If the term of a sequence increases in value what is true about the common difference

The correct option C: r = √(√3)² + (√3)² = √6; θ  = arctan (1) = π/4.

The complex number z=x+iy is represented by the rectangular coordinates (√3,√3) and polar coordinates (6,π/4) respectively.

The polar coordinates r (a radial coordinate) and in Cartesian space (the angular coordinate, generally termed as  polar angle),

x = rcosθ  .....(1)

y = rsinθ,  .....(2)

where is indeed the counterclockwise angle first from x-axis and r is the radial distance to the origin. Considering x and y,

r² = x² + y²  ...eq 3

θ  = arc tan (y/x)

Using the polar coordinates explanation from above, we can deduce that;

r² = x² + y²  .

r² = √3² + √3²  .

r = √(√3)² + (√3)²

and

θ  = arc tan (√3/√3) = arctan (1) = π/4.

Thus, the complex number z=x+iy is represented by the rectangular coordinates (√3,√3) and polar coordinates (6,π/4) respectively.

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The compete question is attached.

1/2 is the scale factor from the cliff in the drawing to the actual cliff.

A scale factor is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller. The scale factor is 2 because the length of each of the sides has been multiplied by 2. If this is reversed: The scale factor is 1/2 because the length of each of the sides has been divided by 2.

A scale factor of 1/2 means that the new shape is half the size of the original shape.

Scale factor = Larger figure dimensions ÷ Smaller figure dimensions

The scale factor for scaling up is always greater than 1. Scaling down means that a larger figure is reduced to a smaller one. The scale factor of a dilated figure is denoted by 'r' or 'k'.

If the scale factor is more than 1, the image is enlarged.

If the scale factor is less than 1, the image is contracted.

If the scale factor is 1 (k = 1), the image remains the same.

The scale factor cannot be zero.

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The correct description will be;

⇒ y = - 2x + 3

4x + 2y = 6

These are independent.

⇒ y = -2x + 3

4x + y = 9

These are consistent.

⇒ y = -2x+3

4x + 2y = 9

These are inconsistent.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expressions are,

1. y = -2x+3

4x + 2y = 6

2. y = -2x+3

4x+y=9

3. y = -2x+3

4x + 2y = 9

Now,

From (1);

1. y = -2x+3

4x + 2y = 6

⇒ 2x + y = 3

4x + 2y = 6

⇒ 2x + y = 3

So We get;

⇒ 2/2 = 1/1 = 3/3

⇒ 1/1 = 1/1 = 1/1

These are independent.

From (2);

1. y = -2x+3

4x + y = 9

⇒ 2x + y = 3

4x + y = 9

So We get;

⇒ 2/4 ≠ 1/1

⇒ 1/2 ≠ 1/1

These are consistent.

From (3);

1. y = -2x+3

4x + 2y = 9

⇒ 2x + y = 3

4x + 2y = 9

So We get;

⇒ 2/4 = 1/2 = 3/9

⇒ 1/2 = 1/2 ≠ 1/3

These are inconsistent.

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If points d and f are on side ab and points e and g are on side ac then line segments de and fg are parallel

What are parallel lines?

Parallel lines are those lines that do not meet at any point. If we draw a triangle ABC and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle

Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.

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Answer:

To find the value of r₂, we need to know how the dilations with scale factors r₁ and r₂ affect the coordinates of the point P.

If a dilation with scale factor r₁ maps a point P with coordinates (x, y) to another point P' with coordinates (x', y'), then the coordinates of P' are related to the coordinates of P by the equation:

x' = r₁x

y' = r₁y

Similarly, if a dilation with scale factor r₂ maps a point P' with coordinates (x', y') to another point P'' with coordinates (x'', y''), then the coordinates of P'' are related to the coordinates of P' by the equation:

x'' = r₂x'

y'' = r₂y'

Since we are given that the dilations map P to P and P' to P, we can set the coordinates of P and P'' equal to each other, and the coordinates of P' and P'' equal to each other. This gives us the following system of equations:

x'' = x

y'' = y

x'' = r₂x'

y'' = r₂y'

Substituting the second set of equations into the first set, we get:

x = r₂x'

y = r₂y'

Since we know that the dilation with scale factor r₁ maps P to P', we can substitute the equations for x' and y' into the above equations to get:

x = r₂*(r₁x)

y = r₂(r₁*y)

Solving for r₂, we find that:

r₂ = 1/r₁

Substituting the value of r₁ = 1/4, we find that:

r₂ = 1/(1/4) = 4

So the value of r₂ is 4.

The solution to the given simultaneous equations are;

x = 5/3 and y = 7/3

We are given the two simultaneous equations as;

x + y = 4  

y = 2x -1

Rearranging the second equation to have all the variables on one side gives; 2x - y = 1

Thus, we have the equations;

x + y = 4   ------(1)

2x - y = 1    -----(2)

Add eq 1 to eq 2 to get;

3x = 5

divide both sides by 3 using division property of equality to get;

x = 5/3

Put 5/3 for x in eq 1 to get;

⁵/₃ + y = 4

y = 4 - ⁵/₃

y = ⁷/₃

Thus, those are the solutions to the simultaneous equations.

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Answer:

The common ratio is 2.

Answer:

Step-by-step explanation:

Plutonium is a radioactive element that is known to release large amounts of energy through the process of nuclear fission. When a nucleus of plutonium atom is split, it releases a tremendous amount of energy in the form of heat, light, and radiation. This energy is released through a chain reaction, in which the energy from one fission event is used to trigger the fission of additional atoms, releasing even more energy. The heat energy produced by plutonium can be harnessed and used in various ways, such as generating electricity or powering spacecraft.

It is important to note that the behavior of plutonium depicted in the movie "Martian" may be based on scientific concepts, but it may also include fictional elements and may not be entirely accurate or realistic. It is important to remember that fictional works are not necessarily scientifically accurate and should not be taken as fact.

The plutonium emit neutrons as a few of its nuclei spontaneously undergo nuclear fission, which is the reason behind the heat generation.

Given is a dug out plutonium.

Plutonium - 238, Pu - 240 and Pu - 242 emit neutrons as a few of their nuclei spontaneously undergo nuclear fission, albeit at a low rate. This is the reason why plutonium acts as a source of heat energy for Matt Damon and helped him save the fuel.

Therefore, the plutonium emit neutrons as a few of its nuclei spontaneously undergo nuclear fission, which is the reason behind the heat generation.

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Answer:

20

Step-by-step explanation:

When you have two minuses, it will result in a plus.

Answer:

it's 20

Step-by-step explanation:

i just hv to know the sign

Step-by-step explanation:

add 100degrees to 15 degrees to get 115degrees. Subtract 180 degrees to 115degrees to get the missing angle which will be 65 degrees

The ratio of boy to girl who play kickball at race is 6 to 2. There are 18 girl on the team. the number of boys who play kickball at race is 12 boys.

The ratio of boy to girl who play kickball at race is 6 to 2

6 boys: 2 girls

Multiply the number of girls by the ratio:

18 girls x (6 boys / 2 girls) = 18 x 3 = 54

Subtract the number of girls from the total to get the number of boys:

54 - 18 = 36

Therefore, there are 12 boys who play kickball at race.

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Ana should choose option (a) because she pays the least in interest.

To determine which option would be the most cost-effective for Ana, you need to consider the total amount of interest she would pay over the course of the loan.

Option (a) is monthly simple interest, which means that the interest is calculated on the principal balance of the loan at the end of each month, based on the annual interest rate. Option (b) is quarterly compound interest, which means that the interest is compounded and added to the principal balance of the loan at the end of each quarter. Option (c) is continuous compound interest, which means that the interest is compounded continuously, rather than at fixed intervals.

Using the formula for simple interest, the total amount of interest that Ana would pay over the course of the loan under option (a) is:

$166.25 = $5,000 * 3.99% * 10

$10.6375 she tip if she wants to give a 23% tip of the whole bill when  tab for the nice supper that Kristyn and her sister had was $ 46.25.

Given that,

The tab for the nice supper that Kristyn and her sister had was $ 46.25.

We have to find how much should she tip if she wants to give a 23% tip of the whole bill.

We know that,

The tab for the nice supper that Kristyn and her sister had was $ 46.25.

So,

23% tip of the whole bill is

=$ 46.25×23%

=10.6375

Therefore, $10.6375 she tip if she wants to give a 23% tip of the whole bill when  tab for the nice supper that Kristyn and her sister had was $ 46.25.

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Each color pencil in the first case costs $0.12. Each color pencil in the second case costs $0.11. The cheapest pencil is in the second case.

The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value. The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to achieve the required value.

Here,

Cost of 24 color pencil=$2.88

Cost of 1 color pencil=$2.88/24

=$0.12

Cost of 18 color pencil=$1.98

Cost of 1 color pencil=$1.98/18

=$0.11

The cost of each color pencil from first case is $0.12. The cost of each color pencil from second case is $0.11. The second case has cheapest pencil.

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To make a 30% alcohol solution, you would need to add 20 liters of 20% alcohol solution to 40 liters of 50% percentage alcohol solution.

50 liters of 50% alcohol solution = 50 liters x 0.50 = 25 liters of pure alcohol

40 liters of 50% alcohol solution = 40 liters x 0.50 = 20 liters of pure alcohol

Total pure alcohol = 25 liters + 20 liters = 45 liters

Required pure alcohol to make a 30% solution = 30 liters

Difference in pure alcohol = 30 liters - 45 liters = -15 liters

Add 20% alcohol solution to make up the difference = -15 liters/0.20 = 75 liters of 20% alcohol solution.

Therefore, 75 liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% percentage solution.

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Según el método de diferenciales, el cambio aproximado del volumen del prisma es aproximadamente igual a 60 centímetros cúbicos.

Las diferenciales son una generalización del concepto matemático de cambio para funciones de una o más variables. Las versiones de una sola variable involucran derivadas ordinarias, mientras las versiones multivariables utilizan derivadas parciales.

El volumen del prisma es igual al producto del área de la base (A), en centímetros cuadrados, y la altura (h), en centímetros.

V(h, A) = h · A

El área de la base es igual al área de un cuadrado, es decir:

A(x) = x²

Donde x es la longitud del lado, en centímetros.

Según el enunciado, la altura del prisma es constante, mientras la longitud del lado de la base es una variable. En consecuencia, tenemos un diferencial que emplea derivadas ordinarias, esto es:

ΔV = (dV / dx) · Δx

V(x) = 15 · x²

dV / dx = 30 · x

Si sabemos que x = 10 cm y Δx = 0.02 cm, entonces el cambio en el volumen del prisma es:

ΔV = 30 · (10 cm)² · (0.02 cm)

ΔV = 60 cm³

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The percentile rank of score 71 on the test is 26.7 and The score of the 60th percentile on the test is 84.

The figure that a particular percentage falls within is referred to as the percentile. For instance, 80% of the kids in a group of 20 are shorter than you, and Ben is the fourth tallest.

Given:

58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

Calculate the percentile of score 71 as shown below,

[tex]Percentile= n / N \times 100[/tex]

Here, n is the number of scores below 71 and N is the total number of scores,

Percentile = 4 / 15 × 100

Percentile = 0.267 × 100

Percentile = 26.7 percentile

Therefore, the percentile rank of score 71 on the test is 26.7

(B)

Substitute the value in the formula given below,

60 = n / 15 × 100

n / 15 = 60 / 100

n = 0.6 ×  15

n = 9

Thus, the 9th term here is 84,

Therefore, the score of the 60th percentile on the test is 84.

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probability that exactly 5  customers pay in cash  is 0.178863

Total number of customer = 20

probability of payment in cash = 0.3

probability of payments via other methods  = 1 - 0.3 =0.7

let probability of payment in cash be p

and probability of payments via other methods be q

To find the probability that exactly y customers pay in cash

p [ x = y ] =  [tex]n_c__x p^x q ^(n-x)[/tex]

here value of y= 5 and n=20 , p =0.3 , q= 0.7

putting the values in above equations we get:

p [ x =5 ] = [tex]20_c__5 * 0.3 ^5 * 0.7 ^15[/tex]

p [ x =5 ] = (15504) * (0.00243) * (0.0047475615)

p [ x =5 ] = 0.178863

so the probability that exactly 5  customers pay in cash  is 0.178863

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Answer:

Step-by-step explanation:

i think i answered another question by you but ill help anyways

ok so you are trying to check the fact that x=2 for both equations

for A. by using substitution

and B. by properties of Equality

A is easy you just substitute 2 into the x values in the given equations

it will look like

-3x+14=18-5x

-3(2)+14=18-5(2)

-6+14=18-10

8=8

and

2x=5-1/2x

2(2)=5-1(2)/2

4=5-2/2

4=5-1

4=4

so now we have proved that both x are eual to 2 by using substitution

i already answered b on a different question

The congruent angles of the statements are;

∠1 + ∠3 = 180° by Vertical angles theorem.

∠5 + ∠6 = 180° by Linear pair theorem.

∠1 + ∠3 = ∠5 + ∠6 by both are supplementary angles.

∠3 = ∠6 by consecutive interior angles

∠1 = ∠5 by corresponding angles.

We want to prove that ∠1 = ∠5.

Corresponding angles; When two parallel lines are intersected by another line, corresponding angles are the angles that are created in matching corners or corresponding corners with the transversal.

From the given question, we see that;

∠1 + ∠3 = 180°: This is because ∠1 and ∠3 are vertical angles by the vertical angles theorem.

∠5 + ∠6 = 180°: This is because ∠5 and ∠6 are linear pairs by the Linear pair theorem.

∠1 + ∠3 = ∠5 + ∠6 ; 180° = 180° ; Both are supplementary angles.

∠3 = ∠6 ; Consecutive interior angles

Now, ∠1 = ∠5, Corresponding angles.

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Electric company charges 7.50 dollars for the first 50 kWh, 10 dollars for the next 50 kWh, 13.50 for the next 100 kWh, 18.50 for the next 100 kWh, 20 dollars for the next 100 kWh and 25 dollars for any kWh over 400.

Electric companies charge customers for the amount of energy they consume, measured in kilowatt-hours (kWh). The cost for each kWh can vary depending on the amount of energy consumed. An electric company may charge 7.50 dollars for the first 50 kWh, 10 dollars for the next 50 kWh, 13.50 for the next 100 kWh, 18.50 for the next 100 kWh, 20 dollars for the next 100 kWh and 25 dollars for any kWh over 400. The higher rate for higher usage reflects the fact that larger consumers of electricity tend to drive up the cost of production and distribution for the company. In addition, electric companies may offer discounts to customers who use more than a certain amount of electricity each month, encouraging conservation and helping to reduce costs.

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Complete Question  is

Economic The table how cot in dollar charged by an electric company for

variou amount of energy in kilowatt-hour

Kilowatt-Hour  Cost in Dollars

0-50 .            7.50

50-100.          10.00

100-200.      13.50

200-300.       18.50

300-400.       20.00

400+.                25.00

Answer:

To solve this equation, we need to perform the operations in the correct order according to the order of operations. The order of operations is a set of rules for determining the sequence in which operations should be performed in a mathematical expression to get the correct result. The order of operations is typically abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Applying the order of operations to the given equation, we first need to evaluate the expression inside the parentheses, which is 3(x - 6). To do this, we need to subtract 6 from x, which gives us 3(x - 6) = 3(11 - 6) = 3(5) = 15. Next, we need to multiply the result of this operation by 3, which gives us 3 * 15 = 45. Therefore, the final result of the equation is 45.

Here is how you can solve the equation step by step:

1. Evaluate the expression inside the parentheses: 3(x - 6) = 3(11 - 6) = 3(5) = 15

2. Multiply the result of the previous step by 3: 3 * 15 = 45

Therefore, the final result of the equation is 45.

Step-by-step explanation:

inverse of function

-

f (x) = 7(x - 5) + 1

y = 7x - 34

x = (y + 34) / 7

g (x) = (x + 34) / 7

____

Answer:

y=16-3x

Step-by-step explanation:

change in x /change in y

Answer:

answer in the picture... .

The rate of increase of the y-coordinate as it approaches the point (1, 5) is 4 cm/s.At that instant, the x-coordinate of the point is not changing; it is staying at 1.

When a point reaches a certain coordinate, it means that the point is not changing anymore. In this case, the point has reached the coordinate (1, 5), which means that the x-coordinate (1) is not changing, while the y-coordinate (5) is increasing at a rate of 4 cm/s. Therefore, the x-coordinate of the point is not changing at that instant.

x = 1

Rate of Change (x-coordinate) = 0 cm/s

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Answer:

19x20

Step-by-step explanation:

The area of a rectangle is given by the formula A = l * w, where l is the length and w is the width of the rectangle. In this case, we are given that the area of the rectangle is 380 square meters and that the length and width of the rectangle are consecutive integers.

We can use this information to create a system of equations to solve for the length and width of the rectangle. Let l be the length of the rectangle and w be the width of the rectangle. Since the length and width of the rectangle are consecutive integers, we have:

l = w + 1

Substituting this equation into the formula for the area of the rectangle, we get:

A = l * w

= (w + 1) * w

= w² + w

Since the area of the rectangle is given as 380 square meters, we can set this equation equal to 380 and solve for w:

w² + w = 380

To solve for w, we can use the quadratic formula, which is given by:

x = (-b ± √(b² - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation, and x is the solution. Substituting the values of a, b, and c into the formula and simplifying, we get:

w = (-1 ± √(1² - 4(1)(380))) / (2(1))

= (-1 ± √(-1519)) / 2

Since the length and width of the rectangle must be positive integers, we can ignore the negative solution and only consider the positive solution. Therefore, the width of the rectangle is 19.

To find the length of the rectangle, we can use the equation l = w + 1 that we derived earlier. Substituting the value of w into this equation, we get:

l = w + 1

= 19 + 1

= 20

Therefore, the length of the rectangle is 20 and the width of the rectangle is 19. The dimensions of the rectangle are 20 x 19.

To identify the congruence postulate used, you need to analyze the given information about the sides and angles of the triangles and choose the postulate that matches the given information.

It's good to use different congruence postulates to identify the congruence of triangles. To identify the congruence postulate used, you need to analyze the given information about the sides and angles of the triangles and see which postulate matches the given information.

For example, if you are given the lengths of two sides and the included angle of one triangle, and the lengths of the corresponding sides and included angle of the other triangle, you can use the SAS Congruence Theorem to conclude that the triangles are congruent. If you are given the lengths of all three sides of both triangles, you can use the SSS Congruence Theorem to conclude that the triangles are congruent.

It's also important to note that the AAS Congruence Theorem is not a valid postulate. The correct postulate is the ASA (Angle-Side-Angle) Congruence Theorem, which states that if two angles of one triangle are congruent to two angles of another triangle, and the included sides are congruent, then the triangles are congruent.

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A quadrilateral whose diagonals do not always bisect each other is a rectangle.

A rectangle is a quadrilateral with four right angles. The diagonals of a rectangle are perpendicular to each other and bisect each other, but not all quadrilaterals with perpendicular diagonals and diagonals that bisect each other are rectangles. For example, a square is a type of quadrilateral with perpendicular diagonals and diagonals that bisect each other, but it has four congruent sides and four right angles, unlike a rectangle.

The word "rectangle" comes from the Latin words "rectus," meaning "right," and "angulus," meaning "angle." This reflects the fact that a rectangle has four right angles.

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