1/4 (8x plus 2) = 20

Answer:

Step-by-step explanation:

(a) Using de Moivre's Theorem, we have that:

z^n = cos(nθ) + i sin(nθ)

1/z^n = cos(-nθ) + i sin(-nθ)

So, we can find z^n + 1/z^n as:

z^n + 1/z^n = (cos(nθ) + i sin(nθ)) + (cos(-nθ) + i sin(-nθ)) = 2 cos(nθ)

And z^n - 1/z^n as:

z^n - 1/z^n = (cos(nθ) + i sin(nθ)) - (cos(-nθ) + i sin(-nθ)) = 2i sin(nθ)

(b) To express the equation 2z^4 - 5z^3 + 7z^2 - 5z + 2 = 0 in terms of cos(θ), we can substitute z with cos(θ) + i sin(θ):

2(cos(4θ) + i sin(4θ)) - 5(cos(3θ) + i sin(3θ)) + 7(cos(2θ) + i sin(2θ)) - 5(cos(θ) + i sin(θ)) + 2 = 0

Expanding the right hand side using the trigonometric identities, we get:

2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0

Note that the real and imaginary parts are separate, so we can simplify this equation to a real equation by equating the real and imaginary parts to 0.

(c) To solve the equation 2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0, we can use numerical methods or analytical methods such as the roots of unity.

Once the roots are found, they can be represented on an Argand diagram by plotting the real and imaginary parts of each root as a point in the complex plane. The magnitude of each point represents the magnitude of the complex number, and the argument (angle) represents the argument of the complex number.

Answer:

Step-by-step explanation:

To simplify the expression X^(12/7) * Y^(35/7) into its simplest form, we need to find the greatest common divisor (GCD) of the exponents 12/7 and 35/7 and divide both exponents by the GCD. Here's the step-by-step process:

Find the GCD of 12/7 and 35/7. To do this, we'll use the Euclidean algorithm method:

a. Divide the larger number, 35, by the smaller number, 12, and get the remainder: 35 ÷ 12 = 2 with a remainder of 11.

b. Divide the smaller number, 12, by the remainder, 11, and get the quotient and remainder: 12 ÷ 11 = 1 with a remainder of 1.

c. The last non-zero remainder, 1, is the GCD of 12/7 and 35/7.

Divide both exponents by the GCD, 1:

a. X^(12/7) becomes X^(12/7 ÷ 1) = X^12.

b. Y^(35/7) becomes Y^(35/7 ÷ 1) = Y^35.

Replace the original exponents in the expression with the simplified exponents: X^12 * Y^35.

So, the expression X^(12/7) * Y^(35/7) is simplified as X^12 * Y^35, which is written as a single radical in its simplest form.

[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ x^{\frac{12}{7}}y^{\frac{35}{7}}\implies \left( x^{12} y^{35} \right)^{\frac{1}{7}}\implies \sqrt[7]{x^{12} y^{35}}\implies \sqrt[7]{x^{7+5} (y^5)^7} \\\\\\ \sqrt[7]{x^7 x^5 (y^5)^7}\implies {\Large \begin{array}{llll} x y^5\sqrt[7]{x^5} \end{array}}[/tex]

Answer: To calculate the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.

20Y1:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share

Common Stock: $6,000 / 50,000 shares = $0.12 per share

20Y2:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share (cumulative preferred stock means that if the company misses a dividend, they still have to pay it in the future, so the dividends per share remain the same)

Common Stock: $45,000 / 50,000 shares = $0.90 per share

20Y3:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share

Common Stock: $0 (there is no information about dividends for the common stock in 20Y3)

So, the dividends per share for each year would be:

20Y1:

Preferred Stock: $2.00 per share

Common Stock: $0.12 per share

20Y2:

Preferred Stock: $2.00 per share

Common Stock: $0.90 per share

20Y3:

Preferred Stock: $2.00 per share

Common Stock: $0.00 per share

Step-by-step explanation:

19.375 pounds is the weight of bike.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that the  frame of a bike weighs16 pounds.

each tire weighs 9 ounces.

In a bike there are 2 tires, so total weight of tires is 2×9=18 ounces.

The seat weighs 12 ounces

The handlebars weigh 24 ounces.

Convert the ounces to pounds.

We know that 1 pound=16 ounces

So The total number of weight in ounces is 18+12+24=54 ounces

Divide by 16 to convert 54 ounces to pounds

54/16=3.375

Now total weight=16+3.375 pounds

=19.375

Hence, 19.375 pounds is the weight of bike.

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Millimeter is the best unit to define the radius of the pencil.

The distance from a circle's centre to any point on its periphery is known as the radius. The radius of a circle is also known as the distance separating any two points on the circle from its centre. The radius of a circle is the separation between its centre and circumference. Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.

The smallest unit of measurement is the millimetre. There are a thousand millimetres in a metre, and a dime is somewhat thicker than a millimetre. When measuring anything's length in metric units, you'll be working with meters and variants on meters, including millimeters.

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Option (c) is correct answer.

(C) DE = 12, DF = 16 and m∠D = 35

which states, length of DE is 12 units , length of DF is 16 units and m/D=35 degrees.

If two figures possess the same shape but not necessarily the same size, they are considered to be similar. We may remark that all circles are similar as an example. Equilateral triangles and squares are similar to one another. Although similar figures need not be congruent, all congruent figures are similar.

Property 1:

Two triangles are similar if their respective sides have the same ratio and their corresponding angles are equal.

Property 2:

The corresponding angles of two similar triangles will have equal values . Equiangular triangles are what they are called.

Now by property 1,

The pairs of  corresponding sides of similar triangles are proportional .

Therefore, in the given triangles,

[tex]\frac{AB}{DE} =\frac{AC}{DF} \\\\\frac{AB}{AC} =\frac{DE}{DF} \\\\\frac{9}{12} =\frac{DE}{DF} \\\\\frac{3}{4} =\frac{DE}{DF}[/tex]

Therefore, in the given options, option (c) satisfies the condition.

Hence, DE = 12 , and DF = 16.

By property 2 we know that , corresponding angles of similar triangles are equal.

hence, /A=/D

therefore, /D=35.

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[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hfill \begin{array}{llll} \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{6x^{-1}y^{-1}}{\sqrt[4]{xy^4}}\implies \cfrac{6}{x^1 y^1 \left( xy^4 \right)^{\frac{1}{4}}}\implies \cfrac{6}{x^1 y^1 \left( x^{\frac{1}{4}}y^1 \right)}\implies \cfrac{6}{x^1x^{\frac{1}{4}} y^1 y^1} \\\\\\ \cfrac{6}{x^{1+\frac{1}{4}} y^{1+1}}\implies \cfrac{6}{x^{\frac{5}{4}} y^2}\implies {\Large \begin{array}{llll} \stackrel{a\quad b \quad ~~ c}{6x^{-\frac{5}{4}}y^{-2}} \end{array}}[/tex]

Answer:

Step-by-step explanation:

Adjacent angles is defined as

Opposite,congruent angles formed when two lines intersect.

Answer:

Answer is in the attached photo

Step-by-step explanation:

The solution is in the attached photo, do take note to find the value of y, we will have to make y the subject.

Answer:

Step-by-step explanation:

To determine whether an ordered pair is a solution to a system of equations or inequalities, we need to substitute the values for x and y into each equation or inequality and see if the resulting expression is true. If it is true for all of the equations or inequalities, then the ordered pair is a solution to the system.

Here's the step-by-step process for each ordered pair:

(1,3):

Substitute x = 1 and y = 3 into y < 4x - 1: 3 < 4(1) - 1 = 3 < 3, which is true.

Substitute x = 1 and y = 3 into y > x: 3 > 1, which is true.

Since both inequalities are true, the ordered pair (1,3) is a solution to the system y < 4x - 1 and y > x.

(0,0):

Substitute x = 0 and y = 0 into y < 4x - 1: 0 < 4(0) - 1 = -1, which is false.

Substitute x = 0 and y = 0 into y > x: 0 > 0, which is false.

Since at least one inequality is false, the ordered pair (0,0) is not a solution to the system y < 4x - 1 and y > x.

y=mx+b

m=slope

b= y-intercept

x=6

y=-5

-5= -1/3(6)+b

-5= 2+b

-2       -2

      -7    =  b

y= -1/3x-7

Answer:

y=-1/3x-3

Step-by-step explanation:

Answer:

1. 18 + 35

2. 6 * 50

3. b - 25

4. x / 4

5. t + 11

6. 100 - k

Step-by-step explanation:

If you get a new job, outline the forms you will have to deal with to file your taxes. The form has to fill in Form W-9 sent by the employer and given use to file your taxes.

The company determines what information to include in the Form 1098 or Form 1099 based on the information provided on the Form W-9.

Information about taxpayers is gathered using Form W-9 to assist with informational reporting to the IRS.

Although it is utilised in other contexts as well, the Form W-9 is most frequently employed when working with businesses that employ independent contractors.

The form requests that a taxpayer enter their name, residence, tax bracket, and withholding specifications.

Therefore, from the following conditions are:

1. Outline the forms you will need to file your taxes if you get a new job. Form W-9 must be completed and returned to the employer in order to file your taxes.

A W-2 will be given to you detailing your profits. New employees are frequently required to complete a Form W-4 rather than a Form W-9 in order to supply their company with information about their taxpayers.

2. Gross income is all income from whatever source derived that is not excluded or deferred from income. AGI is gross income minus "for AGI" deductions. Taxable income is AGI minus "from AGI" deductions.

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Answer:The answer is 20000

Step-by-step explanation:

The actual width and length of the bedroom are respectively; 9 ft and 12 ft

The parameters are given as;

Width of house = 30 feet = 360 inches

Length of house = 45 feet = 540 inches

Scale drawing width of house = 4 inches

Scale drawing length of house = 6 inches

Thus;

Scale factor width = 360/4 = 90

Scale factor length = 540/6 = 90

Scale drawing width of bedroom = 1.2 inches

Scale drawing length of bedroom = 1.6 inches

Thus;

Actual width of bedroom = 1.2 inches * 90 = 108 inches or 9 ft

Actual length of bedroom = 1.6 inches * 90 = 144 inches or  12 ft

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The equation that we want to write is:

193n - 242 = 131

Here we want to write the sentence:

"242 fewer than the quantity 193 times n equals 131"

As an equation.

The first part means that we need to take a number n, multiply it by 193, and then subtract 242.

193n - 242

And that must be equal to 131, then the equation is:

193n - 242 = 131

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The decimal number is -5.690134489..... irrational number. Therefore, option C is the correct answer.

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). Also, the decimal expansion of an irrational number is neither terminating nor repeating.

Here,

-9.121212121212......

This decimal number is non terminating, but repeating

So, the decimal number is rational number

-1.5000000000.....

This decimal number is non terminating, but only zeros are repeating

So, the decimal number is rational number

-5.690134489.....

This decimal number is non terminating and non repeating

So, the decimal number is irrational number

-9.121212121212....

This decimal number is non terminating, but repeating

So, the decimal number is rational number

Therefore, option C is the correct answer.

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The value of x are:

1)

81/2

2)

33/4

3)

13

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

First question:

Since QS is the angle bisector.

We can write as,

PQ/PS = RQ/RS

45/20 = x/18

9/4 = x/18

x = 18 x 9 / 4

x = 9 x 9/2

x = 81/2

Second question:

Since QS is the angle bisector.

We can write as,

PQ/PS = RQ/RS

22/8 = x/6

11/4 = x/6

x = 6 x 11 / 4

x = 66/4

x = 33/4

Third question:

Since QS is the angle bisector.

We can write as,

PQ/PS = RQ/RS

21/15 = (5x - 16)/(3x - 4)

7/5 = (5x - 16)/(3x - 4)

7(3x - 4) = 5(5x - 16)

21x - 28 = 25x - 80

80 - 28 = 25x - 21x

52 = 4x

x = 13

Thus,

The value of x is 81/2, 33/4, and 13.

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Tony can afford the car insurance, and he has enough money($426.33) left over each month to cover other expenses.

Automobile, truck, motorbike, and other types of road vehicles are covered by vehicle insurance. Its main purpose is to offer financial security against property loss or personal injury brought on by auto accidents, as well as against liability that can emerge from related events.

According to the information given,

Tony's yearly pay is $8,320

and his monthly pay is $693.

If we round his yearly pay to $8,000, his monthly car insurance will be 1/30 of that amount, or $266.67.

Since Tony's monthly pay is $693, and his monthly car insurance will cost $266.67, he can afford the insurance. He will have $426.33 remaining each month after paying for the insurance.

Therefore, Tony can afford the car insurance, and he has enough money left over each month to cover other expenses. However, this calculation assumes that Tony has no other major expenses or debts, and it is always a good idea to budget carefully and consider all potential costs before making a significant purchase.

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The polygon DEFG is translated 3 units left to get F'(1, 6)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane. Translation is a rigid transformation that preserves the shape and size.

Polygon DEFG has coordinates D(2, 5), E(3, 1), F(4, 6), and G(6, 6). The polygon is translated 3 units left to get F'(1, 6)

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The product of two rational numbers is 1 . A . Rational number because multiplying two rational numbers is equivalent to the ratio of 3 . Two integers which is 1 . a rational number .

The product of two rational numbers is always a rational number. This is because a rational number is defined as a number that can be expressed as the ratio of two integers.

When you multiply two rational numbers, you are simply multiplying two ratios, which is still a ratio and therefore a rational number.

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The required value of C is 3 which makes 16x² - 24x + C a perfect square.

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.

The expression is given in the question, as follows:

16x² - 24x + C

(4x)² - 24x + C

As we know that the factoring identity:

(a - b)² = a² - 2ab + b²

After comparing, we have a = 4x and 2ab = 24x

Solving for b:

2(4x)b = 24x

b = 24x/8x

b = 3

So 16x² - 24x + 3 = (4x - 3)²

This means the required value of C is 3 which makes a perfect square.

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The probability that in a given week in September, it will rain on at most two days is 0.12.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The probability that it rains on any given day in September = 0.3.

P ( rains ) = 0.3

And,

The probability that it will not rain on any given day in September.

P (no rain) = 1 - 0.3

P(no rain) = 0.7

Now,

The probability is that in a given week in September, it will rain on at most two days.

= P (x ≤ 2)

= P(no rain) + P(rain) + P(rain)

= 0.7 + 0.3 + 0.3

= 0.12

Thus,

The probability that in a given week in September, it will rain on at most two days is 0.12.

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If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. This way, credit cards can be safer than cash.

What is credit card?

A credit card is a small plastic payment card that is provided by a person's bank and enables the cardholder to pay a merchant for products and services depending on the cardholder's accumulated debt.

To be on the safe side in the event that a merchant breaches an agreement, a cardholder may contact the credit bureau to resolve the disputed charges.

So, this way credit cards can be safer than cash.

Hence, option C is the correct solution.

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The average rate of change of the function f(x) over the interval (-1, 2) is; 3.

As evident in the task content; the given function is as represented by the graph of f(x).

Hence, the average rate of change of the function over the given interval; (-1, 2) is;

= ( f (2) - f (-1) ) / (2 - (-1))

where; f (2) = 5 and f (-1) = -4.

Therefore, the average rate of change is;

= (5 - (-4)) / (2 - (-1))

= 9 / 3.

= 3.

Ultimately, the difference quotient of f (x) over the given interval is; 3.

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√55 and √40 are the irrational numbers.

A number system is defined as a system of writing to express numbers.

A rational number is the one which can be represented in the form of P/Q where P and Q are integers and Q ≠ 0.

But an irrational number cannot be written in the form of simple fractions.

√55 is an irrational number

√40 is an irrational number

√49 value is 7 which is a natural number

Hence, √55 and √40 are the irrational numbers.

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You cannot construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm, as the sum of the lengths of the two smaller sides is not greater than the length of the larger side.

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

The lengths for this problem are given as follows:

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