Determine if each infinite geometric series is convergent or divergent.

Determine If Each Infinite Geometric Series Is Convergent Or Divergent.

Answers

Answer 1

The solution to the geometric progression are

a) The geometric progression converges , r = 0.1

b) The geometric progression converges , r = 0.2

c) The geometric progression diverges , r = 5

d) The geometric progression converges , r = 0.2

e) The geometric progression diverges , r = 5

f) The geometric progression converges , r = 0.2

What is Geometric Progression?

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

A geometric progression is said to converge if the common ratio r lies between -1 < r < 1

So , If -1 < r < 1, the geometric sequence converges

a)

The geometric progression is A = 0.3 + 0.03 + 0.003 + ...

The common ratio r = second term / first term

The common ratio r = 0.03 / 0.3

The common ratio r = 0.1

So , -1 < r < 1 and the GP converges

b)

The geometric progression is A = 0.25 + 0.05 + 0.01 + ...

The common ratio r = second term / first term

The common ratio r = 0.05 / 0.25

The common ratio r = 0.2

So , -1 < r < 1 and the GP converges

c)

The geometric progression is A = 0.23 + 1.15 + 5.75 + ...

The common ratio r = second term / first term

The common ratio r = 1.15 / 0.23

The common ratio r = 5

So , r > 1 and the GP diverges

d)

The geometric progression is A = 0.75 + 0.15 + 0.03 + ...

The common ratio r = second term / first term

The common ratio r = 0.15 / 0.75

The common ratio r = 0.2

So , -1 < r < 1 and the GP converges

e)

The geometric progression is A = 0.00025 + 0.00125 + 0.00625 + ...

The common ratio r = second term / first term

The common ratio r = 0.00125 / 0.00025

The common ratio r = 5

So , r > 1 and the GP diverges

f)

The geometric progression is A = 128,750 + 25,750 + 5,150 + ...

The common ratio r = second term / first term

The common ratio r = 25,750 / 128,750

The common ratio r = 0.2

So , -1 < r < 1 and the GP converges

Hence , the geometric progression is solved

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Related Questions

Complete each nuclear fission reaction. 235 92 u 1 0 n → 90 36 kr a 56 ba 3 1 0 n a: 239 94 pu 1 0 n → b c ba 91 38 sr 3 1 0 n b: c:

Answers

a: 235 92 U + 1 0 n → 90 36 Kr + 141 56 Ba + 3 1 0 n

b: 239 94 Pu + 1 0 n → 96 38 Sr + 143 55 Ba + 3 1 0 n

c: It is not possible to complete this nuclear fission reaction as it is not a valid input. There is no nuclide with the atomic number 94 and mass number 239.

What is nuclear fission?

Nuclear reactions are those that involve the nucleus of an atom. Nuclear fission involves the splitting of an atomic nucleus and the formation of two distinct atomic species.

Nuclear fission is a nuclear reaction in which the nucleus of an atom is split into two or more smaller nuclei, along with the release of a large amount of energy. In the first reaction, an atom of Uranium-235 (U-235) is hit by a neutron, which causes the nucleus to split into Krypton-90 (Kr-90) and Barium-141 (Ba-141) along with 3 neutrons. In the second reaction, an atom of Plutonium-239 (Pu-239) is hit by a neutron, which causes the nucleus to split into Strontium-96 (Sr-96) and Barium-143 (Ba-143) along with 3 neutrons.

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The length of a rectangular frame is 15 inches in the diagonal length of the frame is 17 inches what is the width of the frame in inches

Answers

The width of the frame is 8 inches.

Now, According to the question:

The length of a rectangular frame is 15 inches

The diagonal length of the frame is 17 inches.

To find the width of the frame in inches.

Let's take the width of the frame is = w

Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.

This will be:

17² = 15² + w²

289 = 225 + w²

289 - 225 =  w²

64 =  w²

w = [tex]\sqrt{64}[/tex]

w = 8

Hence, The width of the frame is 8 inches.

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divide using long division

Answers

When 392,196 is divided by 87, the answer obtained using long division is 4,508.

What does math's long division mean?

The mathematical procedure for splitting big numbers into several smaller groups or sections is known as long division. The dividend is the number we divide into smaller groups, while the divisor is the number through which we divide. Difficulty difficulty can be solved by breaking it down into manageable parts.

According to the given information:

Dividend : 392,196

Divisor: 87 (number that divides)

39 / 87 = 0

392 / 87 = 4 (87x 4 = 348) - 4 is the first digit of the result

392 - 348 = 44 (remainder)

441 (next digit is one) / 87 = 5 (87x 5= 435) - 5 is the second digit

441-435 = 6 (remainder)

69 / 87 = not possible so add a 0, which is the third digit

696 / 87 = 8 (87x 8 = 696)

696- 696 = 0 (not remainder)

When 392,196 is divided by 87, the answer obtained using long division is 4,508.

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I understand that the question you are looking for is:

392,196 divided by 87 (Using long division)

Punit had 12 tomatoe. He cut each into 6 lice. He ued 4 lice of the 16 andwiche he made. How many lice were remaining?

Answers

If Punit had 12 tomatoes. He cut each into 6 lice. He used 4 lice of the 16 sandwiches he made then 68 slices were remaining.

There were 12 tomatoes and each was cut into 6 slices, giving a total of 72 slices. Here we have to multiply 6 with 12

12×6=72

Of these, 4 slices were used to make sandwiches, leaving 68 slices remaining. Here we have to subtract 4 from 72

72-4=68

Therefore, Punit had 68 slices left, or 11.33 tomatoes, after making the sandwiches. This means that Punit had 68 lice of tomato remaining after making the sandwiches.

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At the gift shop entrance, fans go
through security at a rate of 15 people in
25 seconds. At that rate, approximately
how many people will go through security
in 135 seconds?

Answers

81 people because if you divide 135 seconds by 25 seconds you get 5.4 which you would multiply by 15 to get 81.

What is:
(7*8) + (42-8) / 4

Answers

Answer:

5.5

Step-by-step explanation:

7*8=56

42-8=34

56-34=22

22/4=5.5

what is the half of 8​

Answers

Answer:

4

Step-by-step explanation:

Half means 1/2

Half of 8

= 1/2 x 8

= 8/2

= 4

Hence, half of 8 is 4.

Answer: 4

Step-by-step explanation:4 + 4 is 8 half of 4 is eight.

A cylindrical aluminum soda can is to hold 12 ounces of tasty beverage. What are the dimensions of the can that will minimize the amount of aluminum used

Answers

A cylindrical can with volume 355 ml will use the least aluminum if its radius is about 3.84 cm and its height is about 7.67 cm.

What is a reasonable approximation for the volume of a soda can?

The soda cans are advertised as having a volume of 12 ounces, or 355 milliliters. The remaining head space is just under 25 ml. The can weighs about 13 g by itself. 39 g, or about 11%, of sugar, make up 355 ml of Coke.

How much pressure does a 12 oz. soda can typically hold?

When canned at 4 °C and stored at 20 °C, 12 oz. soda cans typically have pressures of about 120 kPa and 250 kPa, respectively. A 7UP® can that has been refrigerated contains 210 kPa of pressure. Pepsi-Cola®, on the other hand, has 276 kPa at about 16 °C.

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Neil work a a conultant at a oftware company. The amount of hi annual bonu i baed upon the number of hour he work. B = the amount of Neil' bonu
h = the number of hour Neil work

Which of the variable i independent and which i dependent?

Answers

The independent variable is h (the number of hours Neil works) and the dependent variable is B (the amount of Neil's bonus).

In this scenario, the amount of Neil's bonus (B) is dependent on the number of hours he works (h). The number of hours he works is the input or independent variable, while the amount of bonus he receives is the output or dependent variable. It can be said that the number of hours he works is the cause and the amount of bonus is the effect.

The equation is B = f(h) where f is the function that relates the two variables.

Thus, the independent variable is h (the number of hours Neil works) and the dependent variable is B (the amount of Neil's bonus).

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Complete Question is-

Neil works as a consultant at a software company and the amount of his annual bonus is based on the number of hours he works, which variable is independent and which is dependent? With B as the amount of Neil's bonus, and h as the number of hours Neil works.

(6b+ 2) - (4b + 3)
Help pls I don’t know how to do this

Answers

Answer:

2b - 1

Step-by-step explanation:

To solve this problem, we will need to open the parentheses. To do this, we will put an imaginary 1 in front of both sets of parentheses to open them using the distributive property, this gives us:

1(6b + 2) - 1(4b + 3)

We will open the first set of parentheses with no problem, but in the second set, we have -1, so we need to make every positive number negative and every negative number positive, giving us:

6b + 2 - 4b - 3

Then, we group our like terms:

6b - 4b + 2 - 3

Then, we subtract, giving us:

2b - 1

So the most simplified version is 2b - 1.

Hope this helped!

Answer:

Step-by-step explanation:

You begin by distributing the negative so -4b -3

then you will multiply (6b+2) by (-4b -3)

24b^2 - 18b - 8b - 6

answer = 24b^2 - 26b - 6

Condos in Georgetown go up in value by 10% each year. If the Sutton family's condo is now worth $120,000, what will it be worth in 8 years? If necessary, round your answer to the nearest cent.

Answers

The Sutton family's condo's worth in 8 years will be $216000.

What is exponential function?

An exponential function is a mathematical function in the form f(x) = aˣ, where {x} is a variable and {a} is a constant which is called the base.

Given is that Condos in Georgetown go up in value by 10% each year. Sutton family's condo's current worth is $120,000.

We can write the function to calculate the worth after {T} years as follows.

A{T, R} = A{i} {1 + RT}

A{T, R} = {120000} {1 + (10/100) x 8}

A{T, R} = {120000} {1 + 0.1 x 8}

A{T, R} = {120000} {1 + 0.8}

A{T, R} = {120000 x 1.8}

A{T, R} = 216000

Therefore, the Sutton family's condo's worth in 8 years will be $216000.

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Grant reads as part of his homework each week. - he must read for at least 4 hours each week as part of his homework. - This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers,n,of hourse he could read on each of the 5 weekdays this week. The graph is shown. PLEASE HELP ME

Answers

A statement which best describes the solution set of the given inequality 5n + 1.5 ≥ 4 is: C. all rational number values of n that are at least 0.5.

What is a rational number?

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 12, 0.5, √16, etc.

Next, we would translate the word problem into algebraic inequality and then solve for the value of n as follows;

5n + 1.5 ≥ 4

Subtracting 1.5 from both sides of the algebraic inequality, we have:

5n + 1.5 - 1.5 ≥ 4 - 1.5

5n ≥ 2.5

Dividing both sides of the algebraic inequality y 5, we have:

n ≥ 2.5/5

n ≥ 0.5

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Complete Question:

Grant reads as part of his homework each week. he must read for at least 4 hours each week as part of his homework. This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers, n, of hours he could read on each of the 5 weekdays this week. The graph is shown.

Which describes the solution set of the inequality?

A. all whole number values of n that are at least 1

B. all whole number values of n that are greater than 1

C. all rational number values of n that are at least 0.5

D. all rational number values of n that are greater than 0.5

What is the length of ab

Answers

A triangle is a three-sided polygon with three vertices. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The correct answer Is option c) 6.

What is triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

The diagram shows us a triangle [tex]$\mathrm{ABC}$[/tex], which

[tex]$$m \angle A=m \angle C=63^{\circ}, \quad A B=3 x$$[/tex]

units and [tex]$B C=(4 x-2)$[/tex] units.

The task Is to determine the length of the slde [tex]$\mathrm{AB}$[/tex].

[tex]$\mathrm{ABC}$[/tex] has the following

[tex]$$m \angle A=m \angle C$$[/tex]

In a triangle, we understand that

If the measurements of two angles are equal, then the lengths of the sides or each side are also equal.

so we must have

[tex]B C=A B \\\Rightarrow 4 x-2=3 x \Rightarrow 4 x-3 x=2 \Rightarrow x=2 .\end{aligned}$$[/tex]

As a result, [tex]$\mathrm{AB}$[/tex] will be of length

[tex]$$A B=3 x=3 \times 2=6$$[/tex]

As a result, the side [tex]$A B$[/tex] is 6 units long.

Therefore, the correct answer Is option c) 6.

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solve for the missing side length in this triangle ​

Answers

Answer:

10 and 24units

Step-by-step explanation:

Pythagoras' Theorem

Pythagoras' Theorem applies to right angle triangles with the formula:

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

where c is the longest side, with a and b the shorter ones (interchangable)

Solution

With the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.

By Pythagoras' Theorem,

[tex] {26}^{2} = ( {5x)}^{2} + ( {12x)}^{2} \\ 676 = 25 {x}^{2} + 144 {x}^{2} \\ 169 {x}^{2} = 676 \\ {x}^{2} = 676 \div 169 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ = 2[/tex]

Now we can find the side lengths.

[tex]5x = 5(2) = 10units \\ 12x = 12(2) = 24units[/tex]

Therefore the side lengths are 10 and 24 units.

Select all the as that inequalities that have the same solution as -4x<20

A. -x<5
B. 4x>-20
C. 4x<20
D. X<-5
E. X>5
F. X>-5

Answers

Answer:

A, B, F

Step-by-step explanation:

Divide both sides of -4x<20 by 4, and we have A

Multiply both sides of -4x<20 by -1, since -1 is a negative number, we reverse the inequality, and we have B

Multiply both sides of -x<5 (A) by -1, since -1 is a negative number, we reverse the inequality, and we have F

i need help Please will mark brainiest

Answers

The standard form of the polynomial -n²(n² + 5n + 6) is  -n⁴ - 5n³ - 6n².

How to represent polynomial in standard form?

Polynomials are algebraic expressions that consist of variables and coefficients.

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.

Hence, let's represent the polynomial in standard form as follows:

-n²(n² + 5n + 6)

Open the brackets

-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²

Hence,

-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²

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Please Simplify the phrase the first two and find the last one

Answers

Answer:

1)  23x + 6y

2) 8x  - 4y

3)  4x - x² + 7

Step-by-step explanation:

Simplify:

 

Multiply each term of (3x + 6y) by 5 and multiply each term of (2x - 6y) by 4.

5(3x + 6y) + 4 (2x - 6y)  = 5*3x + 5*6y + 4*2x - 4*6y

                                       = 15x + 30y + 8x - 24y

Now, combine like terms. Like terms have same variable with same power.

                                         = 15x + 8x + 30y - 24y

                                           = 23x + 6y

2) 3(4x - 2y) - 2*(2x -y) = 3*4x + 3*(-2y) + (-2)* 2x + (-2)*(-y)

                                     = 12x - 6y - 4x + 2y

                                     = 12x - 4x - 6y + 2y

                                    =  8x - 4y

3) f(x) = 3x + 2

To find f(x +1),  replace x with (x +1)

f(x +1) = 3*(x + 1) + 2

          = 3*x + 3*1 + 2

          = 3x + 3 + 2

          =3x + 5

f(2x) = 3*(2x) + 2

        = 6x + 2

f(2x) + h(x) = 6x + 2 - x² - 2x + 5

                 = 6x - 2x - x² +2 + 5

                 = 4x - x² + 7

What are the 4 quadrants called?

Answers

The 4 quadrants are called as Quadrant I, Quadrant II, Quadrant III and Quadrant IV.

The term quadrant in math is also known as the coordinate grid, cartesian coordinate system, or Cartesian plane, are basically constructed by taking a vertical axis, or the y-axis and setting it against a horizontal axis, or the x-axis and it creates a grid with four quadrants.

According to the cartesian system, here the coordinate plane is divided into four equal parts by the intersection of the x-axis and the y-axis such as the vertical number line.

Here the four quadrants are written as,

Quadrant I that is placed upon the upper right quadrant is the first quadrant, denoted as Quadrant I and the value on the x-axis and the y-axis both have positive numbers.

Next one is Quadrant II which is placed on the upper left quadrant is the second quadrant, denoted as Quadrant II and the value of the x-axis has negative numbers and the y-axis has positive numbers.

Third one is Quadrant III placed on the bottom left quadrant is the third quadrant, denoted as Quadrant III and the value of both the x-axis and the y-axis have negative numbers.

Final one is Quadrant IV which is placed on the bottom right quadrant is the fourth quadrant, denoted as Quadrant IV and here the value of the x-axis has positive numbers and the y-axis has negative numbers.

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How many pieces of 2/3 yard can I cut if I have 6 1/3 yards of material

Answers

Answer:

9

Step-by-step explanation:

6 1/3 yards of material is 19/3 yards total. 6 yards broken into thirds is 18/3. 18 divided by 2 is 9. There are 9 total pieces to cut, and an extra 1/3 left over

help me on this one bro I hate math

Answers

The initial amount of the investment is $800, the investment grows at the rate of 10% each year, and the value of the investment after 12 years is $1760.

What are coordinates in a graph?

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates from the graph.

(0, 800), (1, 880), (2, 968)

x-coordinate is the number of years and the y-coordinate denotes the Value.

Now,

The initial amount of the investment is when x = 0.

= 800

Now,

Rate of change of the value each year.

=(880 - 800) / (1 - 0)

= $80

Rate of percentage.

= 80/800 x 100

= 10%

Now,

The value of the investment after 12 years.

= 800 + 12 x 80

= 800 + 960

= $1760

Thus,

The initial amount of the investment is $800.

The investment grows at the rate of 10% each year.

The value of the investment after 12 years is $1760.

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The number of acres in a landfill is given by the function A=3000e−0. 05t, where t is measured in years. How many acres will the landfill have after 9 years? (Round to the nearest acre. )
Is this exponential growth or decay?

Answers

A function A = 3000 e^(-0. 05t) is an exponential decay function.

And the landfill after 9 years =  1912.8 acres

From given information, the number of acres in a landfill is given by the function A = 3000 e^(-0. 05t), where t is measured in years.

To find:  the landfill after 9 years

Substitute t = 9 years in above function.

A = 3000 × e^(-0. 05t)

A = 3000 × e^(-0.05 × 9)

A = 3000 × e^(-0.45)

A = 3000 × 0.6376

A = 1912.8                 .............(1)

Substitute t = 9 years in given function.

A = 3000 e^(-0. 05t)

A = 3000 × e^(-0.05 × 0)

A = 3000 × e^(0)

A = 3000 × 1

A = 3000

This means, initially a landfill was 3000 acres.

From (1) we can observe that after 9 years, the landfill is  1912.8    acres.

A landfill has been reduced.

So, a function is exponential decay function.

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What is the x-intercept of the graph of y x2 − 4x 4?

Answers

The x-intercept for the graph of y is found to be at x = 2.

Define the term x-intercept?The points where such a line crosses an axis are known as the x-intercept and the y-intercept, respectively.The graph's intersection with the x-axis is known as the x-intercept.Therefore, the y coordinate would be zero at that time.

The quadratic equation given is

y = x² - 4x + 4

Put y = 0

0 = x² - 4x + 4

It becomes perfect square for (x - 2).

It can be written as;

(x - 2)² = 0

Take square root on the both sides

x - 2 = 0

x = 2

Thus, the x-intercept for the graph of y is found to be at x = 2.

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The correct question is-

What is the x-intercept of the graph of y = x² - 4x + 4?

Solve the Linear system by using substitution.

y= -3x -1
4x+3y=2

Answers

The solution for the given system of equations is (-1, 2).

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of linear equations are y=-3x-1 ------(I) and 4x+3y=2 ------(II).

Substitute y=-3x-1 in equation (II), we get

4x+3(-3x-1)=2

4x-9x-3=2

-5x=5

x=-1

Substitute x=-1 in equation (I), we get

y=-3(-1)-1

y=2

Therefore, the solution for the given system of equations is (-1, 2).

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Is gram equal to mole?

Answers

No, 1 gram is not equal to 1 mole. The numerical values of mole and gram are different for an object.

What is 1 gram?

Avogadro number of atoms makes up one mole. It is possible to convert a mole into grams if you know the mole quantity.

Mole: The International System of Units uses the mole (symbol: mol) as the unit of material quantity. How many elementary entities of a particular substance are present in an object or sample is determined by the quantity of that material. It is specified that the mole contains exactly 6.02214076×10²³ elementary entities.

The relation between  gram  and mole is

1 gram = Mole × atomic weight.

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I don't understand help

Answers

Volume of the triangle is 1420m³ given in the question.

What is Volume?

There are various volumes for various geometric shapes. Cubes, cuboids, spheres, cylinders, cones, etc. are examples of common 3D shapes that we encounter on a daily basis.

Finding the volume is simple when dealing with shapes with a flat surface, like a cube or a cuboid. Cones, cylinders, and spheres are examples of curved shapes, and it is necessary to take into account both their curved surfaces' dimensions and their overall curvature. Possibly their diameters or radii

The term "irregular solids" refers to solids that lack precise measurements or shapes. A fixed formula that can be used to calculate the volumes of such solids is typically absent. It is possible to obtain these volumes in a variety of ways, one of which is the liquid displacement method, which is based on the Archimedes Principle.

Now volume triangle = area × height

⇒ 1/2 × 20 × 14.2 × 10

= 1420m³

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What does ∈ mean in math?

Answers

This is a symbol in mathematics that represents "to the power of" or "exponent".

It is used to indicate that a number or expression is being multiplied by itself a certain number of times. For example, if the expression 2aˆ3 is written, it means that 2 is being multiplied by itself 3 times, or 2x2x2. In other words, 2aˆ3 = 2x2x2 = 8.

The number to the right of the symbol is called the "exponent". The number or expression to the left of the symbol is called the "base". When a number is raised to the power of one, it is equal to itself. Any number to the power of zero is equal to one. The exponent can be a positive, negative, or fractional number.

Exponents are used to simplifying calculations and can be used to represent large numbers in a more concise form.

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Which angles are alternate exterior angles?


1. EFH and BCF

2. EFH and DCA

3. EFH and EFC

4. EFH and BCA

Answers

∠EFH and ∠ACD are angles of alternate exterior angles in the figure as  alternate external angles are those that are generated on the outer side of the parallel lines .

what are angles ?

When two straight lines connect at a 90° angle or are perpendicular to one another, an angle is formed. The symbol denotes a right angle. In the picture up above, many right angle formations are visible. Shapes include the correct angles. Triangles classified as right triangles have one of their internal angles at a 90 degree right angle. The three interior angles of a triangle add up to 180 degrees, so the three interior angles of a right triangle must always add up to 90 degrees because one of them is always 90 degrees.

given

The pair of angles known as alternate external angles are those that are generated on the outer side of the parallel lines but on the transverse side.

sum up to 180 degrees, you can calculate the size of the inner angle adjacent to it if you know the size of the outer angle (since together they are the angle on a straight line). The internal angles at the other two vertices are added to create the outer angle of a triangle.

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What line is parallel to 2x 3y 6 at 2 3 )?

Answers

The line parallel to the given line 2x+3y=6 is 2x+3y=13.

The general equation of a line is y=mx+c where m is the slope of the line and c is the y-intercept.

The slope of the given line 2x+3y=6 is

3y=(-2x)+6

y=(-2/3)x+2

y=mx+c where m is the slope of the line

so the slope of the given line is (-2/3)

as the slope of two parallel lines is equal so the slope of the line parallel to the given line is also (-2/3)

(y-y1)=m(x-x1) where x1 is the x-coordinate and y1 is the y-coordinate.

Here x1=2 and y1=3

(y-3)=m(x-2)

y-3=(-2/3)x+4/3

3y-9=(-2x)+4

3y+2x=13

2x+3y=13

The line 2x+3y=13 is parallel to the given line 2x+3y=6.

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Solve the system.
6x - y = -15
x+2y = 17
Enter your answer as a coordinate pair in the blank.

Answers

The coordinate pair of the given system is (-1,9)

What are coordinate pairs?

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

Define Equation.

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.

Multiply the first equation by 2 and add the equation 2(6x - y) = 2(-15)

Add the new equation 12x - 2y = -30 to the second equation

12x - 2y = -30, x+2y = 17, add the two equations to eliminate y

13x = -13

x = -1

Substitute -1 back into the equation x+2y = 17.

-1 + 2y = 17

2y = 18

y = 9

So the solution of the system is x = -1, y = 9

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What is the coefficient of x² in 2 X² x³?

Answers

The coefficient of x² in 2 x² x³ is 2 n with number.

2 x² x³

= 2 x² (x³)

= 2 x² (x  x  x)

= 2 x² x  x  x

The coefficient of x² is 2.The expression 2 x² x³ can be written as 2 x² (x³). This can be further simplified to 2 x² (x  x  x). The coefficient of x² is 2, which means that the coefficient of x² in 2 x² x³ is 2. The coefficient of a term is the numerical factor of the term, or the number that is multiplied with the term. In this case, the coefficient of x² is 2, as it is the number multiplied with x².

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