how do you write a linear equation?

Hence the trigonometry identity is proved [tex]\frac{1-2cos^{2}x}{sinxcosx}=tanx-cotx\\}[/tex]

Cos2x is a key identity in trigonometry that can be expressed in a variety of ways. Many trigonometric functions, such as sine, cosine, and tangent, can be used to characterize it. Cos2x is one of the double angle trigonometric identities because the angle in question is a multiple of 2, or the double of x.

In trigonometry, Cos2x is a crucial identity that can be stated in a variety of ways. It can be described using a variety of trigonometric functions, including sine, cosine, and tangent. Considering that the angle under discussion is a multiple of 2, or the double of x, cos2x is one of the double angle trigonometric identities.

we have to prove

[tex]\frac{1-2cos^{2}x}{sinxcosx}=tanx-cotx\\}[/tex]

We can write

1-2cos²x=sin²x+cos²x-2cos²x

1-2cos²x=sin²x-cos²x

LHS

[tex]\frac{1-2cos^2x}{sinxcosx}=\frac{sin^2x+cos^2x-2cos^2x}{sinxcosx}\\\\=\frac{sin^2x-cos^2x}{sinxcosx}[/tex]

[tex]\frac{sin^2x}{sinxcosx}-\frac{cos^2x}{sinxcosx}\\\\=\frac{sinx}{cosx}-\frac{cosx}{sinx}\\\\=tanx-cotx[/tex]RHS

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1. The value of c that completes the square is c = 36.

2. The value of c that completes the square is c = 16.

What is completing the square?

In algebra, completing the square is a technique used to manipulate quadratic expressions (expressions with variables raised to the second power) into a particular form that is useful for solving equations or analyzing the properties of a quadratic function. Specifically, completing the square involves adding and subtracting a constant term to a quadratic expression to create a perfect square trinomial, which can then be factored into a simpler form.

To complete the square for the expressions 1. x² + 12x + c and 2. x² + 8x + c, we need to add and subtract a constant term that will create a perfect square trinomial.

x² + 12x + c:

We can create a perfect square trinomial by adding and subtracting (12/2)^2 = 36 to the expression:

x² + 12x + 36 - 36 + c

(x + 6)² + (c - 36)

So the value of c that completes the square is c = 36.

x² + 8x + c:

We can create a perfect square trinomial by adding and subtracting (8/2)² = 16 to the expression:

x² + 8x + 16 - 16 + c

(x + 4)² + (c - 16)

So the value of c that completes the square is c = 16.

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Answer:

A college student is buying a used car for $10,000. The student can either pay in full with cash from savings, or finance the car for 60 months at a monthly compounding interest rate of 4.25%, which

results in a monthly payment of $206.05 How much more is paid over the life of the loan versus paying in cash?

O $1,000 25

O $11,000 25

O $12,363 00

Step-by-step explanation:

You're welcome.

base area πr²=64πm²

so r=8m

h=2r=2(8)=16m

volume=πr²h

=(22×64×16)/7

=3218.2m³

it is approximately 3217.0m³

Answer:

The probability of the first marble being blue is 4/9 and the probability of the second marble being green is 2/8 (8 because the first marble you pulled out didn't get put back, therefore you only have 8 marbles to choose from now) and 2/8 in simplest form is 1/4.

"The beautiful thing about learning is that no one can take it away from you." :)

The required surface area of the cylinder is [tex]$40\pi$[/tex] square feet.

Region is the proportion of a locale's size on a surface. The region of a plane district or plane region alludes to the region of a shape or planar lamina, while surface region alludes to the region of an open surface or the limit of a three-layered object.

The formula for the surface area of a cylinder is:

[tex]$A = 2\pi r^2 + 2\pi rh$[/tex]

Where:

A = Surface area

r = Radius

h = Height

Here, r = 4 ft and h = 1 ft.

Plugging in the values:

[tex]$A = 2\pi (4^2) + 2\pi (4)(1)$[/tex]

[tex]$A = 2\pi (16) + 2\pi (4)$[/tex]

[tex]$A = 32\pi + 8\pi$[/tex]

[tex]$A = 40\pi$[/tex]

Therefore, the surface area of the cylinder is [tex]$40\pi$[/tex] square feet.

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The musical theater group should charge $14.25 per ticket to maximize revenue. To find the ticket price that maximizes revenue, we need to determine the revenue function and then differentiate it with respect to the ticket price to find the critical points.

We can then evaluate the revenue at these points to determine the maximum. Let x be the number of dollars charged for admission above the base price of $7.75, and let y be the number of tickets sold at that price. Then, the revenue function is given by:

R(x) = (1200 - 50x)(7.75 + x)

Expanding this expression, we get:

R(x) = 9300 + 650x - 50x^2

To find the ticket price that maximizes revenue, we need to find the critical points of the revenue function. We can do this by differentiating the revenue function with respect to x and setting the derivative equal to zero:

R'(x) = 650 - 100x = 0

Solving for x, we get:

x = 6.5

This means that the additional charge above the base price that maximizes revenue is $6.50. Therefore, the ticket price that maximizes revenue is:

7.75 + 6.50 = $14.25

So, the musical theater group should charge $14.25 per ticket to maximize revenue.

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The changes in the perimeters and areas are stated below

Part (a)

When each dimension of an isosceles trapezoid is multiplied by a scale factor of 3, the perimeter of the trapezoid is also multiplied by 3.

This is because the perimeter is the sum of the lengths of all the sides, and each side is scaled by a factor of 3.

Similarly, when each dimension is multiplied by a scale factor of 4, the perimeter is multiplied by 4.

Part b

When each dimension of an isosceles trapezoid is multiplied by a scale factor of 3, the area of the trapezoid is multiplied by a factor of 9.

Similarly, when each dimension is multiplied by a scale factor of 4, the area is multiplied by a factor of 16, since each dimension is scaled by a factor of 4, and the area is proportional to the square of the scale factor.

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The (+2) and (-8) in y = (x + 2)² - 8 shift the graph up two units and down eight units, respectively.

It is called quadratic because the highest degree of the equation is two. This type of equation is used to calculate the roots of a polynomial, which are the values of x where the equation equals 0.

The (+2) in y = (x + 2)² - 8 shifts the graph up two units on the y-axis.

This is because the addition of two to x before squaring it creates a quadratic equation which will create a graph which is two units higher than the graph created by the original equation.

The (-8) in y = (x + 2)² - 8 shifts the graph down eight units on the y-axis. This is because subtracting 8 from the squared term creates a graph which is eight units lower than the graph created by the original equation.

Therefore, the (+2) and (-8) in y = (x + 2)² - 8 shift the graph up two units and down eight units, respectively.

This creates a graph which is six units lower than the graph created by the original equation.

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The equation used to find the height of the stack is 2+xy and the number of bowls in a stack with a height of 14 inches is 16.

Finding the height of the stack :

To form the equation assume the number of bowls and height increased by stacking one into another with variables x and y and form the equation according to the given condition. Now use the resultant equation to find the number of bowls in the given stack.

Here we have

The diagram below shows 5 identical nesting bowls stacked one inside the other. The height of 1 bowl is 2 inches. The height of a stack of 5 bowls is 5 inches.

Part (A)

Let 'y' be the increase in the height of the stack and 'x' be the number of bowls stacked

Hence, Height of stack  = 2 + xy  

Therefore,

The equation that can be used to find the height of a stack is 2 + xy

From the given data,

Height of 5 bowls = 5 inches

=> 2 + xy = 5

=> xy = 3

Leaving the first bowl number bowls stacked = 4

=> x(4) = 3

=> x = 3/4

=> x = 0.75 inches

Part (B)

Given that height of the stack is 14 inches

Using the above equation

=> Height of stack, 2 + xy = 14

=> 2 + (0.75)y = 14

=> (0.75)y = 12

=>  y = 16

Therefore,

The equation used to find the height of the stack is 2+xy and the number of bowls in a stack with a height of 14 inches is 16.

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A teacher compares the pretest and posttest scores of students is an example of a matched-pairs design. Therefore, option d is the correct answer.

A matched-pairs design is an experimental design where the researcher analyzes the differences between two sets of data that are related.

It is used to minimize the effects of variables that are not of interest, such as individual difference.

Based on the given options,

option d : a teacher compares the pretest and posttest scores of students is an example of a matched-pairs design.

In this design, the teacher compares the students' performance before and after a specific treatment.

The design is used to minimize the differences in the individual differences in the students' academic performance is an example of a matched-pairs design.

option d is the correct answer.

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The volume of the rock is 9.5 mL.

What is the volume ?

To find the volume of the rock using water displacement, we need to subtract the initial volume of water (20 mL) from the final volume of water with the rock in the cylinder (29.5 mL). The difference between the two volumes represents the volume of the rock.

Volume of rock = Final volume - Initial volume

Volume of rock = 29.5 mL - 20 mL

Volume of rock = 9.5 mL

Therefore, the volume of the rock is 9.5 mL.

Volume is the amount of space occupied by an object or a substance. It is a three-dimensional quantity that can be measured in units such as cubic meters (m³), cubic centimeters (cm³), liters (L), or milliliters (mL), depending on the size of the object or substance being measured.

The formula for calculating the volume of a simple geometric shape, such as a cube or a sphere, can be found by multiplying the length, width, and height of the object. For more complex shapes, the volume can be calculated using methods such as water displacement, which involves measuring the amount of water displaced by an object when it is submerged in a container of water.

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Complete question is: A rock has a mass of 27.54 grams. Since it can't be measured to find its volume, water displacement is used. It is placed in a graduated cylinder with 20 mL of water. Once the rock is in the cylinder, the liquid level is 29.5 mL. the volume of the rock is 9.5 mL.

The cost of  each piece of trim is $1.63

To find the cost of one piece of trim, we can use the unitary method, which involves dividing the total cost by the number of pieces. In this case, we can use the following formula

Cost of one piece of trim = Total cost / Number of pieces

We know that Kevin bought 4 pieces of trim for a total of $6.52, so we can substitute these values into the formula

Cost of one piece of trim = $6.52 / 4

Simplifying this expression, we get

Cost of one piece of trim = $ 1.63

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The amount of tickets earned by friends playing an arcade game  is 1 ticket .

what is meaning of term   amount ?

The term "amount" generally refers to a quantity or a sum of something, often related to a numerical value. It can refer to the total value or quantity of something, such as the amount of money in a bank account

what is arcade game?

An arcade game is a type of video game that was originally designed to be played in public places, such as arcades, malls, and restaurants. These games has  gameplay mechanics

In the given question,

To regroup the amounts so that each person has the same amount, we need to find the total number of tickets earned and divide by the number of friends.

Total number of tickets earned = 0 + 0 + 0 + 1 + 1 + 2 + 3 = 7

Number of friends = 7

Each person will have the same amount of tickets if we divide the total number of tickets earned by the number of friends:

7 tickets ÷ 7 friends = 1 ticket per person

Therefore, each person should receive 1 ticket.

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Answer:

Independent: the number of cups, c, that he sells

Dependent: the amount of money, m, that he makes each day

Step-by-step explanation:

* The independent variable determines the value of the dependent variable. The number of cups of frozen juice that Richard sells each day determines the amount of money that he makes each day.

* Side note: For your information, the linear equation that models this relationship would be m = 1.25 c. You would graph that as y = 1.25 x, and since x is independent while y is dependent, you know that c is independent and m is dependent.

* Good luck completing the table! I would help out with that if I could see it!

The correct volume of the prism is 4637 cm² and the mistake that the student made is not getting the base of the prism first.

The correct volume of the prism can be gotten by first determining the base and multiplying this by height. When we apply this formula, the base of the prism will be:

6 * 9.2 * 8 * 1/2

= 220.8 cm²

Having gotten the base, we will now multiply this by the volume.

Volume = 220.8 cm²  * 21 cm

= 4637 cm²

So, the volume of the prism is equal to 4637 cm².

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Answer:

x ≈ 19,47°

Step-by-step explanation:

Use trigonometry:

[tex] \sin(∠cab) = \frac{cb}{ab} [/tex]

[tex] \sin(x°) = \frac{2}{6} [/tex]

[tex]x ≈19.47°[/tex]

Answer:

Step-by-step explanation:

x = 9

Answer:

18

Step-by-step explanation:

Remember, When finding the area of a triangle (especially a right angled one) the equation is 1/2bh or 0.5bh

Meaning we can do 6x6x0.5 = 18

The name of a function identifies it and must be used when the function is called - True

A function serves as its unique identifier and must be used when calling the function. A function in a computer language is given a name when it is created so that the user can invoke it later on in their particular code. The function is identified by its name which also serves to set it apart from similar functions with potentially different titles.

Depending on its definition, the parentheses that come after the function name may or may not contain arguments or parameters when calling a function. A function is called, executed, and its outcomes are returned to the caller code. Due to the reason that it is a crucial part of the function's definition, its name must always be employed when a function is called.

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Let the first number be x and the second number be y. Then we have:

xy/4 = 10 + 9 + 10

Simplifying the right side:

xy/4 = 29

Multiplying both sides by 4:

xy = 116

Now we need to find two numbers whose product is 116. We can start by listing the factors of 116:

1, 2, 4, 29, 58, 116

Since we are looking for two numbers whose product is 116, we can try pairs of factors until we find a pair that works:

1 x 116 = 116 (not a sum of two numbers)

2 x 58 = 116 (sum is 60, not 19)

4 x 29 = 116 (sum is 33, not 19)

So the only pair that works is:

x = 29 and y = 4

Let's check if these values satisfy the original equation:

xy/4 = 29 x 4 / 4 = 29 = 10 + 9 + 10

So the solution is x = 29 and y = 4.

The probability that he will reach out into his pocket and pull out a $10 bill each time is 1/7. The correct option is the second option 1/7

From the question, we are to determine the probability of William pulling out a $10 bill twice without replacement

The probability of pulling out a $10 bill on the first draw is 3/7, since William has three $10 bills out of a total of seven bills in his wallet.

Since William does not replace the first bill when he pulls out the second one, there will be one less bill in the wallet for the second draw. Therefore,

The probability of pulling out another $10 bill on the second draw is 2/6 (since there will be two $10 bills left out of six bills in the wallet).

Thus,

The probability that he will reach out into his pocket and pull out a $10 bill each time is

P(two $10 bill) = 3/7 × 2/6

P(two $10 bill) = 3/7 × 1/3

P(two $10 bill) = 1/7

Hence, the probability is 1/7

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The zeros of the function attached in the graph are

(-6 , 0) and (2, 0)

The zero of a quadratic graph is the point at which the graph intersects the x-axis. It is the value(s) of x for which the function f(x) equals zero. In other words, it is the value(s) of x that make(s) the quadratic equation equal to zero.

The zeros of a quadratic graph are also known as the roots, x-intercepts, or solutions of the quadratic equation.

Tracing the point where the graph cuts the x-axis we can see that it is at the point -6 on the left hand side and 2 on the right hand side.

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Rounding to the nearest whole number, we get that Carson's commute would be longer than 44 minutes about 168 times per year.

What is the normal distribution?

The normal distribution is a probability distribution that is commonly used in statistical analysis. It is a continuous probability distribution that describes a set of data that tends to cluster around a mean value, with fewer observations further from the mean.

We can use the normal distribution formula to solve this problem. Let X be the amount of time it takes Carson to commute to work in minutes.

Then we have:

X ~ N(47, 4²)

We want to find P(X > 44), the probability that Carson's commute takes longer than 44 minutes. We can standardize X using the formula:

Z = (X - μ) / σ

where μ is the mean and σ is the standard deviation. Substituting the given values, we get:

Z = (44 - 47) / 4 = -0.75

We can use a standard normal distribution table or a calculator to find the probability that Z is greater than -0.75. Using a standard normal distribution table, we find:

P(Z > -0.75) = 1 - P(Z ≤ -0.75) = 1 - 0.2266 = 0.7734

Therefore, the probability that Carson's commute takes longer than 44 minutes is 0.7734.

To find the number of times this would happen out of 217 days, we can multiply the probability by the number of days:

0.7734 * 217 = 167.9

Hence, Rounding to the nearest whole number, we get that Carson's commute would be longer than 44 minutes about 168 times per year.

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We are given that the quadratic function has the equation:

y = a(x + 6)(x - 2)

To find the value of a, we can use the fact that the function passes through the point (3, 36). This means that when x = 3, y = 36. Substituting these values into the equation, we get:

36 = a(3 + 6)(3 - 2)

36 = 9a

a = 4

Therefore, the value of a is 4.

Step-by-step explanation:

Question 6,

x+3=2x-23

x- 2x=-23-3

-1x=-26

x=26

The maximum number of tickets the theater can sell is 39,572.

The maximum number means the greatest amount of something possible.

The theater sale each weekend is 761 tickets.

There are eight weekend days in a month and in case the month starts with a Saturday or a Sunday there can be an additional weekend.

To calculate the maximum number of tickets the theater can sell in 1 year, we can multiply the maximum number of tickets sold per weekend by the number of weekends in a year, which is 52.

So, 761 tickets x 52 weekends = 39,572 tickets

Therefore, the maximum number of tickets the theater can sell in 1 year is 39,572 tickets.

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Therefore , the solution of the given problem of unitary method comes out to be [tex]a_n-1[/tex] and [tex]a_n[/tex] is the nth word in the sequence.

A unitary approach is a mathematical problem-solving methodology that includes determining the value or quantity of a single unit or a fraction of a single unit and then utilizing that value to determine the value or quantity of a greater or lesser number of units.

This generally recognized ease, preexisting variables, and any significant elements from the initial Diocesan customizable query may all be used to complete the task. If so, your may have another chance to interact alongside the item. Otherwise, all important influences on how algorithmic proof acts will be eliminated.  

Here,

The museum will have 75 items when it opens, and 3 more pieces will be added each month. The numerals in the pattern for the following eight months are as follows:

=> 75 + 3 = 78

=>  78 + 3 = 81

=>  81 + 3 = 84

=>  84 + 3 = 87

=>  87 + 3 = 90

=>  90 + 3 = 93

=>  93 + 3 = 96

=>  96 + 3 = 99

Each number is 3 more than the one before it, which is another pattern that can be seen in the numerals. With a common difference of three, the series is an arithmetic one. This pattern can be represented numerically as:

=> [tex]a_n = a_{n-1} + 3[/tex]

where the preceding term is called [tex]a_n-1[/tex] and [tex]a_n[/tex] is the nth word in the sequence.

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the cut-off dollar amount for being in the top 3% of patients is approximately $487.32.

To find the cut-off dollar amount for being in the top 3% of patients visiting the emergency room for a sore throat, we need to use the normal distribution with a mean of $320 and a standard deviation of $89.
Find the z-score for the top 3%
To find the z-score, we can use a z-table, which provides the area under the curve of the standard normal distribution. Since we want to find the top 3%, we will look for 0.97 (1 - 0.03) in the z-table. The z-score corresponding to 0.97 is approximately 1.88.
Convert the z-score to a dollar amount
Now that we have the z-score, we need to convert it to a dollar amount using the mean and standard deviation. The formula for this is:
X = μ + (z * σ)
Where X is the dollar amount, μ is the mean ($320), z is the z-score (1.88), and σ is the standard deviation ($89).
Calculate the cut-off dollar amount
Using the formula from Step 2, we can now calculate the cut-off dollar amount:
X = 320 + (1.88 * 89)
X = 320 + 167.32
X ≈ 487.32

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Answer:

2. 1

3. [tex]\dfrac{x(x + 2)(x - 4)}{(x - 2)^2}[/tex]

Step-by-step explanation:

2.

[tex] \dfrac{x^2 - 81}{x + 81} \times \dfrac{x^2 + 81x}{x^3 - 81x} = [/tex]

Multiply the fractions together by multiplying the numerators and multiplying the denominators.

[tex] = \dfrac{(x^2 - 81)(x^2 + 81x)}{(x + 81)(x^3 - 81x)} [/tex]

Factor every numerator and denominator.

[tex] = \dfrac{(x + 9)(x - 9)x(x + 81)}{(x + 81)x(x^2 - 81)} [/tex]

[tex] = \dfrac{(x + 9)(x - 9)x(x + 81)}{(x + 81)x(x + 9)(x - 9)} [/tex]

Now divide the numerator and denominator by terms common to both. This is what is commonly called canceling terms in the numerator and denominator. Every term in the numerator has an equal term in the denominator. All terms cancel out leaving 1.

[tex] = 1 [/tex]

3.

Since you have a division here, first, multiply the first fraction by the reciprocal of the second fraction. Then factor the numerator and denominator and cancel out common terms.

[tex] \dfrac{x^2 + 4x}{x - 2} \div \dfrac{x^2 + 2x - 8}{x^2 - 2x - 8} = [/tex]

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

[tex] = \dfrac{x^2 + 4x}{x - 2} \times \dfrac{x^2 - 2x - 8}{x^2 + 2x - 8} [/tex]

[tex] = \dfrac{(x^2 + 4x)(x^2 - 2x - 8)}{(x - 2)(x^2 + 2x - 8)} [/tex]

Now factor every factorable expression.

[tex]= \dfrac{x(x + 4)(x + 2)(x - 4)}{(x - 2)(x + 4)(x - 2)}[/tex]

Now cancel equal terms in the numerator and denominator.

[tex]= \dfrac{x(x + 2)(x - 4)}{(x - 2)(x - 2)}[/tex]

[tex]= \dfrac{x(x + 2)(x - 4)}{(x - 2)^2}[/tex]