Consider the relation below
Is it a function?
Is the relation a one to one function?
Is the inverse of the relation below itself of function ?

The graph of f(x) = x in a straight line passing through the origin (0,0) and  at an angle of 45 degrees to the x axis. It increases from left to right.

What is graph?

In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs.

A simple graph is one in which no two vertices are connected by more than one edge, and no edge begins or finishes at the same vertex. In other terms, a simple graph is one that doesn't have loops or many edges.

Reflection in the x axis  will convert all positive values of f(x) to negative values of f(x)  and vice versa.  

g(x)  = - x     and is a straight line passing through origin  at angle of 45 degrees but the slope descends from left to right.

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Answer:

x = 2, y = 3

Step-by-step explanation:

Solve the following system:

{-2 y + 3 x = 0 | (equation 1)

{-2 y + x = -4 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x - 2 y = 0 | (equation 1)

{0 x - (4 y)/3 = -4 | (equation 2)

Multiply equation 2 by -3/4:

{3 x - 2 y = 0 | (equation 1)

{0 x + y = 3 | (equation 2)

Add 2 × (equation 2) to equation 1:

{3 x + 0 y = 6 | (equation 1)

{0 x + y = 3 | (equation 2)

Divide equation 1 by 3:

{x + 0 y = 2 | (equation 1)

0 x + y = 3 | (equation 2)

Collect results:

Answer: {x = 2, y = 3

Answer:

2x=4 x=2

Step-by-step explanation:

3x-x=2x

-2y-(-2y)=0

0-(-4)=4

2x=4

x=2

If x=2,3(2)-2y=0

Answer:

Step-by-step explanation:

Answer: CLICK TO VIEW

16x^3+5x?

Step-by-step explanation:

Functions can be represented as equations, and equations can be represented as functions.

The number of people that started the rumor is 10

The function is represented as:

To calculate the number of people that started the rumor, we simply set t to 0.

So, we have:

Evaluate the exponent of e

Express e^0 as 1

Multiply 39 and 1

Add 1 and 39

Divide 400 by 40

When t = 0, N(t) = 10

This means that 10 people started the rumor.

Hence, the number of people that started the rumor is 10

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Answer:

Step-by-step explanation:

To find KLR, we subtract MLR from KLM. We get left with 2x+14=KLR. With this, we can see that 36 degrees = 2x+14.

Now you just solve.

The value of divisor and the dividend for the synthetic division problem will be;

⇒ (x + 3) and 2x³ + 4x² - 4x + 6

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The synthetic division problem is,

⇒ - 3/ 2 4 -4 6

Now,

Since, The synthetic division problem is,

⇒ - 3/ 2 4 -4 6

Hence, The divisor of the synthetic division problem is,

⇒ x - (- 3) = x + 3

And, There are four leading coefficient.

Hence, The dividend of the polynomial must be degree of 3.

So, By the leading coefficient are;

⇒ 2, 4, - 4, 6

Hence, We get;

⇒ 2x³ + 4x² - 4x + 6

Thus, The value of divisor and the dividend for the synthetic division problem will be;

⇒ (x + 3) and 2x³ + 4x² - 4x + 6

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Answer:

Step-by-step explanation:

I hope this letter finds you in good health dear. I am doing well here.

It is been a long time since I haven’t written a letter to you, I finally got some time. I was actually occupied with some practical submissions. I am anyway going to start with the preparation for my exams. They are beginning from next week onward. What about yours?

This time I will be making my own notes by going through each and every topic so that I don’t miss out on topics. If you want I will share my notes with you. I am also going to refer to some extra books for easier explanations. My teacher gave me this idea. This will help me remember the basics in my own words and will help me understand each and every concept well.

Do write me back. I miss our long chats and I wish to hear from you.

On solving the provided question, we got that - y = 4, when x=2 and the hypotenuse of the resulting right triangle is 5.

[tex]AC^2 = AB^2 + BC^2[/tex] is the formula for the Pythagorean theorem, where AB is the perpendicular, BC is the base, and AC is the hypotenuse. All triangles with 90° angles are governed by the Pythagorean equation.

The hypotenuse formula can be used to define the relationship between the sides of a right triangle, making it a specific kind -

[tex]c^2 = a^2 + b^2\\or\\c^2 = x^2 + y^2[/tex]

where,

The triangle's hypotenuse, or c, is the side that faces away from the 90-degree angle.

while the sides closest to the 90° angle are denoted by a and b.

Given that the hypotenuse is 5 = c and one of the sides has a measure of 2 = x in the issue statement, we can calculate for y as follows:

[tex]y^2 = c^2 - x^2\\y^2 = 5^2 - 2^2\\y^2 = 21\\y = 4.58[/tex]

The number before the decimal is known as the natural number. As a result, the response is:

y = 4

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Answer: Because the first washing machine is cheaper

Step-by-step explanation:

Find the first washing machine price by taking 550 times 0.7 = $385

The second machine is first down by 20%, so take 550 times 0.8 =$440

Then 10% off, so take 440 times 0.9 = $396

So the first washing machine is cheaper than the second one $11

Answer:

22.31 minutes

Step-by-step explanation:

First simplify the numbers to decimals to make it easy : 2 1/3 = 2.30( estimated) ,  11 2/3 = 11.67 ( estimated ), and 4 2/5 = 4.4

The we divide how many miles by the total amount of minutes to get 5.07( estimated )

We then multiply it by 4.4 to get 22.308 to be exact.

So it will take him 22.31 minutes

P.S : Correct me if I am wrong. Apologizes.

The data set of favorite sports among 9th graders is univariate and numerical.

Univariate data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.

In bivariate two different variables in this kind of data. The analysis of this kind of data focuses on linkages and causes, and it seeks to understand the causal connection between the two variables.

Given, A set of data of the favorite sports among 9th graders.

Baseball or Softball, Basketball, Lacrosse, Soccer and Field hockey

and the percentage of 9th graders who plays a certain type of sport.

This is a univariate and numerical type of data set not bivariate,

An example of bivariate data is temperature and ice cream sales in the summer season as the sales of ice cream must be related to the temperature.

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Answer:they all end in the same number

Step-by-step explanation:

if you look at the ending of each number they are the same

The domain of the given graph will be equal to -4≤ x ≤ 4. The correct option is A.

The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x).

A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.

The values that we can put in the function of the given graph images vary from -4 to 4.

In the y-axis, the value of x varies from -4 to 4.

Therefore, the domain of the given graph will be equal to -4≤ x ≤ 4. The correct option is A.

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When  (a, b) appears on a graph, it is said to be symmetric around the x-axis if (a ,b) also appears there at the same time. A graph that is symmetric around the x-axis is shown in the following illustration. A graph is said to be symmetric around the y-axis if and only if (a ,b) and (a, b) are both present on it.

We replace all the x's with -x and check to see if we get an equivalent formula to determine algebraically whether a graph is symmetric with regard to the y axis. Example: A) To make y = x2 symmetric with regard to the y axis, we substitute y = (-x)2 = x2 for y = x2.

Ordered pairs (x, y) and and exist in equations or functions that are symmetric to the origin (-x, y). The original equation is symmetric with respect to the origin if you swap -x for x and -y for y in the equation and simplify.

If we reflect a function's graph about the y-axis, we will get the same graph since some functions might be symmetrical about the y-axis. We may reflect various functions about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as even and odd functions.

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The statement that ,"distribution of sample​ mean(μ) will be normally distributed if sample is obtained from population that is normally​ distributed, regardless of sample size(n)" is True .

What is Normal Distribution ?

A Normal Distribution is a distribution that describes a symmetrical plot of data around the mean value, where width of curve is defined by standard deviation.

the Central Limit Theorem states that , for a normally distributed random variable "X" , with mean "μ" and standard deviation "σ" , the sampling distribution of the sample means with size "n" can be approximated to a normal distribution with mean  and standard deviation  is s = σ/√n   .

So , sample size restriction is only for non normal underlying distribution,

Therefore , by Central Limit Theorem the given statement is True .

The given question is incomplete , the complete question is

The distribution of the sample​ mean (μ), will be normally distributed if the sample is obtained from a population that is normally​ distributed, regardless of the sample size . Is the statement True or False ?

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No, the ordered pair (0, 4) is not a solution of the inequality y ≤ x − 3

The solution of the inequality is checked by substituting the value in the ordered pair

If the given function helps in finding the each of the numbers that makes up the ordered pair then it is a solution

The substitution is as below

y ≤ x − 3

substituting x = 0

y ≤ x − 3

y ≤ 0 − 3

y ≤ -3

y is 4 and 4 is not less than or equal to -3, this means that the ordered pair is not a solution

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g(×)=4x+1 when g(×)=4x​ then we are getting No Solution.

What is system of equations?

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution. A solution is not assured even then.

[tex]$$\left[\begin{array}{c}g=4 x+1 \\g=4 x\end{array}\right]$$[/tex]

Substitute g=4 x

[4 x=4 x+1]

Refine 4 x=4 x+1

-1=0

-1=0 is false, therefore the system of equations has no solution

No Solution

Complete Question : Find the solution of the given function g(×)=4x+1 when g(×)=4x​.

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The probability that the randomly selected numbers are divisible by 3 is 3/10.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, the probability that the randomly selected number is divisible by 3:

Numbers under 20 divisible by 3 are: 3, 6, 9, 12, 15, 18

Total numbers: 20

Probability formula: P(E) = Favourable events/Total events

Now, substitute values and calculate as follows:

P(E) = 6/20

P(E) = 3/10

Therefore, the probability that the randomly selected numbers are divisible by 3 is 3/10.

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Answer:

B

Step-by-step explanation:

h = 6.2w + 4.5

using forth week

h = 6.2(4) + 4.5

h = 24.8 + 4.5

h = 29.3

gives a close value

Answer:

The two expressions are equivalent, based on a direct numerical comparison (a) and (b) a methematical comparison.

Step-by-step explanation:

a)  The expressions can be shown to be equivalent by entering the numbers into each expression and comparing the results.  This is easy with a spreadsheet program.  Set up a table with the values of x in the left column.  Then enter the 2 equations in the first entry (-2) in each of two subsequent columns.  These expressions can be copied to the other rows by clicking on the first cell and dragging the lower right corner down until all rows are included.  The copied expressions will select the corresponding value of x for both expressions, as shown in the attached table.  It can be seen that both expressions yield the same results.

b)  Prove the equivalence mathematically:

In other words, do the two expressions equal each other?

(12x^2 - 27)/3  = -(-2x+3)(2x+3)   ??

Simplify both sides

(4x^2 - 9)           =   -(-4x^2 + 9)       ?

4x^2 - 9             =   4x^2 - 9            Yes.  They are equivalent

The number of students travelled by bus and train are 38.

Given that, the Marching Band is traveling from Minnesota to Florida to perform in a national competition

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x = Students traveling by train

Let y = Students traveling by bus

Now equations to represent the situation is

150x+120y=4,800 and 15x+20y=720

30(5x+4y)=4,800

5x+4y=160 ----------(I)

15x+20y=720

3x+4y=144 ----------(II)

Subtract equation (II) from (I), we get

5x+4y-(3x+4y)=160-144

⇒ 2x=16

⇒ x=8

Substitute x=8 in equation (I), we get

5(8)+4y=160

⇒ 4y=120

⇒ y=30

Number of students =38

Therefore, the number of students travelled by bus and train are 38.

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Answer: 0.75x+0.8(x+10)=101

Step-by-step explanation:

Jared:   a=x*0.75

Zach: b= (x+10)*0.8

total a+b=101

final equation

0.75x+0.8(x+10)=101

The power of three halves is equal to 3.

What is power?
Power is the ability to influence or control the behaviour of others, and to make decisions that affect the outcome of any given situation. It is a form of force that can be both positive and negative, and can be used in various ways. Power can come from a variety of sources, such as money, status, knowledge, physical strength, and social standing. It is a form of authority that can be used to motivate and inspire others, or to manipulate and coerce them. Power is an important part of many social and political systems, and is essential for effective leadership. It is an essential tool for achieving desired outcomes and can be used for good or for ill. Ultimately, power is a form of influence, and its use depends on the individual wielding it.

In general, if a is a positive real number and n is a positive integer, then a^(n/2) is equal to the square root of a^n. This can be written as:
a^(n/2) = sqrt(a^n) = a^(1/2) * a^(1/2)
Therefore, 3^(3/2) is equal to 3.

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Answer:

First answer: 10

Second answer: 810 ft^2

Step-by-step explanation:

Hope this helps

Answer:

[tex]2ab(b+4a)[/tex]

Step-by-step explanation:

Given expression:

[tex]2ab^2+8a^2b[/tex]

Rewrite b² as b · b:

[tex]\implies 2abb+8a^2b[/tex]

Rewrite a² as a · a:

[tex]\implies 2abb+8aab[/tex]

Rewrite 8 as 2 · 4:

[tex]\implies 2abb+2 \cdot 4aab[/tex]

Rearrange:

[tex]\implies 2abb+2ab4a[/tex]

Factor out the common term 2ab:

[tex]\implies 2ab(b+4a)[/tex]

Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.

What is division in mathematics?

Division is the process of splitting a number or an amount into equal parts.

To find the number of times Anna will need to fill the measuring cup, divide the number of cups of turnips by the size of the measuring cup:

78 cups/14 cups:

                            = 78/14

                              =5.57 measures

Hence, Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.

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Having sides that are parallel to one another, a parallelogram is a two-dimensional geometric shape. It is a sort of four-sided polygon (sometimes known as a quadrilateral) where each parallel pair of sides is the same length.

In addition, AB = CD and AD = BC.

A = C & B = D are also true.

Therefore,

∠A + ∠D = 180

∠B + ∠C = 180

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The completed reasons that justify the statements in the solution to the equation consisting of an algebraic expression are presented as follows;

Statements        [tex]{}[/tex]                             Reasons

1. (1/2)·x - 5 = 10                        [tex]{}[/tex]     1. Given

2. 2·((1/2)·x - 5) = 20   [tex]{}[/tex]                   2. Multiplication property

3. x - 10 = 20                                 4. Distributive property

4. x = 30                                        5. Additive property

An algebraic equation consists of a statement that sets two expressions, that (at least one) consists of algebraic term, as being equivalent or the same.

The details of the reasons used to justify the steps are presented as follows;

Multiplication property

The multiplication property of equality states both sides of an equation remain equal following the multiplication of both sides of the equation by the same property.

Distributive property

The distributive property states that the multiplication of the sum of two numbers by a specified number has equivalent result as multiplying the individual numbers in the addend by the number

Mathematically; a·(b + c)  = a·b + a·c

Additive property

The additive property states that the equality of both sides of an equation is still true following the addition of the same quantity to both sides of the equation.

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The address of element 0 is T₂₁ in the given matrix.

What are Matrices?

Matrices, the plural form of a matrix, are the arrangements of numbers, variables, symbols, or expressions in a rectangular table that contains various numbers of rows and columns. They are rectangular-shaped arrays, for which different operations like addition, multiplication, and transposition are defined. The numbers or entries in the matrix are known as its elements. Horizontal entries of matrices are called rows and vertical entries are known as columns.

We have given,

the matrix:

[tex]T = \left[\begin{array}{cc}4&2\\5&0\\11&-1\\8&3\end{array}\right][/tex]

To find the denotation of the element 0,

so,

A matrix is the arrangement of numbers in rows and columns in order to form an array.

The horizontal arrangement is called a row and the vertical arrangement is called a column.

If the matrix is denoted as  [tex][T]_{m \times n}[/tex] it means that the matrix T has m rows and n columns and the order of the matrix is m × n.

Each number in the matrix is called an element and the position of the element is represented as [tex]a_{mn}[/tex].

Representation of the standard matrix is:

[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}&........ a_{1n}\\a_{21}&a_{22}&........a_{2n}\\\\a_{m1}&a_{m2} &........a_{mn}\end{array}\right]_{m \times n}[/tex]

from the above information, we can say that the address of element 0 is

T₂₁.

Hence, the address of element 0 is T₂₁ in the given matrix.

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