the first term of arithmetic prog is 12 and sum of first 9 terms is 135 find the common difference

Equivalence relations are important in maths because of the following parts,

A relation R on a set A is called an equivalence relation if and only if the relation R is recursive, symmetric, and transitive. An equivalence relation is a relation on sets, and is generally represented by the symbol “~”. For example: "Equal to (=)" is the equivalence relation on any set of numbers A for all elements a, b, c ∈ A,

Reflexive: a = a ,

Symmetric: a = b ⇒ b = a and

Transitive: a = b, b = c ⇒ a = c.

This means that (=) is recursive, symmetric, and transitive. Equivalence relations are used in several areas of mathematics.

does not satisfy || f || = 0 <=> f=0.

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Complete question:

Why is equivalence relation important in maths?.

The range of the function FX = -2(6x) + 3 is [-3, +∞).

First, let's simplify the equation.

FX = -2(6x) + 3

FX = -12x + 3

To determine the range of the function, start by graphing the equation.

The graph will be a line with a slope of -12 and a y-intercept of 3.

To find the range, we need to determine the y-values of the graph as x-values increase. Since the slope is negative, the y-values will decrease as x-values increase.

The range of the function is all real numbers less than or equal to 3.

Therefore, the range of the function FX=-12x+3 is all real numbers less than or equal to 3.

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Quadratic equations in factored form can be solved by using the Zero Product Property, which states that if the product of two numbers equals zero, then at least one of the values must also equal zero.

The Zero Product Property can be used to resolve any factored quadratic equation, such as (a + b)(a b) = 0. In accordance with the zero product property, if a+b=0, then either an or b must also be equal to zero. This essential characteristic allows us to solve equations like (x+2)(x-5)=0.

The zero product property states that if two quantities are added together and the result is zero, then one or both of the individual quantities must also be zero. You can solve this problem by rewriting it as (x + 3) (2 x 1) = 0.

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Answer:

3 kph

Step-by-step explanation:

speed = x kph

(x-1)*t=8; 8/(x-1)= t units are km

(x+1)t=16; 16/(x+1)=t

Set them equal to each other

8/(x-1)=16/(x+1)

cross multiply

8x+8=16x-16

-8x=-24

x=3 kph

Answer:

it's 8

Step-by-step explanation:

I find it because 96÷8=12

and 64÷8=8

The constant of proportionally with the equation

[tex]$k = \frac{y}{x}$[/tex]  with [tex]$y = \frac{5}{3}x$[/tex]

The constant of proportionality, also known as the coefficient of proportionality, can be found by using the equation:

[tex]$k = \frac{y}{x}$[/tex]

Plugging in the given values of x and y:

[tex]$k = \frac{20}{12}$[/tex]

Which can be simplified to:

[tex]$k = \frac{5}{3}$[/tex]

The equation that relates x and y is:

[tex]$y = kx$[/tex]

Using the equation [tex]$y = kx$[/tex]  to find the constant of proportionality, also known as the coefficient of proportionality, and then substituting that value into the equation to relate x and y is one way to solve the problem.

It is the most common way to express a proportionality between two variables and it is the basic form of all proportional relationships.

So, substituting the value of k found earlier:

[tex]$y = \frac{5}{3}x$[/tex]

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The number of hats Sara bought is 7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Sarah went shopping at a store and bought some hats that cost $6 each and 2 necklaces that cost $12 each.

The number of hats will be calculated as,

12N + 2H = 66

12 x 2 + 2 H = 66

2H = 66 - 24

2H = 42

H = 42 / 2

H = 21

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Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

NOOOOOO FIGURE IT OUT YOUR SELF THATS WHY THEY TEACH YOU DUHHHHHHHHHHHHH

We need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

What is ASA congruence of triangle?

The two triangles are considered to be congruent according to the ASA rule if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.

We are given the following:

1. ∠A ≅ ∠X

2. ∠C ≅ ∠Z

Now, in order to show the triangles as congruent by ASA congruence of triangle, we need the side which is in between both the angles.

The sides in between both the angles are AC and XZ.

Hence, we need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

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The amount of water to add is 45 grams

From the question, we have the following parameters that can be used in our computation:

Sugar = 15 grams

Proportion of syrup = 25%

So organizing the information given in the statement we have that:

In this way, we can calculate the missing value for this percentage as:

25% of x = 15 grams

Express as decimal

So, we have

0.25 * x = 15

Divide both sides by 0.25

x = 60

This means that the total amount is 60 grams

If the syrup contains 25% of sugar, then 75% would be water (assume no other item is present)

So, we have

Water = 75% * 60g

Water = 45g

Hence, the amount is 45 grams

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Answer: 45 g of water

Step-by-step explanation:

No, 0 Infinity is not a real number. It is an undefined mathematical expression.

No, 0 Infinity is not a real number. It is an expression that is undefined in mathematics. This means that it has no numerical value or meaning, and cannot be accurately represented or calculated. In other words, 0 Infinity is not a valid mathematical expression, and so it is not considered a real number.

This means that it has no numerical value or meaning, and cannot be accurately represented or calculated. In other words, 0 Infinity is not a valid mathematical expression, and so it is not considered a real number.

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Answer:

B. Output = (2)(Input) – 3.

Step-by-step explanation:

The correct answer is B. Output = (2)(Input) – 3.

This is because the function is a linear function, and the slope is 2 and the y-intercept is -3.

You can see this by considering the difference in y for each pair of points and the difference in x for each pair of points.

For example, from (negative 1, 1) to (1, 2) the difference in y is 1 and the difference in x is 2.

This means the slope is 1/2 which is the same as 2, and the y-intercept is -3

Writing linear equations given two points can be a useful skill when graphing linear equations.

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Answer:

(x - 5)² + (y + 3)² = 9

Step-by-step explanation:

The standard equation of a circle with center (a, b) and radius r is given by

(x - a)² + (y-b)² = r²

Here the center is (5, -3) and r = 3

Substituting values for a = 5, b = -3 and r = 3

(x - 5)² + (y-(-3))² = 3²

(x - 5)² + (y + 3)² = 9

It is OK to leave it in this form without expanding

Answer:

I'm sorry, but the formula you provided "F G )( X" is not a valid mathematical notation, it doesn't make sense in mathematical or scientific context. Please provide more information or context about the formula or correct the formula if it has any typo.

Due to the absence of an x in the issue, the y-intercept is -4. At the conclusion, it stands on its own and directs you to begin at (0,-4). The slope is -5/1 because the slope of the equation is toward the value of x in the equation.

y = 5x - 4 has a 5 slope. The line's equation, y = 5x - 4, is expressed in the form y = mx + b, as you can see. It is therefore in slope-intercept form. When a line's equation is written in slope-intercept form, we may determine that the slope of the line equals m, the x-coefficient.

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.

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A polynomial of degree 3 is called a cubic polynomial.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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The term "density" refers to the amount of volume (or physical space) occupied by an object or substance in relation to the amount of matter contained therein (its mass).

What is density ?

The quantity of things—which could include humans, animals, plants, or objects—in a given space is referred to as density. To determine density, divide the number of objects by the area's measurement. The number of people in a country divided by its area in square kilometers or miles is known as its population density.

The term "density" refers to the ratio between the volume (the amount of space taken up by an object or substance) and the amount of matter contained therein (its mass). The amount of mass per unit of volume is another method to define density. An object has a high density if it is both heavy and small.

By dividing the mass of an object by its volume, one may determine its density.

This means that if density is D, mass is M, and volume is V.

a)

M = 500 gms

40 cubic cm V

$D=$500/40

$D=12.5$

b)

M = 125 gms

= 1.4 cubic cm

$D = $ 125/1.4

$D=89.28$

D =89.28 gm per cc.

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The term "density" refers to the amount of volume (or physical space) occupied by an object or substance in relation to the amount of matter contained therein (its mass).

The quantity of things—which could include humans, animals, plants, or objects—in a given space is referred to as density. To determine density, divide the number of objects by the area's measurement. The number of people in a country divided by its area in square kilometers or miles is known as its population density.

The term "density" refers to the ratio between the volume (the amount of space taken up by an object or substance) and the amount of matter contained therein (its mass). The amount of mass per unit of volume is another method to define density. An object has a high density if it is both heavy and small.

By dividing the mass of an object by its volume, one may determine its density.

This means that if density is D, mass is M, and volume is V.

a)

M = 500 gms

40 cubic cm V

$D=$500/40

$D=12.5$

b)

M = 125 gms

= 1.4 cubic cm

$D = $ 125/1.4

$D=89.28$

D =89.28 gm per cc.

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After solving, the remainder when [tex]-x+3x^2-1[/tex]  is divided by x + 1 is 3.

In the given question, we have to find the remainder when [tex]-x+3x^2-1[/tex]  is divided by x + 1.

The given polynomial is [tex]-x+3x^2-1[/tex].

We have to find the remainder of the polynomial when we divide this polynomial x + 1.

To find the polynomial we equate x+1 equal to zero to find the value of x.

x + 1 = 0

x = -1

Now putting x = -1 in the given equation [tex]-x+3x^2-1[/tex].

P(x) = [tex]-(-1)+3(-1)^2-1[/tex]

P(x) = 1 + 3×1 - 1

P(x) = 1 + 3 - 1

P(x) = 3

Hence, the remainder when [tex]-x+3x^2-1[/tex]  is divided by x + 1 is 3.

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The complete question is:

When [tex]-x+3x^2-1[/tex]  is divided by x + 1 then remainder will be?

The graph of the linear equation:

y = -x + 4

can be seen on the image at the end.

Here we want to graph the following linear function:

y = -x + 4

To graph it, we need to find two points that lie on that line, and to get that we need to evaluate the line.

When x = 0.

y = -0 + 4

y = 4

So we have the point (0, 4)

When x = 2

y = -2 + 4

y = 2

So we have the point (2, 2)

Now we just need to graph these two poins and connect them with a line, we will get:

The height of the wheel is 63 centimeters that is the diameter of the circular wheel.

Given data :

a) The height of the wheel is 63 centimeters that is the diameter of the circular wheel.

b) The distance traveled by the wheel when it goes all the way around one time is 198 centimeters that is the perimeter of the circular wheel.

c) The distance traveled by the wheel when it goes all the way around one time is the perimeter  of the circle. To estimate the value of t, divide the distance  traveled by the wheel when it goes all the way around by its height.

Completed question :

A bicycle wheel is 63 centimeters from top to bottom. When the wheel goes all the way

around one time, the bicycle travels 198 centimeters. How can this information be used to

estimate the value of ?

63 cm

Click the arrows to choose an answer from each menu.

Because the wheel is circular, the height of the wheel is the Choose...

of

the circle. The distance traveled by the wheel when it goes all the way around one time is the

Choose...

of the circle. To estimate the value of t, Choose... the distance

traveled by the wheel when it goes all the way around by Choose...

y

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Answer:

x > 10.4

Step-by-step explanation:

Isolate X by adding 3.5 to each side of the inequality

That leaves you with x > 6.9 + 3.5

There are a lot of linear solutions to problems. In fact, there are an infinite number of them.

Linear solutions are the most common type of solution. They're also the easiest to solve. These solutions are used in algebra and geometry. There are six different types of equations in which a linear solution exists. These are:

1) One variable equals zero

2) Two variables are equal

3) Three variables are equal

4) Any equation with one constant and one other variable

5) Two variables have an equal ratio to another variable

6) Two variables are equal to a certain number One solution that's linear is a quadratic equation with two variables. It has the form x2 + bx + c = 0 To solve this equation, you can use basic algebraic skills like factorization, substitution, and addition.

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Answer:

I believe the first one

Step-by-step explanation:

Answer:

7 < x < 11

Step-by-step explanation:

Answer:150

Step-by-step explanation:

suppose he asks 300 and only 1/2 say yes,

Answer:

1/32

Step-by-step explanation:

5 counters, 1/2 chance of it being yellow, therefore...

[tex](\frac{1}{2})(\frac{1}{2})(\frac{1}{2})(\frac{1}{2})(\frac{1}{2}) = (\frac{1}{32})[/tex]

Answer: A or C i would go with C but ur instict

Step-by-step explanation:

Answer:

A or C

Step-by-step explanation:

Good Luck!

Answer:

Points B, C, and D are on line n

Step-by-step explanation:

Answer:

лттьло. ьнеь е екбюедку к е. еккд

The commutative property and associative property do not hold for subtraction and division, as the end results are completely different after changing the order of numbers.

The commutative property deals with the arithmetic operations of addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result.

For example, 4 + 5 gives 9, and 5 + 4 also gives 9. The order of two numbers being added does not affect the sum. The same concept applies to multiplication too.

Thus, The commutative property and associative property do not hold for subtraction and division, as the end results are completely different after changing the order of numbers.

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