show that, given one nth root of z, the others are obtained by multiplying it by the nth roots of unity. (z is complex number)

the equation of the required line is 3xâ2y+1=3x1â2y1+1.

(i) We are given the parallel line of the given equation, that is yâ2x=0.

So, the equation of the required line will be yâ2x=c, where c is a constant.

Let the point of intersection of the two lines be (x1, y1).

Then, substituting the values of x1 and y1 in the equation yâ2x=c, we get

y1â2x1=c

or, c=y1â2x1

Hence, the equation of the required line is yâ2x=y1â2x1.

(ii) We are given the perpendicular line of the given equation, that is 2x+yâ5=0.

So, the equation of the required line will be 3xâ2y+1=c, where c is a constant.

Let the point of intersection of the two lines be (x1, y1).

Then, substituting the values of x1 and y1 in the equation 3xâ2y+1=c, we get

3x1â2y1+1=c

or, c=3x1â2y1+1

Hence, the equation of the required line is 3xâ2y+1=3x1â2y1+1.

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Hey there!

Answers;

For part (a):

[tex]v=669,883[/tex]  [tex]miles/day[/tex]

[tex]r=44,423[/tex] [tex]miles[/tex]

[tex](a)V=rw[/tex]

[tex]w=\frac{v}{r}[/tex] [tex]=\frac{669883}{44423}[/tex][tex]=15.0796[/tex] [tex]radians/day[/tex]

[tex]15[/tex] [tex]radians/day[/tex]

For part (b):

[tex]Circumference=2\pi r[/tex]

[tex]2*3.14*44423[/tex]

[tex]278976*44[/tex]

Number of rotations = [tex]\frac{669883}{278976*44}[/tex] =  [tex]2*40[/tex] ⊥ ≈ [tex]2[/tex]

Hence:

(a) [tex]15[/tex] [tex]radiations/day[/tex]

(b) Number of rotations = [tex]2[/tex]

___________________________________________

Hope this helps! If you mark Brainliest, TYSM! :D

Yes, these numbers meet the triangular inequalities, then these can be the measures of the sides of a triangle.

Remember that if A, B, and C are the sides of a triangle, then the triangle inequality says that:

A + B > C

A + C > B

C + B > A

As long as 3 values are solutions of the inequalities, then these can be the sides of a triangle.

if we use:

A = 7

B = 10

C = 10

Then we get:

7 + 10 > 10 ---> 17 > 10

7 + 10 > 10 ---> 17 > 10

10 + 10 > 7 ---> 20 > 7

All the ienqualities are true, thus, these can be the measures of the sides of a triangle.

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A two variable linear equation means an equation having two variables. It is usually represented as ax+by =c. We can solve a two variable linear equation in many ways.

If the linear equation is only given, to solve it we have to calculate the x-intercept and y-intercept. It is one way of solving a two variable linear equation. Lets look into an example.

 2x+5y = 19

The x intercept is when y=0,

then, 2x+ (5×0) = 20

          2x = 20, x=10

y intercept is when x=0, then

2×0 + 5y = 20

   5y = 20,  y= 20/5 =4

So, by solving the equation, we get x=10 at x intercept and y=4 at y intercept.

If one the values are given , we can substitute it in the equation to calculate the other variable.

In the equation, 2x+3y= 12, if y=2, we can calculate by substituting.

    2x + (3×2) = 12

     2x = 12-6

     2x = 6

      x =3

So when y=2 then x=3.

Constraints are the restrictions on the domain of a linear equation, like a number of days or students should be a positive integer.

So, we can solve a two variable linear equation through different ways.

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Since function f andg are continuous and u g subseteq u f, Theorem 2.1.13 states that f circ g is continuous on u g.

In accordance with Theorem 2.1.13, if two functions,f andg, are continuous on open domains [tex]$u f$[/tex]and [tex]$u g$[/tex] respectively, and $g(u g)subseteq u f, then $ circ g is continuous on u g. This is the case since the domain of f, which is u g is a subset of the domain of f, which is u g, and the composition of continuous functions is continuous. The composition of these two functions will be continuous onu g because both of these functions are continuous and u g subseteq u f.

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Answer: 7

Step-by-step explanation:

Patricia has  6 cans of almonds that each contain eight 1/3 cup servings, meaning that Patricia has a total of

6 cans x 8 servings x 1/3 cup = 16 cups of almonds

If she needs 2.25 cups of almonds, that would be equal to

16/2.25 = around 7.1

since you can't have a fraction of a snack bag, Patricia just has 7 snack bags.

The two expressions are written as :

3f+4s+2f this expression that we have here is a mathematical expression that we can  combine by making use of the commutative addition.

We would have the first expression when we write the equation as:

3f+4s+2f = 3f + 2f + 4s

We would have the second expression when we write the equation as

5f + 4s

This is the solution of the expression.

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two expressions that are equivalent to 3f+4s+2f ?

The market share of the vape machine market had sales of $1.4M is given as 63.57%.

To calculate the brand's market share, you would need to divide the brand's sales by the total sales of the market and then multiply by 100 to get the percentage.

In this case, the brand's sales are 10000 units x $89/unit = $890,000.

So the market share would be:

$890,000 / $1,400,000 x 100 = 63.57%.

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Step-by-step explanation:

x² - y² = (x + y)(x - y)

3x - 3y = 3(x - y)

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

Answer:

x^2 - y^2

_______

3x - 3y

(x+y) (x-y)

_______ { (x-y) (x-y) cancels out}

3(x-y)

(x+y)

____

3

Hope this will help you...!!!!

Out of the given vectors is in the span of the other vectors,  b. One of the vectors is in the span of the other vector. Since u and v have the same last component, they are linearly dependent, so u is in the span of v and w.

If a set of vectors is linearly dependent, then one of the vectors can be expressed as a linear combination of the other vectors. This means that one vector is in the span of the other vectors. In this case, u can be expressed as a linear combination of v and w, so u is in the span of the other vectors.  

To check for linear dependence, we can first check for a zero row in the matrix formed by the vectors. If there is a zero row, then the vectors are linearly dependent. In this case, the last row of the matrix formed by the vectors is [3,3,0], which is a zero row, so the vectors are linearly dependent.  We can also check for linear dependence by computing the determinant of the matrix formed by the vectors.

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A line that is parallel to y = -4x + 11 and goes through the point (2, 1) in point slope form is: A. y - 1 = -4(x - 2).

Mathematically, the point-slope form of a line is modeled by this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the given linear equation y = -4x + 11, the slope is given by:

y = -4x + 11

m₁ = -4

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ (m represents the slope.)

At point (2, 1), an equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -4(x - 2)

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The numbers that correctly complete the two-way table are 100,70, 170, 80, 130, 210, 180,200, and 380 as shown in the attached chart.

Total of sweatshirts= 380

Total with no hood= 210

Green sweatshirts= 180

Purple sweatshirts with no hood= 70

Based on this information we can conclude:

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A man who is 1.853m tall would have a z-score of  1.297.

Generally, To find the z-score for a man who is 1.853m tall, we need to use the formula for a z-score:

= (x - mean) / standard deviation.

In this case, the mean height for men is 1.757m and the standard deviation is 0.074m, so the z-score for a man who is 1.853m tall would be:

(1.853 - 1.757) / 0.074 = 1.297297297

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The expression of the side length is 6y - 5

The complete question is added as an attachment

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

Perimeter = 48y - 40

Number of sides = 8

The side length s can be calculated as

s =(48y - 40)/8

Evaluate the quotient

s = 6y - 5

Hence, the side length expression is 6y - 5

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Method 2 is the best option for estimating the average yearly income of the class of 2005.

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Answer:

see attached

Step-by-step explanation:

The critical values for a one-sample t test given the following conditions are  +1.796, -1.796 2. -2.60 3. +2.576, -2.576 4. +1.729.

Value is a term used in many different contexts to refer to the worth or importance of something. It is used to describe the worth of an item or service in terms of its utility, its ability to satisfy a need or desire, or its usefulness in exchange. Value can also refer to the worth of an individual or group in terms of their contribution to society or their inherent worth. Value is subjective and can vary greatly from one person or group to another.

1. +1.796, -1.796
2. -2.60
3. +2.576, -2.576
4. +1.729

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One integral element that defines sport and distinguishes it from play and dramatic spectacle is the concept of competition.

In sports, there are typically opponents or teams competing against each other to achieve a goal or win a match.

This competitive aspect is not present in play or dramatic spectacles, where the focus is typically on individual or group performance rather than competition against others.

Sports are defined as physical activities that involve a set of rules and are typically competitive in nature. They are typically organized and played by people in order to achieve a goal or win a match. Examples of sports include football, basketball, soccer, tennis, baseball, and golf.

Sports are also a form of recreation, entertainment, and physical activity. They can be played individually or in teams. They help to improve physical fitness, and mental health and also promote teamwork and social interaction.

Therefore, One integral element that defines sport and distinguishes it from play and dramatic spectacle is the concept of competition.

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So, the height of the pedestal is ((h1−h2)tanβ+h2tanα)/tanα−tanβ.

To find the height of the pedestal, we can use the concept of angles of elevation. The angle of elevation is the angle between the horizontal line of sight and the line of sight to an object above the horizontal.

From the given information, we know that the angles of elevation of the top and bottom of the statue from a point h2 metres above the ground level are α and β respectively.

We can use the tangent of the angle of elevation to find the height of the object. The tangent of the angle of elevation is equal to the height of the object divided by the distance from the base of the object to the point of observation.

Let's call the height of the pedestal as "h3"

So we can write the following equations:

h1/((h3+h1)-h2)= tan(α)

h1/((h3)-h2)= tan(β)

By solving the above equations we can get the value of h3 which is the height of the pedestal.

((h1−h2)tanβ+h2tanα)/tanα−tanβ

This is the final equation which gives the height of the pedestal.

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Answer: THE CORRECT ANSWER IS 30  

Step-by-step explanation:

After divide, the value of quotient is 0.133.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

⇒ 10 divided by 75.10.

Now, We get;

⇒ 10 divided by 75.10

⇒ 10 ÷ 75.10

⇒ 0.133

Thus, The value of quotient after divide = 0.133

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The average velocity (in m/s) over the given time intervals is [1,2]

Part A.

Keep in mind that the formula for average velocity is

(Y2 - Y1)/V avg = displacement/time interval (t2 - t1)

Given that the rock's position at time t is determined by:

y = 16t - 1.86*t^2

Part 1

for the time period [1, 2]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*2 - 1.86*22 = 24.56 m when t2 = 2 sec.

So

average Velocity = (24.56 - 14.14)/(2 - 1) (2 - 1) = 10.42 m/s V avg

Part 2.

for the time period [1, 2]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.5 - 1.86*1.52 = 19.815 m when t2 = 1.5 sec.

So,

average Velocity  = (19.815 - 14.14)/(1.5 - 1) (1.5 - 1) = 11.35 m/s V avg

Part 3.

During the period [1, 1] .1]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.1 - 1.86*1.12 = 15.3494 m when t2 = 1.1 sec.

So,

average Velocity  = (15.3494 - 14.14)/(1.1 - 1) (1.1 - 1)

average Velocity = 12.094 m/s and equals 12.09 m/s (In two decimal places)

Part 4.

During the period [1, 1] .01]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.01 - 1.86*1.012 = 14.262614 m when t2 = 1.01 sec.

So,

average Velocity = (14.262614 - 14.14)/(1.01 - 1) (1.01 - 1)

12.26 m/s and V avg = 12.2614 m/s (In two decimal places)

Part 5.

During the period [1, 1] .001]

Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.

Y2 = 16*1.001 - 1.86*1.0012 = 14.15227814 m when t2 = 1.001 sec.

So,

average Velocity = (14.15227814 - 14.14)/(1.001 - 1) (1.001 - 1)

12.28 m/s V avg = 12.27814 m/s (In two decimal places)

Part B.

Rock's immediate velocity will be determined by:

d[16t - 1.86t2]/dt = V= dy/dt

Velocity = 16*1 - 2*1.86*t

time = 1 second,

Velocity = 16 - 2*1.86*1

average velocity at time t is equal to V = 12.28 m/s.

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The measure of the side length n is equal to 14 for the right triangle.

Considering the larger acute angle, if we represent it by θ then for the bigger right triangle with adjacent m and hypotenuse 28+7= 35;

cosθ = m/35

for the smaller right triangle with adjacent 7 and hypotenuse m

cosθ = 7/m

m/35 = 7/m

m² = 245 {cross multiplication}

m = √245 = 7√5 {take square root of both sides}

(√245)² = 7² + n² {by Pythagoras rule for the smaller right triangle}

245 = 49 + n²

n² = 245 - 49 {collect like terms}

n² = 196

n = √196 {take square root of both sides}

n = 14

Therefore, the measure of the side length n is equal to 14 for the right triangle

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The charge of each company will be the same at 40 miles.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let us suppose the miles travelled as x.

Given that:

Cassandra's Car Rentals charges $.10 per mile with a service fee of $40.00, this is represented as:

C = 0.10(x) + 40

Carnuba's Car rental charges $.15 per mile and has a service of $20.

D = 0.15(x) + 20

The charge of both the companies would be equal when C = D:

0.10(x) + 40 = 0.15(x) + 20

40 -20 = 0.15x = 0.10x

20 = 0.5x

x = 20/ 0.5

x = 40

Hence, the charge of each company will be the same at 40 miles.

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Answer:

your question is 6=1/v+2

Step-by-step explanation:

6-2=1/v

4v=1

v=1/4

Answer:

47.21

Step-by-step explanation:

Subistitute:-47.4-0.19

Calculate the sum or difference:-47.21

The comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.

Suppose that [tex]$\sum_{n=1}^{\infty} a_{n}$ and $\sum_{n=1}^{\infty} b_{n}$[/tex] are series with positive terms. We assume that does not exist and that [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex]diverges.

To prove that [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] also diverges, we will use the comparison test. Since [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex] diverges, we can find a number M such that [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges. Since [tex]$\lim_{n\rightarrow \infty} \frac{a_{n}}{b_{n}}$[/tex] does not exist, we can find a number N such that for all [tex]$n \geq N$, $\frac{a_{n}}{b_{n}} > 1$[/tex].

Now, for any [tex]$n \geq \max \{M,N\}$[/tex], we have [tex]$\frac{a_{n}}{b_{n}} > 1$[/tex]. Thus, [tex]$a_{n} > b_{n}$[/tex]. By the comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.If the ratio of two series with positive terms,[tex]$\sum_{n=1}^{\infty}a_n$[/tex]  and [tex]$\sum_{n=1}^{\infty}b_n$[/tex], does not converge to a limit as n approaches infinity and [tex]$\sum_{n=1}^{\infty}b_n$[/tex] diverges, then [tex]$\sum_{n=1}^{\infty}a_n$[/tex] must also diverge.

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The radian measure of A = 170° as an exact fraction that contains the π symbol is; ¹⁷/₁₈π

When we want to convert the value of an angle in degree, to its equivalent radians, what we need to do is to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.

Thus, since we want to find the radian measure of 170 degrees, it means that;

If 180° = π radians,

then; 170° = (170 * π)/180

= ¹⁷/₁₈π

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The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.

The unit tactic is a strategy for addressing issues that entails first figuring out the value of a particular unit, then increasing that value to figure out the needed value. Simply put, the unit method is employed to obtain a minimum unit value from a multiple that is supplied. For example, 40 pens may cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its homologue and reciprocal are equal in terms of mathematics, algebra, linear algebra, applied mathematics, or mathematics for matrices or operators.

given

1 pound = 16 ounces

for 2 packages

2 pounds 10 ounces + 4 pounds 12 ounces

6 pounds and 22 ounces

= 7 pounds 10 pounces

The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.

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Answer: yes

Step-by-step explanation:

It's right angled if and only if A^2 + B^2 = C^2

- a^2 = (11-3^2 + 11-5^2) = (64 + 36) = 100

- b^2 = (6-3^2 + 1-5^2) = (9 + 16) = 25

a^2 + b^2 = 125 = sqrt(125)^2