If a group G has exactly one subgroup H of order k, prove that H is normal in G. This problem has been solved! You'll get a detailed solution from a subject ...

Step-by-step explanation:

A) When both parallel lines are secant to the circle:

Let's consider two parallel lines, line l and line m, that intersect a circle at four points. Let A and B be two of the points where line l intersects the circle, and let C and D be two of the points where line m intersects the circle, as shown below:

```

C D

o-----o

/ \

/ \

/ \

/ \

A B

o------------------------o

```

Since line l is parallel to line m, we know that ∠A = ∠C and ∠B = ∠D, because they are corresponding angles. We also know that the sum of opposite angles of a cyclic quadrilateral is 180 degrees. Therefore, we have:

∠ACB + ∠ADB = 180° (opposite angles of cyclic quadrilateral ABCD)

∠A + ∠C + ∠B + ∠D = 180° (sum of angles in quadrilateral ABCD)

Substituting ∠A = ∠C and ∠B = ∠D, we get:

∠ACB + ∠ADB = 180°

2∠A + 2∠B = 180°

∠A + ∠B = 90°

This means that ∠ACB and ∠ADB are complementary angles. Since the intercepted arcs are defined by the central angles ∠ACB and ∠ADB, and these angles are complementary, it follows that the intercepted arcs are congruent.

B) When both parallel lines are tangent to the circle:

Let's consider two parallel lines, line l and line m, that are tangent to a circle at points A and B, as shown below:

```

o

/ | \

/ | \

/ | \

/ | \

A--------o--------B

\ | /

\ | /

\ | /

\ | /

o

```

Since line l is parallel to line m, we know that ∠A = ∠B, because they are alternate interior angles. We also know that the angle between a tangent and a chord that intersects the tangent is equal to the intercepted arc. Therefore, we have:

∠ALB = 2∠A (angle between tangent line l and chord AB)

∠BLA = 2∠B (angle between tangent line m and chord AB)

Substituting ∠A = ∠B, we get:

∠ALB = 2∠A

∠BLA = 2∠A

This means that the intercepted arcs AL and BL are congruent, because they are defined by the central angles ∠ALB and ∠BLA, which are equal.

Therefore, we have shown that in both cases, when two parallel lines intercept a circle, they intercept congruent arcs on the same circle.

Answer:

Step-by-step explanation:

Answer:

1. 39, 46

2. 180

Step-by-step explanation:

1. count up by 7

2. not sure..

Answer:

In linear algebra, an augmented matrix is a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices.

Step-by-step explanation:

Answer:

x (7-4x)

factor x out of 7x-4x^2

Answer:

it still 11/295

Step-by-step explanation:

The two values of x best represent where the two functions are equal will be (12,11)

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

Given data;

Linear function passing through;

(1, 2), (3, 4), (6,7) and (8, 9)

Quadratic function passing through

(3, 4), (5, 0), (7, 4) & (8, 9)

Let x be two values of x best represent where the two functions are equal;

The value of the x is obtained from the graph where the two line meets.

The value of x willl be (12,11)

Hence, the two values of x best represent where the two functions are equal will be (12,11)

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The equation of the function is (d) g(x) = 4ˣ ⁻ ⁴ + 2

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

The functions f(x) and g(x)

In the graph, we can see that

f(x) = 4ˣ

The transformation on the graph is

This means that

g(x) = f(x - 4) + 2

Recall that

f(x) = 4ˣ

So, we have

g(x) = 4ˣ ⁻ ⁴ + 2

This means that the equation of the function is g(x) = 4ˣ ⁻ ⁴ + 2

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Answer:

70 cards bought from Jim

Step-by-step explanation:

the ratio of cards Jim : Alvin = 7 : 2 = 7x : 2x ( x is a multiplier ) , then

7x + 2x = 360

9x = 360 ( divide both sides by 9 )

x = 40

Jim has 7 × 40 = 280 cards

Alvin has 2 × 40 = 80 cards

let n be the number of cards Alvin buys from Jim , then

Jim has 280 - n cards

Alvin has 80 + n cards

Then expressing in fractional form

\(\frac{280-n}{80+n}\) = \(\frac{7}{5}\) ( cross- multiply )

7(80 + n) = 5(280 - n) ← distribute both parenthesis

560 + 7n = 1400 - 5n ( add 5n to both sides )

560 + 12n = 1400 ( subtract 560 from both sides )

12n = 840 ( divide both sides by 12 )

n = 70

Alvin buys 70 cards from Jim

Answer:

111

Step-by-step explanation:

(4×3+3×2-17×-12)÷(×+2)

(12+6+204)÷(2)

(222)÷(2)

222÷2

111

Answer: You can see if the graphs of the two populations meet at a given point.

Step-by-step explanation:

If we have a graph of population vs time

such that y = population and x = time, two different populations will be exactly the same for a given time if we have an intersection of the two graphs. The value (x0, y0) where the graphs cross is the time = x0 and the population y0, this means that both populations have y0 individuals at the same time.

Answer:

C?

Step-by-step explanation:

A) Jared makes x of a goodie bag per hour. How many

can he make in y of an hour?

B) Jared makes x of a goodie bag per hour. How many

can he make in y of an hour?

C) Jared has x of an hour left to finish making goodie  bags. It takes him y of an hour to make each goodie  bag. How many goodie bags can he make?

D) id k

Quotient is the answer to a division problem, so we need to find a problem that needs to divide x and y to find the answer. It isn't A or B, since they are asking for y, not the quotient. I have no idea what D is. C makes sense, so C might be the answer.

It tells us how much time he has(x), and how long it takes him to make 1 bag(y), and we need to find the answer, which is the quotient.

So C is the answer.

---

hope it helps

Answer:

c

Step-by-step explanation:

Length of tree = 8.57 m.

Let AB represent the length of lower CD represent the length of tree.

Now we use the trigonometric ratios formula

tan = Perpendicular / base.

Now, in triangle AEC

tan 28° = AE / EC = AE / 44

= AE = 44 * Tan 28^.

= AE = 23.39 m

Now, in triangle ABD.

Length of tree = Length of  tower

= Length of tree = 31.97 – 23.39

= Length of tree = 8.57 m.

Pythagoras of Samos became an historic Ionian Greek logician and the eponymous founder of Pythagoreanism. His political and religious teachings were widely recognized in Magna Graecia and motivated the philosophies of Plato, Aristotle, and, through them, the West in preferred. knowledge of his life is clouded with the aid of legend; however, he appears to have been the son of Menarches, a gem-engraver at the island of Samos. cutting-edge students disagree concerning Pythagoras's schooling and influences; however, they do agree that, around 530 BC, he travelled to Croton in southern Italy, wherein he based a school in which initiates have been sworn to secrecy and lived a communal, ascetic lifestyle.

This lifestyle entailed some of dietary prohibitions, historically said to have included vegetarianism, despite the fact that current students doubt that he ever encouraged entire vegetarianism. The coaching most securely recognized with Pythagoras is metempsychosis, or the "transmigration of souls", which holds that every soul is immortal and, upon demise, enters into a new body.

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Answer:

860.3

Step-by-step explanation:

43·π·5.93≈860.28954in³

860.28954 = 860.3

The volume of the sphere is V = 859.9 inches³

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the radius of the sphere be r = 5.9 inches

Now , Volume of a Sphere = ( 4/3 ) πr³

On simplifying , we get

V = ( 4/3 ) ( 3.14 ) ( 5.9 )³

V = 859.853 inches³

Hence , the sphere has volume of 859.9 inches³

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Answer:

y = 1/4 x - 1/2

Step-by-step explanation:

Remark

The general equation for a line is y = mx + b

You know that m = 1/4. The problem is what do you do about (2,0)?

Solution

y = 1/4 x + b                  Let x = 2 when y = 0

0 = 1/4 * 2 + b               multiply 2 * 1/4

0 = 1/2 + b                     Subtract 1/2 from both sides

b = - 1/2

equation y = 1/4 x - 1/2

Graph

Answer:

can I get ful question........?

Answer:

Here is the full question

Step-by-step explanation:

Answer:

yes , because -3 is the whole number

Answer:

Step-by-step explanation:

just think of the parts of an equation as just regual number

a = 5      b = 8      a × b  =  5 × 8     =  40

now f(x) =  x² + 3x     and g(x) = 2x²      

f(x) × g(x)      =     (x² + 3x) × (2x²)

                    =     (x² × 2x²) + (3x × 2x²)

                    =     2x^4  + 6x^3

f(x) × g(x)  = 2x^4  + 6x^3    < ------------------ FINAL ANSWER

let x =2   in (x² + 3x) × (2x²)  

        (2² + 3×2) × (2×2²) = (4+6) (8) = (10×8) = 80

f(x) × g(x)  = 2x^4  + 6x^3

      =  2×16 + 6×8

      = 32 + 48

      = 80      it checks as correct

Answer:

>

Step-by-step explanation:

8-4x>-4

4x>8+4

4x>12

x>3

Answer:

7 for each week

Step-by-step explanation:

7:1 = 7 dollars in 1 week

14:2

21:3

28:4

35:5

42:6

49:7

56:8

63:9

70:10

77:11

84:12

Answer:

How many weeks 23 34 85? if its 23 161 if its 34 238 and if its 85 595

Step-by-step explanation:

The money in Shane's account after five years will be $4900.

The formula for simple interest is -

S.I. = PRT/100, where P is principal, R is rate of interest, T is time and SI is simple interest. Interest is calculated semi-annually then t will be 5×2 years.

Keep the values in formula -

S.I. = 3500 × 4 × 5 × 2/100

Performing multiplication in numerator on Right Hand Side of the equation

S.I. = 1,40,000/100

Cancelling common zero on Right Hand Side of the equation

S.I. = $1400

Total amount = Principal + Interest

Keep the values in formula -

Total amount = 3500 + 1400

Performing addition

Total amount = $4900

The total money in account will be $4900.

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Answer: x =400

Step-by-step explanation:

Answer:

180 + 0.4x = 400

Answer:

number of general admission tickets sold = 32

Number of VIP tickets sold = 8

Step-by-step explanation:

Total Number of tickets = 40

Cost of general admission tickets = $20

Cost of VIP tickets = $30

Total revenue = $880

Let

x = number of general admission tickets sold

y = number of VIP tickets sold

The equations are:

x + y = 40 (1)

20x + 30y = 880 (2)

From (1)

x = 40 - y

Substitute x = 40 - y into (2)

20x + 30y = 880

20(40 - y) + 30y = 880

800 - 20y + 30y = 880

10y = 880 - 800

10y = 80

y = 80 / 10

= 8

y = 8

Substitute y = 8 into (1)

x + y = 40

x + 8 = 40

x = 40 - 8

= 32

x = 32

number of general admission tickets sold = 32

Number of VIP tickets sold = 8

Answer:

  34 square units

Step-by-step explanation:

You want the area of the triangle with vertices X(6, 8), Y(3, 3), and Z(13, -3).

There are several ways the area of a triangle can be calculated from the coordinates of the vertices. One relatively easy method is to find half the absolute value of the sum of the determinants of adjacent pairs of points.

This calculation is shown in the second attachment.

The area of ∆XYZ is 34 square units.

A slope calculation will tell you side XY is perpendicular to side YZ. This means you can find the area from the lengths of these two sides. The distance formula can tell you the lengths.

  XY = √((3 -6)² +(3 -8)²) = √(9 +25) = √34

  YZ = √((13 -3)² +(-3 -3)²) = √(100 +36) = 2√34

 Area = 1/2bh = (1/2)(√34)(2√34) = 34 . . . . square units

Pick's theorem tells you the area of a polygon with vertices on grid points can be found by counting the grid points on the boundary and interior to the boundary.

  A = i + (b/2) -1

This triangle has the three given vertices on grid points, along with point (8, 0), which is the midpoint of YZ. There are 33 interior points, so the area is ...

  A  = 33 +(4/2) -1 = 34 . . . . square units

The length of XZ is ...

  XZ = √((13 -6)² +(-3 -8)²) = √(49 +121) = √170

Heron's formula tells you the area is given by ...

  A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter

The third attachment shows this calculation gives an area of 34 square units.

__

Additional comments

The slope calculation tells you the slope of XY is ...

  m = (y2 -y1)/(x2 -x1) = -5/-3 = 5/3

and the slope of YZ is ...

  m = -6/10 = -3/5 . . . . . . . . the opposite reciprocal of the slope of XY

Hence these sides are perpendicular, as we noted above.

We like Pick's theorem for finding the areas of small figures with irrational side lengths (such as this one). It just involves counting, which is often easier than using a bunch of different formulas for slope or length.

The determinant formula is easy to compute, but tedious to enter on a calculator. It is much easier to program a spreadsheet for this. As with Pick's theorem, the method applies to a polygon with any number of vertices.

  \(\left|\begin{array}{cc}a&b\\c&d\end{array}\right|=ad-bc\)

In these 2×2 matrices, the coordinates can be listed in rows or in columns. It makes no difference to the calculation. The key is to work in one direction around the figure. (Here, we went CCW.)

The triangle is drawn in the first attachment. The geometry program that drew it also calculated its area to be 34 square units.

You may have noticed that the "determinant" method and Pick's theorem guarantee that the area of any polygon with integer coordinates will be an integer multiple of 1/2 square unit. That is, it will never be irrational. (You might not see that using Heron's formula.)

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Answer: 1. X=4

2. X=12

3. X=5

4. B=1

Step-by-step explanation:

Answer:

24960 dollars per year

Step-by-step explanation:

(450 + 30) x 52 ( weeks in a year)

Answer:

Step-by-step explanation:

1. $450+$30 = $480

2. $480 x 50(weeks) = $24,000

Answer:

Step-by-step explanation:

The meaning of the translation (x + 6, y + 10) is that all points in a coordinate plane are moved 6 units to the right and 10 units up.

In other words, for any point (x, y) in the original position, after the translation, the new coordinates would be (x + 6, y + 10). This means that the x-coordinate of each point is increased by 6 units, resulting in a shift to the right, and the y-coordinate is increased by 10 units, resulting in a shift upwards.

You have to fist write it in a way you don't confuse yourself

Let the number be x

x+5=17

x=17-5

x=12

It's a step by step process

The Remainder when dividing f(x) by x - 3 is 840

The remainder when dividing the polynomial f(x) = 3x^5 + 4x^3 + 3 by the binomial x - 3, we can use the polynomial remainder theorem. According to the theorem, if we substitute the divisor, x - 3, into the polynomial f(x) and evaluate it at x = 3, the resulting value will be the remainder.

Let's calculate the remainder using this approach:

Substituting x = 3 into the polynomial f(x), we have:

f(3) = 3(3)^5 + 4(3)^3 + 3

    = 3(243) + 4(27) + 3

    = 729 + 108 + 3

    = 840

Therefore, when f(x) = 3x^5 + 4x^3 + 3 is divided by x - 3, the remainder is 840.

In summary, the remainder when dividing f(x) by x - 3 is 840.

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The equation for the plane through p0(−1,1,9) perpendicular to the following line vector is, ( x , y , z ) = ( 0 , 0 , 10)

A quantity that has both magnitude and direction but not position. Examples of such quantities are velocity and acceleration.

Given that,

The equation for the plane through p0(−1,1,9)

The xy-plane has a normal vector of 〈0, 0, 1〉, and any plane parallel to it will have the same normal vector.

Then the equation of the plane through (-1, 1, 9) that is parallel to the xy-plane has equation

〈x - (-1), y - 1, z - 9〉 • 〈0, 0, 1〉 = 0

x + 1 = 0

y - 1 = 0

z - 9 = 1

z = 1 + 9

z = 10

Therefore,

The equation for the plane through p0(−1,1,9) perpendicular to the following line vector is, ( x , y , z ) = ( 0 , 0 , 10)

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