Solve for X, Leave in simplest radical form.

We know,

[tex] \cos(angle) = \frac{base}{hypotenuse} [/tex]

Here, the angle is 45°. Base = x, Hypotenuse = √10

We know,

[tex] \cos(45) = \frac{1}{ \sqrt{2} } [/tex]

Therefore,

[tex] \cos(45) = \frac{x}{ \sqrt{10} } \\ = > \frac{1}{ \sqrt{2} } = \frac{x}{ \sqrt{10} } \\ = > x = \frac{ \sqrt{10} }{ \sqrt{2} } = \sqrt{5} [/tex]

Answer:

√5

Hope it helps.

The steps in the correct order to solve the equation: [tex]3\times 2^{(2t-5)} - 4 = 10[/tex] is given below and the solution to given equation is t = 3.625

Consider given equation: [tex]3\times 2^{(2t-5)} - 4 = 10[/tex]

We arrange the given steps in correct order to solve given equation.

Step 1:

Add 4 to each side of the equation.

⇒ [tex]3\times 2^{(2t - 5)} = 14[/tex]

Step 2:

Divide each side of equation by 3

⇒ [tex]2^{(2t - 5)} =\frac{14}{3}[/tex]

Step 3:

Take the log of each side of equation.

[tex]log 2^{(2t-5)} = log(\frac{14}{3})[/tex]

Step 4:

use the exponential property and write (14/3) in decimal form:

⇒ (2t - 5) log(2) = log(4.67)

Step 5:

Divide each side by log 2

⇒ 2t - 5 = log(4.67) / log(2)

Step 6:

Find the value of log(4.67) / log(2) and substitute  

⇒ 2t - 5 = 2.23

Step 7:

Add 5 to each side of the equation

⇒ 2t = 2.23 + 5

Step 8:

Simplify

t = 3.625

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Answer: C

Step-by-step explanation: a triangle has a measurement of 180 degrees not 120

the answer is c the measure of each angle of an Equlateral triangle in 120 °

According to the concept of differentiation the length of his shadow changing when he is 10 feet from the base of the light is 10 feet.

Here we have given that the height of man = 6 feet

And the Height of light is 15 feet

Then the Rate of walk by man is written as

=>dx/dt = 5 feet per second.

Here we have to find the rate at which the tip of his shadow is moving when he is 10 feet from the base of the light.

Here by using ratio of similar triangles we have write it as,

=> 15/y = 6/(y - x)

When we do the cross multiplication on it, then we get

=> 15(y - x) = 6y

=> 15y - 6y = 15x

=> 9y = 15x

When we dividing by 3 on both sides then we get

=> 3y = 5x

While we differentiating both sides with respect to t then we get

=> 3(dy/dt) = 5(dx/dt)

=> dy/dt = (5/3)(6)

When we simplify this one, then we get

=> dy/dt =  10 ft/s

Hence the rate at which the tip of his shadow is changing is 10 ft/s.

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The type of system of linear equations with infinitely many solutions is called a homogeneous system of linear equations.

A system of linear equations is a set of two or more equations with two or more variables that are related to each other. When a system of linear equations has an infinite number of solutions, it is called a homogeneous system of linear equations. This is because all the equations in the system are multiples of each other, so any solution of one equation is also a solution for all the other equations.

The type of system of linear equations with infinitely many solutions is called a homogeneous system of linear equations.

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Answer: g(f(10)) = g(√2x+5) = 6x-3

We need to substitute x = √2*10 + 5 into g(x) = 6x - 3

g(f(10)) = 6(√2*10 + 5) - 3 = 6√20 + 30 - 3 = 6√20 + 27

So g(f(10)) = 6√20 + 27.

The slope of the original line is 3/5.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the slope of the original line.

To find the slope of the original line, we need to convert the equation to the slope-intercept form (y = mx + b), where m is the slope.

To convert, we'll isolate y:

-3x + 5y = 20

5y = 3x + 20

y = (3/5)x + 4

The slope of the original line is 3/5. The slope of the line perpendicular to this line would be the negative reciprocal of this slope, or -5/3.

Hence, The slope of the original line is 3/5.

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The information shows that f(4)=f(30) tells us that the weight of a particular female panda at 4 years old is the same as her weight at 30 years old.

It is a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

In this case, Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.

The function illustrated shows that the weights are the same.

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The value of fx(1, 0) equal to -(1/√(3)) and  fy(1, 0) is equal to -20/√3.

To find fx(1, 0) and fy(1, 0), we need to take the partial derivative of the given equation with respect to x and y respectively, and then evaluate the derivatives at the point (1,0).

First, we have f(x, y) = √(4 - x² - 4y²)

To find fx(1, 0), we'll take the partial derivative of f(x, y) with respect to x:

fx(x, y) = ∂f/∂x = -(x/√(4 - x² - 4y²))

Therefore, fx(1, 0) = -(1/√(4 - 1² - 4×0²)) = -(1/√(3))

fx(1, 0) = -(1/√(3))

To find fy(1,0), we'll take the partial derivative of f(x, y) with respect to y:

fy(x, y) = ∂f/∂y

= -2y/√(4 - x² - 4y²)

Therefore, fy(1, 0) = -20/√(4 - 1² - 4×0²) = -20/ √3

These numbers, fx(1, 0) and fy(1, 0), can be interpreted as slopes of the equation. The slope in this case represents the rate of change of the function in the x and y directions. A negative value for fx(1,0) means that as x increases by a small amount, the function value decreases by a small amount, while a value of 0 for fy(1,0) means that as y increases by a small amount, the function value does not change.

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Therefore , r its derivation are not present. The dependent variable does not have a transcendental function.

Numbers and their variants, math and nearby tissues, shapes and their real positions, as well as potential placements, are all studied in mathematics. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. An input-output relationship is called a function when each input results in a single, unique output. A realm and a city or municipality, or scope, are assigned to each function.

Here,

Given :  (1+y²)(d²y/dt²)+t(dy/dt)+y=et

The second derivative is the highest derivative in this fractional derivative (). As a result, this differential equation has an order of 2.

The dependent variable's product and its derivative are present, indicating linearity.

The differential equation is hence non-linear.

Second order nonlinear ordinary differential equations are categorized as such.

t²(d²y/dt²)+t(dy/dt) + 2y =sint

The differential equation shown is  t²(d²y/dt²)+t(dy/dt) +2y=sint

Order: This differential equation has a higher order differential equation since the largest derivative it has is.

Lack of the dependent variable's product and/or derivative indicates linearity. Higher powers of the variable or its derivation are not present. The dependent variable does not have a transcendental function.

Therefore , r its derivation are not present. The dependent variable does not have a transcendental function.

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The statement, "two triangles with corresponding congruent angles are congruent," is true.

According to the Triangle Congruence Postulate, if two triangles have three pairs of corresponding congruent angles, then the triangles are congruent.

This means that if two triangles have three pairs of corresponding congruent angles, all six angles are congruent and the triangles are exactly the same size and shape.

Thus, the statement, "two triangles with corresponding congruent angles are congruent," is true.

Congruence is determined by the congruence of angles, sides, and the overall shape of the triangle. If two triangles have the same angles and sides, then they are considered to be congruent.

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Over the past year, Becky has enjoyed watching 7 out of the 9 movies recommended by her local newspaper. She aims to design a spinner that she can use to simulate this scenario and predict the probability that she will be going to enjoy each of the next 5 movies recommended by the newspaper.  Becky should divide her spinner into 9 equal-sized sections in order to best simulate this situation.

Hence, Becky should divide her spinner into 9 equal-sized sections in order to best simulate this situation.

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Answer:

Factors of x are 0, 5, and -4.

Step-by-step explanation:

⇒ x³ = x² + 20x

⇒ x³ - x² - 20x = 0

⇒ x (x² - x - 20) = 0

⇒ x ( x² - 5x + 4x - 20) = 0

⇒ x ( x ( x - 5) + 4 ( x - 5)) = 0

⇒ x (x - 5) (x + 4) =0

⇒ x = 0, 5, and -4

Answer: x = 5

x = -4

x = 0

Step-by-step explanation:The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -20

Step-1 : Multiply the coefficient of the first term by the constant   1 • -20 = -20

Step-2 : Find two factors of  -20  whose sum equals the coefficient of the middle term, which is   -1 .

     -20    +    1    =    -19

     -10    +    2    =    -8

     -5    +    4    =    -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  4

                    x2 - 5x + 4x - 20

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-5)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-5)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x-5)

            Which is the desired factorization  A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.  Solving   x2-x-20 = 0 by Completing The Square .

Add  20  to both side of the equation :

  x2-x = 20

Now the clever bit: Take the coefficient of  x , which is  1 , divide by two, giving  1/2 , and finally square it giving  1/4

Add  1/4  to both sides of the equation :

 On the right hand side we have :

  20  +  1/4    or,  (20/1)+(1/4)

 The common denominator of the two fractions is  4   Adding  (80/4)+(1/4)  gives  81/4

 So adding to both sides we finally get :

  x2-x+(1/4) = 81/4

Adding  1/4  has completed the left hand side into a perfect square :

  x2-x+(1/4)  =

  (x-(1/2)) • (x-(1/2))  =

 (x-(1/2))2

Things which are equal to the same thing are also equal to one another. Since

  x2-x+(1/4) = 81/4 and

  x2-x+(1/4) = (x-(1/2))2

then, according to the law of transitivity,

  (x-(1/2))2 = 81/4

We'll refer to this Equation as  Eq. #4.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(1/2))2   is

  (x-(1/2))2/2 =

 (x-(1/2))1 =

  x-(1/2)

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:

  x-(1/2) = √ 81/4

Add  1/2  to both sides to obtain:

  x = 1/2 + √ 81/4

Since a square root has two values, one positive and the other negative

  x2 - x - 20 = 0

  has two solutions:

 x = 1/2 + √ 81/4

  or

 x = 1/2 - √ 81/4

Note that  √ 81/4 can be written as

 √ 81  / √ 4   which is 9 / 2

1) The function f(x) is defined as follows: B. F(x) = -(x + 2)²(x - 2).

2) The standard definition of function f(x) is given as follows: A. F(x) = ax³ + bx² + cx + d.

4) The approximate solution to the system of equations is given as follows: A. (-3.43, 6.30).

The function f(x) is defined according to the Factor Theorem, with the product of the linear factors of the function, which are dependent on the roots of the functions.

The zeros of the function, along with their multiplicity, are given as follows:

Hence the function is defined as follows:

F(x) = a(x + 2)²(x - 2).

The y-intercept is positive, meaning that:

-8a > 0.

Thus the leading coefficient a is negative, and the correct option is given by option B.

A cubic function, in which the coefficients a and d are positive, is represented as follows:

A. F(x) = ax³ + bx² + cx + d.

The solution to the system of equations is found through graphing, and is the point of intersection of the two functions.

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1. The area of the shaded part = 95π

2. The area of the half circle = 12.5π

3. the distance of the bicycle = 0.0675/π inches

4. The diameter of the circle = 9 unit

radius = 4.5

area = 20.25π unit²

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

The area of a circle = πr²

1. Area of the shaded part = area of big circle - area of small circle

= 12²π - 7²π

= 144π - 49π

= 95π

2. area of semi circle = 1/2πr²

= 1/2×5²× π

= 25π/2

= 12.5π unit²

3. The distance moved by the biycle =

S = tetha/r

tetha = 2π×100 = 200π

S = 200π/13.5

S = 14.8π inches

4. c = πd

c = 9π

d = 9

r =d/2 = 9/2 = 4.5

Area = 4.5²π

A = 20.25π unit²

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The number of outfits Mariam can purchase is 7.

The inequality to represent the situation is 560 ≤ 349.02 + 27.40x.

Mariam has $560 to spend at a bicycle store for some new gear and biking outfits. The price list are as follows:

She plans to spend some or all of the money she has left to buy new biking outfits for $27.40 each.

The inequality that can be used to determine x, the number of outfits Mariam can purchase within her budget can be calculated as follows:

560 ≤ 275.67 + 3(16.32) + 24.39 + 27.40x

where

x = number of biking outfits

560 ≤ 275.67 + 3(16.32) + 24.39 + 27.40x

560 ≤ 275.67 + 48.96 + 24.39 + 27.40x

560 ≤ 349.02 + 27.40x

560 - 349.02 ≤ 27.40x

divide both sides by 27.40

210.98 ≤ 27.40x

divide both sides by 27.40

210.98 / 27.40 ≤ x

7.7 ≤ x

Therefore, the number of outfit he can purchase is 7.

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Answer:41,111

Step-by-step explanation:4-3=1 3-2=1 2-1=1 bring the 1 down and bring the 4down to and you got your answer

The value of x using trigonometry is √6.

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.

The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that may be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.

In the triangle base = [tex]\sqrt{2}[/tex] and height as x

The value of the angle is [tex]60\x^{o}[/tex]

so tanθ = tan[tex]60\x^{o}[/tex]

[tex]\frac{height }{base} = tan60\x^{o} \\[/tex]

⇒ x = √3 * √2

⇒ x = √6

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Answer:

(- 1, 5 )

Step-by-step explanation:

y = x + 6 → (1)

y = 2x + 7 → (2)

since both equations have y on the left side, then equate the right sides

2x + 7 = x + 6 ( subtract x from both sides )

x + 7 = 6 ( subtract 7 from both sides )

x = - 1

substitute x = - 1 into either of the 2 equations for y

substituting into (1)

y = x + 6 = - 1 + 6 = 5

solution is (- 1, 5 )

Step-by-step explanation:

We would make these two equations equal to each other since both equations are in y= form

[tex](x + 6) = (2x + 7)[/tex]

Now to get numbers on one side and X's on the other.

Let's start by subtracting 6 from both sides

[tex]x = 2x + 1[/tex]

Next we can subtract 2X

[tex] - x = 1[/tex]

Last but not least, we can divide by -1 to reverse the signs

[tex]x = - 1[/tex]

The trigonometric equation for the function with a period of 6 is [tex]f(x) = A sin (\frac{\pi}{3}t)[/tex].

The simplest definition of a trigonometric function is the function of an angle in a triangle, often known as a circular function. It implies that these trig functions can be used to determine the relationship between a triangle's angles and sides.

The general equation of the wave is given by the formula:

f(x) = A sin(wt)

Where, [tex]w = \frac{2\pi}{T}[/tex]

where, T is the time period.

Given that T = 6, substituting the value in the formula we have;

[tex]w = \frac{2\pi}{6}[/tex]

[tex]w = \frac{\pi}{3}[/tex]

Substituting the value of w in the general equation:

[tex]f(x) = A sin (\frac{\pi}{3}t)[/tex]

Hence, the trigonometric equations for the function with a period of 6 is [tex]f(x) = A sin (\frac{\pi}{3}t)[/tex].

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Answer:

80% of the flour is left.

Answer:

I hope may answer is correct! I am sorry if it is not!

The chef used 800g out of a 5kg bag of flour, so the amount of flour left is 5,000g - 800g = 4,200g. To find the percentage of flour left, divide the amount of flour left by the total amount of flour and multiply by 100: (4,200g / 5,000g) * 100 = 84%. So 84% of the flour is left.

The measurements of all the angles, if one angle is a right angle (90 degrees), and the second angle's measurement is six times smaller than the third angle's measurement of 180 degrees.

As per the data given in the above question are as bellow,

The data provided are as bellow.

The known angle (90) a pronumeral of r.

give the second angle (the one with all the subtraction) a pronumeral or x.

The third angle the pronumeral of y

x = 7y - 6

90 + x + y = 180

90 + 7y - 6 + y = 180

90 + 8y - 6 = 180

90 + 8y =186

8y = 96

y = 12.  

the third angle is 12

so 12 + 90 = 102

the second angle must equal 88 to make it to 180

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Note the correct question is as bellow,

Given a right triangle, find the measures of all of the angles, if one angle is a right angle (90 degrees) and the measure of the second angle is six less than seven times the measure of the third angle. This is represented by the equation x=7y - 6

The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level.

not significantly more than 3 minutes.

The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.

1. The null hypothesis is that the population mean is equal to 3 minutes.

2. A sample of 100 customers was taken, with an average length of calling time of 3.1 minutes and a sample standard deviation of 0.5 minutes.

3. The p-value from the sample data is 0.28, which is higher than the 0.05 significance level.

4. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.

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The flowers was 8 roses, 2 lillies and 2 irises in each of the identical bouquet.

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the number of roses in each bouquet, y represent the lillies in each bouquet, and z represent the irises.

A florist must make 5 identical bridesmaid bouquets for a wedding. She has a budget of $160, hence:

Cost of flowers in each bouquet = $160/5 = $32

She wants 12 flowers in each bouquet, hence:

x + y + z = 12   (1)

She wants twice as many roses as the other two types of flowers combined, hence:

x = 2(y + z)

x - 2y - 2z = 0   (2)

Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each, hence:

2.5x + 4y + 2z = 32    (3)

From the equations:

x = 8, y = 2, z = 2

There was 8 roses, 2 lillies and 2 irises.

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Note if Tommy were to hire a car to drive 850 miles in 8 days under the price conditions given, it would cost him £575 to go with the cheaper company which is company B.

To compute the cheaper price, we need to work out how much it comes to if he went with either company.

Company A:

Daily Charge £20

Cost per mile 50p

Given that he goes 850 Miles ;

For 8 days,

His Total cost with Company A is

(20 x 8) + [ (50 *850)/100); recall that 100 pence (p) make 1 British Pound (£)

Thus, 160 + 425

= £585

Thus, to go with Company A, Tommy will spend £585

On the other hand, Tommy's Total cost with Company B is computed as follows;

Daily Charge £40

Cost per mile 30p

Total cost will come to: (40 x 8) + [(30 *850)/100)

= 320 + (25500/100)

= £575

Since Company will charge a total of £585 and Company B will charge a total of £ 575, we can conclude that the cheaper company is company B.

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Full Question:

Tommy wants to hire a car to drive 850 miles in 8 days how much would it cost him to hire a car from the cheaper side. See the attached for the pricing conditions.

Answer:

-15

Step-by-step explanation:

im thinking +[-15] and [-15] are the same thing

An equation that models the numbers is x, x+1, x + 2

The term equation is known as a condition on a variable such that two expressions in the variable have equal value

Here we know that Chloe is trying to find three consecutive, positive integers such that six times the largest is equal to the twice sum of the two smaller integers.

Then the given parameters are written as the three consecutive positive numbers Chloe is trying to find are x, x+1, x + 2

Here we have the conditions of the three positive numbers are written as,

=> 6 × (x + 2) = 2 × (x + x + 1)

Now, we have to check if the three consecutive numbers can be 4, 5, and 6 by substituting the values as written as,

=> x + 2 = 6

=> x + 1 = 5

Then the value of x is 4

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To find the ratio equivalent to another ratio, divide both parts of the ratio by the same number. This will create a new ratio that is equal to the original ratio. For example, to find the ratio equivalent to a ratio of 4:6, divide both 4 and 6 by 2. This results in a new ratio of 2:3, which is equivalent to 4:6.

1. Start by identifying the ratio that you need to find the equivalent of.

2. Divide both parts of the ratio by the same number.

3. This will create a new ratio that is equal to the original ratio.

To find the ratio equivalent to another ratio, divide both parts of the ratio by the same number. This will create a new ratio that is equal to the original ratio.

To find the ratio equivalent to another ratio, divide both parts of the ratio by the same number. This will create a new ratio that is equal to the original ratio. For example, to find the ratio equivalent to a ratio of 4:6, divide both 4 and 6 by 2. This results in a new ratio of 2:3, which is equivalent to 4:6.

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Therefore, 24 square units are the answer to the surface area problem that has been given.

Shape is a term used to express how much total area a material's surface takes up. Surface area of a three-dimensional shape is determined by its surrounds added together. Surface area refers to a multi-total shape's surface area covering. A cube with five rectangular sides has a volume of water equal to the sum of the areas of each face. Alternately, you can get the box's dimensions by using the following formula: Surface (SA) equals twice twice twice twice.

Here,

The height of the square in the example is 5-2 = 3.

The base of the provided square is composed of units => 7 -(-1) units => 8 units.

The given square therefore contains an area equal 8 * 3 = 24 square units.

The preceding area problem must therefore be solved using 24 square units.

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The value of p, q, and r cannot be found without more information about what the variables represent and any equations or relationships that they may be a part of.

Please provide more context or information about the problem you are trying to solve.

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