prove that every subgroup of order $p^{n-1}$ with g order p n is a normal subgroup math.stackexchange

Answer:

x = 2

Step-by-step explanation:

Let's find our third angle:

60 + 60 + A = 180

A = 60

Because all of our angles are the same, the triangle must be equilateral, meaning all of the sides are the same length as well!

(Pick any two sides):

2x + 3 = 4x - 5

(add 5 to both sides):

2x + 8 = 4x

(Subtract 2x from both sides):

2x = 4

(divide both sides by two):

x = 2!

Applying the triangle midsegment theorem, the length of HJ is: 8 units.

The triangle midsegment theorem states that when a line connects the midpoints of two sides of a triangle, it is parallel to the third side and also has a length that is half of the length of the third side.

In the image attached below, segment LK is a midsegment of the triangle which is parallel to a third side, segment HJ.

Therefore:

LK = 1/2(HJ) [triangle midsegment theorem]

Substitute

4 = 1/2(HJ)

Multiply both sides by 2

4 × 2 = 1/2(HJ) × 2

8 = HJ

Length of HJ = 8 units.

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Using the congruence angel theorem, the value of ST is 38.

In the given question given that, UV||RT.

We have to find the value of ST.

Given: UV||RT

Prove: Value of ST.

From the given diagram we can see that;

UT = 19

VS = 39

RS = 26

Using the Congruence Triangle Theorem;

∆USV≈∆TSR

So using the theorem;

US/VS = ST/RS………………(1)

From the given diagram we can see that

US = UT+ST

US = 19+ST

Now putting the value to the condition 1

(19+ST)/39 = ST/26

Simplifying

26(19+ST) = 39ST

494+26ST = 39ST

Subtract 26TS on both side, we get

13ST = 494

Divide by 13 on both side, we get;

ST = 38

Hence, the value of ST is 38.

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Among any group of d+1 integers there are two with exactly the same remainder when divided by d.

Positive integers are those bigger than 0 that don't contain any fractional portions. On the number line, these figures are located to the right of 0.

Since it is neither positive nor negative, 0 is not a positive integer. Positive integers are defined as numbers greater than 0 in mathematics.

The possible remainders after dividing an integer by d are 0, 1, 2,..., d-1.

The number of remainders that can be obtained is d, or |0, 1, 2,..., d-1|=d0,1,2,...,d-1=d.

According to the Pigeonhole Theory:

objects are the number of integers in d+1.

"holes" = "remainders" + "d"

[d+1/d]=2

According to the Pigeonhole Principle, there are always two d+1 integers in every group that have precisely the same residual after being divided by d.

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There are always two d+1 numbers in any group that have the exact same residual after division.

An integer, pronounced "IN-tuh-jer," is an entire number which can be positive, minus, even zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, among 3,043. 1.43, 1 3/4, 3.14, and other values which aren't integers seem to be some examples.

The potential remainders after dividing an integer by d are 0, 1, 2,..., d-1.

The possible number of remainders is d, or I{0,1,2,.......d-1}I = d

By the Pigeonhole Principle:

Objects = umber of integers = d+1

Holes = number of remainders = d

[tex]\frac{d+1}{d} = 2[/tex]

According to the Pigeonhole Principle, there are always two d+1 numbers in every group that have precisely the same residual after being divided by d.

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Answer:15i-25/34

Step-by-step explanation:

You have to multiply by 3+5i to get rid of the i on the bottom since you can't have it.

5i/3-5i x 3+5i/3+5i

Answer:

x = 2

<1 = 28

Step-by-step explanation:

The two angles equal each other.

4x + 20 = 5x + 18  Subtract 4x from both sides

20 = x + 18  Subtract 18 from both sides

2 = x

4x + 20

4(2) + 20

8 + 20

28

The remaining material for sewing is 5/2 material.

Fractions are used to represent smaller pieces (or parts) of a whole.

Given that, Keith buys 3 yards of material to make a blanket. He trims off a total of 1/6 yard before he begins sewing.

1/6 of 3 = 3x1/6 = 1/2

The remaining material = 3-1/2

= 5/2

Hence, The remaining material for sewing is 5/2 material.

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With the application of Arithmetic operators altitude must the airplane make in order to land is 21350 feets.

What is Arithmetic operators ?

By combining operands with one arithmetic operator, an arithmetic operation is given. The built-in functions ADD, SUBTRACT, DIVIDE, and MULTIPLY additionally allow for the specification of arithmetic operations.

solution:

An airplane was flying at an altitude above the sea level is 11,200 feet

The airplane then increased its altitude by 10,150 feet.

By adding both the altitude 11,200 + 10,150 = 21350 feets

Therefore, altitude must the airplane make in order to land is 21350 feets

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The solution is

a) The slope/rate of change between the inputs in m = -1/2

b) Slope/rate of change between the domain values of 4 and 8 is m = -1/2

c) The slope/rate of change is constant

d) The function is a linear function

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be = A

Now , the value of A is

a)

when the inputs are 0 and 4 , the values of x = 0 and x = 4

So , the values of y = 5 and y = 3 respectively

Let the first point be P = P ( 0 , 5 )

Let the second point be Q = Q ( 4 , 3 )

Now , the slope of the line between the two points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 3 - 5 ) / ( 4 - 0 )

Slope m = -2/4

Slope m = -1/2

So , the slope of the line m = -1/2

b)

when the domain values are 4 and 8 , the values of x = 4 and x = 8

So , the values of y = 3 and y = 1 respectively

Let the first point be Q = Q ( 4 , 3 )

Let the second point be R = R ( 8 , 1 )

Now , the slope of the line between the two points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 1 - 3 ) / ( 8 - 4 )

Slope m = -2/4

Slope m = -1/2

So , the slope of the line m = -1/2

c)

The slope of the line m = -1/2 and it is constant

d)

The function is a linear function and the equation of line is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = -1/2 ( x - 0 )

On simplifying the equation , we get

y - 5 = -1/2 ( x )

Adding 5 on both sides of the equation , we get

y = ( -1/2 )x + 5

Therefore , the equation of line is y = ( -1/2 )x + 5 and it is linear

Hence , the equation of line is y = ( -1/2 )x + 5 and it is linear where the slope of the line is m = -1/2

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Answer:

C. Higher Demand from customers

Step-by-step explanation:

Higher Materials cost leads to higher production cost

Higher minimum wage leads to higher production cost

The demand for the final product does not increase the production cost of the products

Answer: C. Higher Demand from customers

Step-by-step explanation:

The required simplified expression is 2x + 3xy² - 3y⁴ which is determined by using the distributive property.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question as:2x + 3y²(x - y²)

We have to simplify the given expression.

As per the question, we have

⇒ 2x + 3y²(x - y²)

Apply the distributive property of multiplication

⇒ 2x + 3xy² - 3y⁴

Therefore, the simplified expression is 2x + 3xy² - 3y⁴.

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Answer:

MAY BE IT'S HELP UHHH=^._.^

Answer:

The answer to the expression 3(6x-4y)-5 is 18x - 12y - 5. This is the result of following the order of operations and performing the necessary operations in the correct sequence.

Step-by-step explanation:

To solve this problem, you need to follow the order of operations, which is a set of rules that dictate the sequence in which operations should be performed in a mathematical expression to get the correct result. The order of operations is often abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

According to the order of operations, the first step in solving this problem is to evaluate anything inside parentheses. In this case, there are no parentheses, so we can move on to the next step, which is to evaluate any exponents. Again, there are no exponents in this expression, so we can move on to the next step, which is to perform any multiplication or division.

In this case, there is a multiplication operation: 3 * (6x - 4y). So we need to evaluate this first. To do that, we need to multiply 3 by each of the terms inside the parentheses: 3 * 6x and 3 * -4y. This gives us 18x - 12y.

Now that we have performed all of the multiplication and division operations, we can move on to the final step, which is to perform any remaining addition or subtraction operations. In this case, there is only one subtraction operation: 18x - 12y - 5. So we need to subtract 5 from 18x - 12y to get our final answer: 18x - 12y - 5 = 18x - 12y - 5.

Therefore, the result of evaluating the expression 3(6x-4y)-5 is 18x - 12y - 5. I hope this helps! Let me know if you have any other questions.

You would need to purchase 89.25 square feet of tiles to cover the floor of a 10.5-foot by 8.5-foot bathroom.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

To determine the number of square feet of tiles needed to cover a 10.5-foot by 8.5-foot bathroom floor, we can use the formula for the area of a rectangle, L × W

As per the question, the length of the floor is 10.5 feet and the width is 8.5 feet, so the total area of the floor is 10.5 feet × 8.5 feet = 89.25 square feet.

Therefore, you would need to purchase 89.25 square feet of tiles to cover the floor of a 10.5-foot by 8.5-foot bathroom.

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The total cost of kim's car is $30,021.61

What is total ?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.

20% of the car price

= (20 * 28,000 ) / 100

= $5600

She paid $5600 as down payment for new car

Financed remaining for 48 months = 4 years

APR = 4.3%

Loan amount = 28000 - 5600

                      = 22400

Monthly payment = [tex]\frac{P * R * (1+R)^{n} }{(1+R)^{n} - 1}[/tex]

Rate of interest = (R/12)/100

For 4.3 % R will be = 0.00358333

Monthly payment is = $508.78

So the total interest paid will be = $ 2021.61

Total cost of the car = cost price + interest

              = 28000 + 2021.61

              =  30021.61

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Answer:

-3

Step-by-step explanation:

A (0,2)

B (2,-4)

slope = (-4-2)/(2-0)

-6/2

-3

a parallel line has the same slope

Answer:

D

Step-by-step explanation:

[tex]m\angle BCA+m\angle ACD=180^{\circ} \\ \\ 2x-5+3x+10=180 \\ \\ 5x+5=180 \\ \\ 5x=175 \\ \\ x=35 \\ \\ \\ m\angle ACD=3(35)+10=115^{\circ}[/tex]

The dimensions of the field are 17 meters and 8.5 meters.

What is dimensions?

The minimal set of coordinates required to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one because a point on it can be specified by a single coordinate, such as the point at 5 on a number line.

Given:

Brianna has 34 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank.

Since,

Area of rectangle = A = l x w        ..(1)

where l = length and w = width

Perimeter = 2w + l

34 = 2w + l

  l = 34 - 2w             ..(2)

Plug this value in equation (1).

A = (34 - 2w) x w

140 = 34w - 2w^2

2w^2 - 34w + 140 = 0

The dimension w can be found as follows;

w = - b / 2a

Here a = 2, b = -34

⇒ w = -(-34)/2(2) = 34/4 = 8.5

Hence, the width is 8.5 meters.

Now to find the length.

Plug w = 8.5 in equation (2)

l = 34 - 2(8.5)

l = 34 - 17

l = 17

Hence, the dimensions of the field are 17 meters and 8.5 meters.

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Complete question:

Brianna has 34 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 140 square meters.

List each set of possible dimensions (length and width) of the field.

Answer:

10

Step-by-step explanation:

[tex]-2-(-12)\\=-2+12\\=12-2 \\=10[/tex]

The measure of arc DA is  104°.

What is inscribed angle?

In terms of geometry, an inscribed angle is the angle created when two chords intersect within a circle. It can also be described as the angle formed by two specified points on a circle at a given point on the circle. Two chords of the circle sharing an endpoint are equivalently used to define an inscribed angle.

We have to find the measure of arc DA.

In the given diagram the angle DBA is the inscribed angle.

Since, the measure of arc formed by inscribed angle is twice the measure of inscribed angle.

Here, m ∠DBA = 52°

Hence,

measure of arc DA = 2 (m ∠DBA)

                               = 2(52°)

measure of arc DA = 104°

Hence, the measure of arc DA is  104°.

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Answer: If the rate is constant, then the situation is a proportional relationship. If the rate is not constant, then the situation cannot be a proportional relationship.

Answer:

57 years old

Step-by-step explanation:

Bob=31

Mark= 31 x 2 - 5

31 x 2= 62

62- 5 = 57

Mark is 57 years old

Answer:

Mark is 18

Step-by-step explanation:

The triangle has three side x,y and √(x²+y²), the slope of x is zero, the slope of y is undefined, the slope of √(x²+y²) is tanα. The coordinate of the midpoint of x is x/2,0 and y is 0, y/2

suppose the triangle is right-angled and the sum of other two angles are also 90 degrees. we know that the side opposite to the right angle is called hypotenuse. let the other two side is denoted by x and y. Now, x is the base of triangle, and the rest of the side is y. The angle between hypotenuse and base is denoted by α . As per Pythagorean theorem, hypotenuse = √(x²+y²).

slope can be calculated by tanα or using the formula (y₂-y₁)/(x₂-x₁)

according to trigonometric ratio, tanα = opposite side/base = x/y

 tanα is the slope of hypotenuse.

the side length x is along the horizontal axis, so its y coordinate is zero and slope is also zero.

the side length y is along the vertical axis whose x coordinate is zero that means slope is undefined.

As per the formula (y₂-y₁)/(x₂-x₁) used to calculate slope, whenever x coordinate is zero the result is written as undefined.

hence, the triangle is right-angled, and the biggest side has a slope only.

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Answer:

The missing term in the output of the function [tex]g(f(x))[/tex] is -18.

[tex]g(f(x))=10x^2-18[/tex]

Step-by-step explanation:

In mathematics, function composition is a term that encompasses a relationship between two functions wherein the output of one function is used as the input for another function. This relationship combines two functions to form a single function, known as a composite function. For future reference, function composition may also be denoted by a small circle, see below:

[tex](g\circ f)(x)=g(f(x))[/tex]

In the given problem, we must evaluate the composite function [tex]g(f(x))[/tex] / [tex](g\circ f)(x)[/tex] to identify the unknown term.

With composite functions, we begin evaluating from the inside. To evaluate [tex]g(f(x))[/tex], we must substitute the output of the function [tex]f(x)[/tex] (given as the expression [tex]2x^2-5[/tex]) as the input ([tex]x[/tex]) for the function [tex]g(x)[/tex]:

[tex]g(f(x))=g(2x^2-5)[/tex]

Now, using [tex]f(x)[/tex] as the input ([tex]x[/tex]) for the function [tex]g(x)[/tex] (given as the expression [tex]5x+7[/tex]), we can substitute [tex]2x^2-5[/tex] into the output for the function [tex]g(x)[/tex]:

[tex]g(f(x))= 5(2x^2-5)+7[/tex]

From here, we can go ahead and distribute the 5:

[tex]g(f(x))=10x^2-25+7[/tex]

Combine like terms:

[tex]g(f(x))=10x^2-18[/tex]

With the composite function evaluated, we can identify our missing term as [tex]-18[/tex].

Answer:

The profit percent is 30%.

Step-by-step explanation:

Answer: 30%

Step-by-step explanation:

Your profit is $0.30 so you have to calculate what percent 30 is of 100 (I converted both numbers to cents) and you would get 30%

The theory tells us that the sphere is a three-dimensional body that arises by rotating a semicircle around its diameter.

The sphere has been a three-dimensional body. The main characteristics of this body are:

In the attached image let's see an example of a sphere.

¡Hope this helped!

The solution is

A) The domain to plot the growth function is Domain = [ 0 , 8 ]

B) The y-intercept of the graph of the function f ( a ) is f ( 0 ) = 3 cm

C) The average rate of change of the function f ( a ) from m = 2 to m = 8 is given by T = 0.4022 cm per month

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Now , the value of A is given by

f ( a ) = 3 ( 1.09 )ᵃ

A)

To find the domain of the function f ( a )

The length of the fish was approximately 5.98 cm

So , substituting the value of f ( a ) as 5.98 cm , we get the value of m,

And , f ( a ) = 5.98 cm

So , 5.98 = 3 ( 1.09 )ᵃ

Solving for a , we get

Divide by 3 on both sides of the equation , we get

1.9933 = ( 1.09 )ᵃ

a = 8

So , the value of a is 8

So , the domain of the function is [ 0 , 8 ]

B)

The y-intercept of the graph is given by substituting the value of a = 0,

So , f ( a ) = 3 ( 1.09 )ᵃ

when a = 0 , we get

f ( 0 ) = 3 ( 1.09 )⁰

f ( 0 ) = 3 cm

Therefore,  the value of f ( 0 ) = 3 cm

C)

The average rate of change from m =2 to m = 8 is given by the equation ,

when m = 2 ,

f ( a ) = 3 ( 1.09 )ᵃ

f ( 2 ) = 3 ( 1.09 )²

f ( 2 ) = 3 x 1.1881²

f ( 2 ) = 3.5643

And , when a = 8

f ( a ) = 3 ( 1.09 )ᵃ

f ( 8 ) = 3 ( 1.09 )⁸

f ( 8 ) = 3 x 1.99256

f ( 8 ) = 5.97768

So , the average rate of change is the slope of the graph

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope = f ( 8 ) - f ( 2 ) / ( 8 - 2 )

Slope = ( 5.97768 - 3.5643 ) / 6

Slope = 2.4133879 / 6

Slope = 0.40223 cm per month

Therefore ,

The average rate of change of the function f ( a ) from a = 2 to a = 8 is given by T = 0.4022 cm per month

Hence ,

A) The domain to plot the growth function is Domain = [ 0 , 8 ]

B) The y-intercept of the graph of the function f ( m ) is f ( 0 ) = 3 cm

C) The average rate of change of the function f ( m ) from m = 2 to m = 8 is given by T = 0.4022 cm per month

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The value of x and y are 3 and 11.

What is the congruent triangle?

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

Given that,

△LMN = △PQR

Thus ∠L = ∠P, ∠M = ∠Q, and ∠N = ∠R.

Also,  ∠L = 40°, ∠M = 90°, ∠P = (17x − y)°, ∠R = (2x + 4y)°.

The sum of interior angles of a triangle is 180°.

∠L + ∠M + ∠N = 180°

40° + 90° + ∠N = 180°

∠N = 50°.

Therefore,

17x − y = 40   .....(i)

2x + 4y = 50  .....(ii)

Multiply equation (i) with 4 and add with equation (ii)

68x - 4y = 160

2x + 4y = 50

_________

70x     = 210

x = 210/70

x = 3

Putting x = 3 in equation (ii)

6 + 4y = 50

4y = 44

y = 11

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