased by 77% is 70.80. The increase is 30.80.
Answer:
$70.80
Step-by-step explanation:
The dress was $40 to add the 77% increase, you would multiply 40 x .77= 30.80, then you would add the 30.80 to the original 40, giving you a total of $70.80
Can the side lengths 5 12 and 13 form a right triangle?.
Answers
The sum of two sides is always greater than the third side. So the side lengths 5, 12 and 13 can form a right triangle.
In the given question, we have to define the side lengths 5, 12 and 13 form a right triangle.
A side can form a right triangle if the sum of two sides is greater than the third side.
To check the given sides can from a right triangle or not we add them.
5 + 12 > 13
17 > 13 (True)
5 + 13 > 12
18 > 12 (True)
12 + 13 > 5
25 > 5 (True)
Hence, we can see that the sum of two sides is always greater than the third side. So the side lengths 5, 12 and 13 can form a right triangle.
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Plumber W charges $95 per hour and an additional $32 for parts. What is the difference in cost between Plumber W and Plumber T if the repair takes 5 hours?
Answers
The difference in cost between Plumber W and Plumber T if the repair takes 5 hours will be $36.
How to calculate the difference in rate?From the information, Plumber W charges $95 per hour and an additional $32 for parts. Plumber T charges $86 per hour and an additional $41 for parts.
The difference in cost between Plumber W and Plumber T if the repair takes 5 hours will be:
= 86 + (41 × 5) - 95 + (32 × 5)
= 86 + 205 - 95 + 160
= 291 - 255
= 36
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Complete question
Plumber W charges $95 per hour and an additional $32 for parts. Plumber T charges $86 per hour and an additional $41 for parts.
What is the difference in cost between Plumber W and Plumber T if the repair takes 5 hours?
One atom i ×110−8 centimeter in length. How many atom could be laid end-to-end on a metertick (which i 100 cm in length)? Leave the anwer in cientific notation. Round to two decimal place, if neceary
Answers
The number of atoms that can be laid end-to-end on a meter stick is equivalent to 10^8 atoms.
A meter is equivalent to 100 centimeters (cm), and an atom is about 10^-8 centimeters in length. So, when we divide the length of a meter stick (100 cm) by the length of one atom (10^-8 cm).
we are essentially dividing 100 by a decimal number on the order of 0.00000001.
This is the same as multiplying 100 by a number on the order of 100,000,000. In other words, we are multiplying 100 by 10^8.
So, 100 cm / (1*10^-8 cm) = 10^8 atoms
This means that the number of atoms that can be laid end-to-end on a meter stick is equivalent to 10^8 atoms which is a very big number, this is why we use scientific notation to represent it.
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What is the completely factored form of 12xy 9x 8y?.
Answers
Given that the polynomial is 12xy - 9x - 8y + 6, we must determine its fully factored form.
There are two variables in the given polynomial.
12xy - 9x - 8y - 6 = 3x(4y - 3) Now, 12xy - 9x - 8y - 6 = 3x(4y - 3) - 2(4y - 3) = (3x - 2)(4y - 3) The polynomial's fully factored form is (3x - 2)(4y - 3)
(3x - 2)(4y - 3) is the fully factored form of 12xy - 9x - 8y + 6.
One approach to factoring expressions is factoring by grouping. If the expression can be broken down into its component parts, this approach is helpful. On the other hand, we can employ additional strategies.
A polynomial is an expression made up of variables, constants, and exponents that are added, subtracted, multiplied, and divided using mathematical operations (no division by a variable).
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Full Question = What is the completely factored form of 12xy - 9x - 8y + 6?
Find the Value of X in the Problem shown.
Answers
Answer:
X = 20
Step-by-step explanation:
The two quadrilaterals are similar to each other. So the ratio of each side of the larger quadrilateral to the corresponding side of the smaller quadrilateral must be the same.
Examining the two figures we see the side which has 68° and 128° pf the smaller quadrilateral has length 2
The corresponding side of the larger quadrilateral on the right is 6
So each side of the larger quadrilateral =6/2 = 3 times each side of the smaller one
Side which has length 10 pf the smaller quadrilateral corresponds to the side with length x+10 of the larger one. This ratio must also be 1:3
So
[tex]\dfrac{10 + x}{10}= 3\\\\[/tex]
Cross-multiplying we get
10 + x = 10 x 3
10 + x = 30
x = 30-10
x =20
ANSWER
Test Scores
100
90
80
70
60
50
40
30
20
10
0
Test Scores in Relation to Homework
3
4
5 6
Hours of Homework
+x
7 8 9 10
Draw a line of best fit for the
graph.
Based on the line your drew,
what is the likely test score of a
student who does not study for
the test?
Answers
Test score of a student who does not study for the test 70%.
What is percentage?A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The sign "%" is used to denote it.
Out of a hundred is what the word "percent" refers to. Percentages are used in mathematics to represent subsets of a whole, just like fractions and decimals are. The whole is thought of as being composed of 100 equal parts when using percentages. As a less common alternative, the abbreviation "pct" may be used to indicate that a number is a percentage.
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Is 52 a perfect square?.
Answers
No, the number 52 is not a perfect square. Because the square root of 52 is an irrational number.
An irrational number is a real number that cannot be expressed as a ratio of two integers, or in other words, as a fraction. Irrational numbers include numbers such as pi (π), the square root of 2, and the square root of 3, which are not terminating or repeating decimals. They cannot be written as a finite decimal or a fraction of integers. Irrational numbers have an infinite number of decimal places, which means they cannot be represented exactly as a decimal.
They are also non-repeating and non-terminating decimals. Irrational numbers have many important properties and applications in mathematics, such as in geometry, where they are used to calculate the lengths of curves and the areas of circles. They also appear in trigonometry and calculus. Irrational numbers are also important in physics and engineering as well as other branches of science and technology. They are often used to express the precise measurements and calculations that are essential in these fields.vb
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Solve the quadratic equation by completing the square. 2+x=6x^2 Completing the square gives us: (x- Answer )^2 = Answer Enter your solutions below from smallest to largest. If a solution is repeated type that answer for both values of x. If your answer is not an integer then type it as a decimal rounded to the nearest hundredth. x=Answer and x=Answer
Answers
Answer:
6xˆ2 - x - 2 = 0
D = 1 + 1*2*6*4=49=7ˆ2;
using formula of discriminant you get
x1= -1/2
x2= 2/3
answer = x1, x2
Your chool i putting on a production of Wet Side Story. Ticket cot $5 for tudent and $9 for non-tudent. On one night there were three time a many tudent a there were non-tudent. On thi night, they old $4,608 in ticket. How many tudent ticket were old? How many non-tudent ticket were old?
Answers
On that particular night, there were 144 student tickets and 432 non-student tickets sold.
Let x be the number of student tickets sold that night
y be the number of non-student tickets sold that night
On that night, there were three times as many student as there were non-students. Hence, we can write that as an algebraic expression such that
3x = y
If tickets cost $5 for students and $9 for non-students, and on that night, they sold $4,608 in tickets, then we can express that as
$5x + $9y = $4608
5x + 9y = 4608
Substitute the value of y from the first expression to the second and solve for x.
5x + 9y = 4608
5x + 9(3x) = 4608
5x + 27x = 4608
32x = 4608
x = 144
Plug in the value of x into the first expression and solve for y.
y = 3x
y = 3(144)
y = 432
Hence, the number of tickets sold on that night to students and non-students were 144 and 432, respectively.
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You survey your class and 4 like vanilla ice cream
and 14 like chocolate ice cream. Write the ratio of
people who like vanilla to people who like chocolate ice
cream, then write the ratio in simplest form.
Answers
Answer: 2:7
Step-by-step explanation:
Vanilla icecream = 4
Chocolate icecream = 14
4:14=2:7
2X2=4
7X2=14
Step-by-step explanation:
a ratio is simply relating 2 (or more) groups and their sizes.
in our case here the ratio is
4/14 = 2/7
this is often written as
4:14 = 2:7
it means that for every 2 people liking (I assume "preferring") vanilla ice cream there are 7 people liking (preferring) chocolate ice cream.
FYI
in total, a ratio also tells us about the size of the sample for the observation or analysis. 4/14 tells us there are 18 (4+14) people in the survey. and the simplified form 2/7 tells us that we can split the whole survey group into units of 9 (2+7) people with the same behavior as the total group.
a ratio is a fraction (incl. all the calculation and comparison rules) with a special meaning.
so, don't mix the ratio up with e.g. the fractions of the different behaviors in the group :
4/18 = 2/9 of the whole group prefer vanilla.
14/18 = 7/9 of the whole group prefer chocolate.
the ratio is now the relative size relationship between both : 2/9 / 7/9 = 2/7
(5+7)*200
[tex]please \: excuse \: my \: dear \: aunt \: sally[/tex]
How would I solve this equation using my formula
Answers
Answer:This is a mathematical expression. To solve it, we can use the order of operations (PEMDAS)
First, we simplify the expressions inside the parentheses.
5+7 = 12
Then, we simplify the multiplication
12 * 200 = 2400
So the result of (5+7)*200 is 2400.
please help!!
<RQT is a straight angle. What are m<RQS and m<TQS?
Answers
angle RQS = 101 degrees
angle TQS = 79 degrees
===================================================
Explanation:
A straight angle has a measure of 180 degrees. It's another way of saying "straight line".
The two angles shown add to 180.
We'll use this fact to solve for x.
(angleRQS) + (angleTQS) = angle RQT
(9x+2) + (7x+2) = 180
16x+4 = 180
16x = 180-4
16x = 176
x = 176/16
x = 11
Use this x value to determine the angles we're after.
angle RQS = 9x+2 = 9*11+2 = 99+2 = 101 degreesangle TQS = 7x+2 = 7*11+2 = 77+2 = 79 degreesCheck:
(angleRQS) + (angleTQS) = 101+79 = 180 which confirms the answer is correct.
(X^2+y^2-1)^3=x^2y^3 Write the mapping notation to transform the parent function then describe the transformations made to the parent function.
Answers
The relation's graph can be seen in the graphic at the bottom, where it is clear that it is function.
How to determine if the relation is a function?The actual function can be specified using this "mapping" notation. Writing f:(x,y)x+y would allow us to define the above f(x, y). Real numbers are referred to as scalars to distinguish them from vectors. Each input is translated into a single output in a relation known as a function (input, output).
The horizontal axis is used for inputs, and the vertical axis is used for outputs. Here, we have the relationship shown below:
(-5,-1), (-4,1), (-3,3), (-1,5), (1,7) (1,7)
The figure below shows the graph of these points. Since there are no two points on the same vertical line, the relation is a function, as you can see.
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The price at Yogurt World is $2.56 for 8 ounces. How much-frozen yogurt could you get for $3.52? ____Ounces
Answers
Answer: 11
Step-by-step explanation: (8/2.56) x 3.52 = 11 ounces
How is FG calculated?.
Answers
To calculate the composition of two functions, "F" and "G", represented by the notation "FG", you first need to have a specific input value, usually represented as "x".The first step is to apply the function "G" to the input "x", resulting in G(x).
The next step is to take the output of the function G, which is G(x), and use it as the input for the function F.
The final step is to apply the function F to the output of G(x) resulting in F(G(x)), which is the composition of the two functions F and G.
In other words, you apply the function G to the input x, and then you apply the function F to the result of G(x). The final result is the function F(G(x)), which is the composition of the functions F and G.
It's important to note that the order of the functions in composition matters and can change the result of composition. The notation "FG)(x)" is different from "GF)(x)" which means that the order of the functions matter in composition.
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