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let n>=2. Calculate the sum of the nth roots of the unity.

Prime factors  from the factors of the given numbers are as follow :

a. 256 = { 2 }

b. 361 = { 19 ]

c. 225 = { 3, 5 }

As given in the question,

Given numbers are as follow:

a. 256     b. 361     c. 225

Prime numbers are those numbers which has only two factors 1 and number itself.

Simplify given numbers to get the prime factors from the factors of the followings  are as follow:

a. 256 = 16 × 16

      = 2⁴ × 2⁴

      = 2⁸

Prime factor of 256 = { 2 }

b. 361 = 19 × 19

19 itself is prime number.

Prime factor of 361 = { 19 }

c. 225

225 = 15 × 15

      = ( 3 × 5 )²

Prime factors are { 3, 5 }

Therefore, prime factors from the factors of the given numbers are as follow :

a. 256 = { 2 }

b. 361 = { 19 ]

c. 225 = { 3, 5 }

The complete question is :

Find the prime factorization of the following:

a. 256     b. 361     c. 225

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A graph of f(x) is shown in the image below.

A graph of f(x) is shown in the image below.

The vertex form equation for g(x) is g(x) = -x²

In Mathematics and Geometry, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Since the parent function is f(x)= (x + 3)² - 2, g(x) would be created by translating f(x) three units to the right, two units up, and reflected vertically over the x-axis as follows;

f(x) = (x + 3)² - 2

g(x) = -[(x + 3 - 3)² - 2 + 2]

g(x) = -x²

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Answer:

Step-by-step explanation:

Always work from the inside out. That means we will deal with the parenthesis first: (4 - 1)

That gives us

2[32 - (3)³]. Next deal with the exponents. That gives us

2[32 - 27]. Next, the last set of parenthesis, which are actually brackets:

2[5] which then, finally, becomes 10

Order of operations...PEMDAS

Answer:

thanks me later mark me the brainliest

Answer:

y= -6x-6, I think, hope it helped

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

I took the test :)

Answer:

Explanation:

Here, we want to get the missing side length

From the question, it was said that the area is greater than 50 square units

What this mean is that the product of the width and length of the rectangle is greater than 50 square units

Therefore, the number in whch we will multiply by 6 must give us a result greater than 50 square units

The highest multiple of 6 closest to 50 is 48 while the closest multiple after 50 is 54

9 multiplied by 6 will give 54 square units

In essence, we can say that the missing side length is 9 square units

The angles that we have in the image here are:

When two angles are measured, they sum up to 180. They are said to be supplementary angles.

On the question, we have two angles that are 90 degrees on a straight line. Hence they are supplementary.

This is an angle that is at 90 degrees. We have to two right angles on the diagram that we have here.

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Based on the information, there are 25 cars with good brakes and good tires.

Total cars = 50

Cars with faulty brakes = 10

Cars with faulty tires = 15

Cars with faulty brakes and good tires = 2

Let's calculate the number of cars with good brakes and good tires:

Cars with faulty brakes or faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with faulty brakes and good tires

= 10 + 15 - 2

= 25

Cars with good brakes and good tires = Total cars - Cars with faulty brakes or faulty tires

= 50 - 25

= 25

Therefore, there are 25 cars with good brakes and good tires.

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Answer:

\(Area =6.41mi^2\)

Step-by-step explanation:

Given

\(a = 5.7\)

\(b = 9.3\)

\(c = 14^\circ\)

Required

The area of the triangle

This is calculated as:

\(Area =\frac{1}{2}* a * b * sin(c)\)

So:

\(Area =\frac{1}{2}* 5.7 * 9.3 * sin(14)\)

\(Area =\frac{1}{2}* 5.7 * 9.3 * 0.2419\)

\(Area =6.41mi^2\)

Answer:

The answer is 6.41!

Step-by-step explanation:

I took the test and this is correct

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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The percentile of the top students will be 88%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state.

The percentile of the top student is given as,

⇒ 100% - 12%

⇒ 88%

The percentile of the top students will be 88%.

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Answer:

3+jk+k^6

j=2 & k=6

substituting the values, we have

= 3+2(6)+6^3

= 3+12+216

= 231

Ans=231

Step-by-step explanation:

j=2 and k=6

Now

Answer:64

Step-by-step explanation:16 × 4

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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It would take them approximately 6.24 hours (or 6 hours and 14 minutes) to complete the order if they work together.

To solve this problem, we can use the formula:

Time = Work ÷ Rate

Time is the time it takes to complete the job, Work is the amount of work to be done, and Rate is the rate of work.

Let's assume that the amount of work to be done is 1 (it doesn't matter what unit we use as long as we are consistent).

Then, Maria's rate of work is 1/12 (she can do 1 job in 12 hours) and the new clerk's rate of work is 1/13 (he can do 1 job in 13 hours).

If they work together, their combined rate of work is the sum of their individual rates:

Rate = Maria's rate + New clerk's rate

Rate = 1/12 + 1/13

Rate = (13 + 12) / (12 x 13)

Rate = 25 / 156

So, their combined rate of work is 25/156 jobs per hour.

Now, we can use the formula to find the time it takes for them to complete the job together:

Time = Work ÷ Rate

Time = 1 ÷ (25/156)

Time = 156/25

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Answer:

Step-by-step explanation:

Comment

If you know this formula

tn = t1 + (n - 1)*d then you don't even have  to count how many odd numbers there are. If you don't know the formula, then you have to count how many odds there are between 1 and 25 inclusive. Just to save you the trouble, there are 13.

Givens

1 = t1

25 = tn

d = 2

Solution

25 = 1 + (n - 1)*2                 Subtract 1 from both sides?

25-1 = 1-1 + (n - 1)*2            Combine

24 = (n  -  1) * 2                   Divide by 2

24/2 = (n - 1)*2/2                

12 = n - 1                               Add 1 to both sides

12 + 1 = n - 1 + 1                     Combine

13 = n

Answer

So you have 13 cards that  will bring success.

Answer:

7/20 participate in art.

Answer:

7/20 hcjauwauhfehhfieafuewaueiwavibiurbviubwibvebaiubj

Answer:

80

Step-by-step explanation:

To find the value of n when d = 3, we can use the given inverse proportionality relationship between n and d²:

n ∝ 1/d²

This can also be written as:

n = k / d²

where k is a constant of proportionality.

We are given that n = 5 when d = 12. Plugging in these values into the equation, we get:

5 = k / 12²

To solve for k, we can multiply both sides of the equation by 12²:

5 * 12² = k

k = 720

Now that we have the value of k, we can use it to find the value of n when d = 3:

n = k / d²

n = 720 / 3²

n = 720 / 9

n = 80

So, the value of n when d = 3 is 80.

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

9514 1404 393

Answer:

  A' = {1, 4, 6}

Step-by-step explanation:

The complement can be found by deleting all of the members of A from U.

Here, we have highlighted the elements of A in U, so the complement is all of the elements that are not highlighted.

  U = {1, 2, 3, 4, 5, 6}

  A' = {1, 4, 6} . . . . . . . . complement of A

The unit price is $0.82

A four pack of granola costs $3.28

Hence the unit price can be calculated as follows

= 3.28/4

= 0.82

Therefore, the unit price is $0.82

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The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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The value of the third number is 25.5

An algebraic expression can be defined as an expression can be defined as an expression that consists of variables, coefficients, terms, constants and factors.

From the information given as;

Now, substitute the values, we get;

x - 9 + 2(x-9) + x = 75

expand the bracket

x - 9 + 2x - 18 + x = 75

collect like terms

x +2x + x = 75 +27

add or subtract the like terms

4x = 102

Make 'x' the subject of formula by dividing both sides by 4

x = 102/4

x = 25.5

Hence, the third number is 25.5

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Complete question

the sum of three numbers is 75 the First number is 9 less than the third the second number is 2 times the third what are the numbers. Find the third number

The three numbers are 19, 28 and 56

Word problem in mathematics is expressing mathematical problems in words. In other words, a word problem is a verbal description of a problem situation wherein one or more questions are posed, the answers to which can be obtained by the application of mathematical operations to information available in the text.

Represent the three numbers with x, y, z

x = z-9

y = 2z

x+y+z = 75

substitute 2z for y in x+y+z

2z+x+z = 75

substitute z-9 for x

2z+z-9 = 75

3z- 9 = 75

3z = 75+9

3z = 84

z = 28

y = 2z

y = 2× 28

y = 56

to find the value of x;

x = 28-9

x = 19

therefore the value of the three numbers (x,y,z) is 19, 28, 56

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Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

\(\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}\)

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

\(\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}\)

\(\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}\)

\(\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}\)

\(\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}\)

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

The northerly component of the wind blowing at 15 m/s from the South East is approximately 10.605 m/s.

To determine the northerly component of a wind blowing from the South East, we need to consider the direction from which the wind is coming and its magnitude.

A wind blowing from the South East means it is coming from the South East direction towards the opposite direction, which is the North West. Since the wind is coming from the South East, we can say it has a southeasterly direction.

To find the northerly component, we need to break down the wind vector into its north and east components. The northerly component represents the part of the wind that is directed towards the north.

If we assume that the wind is blowing at an angle of 45 degrees with respect to the North, we can use trigonometry to find the components. Since the wind is blowing at 15 m/s, we can consider it as the hypotenuse of a right triangle.

The northerly component can be found using the sine of the angle:

Northerly Component = Wind Speed * sin(Angle)

Northerly Component = 15 m/s * sin(45°)

Using the value of sin(45°) (which is √2 / 2 ≈ 0.707), we can calculate the northerly component:

Northerly Component ≈ 15 m/s * 0.707

Northerly Component ≈ 10.605 m/s

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Answer:

Answer:

a. 462

b. 49

Step-by-step explanation:

take pi as 22/7

a. volume= π r² h/3

22/7 × 3² × h/3

22/7 × 3 × h

22/7×3

cross multiply

462

b. h= 3 × v/π r²

3 × 462 over 22/7 × 3²

multiply each term by 7

7×3×7×462over22/7×3²

21×462over22×3²

21/1×462/198

= 9702/198

= 49

Given:

Number of Shares =400

Total paid=$11580

Sold stock=$29.50/share

commission=1%

Find:

a. What was the amount of the sale?

b. What was the net sale?

c. What was the profit or loss?

Explanation:

a) Amount of the sale=29.50 * 400=$11800.

commission=

b)Net sale = Amount of sale - commission

= 11800- 118 =$11682

c)Profit = Net sale - Total paid

= 11682 - 11580

= 102

\(\huge{ \mathcal{ \underline{ Answer }}}࿐\)

Cos 210° is equal to \(-Cos(30°)\)

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