introduction paragraph about Peter G. L. Dirichlet

In common inverse meaning is “something that is contrary or reverses”. When we define inverse meaning we will talk mostly from the mathematics point of view where we find the inverse of different operations and functions

The inverse of a given number is equal to number that is obtained by solving the operation 1/x where x is the initial number.

The inverse operation of subtraction is addition, the inverse operation of division is multiplication.

The inverse of a number should not be muddled with its opposite. While the inverse is 1/x, the opposite is equal to -x. That is, the inverse of 3 is equal to 1/3 while its opposite will be equal to -3.

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The weight of the cat is equal to 24.5 Newton.

In Science, weight can be defined as the force acting on an object or a physical body due to the effect of gravity. Mathematically, the weight force on a physical body can be calculated by using this formula:

Fg = mg

Where:

Note: Acceleration due to gravity is equal to 9.8 m/s².

Substituting the given parameters into the weight formula, we have;

Weight, Fg = 2.5 × 9.8

Weight, Fg = 24.5 Newton.

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Answer:

x⁴-2x³-x²+2x = (x²-2x+2)(x²+2x+1)

Answer:

x(x-2)(x+1)(x-1)

Step-by-step explanation:

just add and subtract the second term to the expression and factor by grouping

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A triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 90 degrees.

No, a triangle is not 90 degrees. In geometry, a triangle is a three-sided polygon with three angles. The sum of the angles in a triangle is always 180 degrees.

This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.

For example, if a triangle has angles of 90 degrees, 60 degrees, and 30 degrees, the sum of these angles is 180 degrees (90+60+30=180).

Therefore, In short, a triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 90 degrees.

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The value x = 0 is zero of function p(x) = x²

Consider given function  p(x) = x²

We know that from the definition of zeros of function, the zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.

To find the zeros of function p(x), we need to equate p(x) to zero then solve it for x.

Here we need to check whether x = 0 is zero of function p(x)

If for x = 0, p(x) = 0 then x = 0 is zero of function p(x).

Substitute x = 0 in given function p(x)

⇒ p(x) = x²

⇒  p(0) = 0²

⇒ p(0) = 0

Thus x = 0 is a zero of given function.

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The complete question is:

Is x = 0 a zero of p(x)=x² ?

ABCD is an isosceles triangle

No, 36 is not a prime number. Because the number 36 is divisible by 1, 2, 3, 4, 6, 9, 12, 18, 36.  

A prime number is a natural number more than 1 that has no positive divisors aside from 1 and itself. Prime numbers have several important properties and applications in mathematics, such as the fundamental theorem of arithmetic, which states that every positive integer can be written as a unique product of primes. They are also used in number theory, cryptography, and coding theory.

In addition, prime numbers are of interest in studying patterns and properties in the distribution of numbers, such as the distribution of twin primes and Mersenne primes. They play a crucial role in number theory, which is a branch of mathematics that studies the properties of integers. Prime numbers are infinite in number, and it is an open question whether there are infinitely many prime pairs or twin primes, which are pairs of prime numbers that differ by 2.

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The additive inverse of 7/5 will be -7/5.

The additive inverse of any numeral is the opposite of that numeral. If a number is added to its additive inverse, the sum of both numbers becomes zero. In other words, the additive inverse is the number that is added to a given number to make the sum zero. That is what you add to a number to get zero is called its additive inverse.

That is, Number + Additive inverse = 0

OR

The negative of a number.

Now we are given the number

7/5

So, the additive inverse of 7/5:

⇒7/5 + Additive inverse = 0

⇒Additive inverse = -7/5

Thus the additive inverse of is 7/5 is -7/5.

--The given question is incorrect; the correct question is

"What will be the additive inverse of 7/5?"--

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The value of the number x such that the quotient of the number,x and 19 is 10 is; 190.

As evident in the task content, the value of x is to be determined such that the quotient of a number, x and 19 is 10.

Since the statement given above can be written algebraically as;

x / 19 = 10

By multiplying both sides of the equation by 19; we have that;

x = 10 × 19

x = 190.

Ultimately, the value of x is; 190.

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Answer:

Choose whichever format you want to give the answer

[tex]\boxed{\dfrac{2}{9} \textrm{ hour}}[/tex]

[tex]\boxed{0.2222 \textrm{ hour}}[/tex]

[tex]\boxed{13.3333 \textrm{ minutes}}[/tex]

Step-by-step explanation:

[tex]\sf{Travel\: time = \dfrac{Distance}{Speed}}[/tex]

The time taken to travel the first 600 km

[tex]= \dfrac{600}{90} = \dfrac{20}{3}\; \sf{hours}[/tex]

This leaves 200 km which was travelled at a speed of 100 km/hr

Time taken for this stretch = 200/100 = 2 hours

If the entire trip were driven at 90 km/h, it would take the same time as the first case. Therefore we only need to be concerned about the last 200km

If the last 200km were traveled at 90 km/h instead of 100 km/h, time taken

[tex]=\dfrac{200}{90} = \dfrac{20}{9}\\\\[/tex]

The difference in time then would be:
[tex]=\dfrac{20}{9} - 2\\\\\\= \dfrac{20}{9} - \dfrac{18}{9}\\\\=\dfrac{2}{9}\; hour[/tex]

= 0.22 hour in decimal

= 13.33 minutes

The equation A = 2x²y + 4x²y² is a polynomial

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 2x²y + 4x²y²   be equation (1)

On simplifying the equation , we get

A = 2xy ( x + 2xy )

Now , it is a mathematical expression with variables and coefficients

Hence , the equation A = 2x²y + 4x²y² is a polynomial

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Answer:

x²+2x

x(x+2)

Step-by-step explanation:

take x common and thats it either tou gave incomplete question or wrong ans

Answer:

See below

Step-by-step explanation:

This should be your expressions: [tex]\displaystyle{x^2+2x-24}[/tex], this can be factored by applying in the form of:

[tex]\displaystyle{x^2+(\alpha + \beta)x+\alpha \beta = (x+\alpha)(x+\beta)}[/tex]

This simply means you have to find two numbers that add up or subtract and obtain the middle term, and that two numbers must also satisfy the last terms as well. (Hence, two numbers adding up to middle term and multiply to last term.)

We can check by seeing into the factor of 24 which are:

These numbers have product of 24. Next, we find the middle term -- since the middle term is positive value. This means that the highest value is in positive.

From factors that we list, we can cancel off the followings:

Therefore, the only factors left are 4 and 6. These two also make 2 (6-4), so we will have [tex]\alpha[/tex] = 6 and [tex]\beta[/tex] = -4. Therefore:

[tex]\displaystyle{x^2+(6-4)x+6(-4) = (x+6)(x+(-4))}\\\\\displaystyle{x^2+2x-24= (x+6)(x-4)}[/tex]

And there you have it, the factor of x² + 2x - 24

Shapes that are identical to each other are considered congruent. There are no differences in the matching sides or angles.

What is a congruent shape?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

Here is the format you requested:

△ABC = △DEC due to AAS

Angle A = Angle D Given

Angle B = Angle E Alternate Interior

Angle C1 = Angle C2 Vertically Opposite

AB = DE Congruent Sides

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The dividend is influenced by both the quotient and the divisor when the remainder is zero.

Any integer that divides a different number is the divisor. A factor, on the other hand, is a divisor that completely divides a number and leaves no remainder. Therefore, all factors are also divisors of a number. But not every divisor will also be a factor. The factors of 20 in the aforementioned case are 4 and 5.

We are left with a value after division if a number (dividend) cannot be divided entirely by another number (divisor). The term "remainder" refers to this amount.

When the remainder is zero, the dividend is affected by both the quotient and the divisor. When the remainder does not equal zero, neither the quotient nor the divisor are dividend factors.

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"Segment GT is congruent to segment PD on the number line." this statement is True.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

The number line is used to represent the coordinates G, T, Y, B, M, P, D, W.

The point of G is -10 and the point of T is -9.

To get the measurement subtract G from T -

= -9 - (-10)

= -9 + 10

= 1

The point of P is 5 and the point of D is 6.

To get the measurement subtract P from D -

= 6 - 5

= 1

The measurement of GT and PD both is 1.

Therefore, segment GD is congruent to segment PD on the number line.

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The conjecture regarding a number and it's absolute value being always opposites is incorrect.

The counterexample is that the absolute value of any positive number is always the own number.

The absolute value of a number is the number without the signal, representing the difference between the number and zero.

For example:

|-2| = |2| = 0.

Hence the conjecture is false, as the absolute value of any positive number is always the own number.

The conjecture would be true if it stated this only for negative numbers, then the absolute value of a negative number is in fact always the opposite of the number.

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Here, b = 6 is a solution for the equations 8b = 48, b + 3 = 9 and 54  ÷ b = 9 but not a solution for 4 = b + 11 - 3b.

Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and typically consist of two expressions connected by an equals sign, is known as solving an equation in mathematics.

One or more variables are designated as unknowns when looking for a solution. An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.

To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. The term "equation's root" is frequently used to refer to an equation's solution, especially but not exclusively for polynomial equations.

Given to prove b = 6

a. 8b = 48

   b = 48/8

   b = 6

b = 6 is a solution

b. 4 = b + 11 - 3b

   3b - b = 11 - 4

   2b = 7

   b = 7/2

   b = 3.5

b = 6 is a not solution

c. b + 3 = 9

   b = 9 - 3

   b = 6

b = 6 is a solution

d. 54  ÷ b = 9

   9b = 54

   b = 54/9

   b = 6

b = 6 is a solution

Thus,  b = 6 is a solution for the equations 8b = 48, b + 3 = 9 and 54  ÷ b = 9 but not a solution for 4 = b + 11 - 3b.

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Answer:the a would be 10

and the b would be 6

Step-by-step explanation:

The sixth term of the arithmetic progression is 94.

An arithmetic progression is a sequence of numbers such that the difference between any two successive members of the sequence is a constant.

Let's call the first term of the arithmetic progression "a" and the common difference "d". Then the nth term of the progression can be found using the formula:

an = a + (n-1)d

We know that the sum of the first four terms is 14, so we can set up the following equation:

a + (a+d) + (a+2d) + (a+3d) = 14

We also know that the sum of the first eight terms is 108, so we can set up another equation:

a + (a+d) + (a+2d) + (a+3d) + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108

Now we can use the first equation to substitute for the first four terms of the second equation:

14 + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108

This gives us:

a + 4d = 94

So the sixth term can be found by substituting n = 6 into the first formula:

a + (6-1)d = a + 5d = 94

Therefore, the sixth term of the arithmetic progression is 94.

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A segment drawn from a vertex to the midpoint of the opposite side is the correct option.

Lines that cross each other at a correct angle are considered to be perpendicular. Examples are the ends of a horizontal ladder and the opposing sides of a rectangle. the symbol that denotes two parallel lines In geometry, a pair of lines that meet or intersect with right angles (90°) are said to be perpendicular.

Drawing the dotted line for the specified measurement is the first step in the line segment construction process. Then, make a mark at that location on the line and set the compass at that location. Now, draw an arc across each side of the indicated line. Draw another arc without adjusting the compass.

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Megan has to pay 29.10 dollars for the sweater after 20 % decrease in cost and a tax of 7 %.

After the discount and the tax is applied, Megan will pay 29.10 dollars for the sweater.

Here we have to determine that how much did Megan pay in total

We know that originally, the sweater costs $ 34.00, and there is a 20 % decrease in that cost and a tax of 7 %.

The decrease of 20 % is written as a factor:

[tex]$1- \frac{20}{100}[/tex] = (1 - 0.2)

The decrease of 20 % is (1 - 0.2).

And an increase of 7 % is written as a factor:

[tex]$1+\frac{7}{100}[/tex] = (1 + 0.07)

The increase of 7 % is (1 + 0.07).

Then the amount that Megan pays for the sweater is:

P = 34.00 × (1 - 0.2) × (1+0.07)

P = 34.00 × (0.8) × (1.07)

P = 29.10

She pays 29.10 dollars for the sweater.

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Megan purchased a sweater that costs $34.00. She used a 20% off coupon and had to pay 7% sales tax how much did her purchase cost on total

Answer:

283.5 square inches

Step-by-step explanation:

W = L ÷ 2 - 3

width  = 27 ÷ 2 - 3

width  = 13.5 - 3

width = 10.5

Area = length · width

Area = 27 · 10.5

Area = 283.5

Answer:

1 kilogram

Step-by-step explanation:

Answer:

Step-by-step explanation:

A vertical line has undefined slope, but will always have an x-intercept. In this case, since the line goes through the point (-2,-9) we know that x will always equal -2. So therefore the equation of this vertical line will be x=-2.

The perimeter of your new patio is 52.

Given that,

In order to match the shape of your backyard, your family has decided to build a rectangular patio there. The dimensions of your backyard are 20 feet wide by 45 feet long. Your new patio measures 18 feet in length.

To find :  The perimeters of your backyard and of the patio.

The dimensions of the yard are length 45 and width 20.

The patio is going to have the same shape, only smaller.

The length of the patio is 18 feet.

The ratio of the length of the patio to the length of the yard is 18/45.

Since the patio and the yard are to have the same shape, then that same ratio of 18/45, applied to the width of 20, gives you a patio width of 18/45* 20 = 8

Therefore, The perimeter of your new patio is 2 * (18 + 8) = 2 * 26 = 52.

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If and only if a function is a bijective function, it has an inverse that is also a function.

Only in the condition, if a function is bijective, meaning it is both onto (surjective) and one-to-one (injective), it has an inverse that is itself a function. If there are no two random input values resulting in a similar output value, then the function is said to be injective. As a result, there is only one x-value that can yield a given y-value.

A unique inverse function cannot be determined for a function if it is not injective. Whereas, a function is surjective if at least one input value is required to produce each output value. As a result, there is at least a single x-value in the domain of the function that yields each y-value in the function's range. A function's inverse would not be defined for values in the range if it were not surjective.

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Step 1: The greatest common factor (GCF) in this equation is x^3. So we can factor it out:

y = x^3(x - 343)

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Step 2: We can not take root of a³ and b as there is no square term in the equation.

Step 3:

a= x^3

b= - 343

Step 4: Plugging in a and b into the original equation, we get

y = x^3(x - 343)

This is the simplified form of the equation.

So, the equation is a polynomial equation of degree 4, with the leading coefficient a = x^3 and the constant term b = -343, and it can be written as y = a(x-b) which is y = x^3(x-343)

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The measure of each angle is 136.9 and 43.1.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

An angle measures 93.8° more than the measure of its supplementary angle.

This means,

There are two angles whose sum is 180.

x + y = 180 ____(1)

x = y + 93.8 _____(2)

Now,

From (1) and (2) we get,

y + 93.8 + y = 180

2y = 180 - 93.8

2y = 86.2

y = 43.1

Now,

x = 43.1 + 93.8

x = 136.9

Thus,

The angles are 136.9 and 43.1.

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Divide the numerator by denominator. Carry the quotient as a whole number and the remainder as the numerator of the proper fraction, maintaining the denominator the same.

A mixed fraction is a type of fraction described as having a fraction and a whole number.

Let's take an example to understand the process completely.

For example, 3(1/7), where 3 is a whole number and 1/7 is a fraction.

Step 1: Divide the Fraction’s numerator by the denominator, i.e. 22/7.

Step 2: The integer portion of the answer will be the integer portion for a mixed fraction, i.e. 3 is an integer.

Step 3: The Denominator will be the same as the original fraction, i.e. 7.

Step 4: So, the improper fraction 22/7 is changed to a Mixed fraction as 3 (1/7).

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The solutions of the quadratic equation 3x^2 + 14x + 5 = 0 can be found by factoring the equation into the product of two binomials, which are equal to zero.

3x^2 + 14x + 5 = (3x+1)(x+5) = 0

To find the solutions, we set each factor equal to zero and solve for x:

3x+1 = 0 or x+5 = 0

x = -1/3 or x = -5

Therefore, the solutions of the quadratic equation 3x^2 + 14x + 5 = 0 are x = -1/3, x = -5.

Alternatively, you can use the Quadratic formula to find the solutions.

The Quadratic formula is: x = (-b ± √(b^2-4ac))/(2a)

Where a,b and c are the coefficients of the equation.

x = (-14 ± √(14^2-435))/(2*3) = (-14 ± √(196-60))/6 = (-14 ± √(136))/6

It's worth noting that both solutions x = -1/3 and x = -5 are correct.

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