For which value(s) ofcdoes the equationx​+4​−c​=0has a solution. (A)c=−4(B)c=0(C)0

The runner should choose the second cooler, because the probability of selecting a sports drink and a water from the first cooler is about 24.98% and the second cooler is about 25.86%.

To calculate the probability of selecting a sports drink and a water bottle from each cooler, we need to use the following formula:

Probability of selecting a sports drink and a water bottle = (number of sports drinks / total number of bottles) x (number of water bottles / (total number of bottles - 1))

For the first cooler, the probability of selecting a sports drink and a water bottle is:

(19/39) x (20/38) = 0.2498, or about 24.98%

For the second cooler, the probability of selecting a sports drink and a water bottle is:

(14/29) x (15/28) = 0.2586, or about 25.86%

Therefore, the runner should choose the second cooler, because it has a slightly higher probability of selecting a sports drink and a water bottle.

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The sunflower would be 30 inches tall after 30 weeks. The sunflower be after w weeks would be 25 + 0.5 * w inches tall.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

To calculate the height of the sunflower after 10 weeks, we can use the formula:

=>height = starting height + growth rate * time elapsed

where the starting height is 25 inches, the growth rate is 0.5 inches per week, and the time elapsed is 10 weeks.

So the height after 10 weeks would be:

=>height = 25 + 0.5 * 10 = 25 + 5 = 30 inches

Therefore, the sunflower would be 30 inches tall after 10 weeks.

To calculate the height after w weeks, we can use the same formula:

=>height = 25 + 0.5 * w

So the height after w weeks would be:

=>height = 25 + 0.5 * w inches

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Answer:

29+3374=32483 that is the solution for the question

hope this helps <3

Answer:

X=5

Step-by-step explanation:

instructions refer to the image

The expression to represent the total cost of hiring a plumber is y = 50 + 40x

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

Charges = $50 for visiting

Rate = $40 every hours

Represent the number of hour with x and the total charge with y

Using the above as a guide, we have the following:

y = Charges + Rate * x

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

y = 50 + 40x

Hence, the equation is y = 50 + 40x

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The given sequence is not a geometric sequence, the quotients between consecutive numbers are different.

Remember that the recursive formula for a geometric sequence is:

f(n) = r*f(n - 1)

Where r is the common ratio.

Here we have the terms:

5, 11, 29, 83

To get the value of r, take the quotient between consecutive terms:

r = 11/5 = 2.2

r = 29/11 = 2.63

r = 83/29 = 2.86

We should get the same value of r for every ofthese quotients, then we can conclude that the given sequence of numbers is not a geometric sequence, is other type of sequence.

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The function that represents an exponential growth would be = f(X) = 0.3 ( 1.05) ^x. That is option C.

An exponential growth of a function is defined as the growth that shows increase rates with respect to a given time.

There are two types of exponential functions: exponential growth and exponential decay.

The function that shows an exponential growth has the formula = f (x) = b^x, when b > 1.

From the examples given in the options above, the correct option that represents the exponential growth is f(X) = 0.3 ( 1.05) ^x. Thai so because 1.05 is greater than 1.

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The exponential function that satisfies the given conditions is y = 2ˣ- 6.

An exponential function with a parent base of 2 can be written as y = 2ˣ. To ensure that the range is {y|y>-5}, we need to add a constant term to the function.

We can write the exponential function as y = 2ˣ + k, where k is a constant term.

To find the value of k, we can plug in the smallest value in the range, which is -5, and solve for k:

-5 = 2ˣ + k

k = -5 - 2ˣ
Since the domain is {x|x∈R}, we can plug in any value for x. Let's plug in 0 for x:

k = -5 - 2⁰

k = -5 - 1

k = -6

So, the exponential function with a parent base of 2 that has a domain of {x|x∈R} and a range of {y|y>-5} is y = 2ˣ - 6.

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Perimeter would not be used to solve the problem of determining the cost of replacing a linoleum floor with a wood floor. Perimeter is a measure of the boundary of a two dimensional shape, such as a square, rectangle, or triangle. This measure would not be useful in calculating the cost of replacing a floor, as the cost of the flooring materials will depend on the total area of the floor, rather than its perimeter.

Area is the measure of the two dimensional space of a shape, and would be the correct measure to use when calculating the cost of replacing a floor. Area is calculated by measuring the length and width of the floor, then multiplying them together. The cost of the flooring materials can then be calculated by multiplying the area of the floor by the cost of the materials per square foot. This would give an accurate figure for the total cost of the flooring materials.

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Answer:

[tex] - \frac{5x}{34} + 14y + 9[/tex]

Step-by-step explanation:

Just making sure. If the way the equation is written is

[tex]1 + 1 - \frac{5}{34} x + 14y + 7[/tex]

then yeah, that's the answer. If it's formatted differently, send a comment so that I could give you the proper answer.

Two families attended a baseball game bought popcorns and souvenir, the cost of each pack of popcorn is $4 and cost of each pack of souvenir is $7.

An expression that depicts the relationship between two or more variables and numbers is called an equation. The provided information can be represented as, using equations:

let x be the price of popcorn and y be the price of souvenir.

First family:

[tex]3x+4y=40[/tex](equation 1)

Second family:

[tex]8x+4y=60[/tex] (equation 2)

We have a system of 2 equations with 2 variables.

3x + 4y = 40

8x + 4y = 60

We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.

from equation 2,

[tex]8x+4y=60\\4y=60-8x[/tex]

divide both sides by 4

[tex]\frac{4y}{4} =\frac{60-8x}{4} \\y=15-2x[/tex]

now putting the value of y in equation 1

[tex]3x+4(15-2x)=40\\3x+60-8x=40\\-5x=-20\\x=4\\[/tex]and [tex]y=7[/tex]

Hence, the cost of popcorn is $4 and cost of souvenir is $7.

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The  product of 3∛6 and 2∛6 is equals to 18.

What is underroot ?

In mathematics, the symbol "√" is called the radical symbol, and the expression written under it is called a radicand.

To simplify 3∛6, we can use the fact that the cube root of a number can be written as a power of that number with an exponent of 1/3. Therefore, 3∛6 can be rewritten as 6^(1/3) raised to the power of 3.

D) To add 3∛6 and 2∛6, we can first factor out the common term of ∛6:

3∛6 + 2∛6 = (3 + 2)∛6 = 5∛6

So the sum of 3∛6 and 2∛6 is 5∛6.

E) To subtract 2∛6 from 4∛6, we can again factor out the common term of ∛6:

4∛6 - 2∛6 = (4 - 2)∛6 = 2∛6

So the difference between 4∛6 and 2∛6 is 2∛6.

F) To multiply 3∛6 by 2∛6, we can use the fact that the product of two roots with the same index can be found by multiplying the radicands together:

3∛6 x 2∛6 = (3 x 2)∛(6 x 6) = 6∛36

Since the cube root of 36 is 3 (3 x 3 x 3 = 27 and 4 x 4 x 4 = 64), we can simplify this further:

6∛36 = 6 x 3 = 18

Therefore, the product of 3∛6 and 2∛6 is equals to 18.

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Answer:

  50 people

Step-by-step explanation:

Given a research project that take 16 people 125 days to complete, you want to know the number of people needed to complete the project in 40 days.

In math, project effort is measured in people×days. That value is considered to be a constant for a given project. This makes the number of people inversely proportional to the number of days, and vice versa.

  (16 people)×(125 days) = 2000 people·days = (p people)×(40 days)

Dividing by 40 days, we have ...

  p people = (2000 people·days)/(40 days) = 50 people

50 people are needed to complete the research in 40 days.

__

Additional comment

In real life, more people may get in each other's way. Or too few people may cause motivation, cooperation, and synergy to be lost. The maxim, "adding people to a late project makes it later" has a certain basis in reality.

Therefore , the solution of the given problem of triangle comes out to be NL =  √(100 + 20LM2) * 10 * 4 .

A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular. The intersection of a quadrilateral's three edges is known as an angle. The sum of a triangle's edges is 180 degrees.

Here,

By removing NP:, we can resolve this system of equations.

NL Equals NP(LM + NL + 5). (5 - LM)

NL = NP(LM - PQ + 5) (LM)

NL(5 - LM) = NP(LM + NL + 5)(LM - PQ + 5) (LM)

By enlarging and condensing, we obtain:

NP = 2NL Plus LM / 5LM

Now that we know this, we can put it into one of the equations to find NL:

(2NL Plus LM / 5LM)

NL = (LM Plus NL + 5) (5 - LM)

By condensing and rearrangeing, we obtain:

(2NL Plus LM) = 0 when (NL2 - 10NL - 5LM2)

The quadratic algorithm yields:

NL =  √(100 + 20LM2) * 10 * 4 alternatively,

=> NL = (10 -  √(100 + 20LM2)) / 4

NL can never be negative, so we pick the positive root:

NL =  √(100 + 20LM2) * 10 * 4

Now that we have this, we can put it into one of the equations to find NP:

NP = 2NL Plus LM / 5LM

NP = 5LM / (2(10 + √100 + 20LM^2)) / 4 + LM)

NP is equal to 5LM / (5 +  √(25 + 5LM2)).

The widths of NP and NL are as follows:

NP is equal to 5LM / (5 + sqrt(25 + 5LM2)).

NL = (10 -  √(100 + 20LM2)) / 4

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The given operation (x²-11x+30)/(x-6)-(x²-12x+35)/(9x³)  expressed in simplest form is x - 11 + 29.89x⁻¹- 2x⁻²+ 8x⁻³ - (3.89)x⁻⁴.

To express this operation in simplest form, we need to find the common denominator and combine the numerators.

Find the common denominator. The common denominator of (x-6) and (9x^(3)) is (9x^(3))(x-6).

Multiply each fraction by the common denominator to get the same denominator for both fractions.

(x²-11x+30)/(x-6) * (9x³)/(9x³) = (9x³)(x²-11x+30)/(9x³)(x-6)

(x²-12x+35)/(9x³) * (x-6)/(x-6) = (x-6)(x²-12x+35)/(9x³)(x-6)

Combine the numerators and keep the same denominator.

(9x³)(x²-11x+30) - (x-6)(x²-12x+35) / (9x³)(x-6)

Simplify the numerator by distributing and combining like terms.

(9x⁵-99x⁴+270x³) - (x³-18x₂+72x-35) / (9x³)(x-6)

9x⁵-99x⁴+269x³-18x²+72x-35 / (9x³)(x-6)

Simplify the denominator by multiplying.

9x⁵-99x⁴+269x³-18x²+72x-35 / 9x⁴-54x³

Simplify the fraction by dividing each term in the numerator by the term in the denominator with the highest power.

(9x⁵/9x⁴)-(99x⁴/9x⁴)+(269x³/9x⁴)-(18x²/9x⁴)+(72x/9x⁴)-(35/9x⁴)

Simplify each term.

x - 11 + (269/9)x⁻¹- (18/9)x⁻²+ (72/9)x⁻³ - (35/9)x⁻⁴

Combine like terms.

x - 11 + (29.89)x⁻¹ - (2)x⁻² + (8)x⁻³- (3.89)x⁻⁴

Therefore, the operation  (x²-11x+30)/(x-6)-(x²-12x+35)/(9x³)   expressed in simplest form is  x - 11 + 29.89x⁻¹- 2x⁻²+ 8x⁻³ - (3.89)x⁻⁴.

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The polyhedron that can be constructed using this net is a triangular pyramid.

A triangular pyramid is a polyhedron that has four faces, with one of the faces being a square and the other three faces being equilateral triangles. The given net shows a square in the center, with three equilateral triangles attached to each of its sides. When the net is folded along the edges, the square becomes the base of the pyramid and the three equilateral triangles become the sides of the pyramid. Therefore, the polyhedron that can be constructed using this net is a triangular pyramid.

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The exact solutions to the equation sin^2(x) - cos^2(x) - sin(x) = 0 in the interval [0, 2π) are π/2, 7π/6, and 11π/6.

Given that

sin^2(x) - cos^2(x) - sin(x) = 0

Let's use the identity cos^2(x) + sin^2(x) = 1 to rewrite the equation:

sin^2(x) - (1 - sin^2(x)) - sin(x) = 0

Open the bracket and evaluate the like terms

2sin^2(x) - sin(x) - 1 = 0

Now we can solve for sin(x) using the quadratic formula:

sin(x) = [-b ± √(b² - 4ac)]/2a

Where

a = 2, b = -1 and c = -1

So, we have

sin(x) = [1 ± √((-1)² - 4 * 2 * -1)]/2*2

sin(x) = [1 ± √9]/4

sin(x) = (1 ± 3) / 4

Evaluate and split

sin(x) = 1 or sin(x) = -1/2.

If sin(x) = 1, then x = π/2.

If sin(x) = -1/2, then we can use the unit circle to find the solutions in the interval [0, 2π):

sin(x) = -1/2 when x = 7π/6 or 11π/6.

Therefore, the solutions in the interval [0, 2π) are π/2, 7π/6, and 11π/6.

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The moments of a variate 'X' are defined by the expected value of the variate raised to the power of r, where r is an integer. In this case, the moments of 'X' are defined by E(X^r) = 0.6, for r = 1, 2, 3. This means that the expected value of X, X^2, and X^3 are all equal to 0.6. The probability of an event occurring is represented by P(X). In this case, P(X > 0) = 0.4, P(X = 1) = 0.6, and P(X^2 = 1) = 0.2. Convergence in probability refers to the concept that a sequence of random variables converges to a specific value with a probability of 1 as the number of trials approaches infinity.

These probabilities represent the likelihood of X being greater than 0, equal to 1, and squared equal to 1, respectively. This means that the probability of the sequence being within a certain distance of the specific value approaches 1 as the number of trials increases.

Two laws of convergence in probability are the Law of Large Numbers and the Central Limit Theorem. The Law of Large Numbers states that the average of a sequence of random variables converges to the expected value as the number of trials approaches infinity. The Central Limit Theorem states that the distribution of the sum of a sequence of random variables approaches a normal distribution as the number of trials approaches infinity.

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The roots of equation A are  2 and 0.25.

The roots of equation B are 3.14 and -0.64.

To solve for the roots of a quadratic equation using the Quadratic Formula, we can use the formula:

x = (-b ± √(b² - 4ac)) / (2a)

Where a, b, and c are the coefficients of the equation.

For equation A, a = 4, b = -9, and c = 2. Plugging these values into the Quadratic Formula, we get:

x = (-(-9) ± √((-9)² - 4(4)(2))) / (2(4))
x = (9 ± √(81 - 32)) / 8
x = (9 ± √49) / 8
x = (9 ± 7) / 8

This gives us two possible values for x:

x = (9 + 7) / 8 = 2
x = (9 - 7) / 8 = 0.25

Therefore, the roots of equation A are 2 and 0.25.

For equation B, a = 2, b = -7, and c = -1. Plugging these values into the Quadratic Formula, we get:

x = (-(-7) ± √((-7)² - 4(2)(-1))) / (2(2))
x = (7 ± √(49 + 8)) / 4
x = (7 ± √57) / 4

This gives us two possible values for x:

x = (7 + √57) / 4 ≈ 3.14
x = (7 - √57) / 4 ≈ -0.64

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Answer:

You are distributing (multiplying) the three to all the terms in the parentheses.

Start:

3(x-2) = 4x + 2

Next:

3x - 6 = 4x +2

After that simplify:

-8 = x

Hope this helps!

Answer:

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The property we use,

→ Distributive property.

The equation is,

→ 3(x - 2) = 4x + 2

Then the value of x will be,

→ 3(x - 2) = 4x + 2

→ 3(x) - 3(2) = 4x + 2

→ 3x - 6 = 4x + 2

→ 3x - 4x = 2 + 6

→ -x = 8

→ [ x = -8 ]

Hence, the value of x is -8.

Answer:

To graph y = 1/2x and y = x + 2, follow these steps:

Make a table of values for each equation. Choose several values of x, plug them into the equation, and solve for y. For y = 1/2x, you might choose x = -2, -1, 0, 1, and 2. For y = x + 2, you might choose the same values of x.

For y = 1/2x:

x | y

-2 | -1

-1 | -1/2

0 | 0

1 | 1/2

2 | 1

For y = x + 2:

x | y

-2 | 0

-1 | 1

0 | 2

1 | 3

2 | 4

Plot the points from each table on a graph. For y = 1/2x, plot the points (-2, -1), (-1, -1/2), (0, 0), (1, 1/2), and (2, 1). For y = x + 2, plot the points (-2, 0), (-1, 1), (0, 2), (1, 3), and (2, 4).

Draw a line through each set of points. The line for y = 1/2x should have a slope of 1/2 and pass through the point (0, 0). The line for y = x + 2 should have a slope of 1 and pass through the point (0, 2).

Label the axes and the lines. You can label the x-axis "x" and the y-axis "y". Label the line for y = 1/2x "y = 1/2x" and the line for y = x + 2 "y = x + 2".

Check your graph. Make sure each point is plotted correctly and the lines are drawn accurately. You can also check your graph by plugging in other values of x and making sure the corresponding points are on the lines.

Use simultaneously equation to eliminate one value and find the other then you find the value of the other one by substituting the value that u find from the other one eg: eliminate X find the value of y and then substitute y in one of your equation to find the value of X.

Answer:

Step-by-step explanation: I don’t know

The center of the ellipse is,

⇒ (3, 1)

An expression which is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division is called an mathematical expression.

We have to given that;

The equation of ellipse is,

⇒ (x - 3)²/4 + (y - 1)²/9 = 1

Now, We know that;

General form of the ellipse is,

⇒ (x - h)²/a + (y - k)²/b = 1

Where, (h, k) = the center of the ellipse.

Hence, We get;

The equation of ellipse is,

⇒ (x - 3)²/4 + (y - 1)²/9 = 1

By comparing;

The center of the ellipse is,

⇒ (h, k) = (3, 1)

Thus, The center of the ellipse is,

⇒ (3, 1)

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37. sec x / tan x = (1/cos x) / (sin x/cos x) = cos x / sin x = cot x
38. cot x / csc x = (cos x/sin x) / (1/sin x) = cos x / sin^2 x = cos x * (1/sin^2 x) = cos x * (csc^2 x)
39. sin x / csc x + cos x / sec x = (sin x / 1/sin x) + (cos x / 1/cos x) = sin^2 x + cos^2 x = 1
40. 1/sin²x - 1/tan^2 x = (1/sin^2 x) - (1/(sin^2 x/cos^2 x)) = (1/sin^2 x) - (cos^2 x/sin^2 x) = (1 - cos^2 x)/sin^2 x = sin^2 x/sin^2 x = 1
41. (1 - sin a)(1 + sin a) = 1 - sin^2 a = cos^2 a
42. (sec a - 1)(sec a + 1) = sec^2 a - 1 = tan^2 a
43. (cos B tan B + 1)(sin B - 1) = (cos B * sin B/cos B + 1)(sin B - 1) = (sin B + 1)(sin B - 1) = sin^2 B - 1 = -cos^2 B
44. (1 + cos B)(1 - cot B sin B) = (1 + cos B)(1 - cos B/sin B * sin B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B - cos^2 B/sin^2 B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B) = (1 + cos B) * 1 = 1 + cos B
45. 1 + cos a tan a csc a / csc a = 1 + (cos a * sin a/cos a * 1/sin a) / (1/sin a) = 1 + (sin a / sin a) / (1/sin a) = 1 + 1/(1/sin a) = 1 + sin a = sin a + 1
46. (cos a tan a + 1)(sin a - 1) / cos^2 a = (cos a * sin a/cos a + 1)(sin a - 1) / cos^2 a = (sin a + 1)(sin a - 1) / cos^2 a = (sin^2 a - 1) / cos^2 a = -cos^2 a / cos^2 a = -1

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By forming and solving the equations we know that the speed of the plane was 220 mph.

In mathematical formulas, the equals sign is used to indicate that two expressions are equal.

A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.

like 3x + 5 = 15, for instance.

Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.

So, d = rt.

t = d/r

The distances are equal.

140/r = 440/(r + 150)

Cross multiply:

140(r + 150) = 440r

140r + 21,000 = 440r

300r = 21,000

r = 70

70 + 150 = 220 mph

Therefore, by forming and solving the equations we know that the speed of the plane was 220 mph.

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Completing the table to show the total cost of uniforms with tax, for groups of students from the four states is as follows:

State              Number     Total Cost

                  of Students    (After-tax)

Idaho                     10        $1,431.00

Mississippi             5          $722.25

Hawaii                  15        $2,106.00

Wisconsin             8          $1,134.00.

The total cost for each group of students from the four states can be determined by multiplication.

The multiplication operation for each group or state first computes the total cost before tax and the total cost after tax.

The total cost after tax uses the sales tax factor or rate to multiply the total cost before tax.

Generally, sales taxes are levied by state and local governments to check the consumption and production of certain items and to increase the revenue of the government.

The price before state sales tax of each uniform = $135

Relevant Taxes and Number of Students:

State           Number of Students     Sales Tax Rate

Idaho                     10                                 6%

Mississippi             5                                  7%

Hawaii                  15                                  4%

Wisconsin             8                                  5%

State              Number      Total Cost     Total Cost

                  of Students    (Before tax)    (After-tax)

Idaho                     10        $1,350            $1,431.00 ($135 x 10 x 1.06)

Mississippi             5           $675             $722.25 ($135 x 5 x 1.07)

Hawaii                  15        $2,025          $2,106.00 ($135 x 15 x 1.04)

Wisconsin             8         $1,080            $1,134.00 ($135 x 8 x 1.05)

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The graph that shows the number of bottles that need to be sold to earn back the money spent on water is Graph C.

The number of bottles that need to be sold to earn back the amount spent on water is :

= Total spent / profit per bottle

= 50 / 2

= 25 bottles

Graph C starts from - $ 50 to show that the amount you have is - $ 50 to show the amount spent on the bottles.

Graph C then ends at 25 bottles to show that this is where you would need to stop to have made back what you spent.

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The Cartesian equation ( y = f(x)) for the curve is y = -x.

To find the Cartesian equation of the curve, we need to eliminate the parameter θ from the given parametric equations. We can do this by rearranging the equations and solving for θ in terms of x or y, and then substituting that value into the other equation.

First, let's rearrange the first equation to solve for cotθ:
2x = cotθ - cscθ
2x + cscθ = cotθ
cscθ - cotθ = -2x

Next, let's rearrange the second equation to solve for cscθ:
4y = 2cscθ - 2cotθ
2cscθ = 4y + 2cotθ
cscθ = 2y + cotθ

Now, let's substitute the value of cscθ from the second equation into the first equation:
2y + cotθ - cotθ = -2x
2y = -2x
y = -x

Therefore, the Cartesian equation of the curve is y = -x.

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