What is the domain of this function?

A function increases if the output value of function increases on increasing the input value and the function decreses if the output value of function decreases on increasing the input value

As we know a function is nothing but a relation between input values and output values where each input has exactly one output.

Consider a function y = f(x)

For a given function if the value of y increases on increasing the value of x, then the function is an increasing function

If the y-value decreases on increasing the value of x, then the function is a decreasing function.

Another method is that if we need to determine whether a function f(x) is increasing or decreasing at point 'a'.

If a function is differentiable on an open interval, we calculate the derivative of function f(x)

If the derivative f′(x) > 0 on an open interval, then function f(x) is increasing on that interval.

If the derivative f′(x) < 0 on an open interval, then function f(x) is decreasing on that interval.

Therefore, if the output value of function increases on increasing the input value then the function is an increasing function and if the output value of function decreases on increasing the input value then the function is an decreasing function.

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Answer:

70 it's a irrational number

Answer:

√70

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a simple fraction and has an infinite, non-repeating decimal representation. Examples of irrational numbers include √2, π, and e.

Of the numbers you listed, √70 is an irrational number. The other numbers are not irrational because they can be expressed as simple fractions: √16 = 4, √1 = 1, and √81 = 9.

Areas of Circles are for [tex]490.873m^2[/tex] radius 12.5m, [tex]706.858m^2[/tex] for radius 15m, [tex]1256.637m^2[/tex] for radius 20m.

The region encircled by a circle with radius r is known as πr² in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.

This formula, which was first discovered by Archimedes, can be derived by considering the circle as the boundary of a series of regular polygons. A regular polygon's area is equal to half its perimeter times the distance from its center to its sides. The equivalent formula,  [tex]A=\frac{1}{2} *2\pi r*r[/tex] states that the area is equal to half the perimeter times the radius.

The limit for a circle is held by [tex]\pi r^{2}[/tex].

Given;

1) r=12.5m

[tex]A=\pi r^2=\pi (12.5)^2=490.873m^2[/tex]
2) r=15m;

[tex]A=\pi r^2=\pi (15)^2=706.858m^2[/tex]

3) r=20m;

[tex]A=\pi r^2=\pi (20)^2=1256.637m^2[/tex]

Areas of Circles are for [tex]490.873m^2[/tex] radius 12.5m, [tex]706.858m^2[/tex] for radius 15m, [tex]1256.637m^2[/tex] for radius 20m.

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The probability that an arrangement of a, b, c, e, f, g begins and ends with a vowel is 1/ 5, that is 0.2.

Therefore, the answer is 0.2.

In an arrangement of a, b, c, e, f, g, the total number of alphabets is 6 and number of vowels is 2.

The probability that an arrangement of a, b, c, e, f, g begins with a vowel is

P1 = 2/ 6

P1 = 1/ 3

The probability that an arrangement of a, b, c, e, f, g ends with a vowel given it begin with a vowel( In this case the total number of alphabets left is 5 and number of vowels left is 1)  is

P = 1/ 5

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Answer:

9

Step-by-step explanation:

The top of the slope starts at 1, and it repeats at 9

Answer:

Step-by-step explanation: 6* (N + 6) = -24

                                              6*n + 6*6=-24

                                               6n+36=-24

                                                   -36   -24

                                                   6n=-60

                                                    n=-10

Answer:

[tex]17.5[/tex]

Step-by-step explanation:

[tex]2.5x15-20[/tex]

[tex]37.5-20[/tex]

[tex]17.5[/tex]

Hope this helps you

The multiplicity of 0 is the number of times that 0 appears as a root of a polynomial equation.

In other words, it is the number of times that 0 is a solution to the equation. For example, the equation x^2 - 4x + 4 has two solutions, 0 and 4. The multiplicity of 0 is therefore 2, since 0 is a repeated solution.

If a polynomial equation has only one 0 as a solution, the multiplicity of 0 is 1. In some cases, a polynomial equation may have no 0s as a solution, in which case the multiplicity of 0 is 0.

In general, the multiplicity of a number is the number of times it appears as a solution to a polynomial equation. For example, the equation x^2 - 2x + 8 has two solutions, 2 and 4. The multiplicity of 2 is 1, since 2 appears only once as a solution, while the multiplicity of 4 is 2, since 4 appears twice as a solution.

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99

There are a total of 50 odd numbers between 1 to 100.

1 is the smallest, odd number:

The sum of all the odd numbers from 1 to 100 is 2500.

The average or mean of all odd numbers 1 to 100 is 50.

[tex]\boxed{ 3 + 2 = 5, 5 + 2 = 7, 7 + 2 = 9}[/tex]

The last number in the chart of odd numbers 1 to 100 given below is 99, as, if we add 2 to 99, we will get 101 which is greater than 100. So, 99 is the last odd number in the list of odd numbers from 1 to 100.

Therefore, the odd integers from 1 to 100 is 99

A picture is given below of all the odd numbers of 1 to 100:

The independent variable x represents the initial amount of her savings account, and the dependent variable y represents the deposited amount into her savings account.

What is the independent and dependent variable?

In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are studied in an experiment under the assumption or demand that they are dependent, by some law or rule, on the values of other variables.

We have,

On week 9, her savings account has a balance of $496,

on week 16, her savings account has a balance of $664.

The equation which represents the situation is:

consider x for the initial amount in the account and y for the weekly deposited amount into her savings account.

so,

x + 9y = $496,

x + 16y = $664.

Hence, the independent variable x represents the initial amount of her savings account, and the dependent variable y represents the deposited amount into her savings account.

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[tex] - x {}^{2} - 36 \\ - (x {}^{2} + 36) \\ - (x {}^{2} - (6i) {}^{2} ) \\ - (x - 6i)(x + 6i) \\ ( - x + 6i)(x + 6i) \: \: or \: \: (x - 6i)( - x - 6i)[/tex]

Answer:

D: (-x-6i)(x-6i)

Step-by-step explanation:

(-x-6i) (x-6i)

-x^2 +6ix -6ix -36

-x^2 -36

So, D is the correct

Answer:

B. 2 x 6

Step-by-step explanation:

The expression doesn't have an equal sign, so C and D is wrong.

So, the correct answer is B

B is correct answer.

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Answer:

Step-by-step explanation:

AW=10

Step-by-step explanation:

In a parallelogram opposite sides are congruent meaning XA and AZ are congruent. YA and AW are congruent. So...

Solving for XA and AZ

XA=AZ

3m=5m-4

-2m=-4

m=2

If YW=10m then 10 x 2 = 20

20 divided by 2 = 10

The y-intercept of the equation 2x - y = -3 is 3 and in ordered pair form is (0,3).

The slope-intercept formula is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation in the question

2x - y = -3

First, we solve form for y and reorder in slope intercept form.

2x - y = -3

Subtract 2x from both sides

2x - 2x- y = -3 - 2x

- y = -3 - 2x

Divide each term by -1

y = 3 + 2x

Reorder in slope intercept form

y = 2x + 3

To find the y-intercept, replace x with zero and solve for y

y = 2(0) + 3

y = 3

Therefore, the y-intercept is 3.

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discontinuity point of a function is a point at which the function is not continuous. There are three types of discontinuities: removable, jump, and essential.

A removable discontinuity is a point at which the function is not defined, but the limit of the function as x approaches the discontinuity point from both sides is equal to a finite value.

A jump discontinuity is a point at which the function is defined, but the limit of the function as x approaches the discontinuity point from both sides is not equal.

An essential discontinuity is a point at which the function is not defined and the limit of the function as x approaches the discontinuity point from both sides is infinite or does not exist.

To find the discontinuity points of a function, you can:

Plot the function on a graph and look for any breaks or gaps in the graph.

Use the algebraic definition of continuity to determine whether the function is continuous at a given point.

Use the limit definition of continuity to determine whether the function is continuous at a given point.

Use a computer algebra system (CAS) to find the discontinuity points of a function.

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A point where the function is not defined and the limit of the function as x approaches the discontinuity point from both sides is infinite or does not exist is referred to as an important discontinuity.

A function's discontinuity points can be located by:

Plot the function on a graph and check the graph for any splits or gaps.

To ascertain whether the function is continuous at a specific point, use the algebraic notion of continuity.

Answer:

in ratio 4:14

Step-by-step explanation:

Step-by-step explanation:

first we come up with a formulae:
Amount of money saved = 2.25+0.25x,

where x is the number of days

Answer:

1. 7.75 = 2.25 + 0.25(x)

7.75 - 2.25/ 0.25 = x

x = 20

2. 2.25+0.25(25) - 2.25 +0.25(14)

= 9.75

3. 2.25 + 0.25(10)

= 4.75

I hope i explained it well...

( i ) 21st day he saves 7.75

(ii) the difference between the amount saved by Rajiv on the 25th day and the 14th day is 2.75 rupees.

(iii) the sum of the amount saved in the first 10 days is 5 rupees.

Solution: (i)  given: on each succeeding day he increases his saving by 25 paise.

                2.75 rupees he saves on the  first day

        so    = 2.75 +(0.25×20)

                = 2.75+5

                = 7.75 rupees

         (ii)   amount saved by Rajiv on the 25th day is:

                = 2.75+(0.25×24)

                = 2.75 + 6

                = 8.75

               amount saved by Rajiv on the  14th day is :

                =2.75+(0.25×13)

                =2.75+3.25

                =6

therefore the difference between Rajiv' saving on the  25th day and the  14th day   is :         =   8.75-6                                    

                     =     2.75

          (iii)   the sum of the  amount saved in the first 10 days is :

                =  2.75+(0.25 ×9)  

                =  2.75+2.25

               =   5          

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Answer:

25 it's easy as 123 ABC 123 abc

A function is a group of components or inputs that have a relationship and produce an outcome. A function's inverse is the function's opposite. When a function's inverse is applied, its domain changes to its range, and conversely.

The core of calculus in math is the concept of functions. The unique types of connections are the ones with functions. Mathematical functions are represented as a rule that, for each input x, produces a distinct result.

As per the question, the relationship between a function and its inverse will be:

1. A group of elements or inputs that are related to one another and produce an output is referred to as a function.

2. A function's reverse is called a function's inverse.

3. When a function is inverse, the domain becomes the range, and vice versa.

4. The graphs of the two concepts—function and inverse—will resemble one another in reverse.

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The required equation of the line is y = 4x - 15

The slope-intercept form of a line is given by

Where m = slope and c =  y-intercept

Given slope of line m = 4 and the point is (2, -7)

As we know

The slope-intercept form is, y = mx + c --- (1)  

From the given data, m = 4

Substitute m = 4 in (1)

=> y = 4x + c ---- (2)

Here (2) will pass through (2, -7)

(2) =>  - 7 = 4(2) + c  

=> - 7 = 8 + c

=> c = - 8 - 7

=> c = - 15  

=> (2) => y = 4x - 15

Therefore,

The required equation of the line is y = 4x - 15

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Answer:

x-intercepts: x=3, -5

Step-by-step explanation:

y = x^2 + 2x − 15

y = x^2 + 5x - 3x − 15  ==> 5*(-3)=-15 and 5+(-3) = 5-3=2

y = x^2 + 5x - 3x − 15

y = x(x+5) - 3(x+5)

y = (x-3)(x+5)

x-3=0  ==> x=3

x+5=0 ==> x=-5

x-intercepts: x=3, -5

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The probability that Milo selected either a science course or a math course is 7/19 (or 0.3684210526).

Using this strategy, Milo has a 36.84% chance of selecting either a science or math course. This strategy is highly risky and unreliable, as there is no guarantee that Milo will select a course he is interested in or capable of taking. Additionally, Milo has a 63.16% chance of selecting a course he may not be interested in or able to take. There is no assurance that Milo will succeed with this strategy, and it could put him at a disadvantage in his academic career. As such, it is not recommended that Milo use this strategy to register for classes.

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Answer:

The total area of the surface of a three-dimensional object. Example: the surface area of a cube is the area of all 6 faces added together.

Step-by-step explanation:

The required equation of the line is y = 3x + 2 in slope-intercept form.

To write the equation of a line in slope-intercept form, we need to know the slope of the line and the y-intercept. The slope of a line is defined as the change in y divided by the change in x for two points on the line.

According to the given graph, the required solution would be as:

For the given points (2, 2) and (4, 8),

So, the slope is : m = 8 - 2 / 4 - 2 = 6 / 2 = 3.

With the slope and y-intercept, we can write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

For the point (2, 2), the y-coordinate is the y-intercept, so the y-intercept is 2.

So, the equation is y = 3x + 2

Therefore, the required equation of the line is y = 3x + 2 in slope-intercept form.

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The value of k in the quadratic equation is k = 2

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + kx - 5/4 = 0   be equation (1)

Now , on simplifying the equation , we get

If 1/2 is the root of given equation, then it will satisfy it.

So , when x = 1/2

( 1/2 )² + k ( 1/2 ) - 5/4 = 0

( 1/4 ) + k/2 - 5/4 = 0

k/2 - 1 = 0

Adding 1 on both sides of the equation , we get

k/2 = 1

Multiply by 2 on both sides of the equation , we get

k = 2

Therefore , the value of k is 2

Hence , the value of k in the equation is 2

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To translate an entire triangle, find the coordinates of each of the triangle's vertices, add the horizontal translation then plot the three translated points.

Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.

There are some steps of translating the triangle:

Step 1: Find the coordinates of each of the triangle's vertices in step one.

Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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Step-by-step explanation:

(3x7x11x13)+1=3004

n=3004

The types of roots in math are known as real roots , imaginary roots or repeated roots.

roots > 0  imaginary

roots < 0  real

roots = 0  repeated

When the roots are bigger than zero, they are referred to as real roots. When the value of the obtained roots is less than zero, the obtained roots are referred to be not real or imaginary roots.

When the sum of the obtained roots equals zero, we conclude that the roots are repeated.

In order to find the roots of a equation we can plot them on a graph and the solve them or we can factorize the given equation. We can also use the formula to calculate graph using determinant method.

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Yes, the given statement is true the volume of the prism is greater than the volume of the pyramid when they have same base and same height.

As given in the question,

Formula required to calculate the volume of the pyramid and volume of the prism is given by :

Volume of a pyramid = (1/3) × (base area )× ( height )

Volume of a prism = (Base area) × (height)

When the base and height of the pyramid is same as that of the base and height of the prism then

Volume of the pyramid =  ( 1/3) × ( Base area  × height )

⇒Volume of the pyramid =  ( 1/3) × ( Volume of the prism )

⇒Volume of the prism = 3 × ( Volume of the pyramid )

⇒Volume of the prism >  Volume of the pyramid

Therefore, the volume of the prism is greater than the volume of pyramid is a true statement.

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