Translate and solve using proportions: What number is 115% of 95?
Provide your answer below:

Simplificando ambos lados de la razón, obtendremos la razón simplificada:

657 : 352

Tenemos la razón:

(3 + 7)*10^2 - 7^3:7^3 + √81

Primero, debemos simplificar ambos lados de la razón, comenzamos con el lado izquierdo, donde primero resolvemos a primer suma, luego el producto, y luego la diferencia.

(3 + 7)*10^2 - 7^3 = 10*10^2 - 7^3 = 10^3 - 7^3 = 657

Para el lado derecho tenemos que recordar que 9 al cuadrado es igual que 81, entonces la raiz quadrada de 81 será igual a 9, reemplazando eso y resolviendo la resta obtendremos:

7^3 + √81 = 7^3 + 9 = 352

Así, podemos simplificar la razón a:

657:352

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The solution to the inequality is x >= -2 for inequality 3x-5≥-11

The given inequality is 3x-5≥-11

Three times of x greater than or equal to minus eleven

x is the variable

3x - 5≥ -11:

Adding 5 to both sides, we get:

3x ≥ -6

Dividing both sides by 3, we get:

solution is  x≥-2

Therefore, the solution to the inequality is x >= -2.

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It is important to note that sharing or requesting specific keys or answers to educational materials, including guided notes, would be considered unethical and potentially a violation of academic integrity.

Guided notes are intended to assist students in actively engaging with course material and enhancing their learning experience. It is recommended that you approach your teacher or instructor for any clarification or additional resources you may need to fully understand the content.

They are in the best position to provide you with the necessary guidance and support.

Instead of seeking shortcuts or unauthorized access to answers, it is more beneficial to invest time and effort in studying, asking questions, and actively participating in your educational journey.

This approach will not only help you grasp the subject matter more effectively but also promote personal growth and knowledge development.

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Answer:

c) 1

Step-by-step explanation:

Solving for the value of s,

→ 3s - 12 = -9

→ 3s = -9 + 12

→ s = 3/3

→ [ s = 1 ]

Thus, option (c) is correct.

If one number is increased by a factor of 12 and the other is decreased by a factor of 4, the product of the two numbers will be multiplied by a factor of 3.

Let's suppose we have two numbers, A and B, and we want to know how their product will change if one number is increased by a factor of 12 and the other is decreased by a factor of 4.

The initial product of the two numbers is:

A x B

If we increase A by a factor of 12, the new value of A will be 12A. If we decrease B by a factor of 4, the new value of B will be B/4. Therefore, the new product of the two numbers will be:

(12A) x (B/4) = (12/4) x A x B = 3AB

So the new product of the two numbers will be three times the initial product. In other words, if one number is increased by a factor of 12 and the other is decreased by a factor of 4, the product of the two numbers will increase by a factor of 3.

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The correct value of Z for the solution to true system is -2

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

2x + 3y - z = 4

x - 3y + 2z = -3

3x + y - z = 5

Transform the third equation

So we have

2x + 3y - z = 4

x - 3y + 2z = -3

9x + 3y - 3z = 15

Eliminate y in the equations by subtraction

So we have

x - 3z = 7

10x - z = 12

Multiply x - 3z = 7 by 10

10x - 30z = 70

10x - z = 12

Subtract the equations

-29z = 58

So, we have

z = -2

Hence, the correct value of Z  is -2

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Answer: c and d

Step-by-step explanation: they’re both even

The function is even will be y = sec x and y = cos x. Then the correct options are C and D.

Even Function - A true function f(x) is said to be an even function if the output value of f(-x) is the same as the f(x) for all values of x in the domain of f.

The equation should be stored in an even function:

f(-x) = f(x)

Check all that apply.

a. y = csc x, then replace x with -x. Then we have

y = csc -x

y = 1/sin -x

y = - 1/ sin x

y = -csc x

b. y = sin x, then replace x with -x. Then we have

y = sin -x

y = - sin x

c. y = sec x, then replace x with -x. Then we have

y = sec-x

y = 1/cos -x

y = 1/ cos x

y = sec x

d. y = cos x, then replace x with -x. Then we have

y = cos -x

y = cos x

Thus, the function is even will be y = sec x and y = cos x.

Then the correct options are C and D.

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The centre and the radius of the circle is (-7, -1) and 6 units

The equation of the circle in standard from is expressed as:

x^2+y^2+2gx+2fy+C = 0

where;

(-g, -f) is the centre

r= √g²+f²-C

Given the equation below

x^2+y^2+14x+2y+14 = 0

2g = 14

g = 7

2f = 2

f =1

Hence the centre of the circle is (-7, -1)

Radius = √49+1-14

Radius = √36 = 6 units

Hence the centre and the radius of the circle is (-7, -1) and 6 units

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Answer:

is x multiplied by p/q??

Answer:

a) 0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire

b) 0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.

Step-by-step explanation:

For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The sprinklers activate correctly or not independently, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.

This means that \(p = 0.7\)

10 sprinklers.

This means that \(n = 10\)

a. What is the probability that all of the sprinklers will operate correctly in a fire?

This is \(P(X = 10)\). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282\)

0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire.

b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?

This is:

\(P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)\)

So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 7) = C_{10,7}.(0.7)^{7}.(0.3)^{3} = 0.2668\)

\(P(X = 8) = C_{10,8}.(0.7)^{8}.(0.3)^{2} = 0.2335\)

\(P(X = 9) = C_{10,9}.(0.7)^{9}.(0.3)^{1}= 0.1211\)

\(P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282\)

Then

\(P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.2668 + 0.2335 + 0.1211 + 0.0282 = 0.6496\)

0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.

The measure of the central angle is 0.75 radians

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

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Answer:

6 ln x + 3 ln y

Step-by-step explanation:

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer:

1,870

Step-by-step explanation:

Step-by-step explanation:

The total price of sneakers including tax will be equal to $20.75.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Price of sneakers = $20

Tax on sneakers = 3.75%

Then, the amount of tax will be,

(20 × 3.75)/100

= 75/100

= $0.75

Then, the total price of the sneakers will be,

$20 + $0.75

= $20.75

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The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.

To write the equation for calculating the yearly interest earned on an investment, we can use the formula:

Interest = Principal * Rate

Where:

- Principal is the initial investment amount.

- Rate is the interest rate expressed as a decimal.

In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:

Rate = 16% = 16/100 = 0.16

Substituting the values into the equation:

Interest = $750 * 0.16

To calculate the interest, we multiply the principal by the interest rate:

Interest = $750 * 0.16 = $120

Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:

Interest = $750 * 0.16

Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.

Year | Initial Investment | Interest Earned | Total Value

---------------------------------------------------------

 1        $750                 $120              $870

 2        $870                 $139.20          $1009.20

 3        $1009.20            $161.47          $1170.67

 4        $1170.67            $187.31          $1357.98

 5        $1357.98            $217.28          $1575.26

In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.

The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.

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The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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This function gives the same result as the previous function we derived, but it expresses the calculation as a composition of the two separate functions that represent each raise separately.

A function is a set of instructions or statements that perform a specific task or computation and returns a value or result. In programming, a function is typically defined using a specific syntax and can be called or invoked by other parts of the program to carry out a particular operation.

Functions are used in programming to break down complex tasks into smaller, more manageable pieces of code, which can then be reused in multiple parts of the program. They can also help to improve the organization, readability, and maintainability of code.

by the question.

let the worker's original hourly wage be represented by the variable x. Then the function for the worker's new hourly wage when the 20% raise is applied before the $2 raise can be expressed as follows:

\(f(x) = (1.20x) + 2\)

In this function, the expression (1.20x) represents the worker's hourly wage after the 20% raise is applied, and the additional $2 raise is added to this amount to determine the final hourly wage.

We can also express this function using function composition notation. Let g(x) represent the function that applies the 20% raise to the worker's hourly wage and let h(x) represent the function that adds the $2 raise to the resulting hourly wage. Then we have:

\(g(x) = 1.20x\)

\(h(x) = x + 2\)

Using function composition, we can write the function for the worker's new hourly wage as:

\(f(x) = h(g(x)) = h(1.20x) = 1.20x + 2\)

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no lol ;0 you should ask your teacher for help ;(

The length of u, to the nearest inch, is 1818 inches.

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

In this case, we'll use the following formula:

a/sin(A) = b/sin(B) = c/sin(C)

Let's label the sides and angles of the triangle:

Side a = u (length of u)

Side b = t (820 inches)

Side c = v (length of v)

Angle A = m/U (132°)

Angle B = m2V (25°)

Angle C = 180° - A - B (as the sum of angles in a triangle is 180°)

Now, we can use the Law of Sines to set up the equation:

u/sin(A) = t/sin(B)

Plugging in the given values:

u/sin(132°) = 820/sin(25°)

To find the length of u, we'll solve this equation for u.

u = (820 \(\times\) sin(132°)) / sin(25°)

Using a calculator, we can evaluate the right side of the equation to get the approximate value of u:

u ≈ (820 \(\times\) 0.9397) / 0.4226

u ≈ 1817.54 inches

Rounding to the nearest inch, we have:

u ≈ 1818 inches

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Step-by-step explanation:

To solve the problem, we'll use the information given to find the values of A and k in the equation T = 20 + Ae^(-kt), where T is the temperature in degrees Celsius at time t.

a. Finding the value of A:

We're given that the initial temperature of the tea was 70℃. Substituting this into the equation, we get:

70 = 20 + Ae^(0) (since e^0 = 1)

70 - 20 = A

A = 50

So the value of A is 50.

b. Finding the value of k:

We're told that it takes 4 minutes for the tea to decrease in temperature from 70℃ to 50℃. We can use this information to set up an equation and solve for k.

Substituting T = 70 and t = 4 into the equation, we have:

70 = 20 + 50e^(-4k)

Subtracting 20 from both sides:

50 = 50e^(-4k)

Dividing both sides by 50:

1 = e^(-4k)

Taking the natural logarithm (ln) of both sides:

ln(1) = ln(e^(-4k))

0 = -4k

Dividing both sides by -4:

0 = k

However, we need to check if this solution satisfies the condition for the tea to decrease in temperature from 70℃ to 50℃ in 4 minutes.

Substituting T = 50 and t = 4 into the equation, we have:

50 = 20 + 50e^(-4(0))

50 = 20 + 50e^0

50 = 20 + 50(1)

50 = 20 + 50

50 = 70

Since 50 is not equal to 70, the value of k = 0 does not satisfy the given condition.

Let's try another approach:

Substituting T = 50 and t = 4 into the equation, we have:

50 = 20 + 50e^(-4k)

Subtracting 20 from both sides:

30 = 50e^(-4k)

Dividing both sides by 50:

0.6 = e^(-4k)

Taking the natural logarithm (ln) of both sides:

ln(0.6) = ln(e^(-4k))

ln(0.6) = -4k ln(e)

ln(0.6) = -4k(1)

ln(0.6) = -4k

Simplifying further:

k = ln(0.6) / -4

Using a calculator or computer to evaluate ln(3/5) / -4, we get approximately:

k = ln(5/3) / 4

To recap:

a. The value of A is 50.

b. The value of k is approximately k = ln(5/3) / 4

.

Note: The calculations provided are based on the given information and assumptions. If there are any additional details or specific conditions provided, please let me know, and I'll be happy to assist you further.

Answer:

Umm is it division or what I’m confused but I want to help.

Step-by-step explanation:

(m + n) has a magnitude of approximately 25.8.

We have,

Consider the two vectors as m and n.

To find (m + n), we need to add the two vectors.

To do this, we first need to determine the components of each vector.

Let's call the angle between vector m and the x-axis α, and the angle between vector n and the x-axis β.

Then we have:

|m| = 10, so the x-component of vector m is m_x = 10 cos α and the

y-component is m_y = 10 sin α.

|n| = 15, so the x-component of vector n is n_x = 15 cos β and the

y-component is n_y = 15 sin β.

We also know that the angle between vectors m and n is 75 degrees. Using the dot product, we can find the cosine of this angle:

m · n = |m| |n| cos 75

m · n = 10 * 15 * cos 75

m · n = 37.32

We also know that the dot product is equal to the sum of the products of the corresponding components:

m · n = (m_x) x (n_x) + (m_y) x (n_y)

37.32 = 10 cos α x 15 cos β + 10 sin α * 15 sin β

Now we have two equations with two unknowns:

m_x + n_x = (10 cos α) + (15 cos β)

m_y + n_y = (10 sin α) + (15 sin β)

We can solve for α and β using the equations we just derived:

m_x + n_x = (10 cos α) + (15 cos β)

10 cos α = (m_x + n_x - 15 cos β)

cos α = (m_x + n_x - 15 cos β) / 10

α = arccos[(m_x + n_x - 15 cos β) / 10]

m_y + n_y = (10 sin α) + (15 sin β)

10 sin α = (m_y + n_y - 15 sin β)

sin α = (m_y + n_y - 15 sin β) / 10

α = arcsin[(m_y + n_y - 15 sin β) / 10]

Now we can substitute these values into the equations for m_x + n_x and m_y + n_y to find (m + n):

m_x + n_x = 10 cos α + 15 cos β

m_y + n_y = 10 sin α + 15 sin β

We can use a graphical method to estimate the values of α and β. Start by drawing vector m with length 10 and angle α with respect to the x-axis. Then draw vector n with length 15 and angle β with respect to the x-axis, starting the tail of n at the head of m.

The parallelogram formed by the two vectors will have a diagonal that represents (m + n). Use a ruler to measure the length of this diagonal to the nearest hundredth.

We can use the law of cosines to find the magnitude of (m + n):

|(m + n)|² = |m|² + |n|² + 2|m||n| cos 75

|(m + n)|² = 10² + 15² + 2(10)(15) cos 75

|(m + n)|² = 665.19

|(m + n)| = 25.8 (to the nearest hundredth)

Therefore,

(m + n) has a magnitude of approximately 25.8.

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The exponential function that can model the county population, y, x decades after Tiana was born, is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 in 6.6 decades after Tiana was born.

The definition of the exponential function is presented as follows:

\(y = a(b)^x\)

In which the parameters of the exponential function are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the function is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 when y = 600000, hence:

\(y = 641000(0.99)^x\)

\(600000 = 641000(0.99)^x\)

\((0.99)^x = \frac{600000}{641000}\)

\(\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}\)

\(x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}\)

\(x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}\)

x = 6.6 decades.

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Answer:

C

Step-by-step explanation:

Answer: C is the correct answer on edge

1) The area of a circle circumscribed about a square is 307.7 cm².

2.a.) The angle ACB is 39 degrees.°.

2b.) The value of x is 5.42.

We shall find the radius to determine the area of a circle.

First,  find the side length of the square:

Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.

Next, find the diagonal of the square, using the Pythagorean theorem:

Diagonal = the diameter of the circumscribed circle.

Diagonal² = side length² + side length²

= 14 cm² + 14 cm²

= 196 cm² + 196 cm²

= 392 cm²

Take the square root of both sides:

Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)

Then, the radius of the circle which is half the diagonal:

Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)

Finally, compute the area of the circle using the formula:

Area = π * Radius²

Area = 3.14 * (9.90 cm)²

Area ≈ 307.7 cm² (rounded to two decimal places)

Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².

2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.

Given that arc AB has a measure of 78°, we can find angle ACB as follows:

Angle ACB = 1/2 * arc AB

= 1/2 * 78°

= 39°

Therefore, the angle ACB is 39 degrees.

2b.) To solve for the value of x, we use the information that the angle ADB =  (3x - 12)⁴.

Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:

(3x - 12)⁴ = 78

Solve the equation for x, by taking the fourth root of both sides:

∛∛((3x - 12)⁴) = ∛∛78

Simplify,

3x - 12 = ∛(78)

Isolate x by adding 12 to both sides:

3x - 12 + 12 = ∛(78) + 12

3x = ∛(78) + 12

Finally, divide both sides by 3:

x = (∛(78) + 12) / 3

x = (4.27 +12) / 3

x = 5.42

So, x is 5.42

Therefore,

1) The area of the circle is 154 cm².

2a.) Angle ACB is equal to 102°.

2b.) The value of x is 5.42

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To find the length of DE in circle D, we can use the properties of a circle and the given information.

In a circle, if two chords intersect, the product of the segments of one chord is equal to the product of the segments of the other chord. In this case, we have chord EF intersecting chord DE at point D.

Let x represent the length of segment DE, and y represent the length of segment DF. Therefore, the length of segment EF would be (x + y).

According to the chord-chord power theorem:

DE * EF = DF * DF

Substituting the given values:

x * (x + y) = y * y

x^2 + xy = y^2

We are also given that angle EDF measures 70 degrees. According to the angle intercepting chord theorem, the intercepted arc EF is twice the measure of angle EDF. So, the measure of arc EF is 2 * 70 = 140 degrees.

Now, we can use the length of arc EF to find the ratio of the lengths of segments EF and DF.

The ratio of the lengths of the intercepted arcs is equal to the ratio of the lengths of the corresponding chords. Therefore:

EF / DF = arc EF / arc DF

(x + y) / y = 140 / 360 [Using the measure of the intercepted arcs]

Simplifying this equation:

(x + y) / y = 7 / 18

Cross-multiplying:

18(x + y) = 7y

18x + 18y = 7y

18x = 7y - 18y

18x = -11y

Dividing by -11:

x = -11y / 18

We need to find the value of x, which represents the length of segment DE. Since segment lengths cannot be negative, we can disregard the negative sign.

x = 11y / 18

Substituting this value of x in the equation x^2 + xy = y^2:

(11y / 18)^2 + (11y / 18) * y = y^2

Simplifying:

121y^2 / 324 + 11y^2 / 18 = y^2

Multiplying through by 324:

121y^2 + 594y^2 = 324y^2

715y^2 = 324y^2

715y^2 - 324y^2 = 0

391y^2 = 0

y^2 = 0

Since y^2 = 0, it implies that y = 0. This means that segment DF has zero length.

Now, substituting y = 0 into the equation x = 11y / 18:

x = 11 * 0 / 18

x = 0

Therefore, the length of DE is 0.

In conclusion, the length of DE is 0.

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