prove that cos 2theta - cos 4theta + cos 6theta - cos 12theta = 4 sin 3theta sin 5theta cos 4theta

Explanation:

This problem is a simple percent chage problem. The absoluge change in price was $12−$8=$4. Relative to the original price, it was 412, which is 0.3333 or 33.33%.

Answer:

X = 5

Y = 2

Step-by-step explanation:

y=2x-8

x-4(2x-8)=-3 -> x-8x+32=-3 -> -7x = -35 -> x=-35/-7 = 5

x=5 -> y=2x-8 -> y=2(5)-8=2

Answer:

x=5  y=2

Step-by-step explanation:

Answer: 117

Step-by-step explanation:

first i found x which is 13

4x+11=6x-15

   +15     +15

4x+26=6x

-4x       -4x

  2x=26

26÷2 2÷2

x=13

then i just put 13 nto the equation and got

m<B=117

if you know how to please mark brainlyest!

Answer:

The equation that matches the table is y = -5x + 7 ⇒ C

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m =  \(\frac{y2-y1}{x2-x1}\) , where

From the given table

→ Choose any two points from the table

∵ Points (0, 7) and (1, 2) are in the table

∴ x1 = 0 and y1 = 7

∴ x2 = 1 and y2 = 2

→ Substitute them in the rule of the slope above

∵ m = \(\frac{2-7}{1-0}=\frac{-5}{1}\)

∴ m = -5

→ Substitute it in the form of the equation above

∵ y = -5x + b

∵ b is the value of y at x = 0

∵ At x = 0, y = 7

∴ b = 7

∴ y = -5x + 7

∴ The equation that matches the table is y = -5x + 7

The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.

To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.

We are given that the area of the square is 25, so we can find the side length of the square:

Area of square = \(s^2 = 25\)

Taking the square root of both sides, we get:

s = √25 = 5

Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:

Diagonal = Diameter = s√2 = 5√2

The radius of the circle is half the diameter, so:

Radius = 5√2 / 2 = (5√2)/2

Now, we can calculate the area of the circle using the formula:

Area of circle = \(\pi r^2\)

Substituting the value of the radius, we get:

Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2

Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.

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Answer: 71

Step-by-step explanation: 100x (5\7) = 71.4

Answer:

71.5

Step-by-step explanation:

5/7 of 100=(5×100)÷7=500÷7=71.5

The equation y² - y²x = 6  can be describe as a function of x as:

y = √(6/(x - x)).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y² - y²x = 6

Taking y² as common.

y²(1 - x) = 6

Divide both sides with (1 - x).

y² = 6/(1 - x)

Square root on both sides.

y = √(6/(x - x))

This is a function of x.

Thus,

y = √(6/(x - x)) is a function of x.

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Answer: y=1.25

Step-by-step explanation:

First things first you have to find what is in the bracket things (i don’t know what it’s called) So 3 - 7 is -4y but since it’s absolute it’s going to be 4y.

So now you’ve got 4y - 10 = -5. Your going to want to eliminate 10 so, subtract 10 to both sides giving you 4y = -5

Lastly to get y by itself you need to divide it by its self so, 4y divided by 4. Do it to both sides. This gives you…

Y = 1.25

To factor the expression, we need to identify any common factors that can be pulled out of the terms.

The terms g²r and 9²₂² have a common factor of g². The terms 6g²rs²t and -6g²rs²t have a common factor of -6g²rs²t. The term 5422 does not have any factors in common with the other terms.

Therefore, the expression can be factored as:

(-6g²rs²t)(g²r + 9²₂²) + 5422

This is the fully factored form of the expression.


????

Using the z-distribution, it is found that the 95% confidence interval is (0.45 , 0.52), and it does not provide strong evidence against that belief.

A confidence interval of proportions is given by:

\(\pi\) ± \(z\sqrt{\frac{\pi (1-\pi )}{n} }\)

where \(\pi\) is the sample proportion, z is the critical value and n is the sample size.

In this problem, we have 95% confidence level, hence \(\alpha\) = 0.95, z is the value of Z that has a p-value of \(\frac{1+0.95}{2}\) = 0.975, so the critical value is z = 1.96

We have that a random sample of 860 births in a state included 423 boys, hence the parameters are given by:

n = 864, \(\pi =\frac{423}{860}\) = 0.49

Then the bounds of the interval are given by:

\(\pi\) + \(z\sqrt{\frac{\pi (1-\pi )}{n} }\) = 0.49 + \(1.96\sqrt{\frac{0.49(0.513)}{860} }\) = 0.52

\(\pi\) - \(z\sqrt{\frac{\pi (1-\pi )}{n} }\) = 0.49 - \(1.96\sqrt{\frac{0.49(0.513)}{860} }\) = 0.45

The 95% confidence interval estimate of the population of boys in all births is (0.45 , 0.52). Since the interval contains 0.513, it does not provide strong evidence against that belief.

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Answer:

x = 2.4

Step-by-step explanation:

4x + 5 / x + 7
combine like terms

X + 4x = 5x

5 + 7= 12

12/ 5x

Divide

12 /5= 2.4

X= 2.4

Experience shows that few students hand in their statistics exams early and most prefer to hand them in near the end of the test period. This means that the time taken by students to write exams is positively skewed.

In statistics, a positively skewed (or right-skewed) distribution is a type of distribution in which most values are clustered around the left tail of the distribution while the right tail of the distribution is longer. The positively skewed distribution is the exact opposite of the negatively skewed distribution.

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Answer:

4x²+1 which is the answer

When all liabilities have been paid for a business, what is left over are referred to as the stockholders' equity.

After all liabilities have been paid, a company's residual assets are referred to as its stockholders' equity. This amount is computed by deducting total liabilities from total assets, or alternatively, by adding share capital and retained earnings and deducting treasury stock.

Total Assets - Total Liabilities = Shareholders' Equity

The aforementioned equation is known as the fundamental accounting equation and is fairly simple to apply. The value of all obligations is subtracted from the total amount of assets on the balance sheet.

SE is therefore the owners' remaining claim to the assets after all debts have been paid. Total assets less total liabilities gives a company's shareholder equity. Shareholder equity includes retained earnings as well as any invested capital.

The complete question is:

Statement of stockholders' equity

The revenues and expenses of Paradise Travel Service for the year ended May 31, 20Y6, follow:

Fees earned $900,000

Office expense 300,000

Miscellaneous expense 15,000

Wages expense 450,000

Everett McCauley invested an additional $40,000 in the business in exchange for common stock, and $10,000 of dividends were paid during the year. Common stock had a balance of $60,000 and retained earnings had a balance of $300,000 as of June 1, 20Y5.

Prepare a statement of stockholders' equity for the year ended May 31, 20Y6.

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When all liabilities have been paid for a business, what is left over are referred to as the stockholders' equity.

After all liabilities have been paid, a company's residual assets are referred to as its stockholders' equity. This amount is computed by deducting total liabilities from total assets, or alternatively, by adding share capital and retained earnings and deducting treasury stock.

Total Assets - Total Liabilities = Shareholders' Equity

The aforementioned equation is known as the fundamental accounting equation and is fairly simple to apply. The value of all obligations is subtracted from the total amount of assets on the balance sheet.

SE is therefore the owners' remaining claim to the assets after all debts have been paid. Total assets less total liabilities gives a company's shareholder equity. Shareholder equity includes retained earnings as well as any invested capital.

The complete question is:

Statement of stockholders' equity

The revenues and expenses of Paradise Travel Service for the year ended May 31, 20Y6, follow:

Fees earned $900,000

Office expense 300,000

Miscellaneous expense 15,000

Wages expense 450,000

Everett McCauley invested an additional $40,000 in the business in exchange for common stock, and $10,000 of dividends were paid during the year. Common stock had a balance of $60,000 and retained earnings had a balance of $300,000 as of June 1, 20Y5.

Prepare a statement of stockholders' equity for the year ended May 31, 20Y6.

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Answer:

Step-by-step explanation:

4/mx

if b is the span of the given vectors, so we can express b as the linear combination of the other given two vector.

given that,

\(a_{1} =\left[\begin{array}{ccc}-1&\\3&\\-1\end{array}\right] , a_{2} =\left[\begin{array}{ccc}-2\\-3\\6\end{array}\right] , b=\left[\begin{array}{ccc}-6\\9\\2\end{array}\right] \\\\\\\\\\\\\\\\\\\\\\\\\)

We have determined that b is span of given vector a1 and a2.

we can write.   \(a_{1} =(-1,-3,-1) ,a_{2}=(-2,-3,6) , b=(-6,9,2)\) .

A vector is a quantity that has magnitude and direction.

if x,y,z...., v are vectors and a,b,c....k are scalars then the linear combination is ax+by+cz+......+kv  

The set of linear combinations is called span for set of vectors.

So, b is span of given vector.

\(b=(c)a_{1} +(d)a_{2}\)   ...... equation (A)

where c and d are scalars.

Now,

\((-6,9,2)=c(-1,3,-1)+d(-2,-3,6)\\(-6,9,2)=(-c,3c,-c)+(-2d,-3d,6d)\\(-6,9,2)=(-c-2d,3c-3d,-c+6d)\\\)

equating the equations,

\(-c-2d=-6\\3c-3d=9\\-c+6d=2\\\)

now we shall solve the above linear equations.\(subtract \\-c-2d-(-c+6d) = -6-2\\-8d=-8\\d=1\\now, \-c=-6+2d\\c=6-2=4\\c=4\)

So, value of scalars c, d satisfied equation A,

thus, b is span of given vector a1 and a2.

The complete question is.

Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors. a1=[-1 3 -1], a2=[-2 -3 6]= [-6 9 2]

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Answer: A

In looking for solutions in the graph of y=f(x) where f(x) = 0, you're looking for the x-intercepts.  The catch is that you only want the x-value of the intercepts.

The intercepts are (-4,0) and (7,0), so the solutions are -4 and 7.

Answer:

She would have scored 75 points.

Step-by-step explanation:

Points scored in a basketball game vary directly with shots taken.

This means that this question can be solved by proportions, using a rule of three.

How many would she have scored if she takes 60 shots?

Using a rule of three:

50 points - 40 shots

x points - 60 shots

Applying cross multiplication:

\(40x = 50*60\)

Dividing both sides by 40

\(x = 50*1.5 = 75\)

She would have scored 75 points.

The unit of the rate of change is (b) dollars per month

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

The table of values

Where we have

y = total amount in dollars

x = number of months

The rate of change is calculated as

Rate  = y/x

substitute the known values in the above equation, so, we have the following representation

Rate = total amount in dollars/number of months

So, we have

Unit = dollars per month

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Answer:

42

Step-by-step explanation:

42÷6 = 7

If you want to find out on your own, you can do 6 * 7 and get 42

Answer:

The value of the third side  c = 12.52

Step-by-step explanation:

Step(i):-

Given thatΔABC is a right angle triangle

                                     AB =  a = 6

                                     BC = a =11

                         Find    AC = ?

Step(ii):-

By using Pythagorean theorem

                               AC² = AB²+BC²

                      ⇒    c² = 6² +11²

                      ⇒  c² = 36 +121

                       ⇒  c² = √157

                           c = 12.52

The value of the third side  c = 12.52

Answer:

Step-by-step explanation:

Describe a functiDescribe a function that takes an input, adds 2, and then multiplies by 4on that takes aDescribe a function that takes an input, adds 2, and then multiplies by 4n inpDescribe a function that takes an input, adds 2, and then multiplies by 4ut, adds 2, and then multiplies by 4

Answer:

1/6  

Step-by-step explanation:

8x - 34 and 5x + 2 are corresponding angles and, by the Corresponding Angles Theorem, are congruent.

8x - 34 = 5x + 2
8x - 34 + 34 = 5x = 2 + 34
8x = 5x + 36
8x - 5x = 5x + 36 - 5x
3x = 36
3x/3 = 36/3
x = 12

figure A :

step 1: multiply

3 x 4 x 4 x5=240m

figure B:

step 1: add

17+12+5+ 15=49cm

Answer:

Answer D

Step-by-step explanation:

The answer here is D since all of the other ones have at least one option that is perpendicular to segment EF.

Answer:

Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.

Step-by-step explanation:

The given equation is:

-x + 3y = 11

To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.

Let's suppose we have another equation with x, for example:

2x + 5y = 7

We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:

-2x + 6y = 22 (multiply the first equation by -2)

2x + 5y = 7 (the second equation)

Now we can add the two equations to eliminate x:

-2x + 2x + 6y + 5y = 22 + 7

Simplifying the equation, we get:

11y = 29

Dividing both sides by 11, we get:

y = 29/11

Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

-x + 3y = 11

Substituting y = 29/11, we get:

-x + 3(29/11) = 11

Simplifying the equation, we get:

-x + 87/11 = 11

Subtracting 87/11 from both sides, we get:

-x = 11 - 87/11

Multiplying both sides by -1, we get:

x = 87/11 - 11

Simplifying the equation, we get:

x = (87 - 121)/11

x = -34/11