If the length of FH is 18 units, what is the value of x?
3
4
6
12

The cosine ratio of ∠Z in the right triangle XYZ is 3/5.

In a right triangle XYZ, angle Y is the right angle. We are given the lengths of two sides of the triangle: YZ = 12 and XY = 16. We are tasked with finding the cosine ratio of ∠Z.

The cosine ratio is defined as the adjacent side divided by the hypotenuse. In this case, the adjacent side is XZ, and the hypotenuse is XY.

Using the Pythagorean theorem, we can find the length of the remaining side XZ:

XZ^2 = XY^2 - YZ^2

XZ^2 = 16^2 - 12^2

XZ^2 = 256 - 144

XZ^2 = 112

XZ = √112

XZ = 4√7

Now that we know the lengths of the adjacent side (XZ) and the hypotenuse (XY), we can calculate the cosine ratio of ∠Z:

cos(∠Z) = XZ / XY

cos(∠Z) = (4√7) / 16

cos(∠Z) = √7 / 4

To simplify the expression further, we rationalize the denominator by multiplying both the numerator and denominator by √7:

cos(∠Z) = (√7 / 4) * (√7 / √7)

cos(∠Z) = (√49 / 4√7)

cos(∠Z) = 7 / (4√7)

cos(∠Z) = (7√7) / (4 * 7)

cos(∠Z) = √7 / 4

Therefore, the cosine ratio of ∠Z in the right triangle XYZ is √7 / 4, or equivalently, 3/5.

In summary, to find the cosine ratio of ∠Z in the right triangle XYZ, we use the lengths of the adjacent side (XZ) and the hypotenuse (XY). By applying the cosine ratio definition and simplifying the expression, we find that the cosine ratio of ∠Z is 3/5.

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Answer:

I'm pretty sure it is (c)

Step-by-step explanation:

bc the angle is not read in the right order

At least 75% of the flights (or 15 out of the 20 flights) will last between 3 days and 11 days, according to Chebyshev's Theorem.

Chebyshev's Theorem states that for any given number k greater than 1, at least (\(1-\frac{1}{k^2}\)) of the data values in any data set will fall within k standard deviations of the mean.

In this case, we can use Chebyshev's Theorem to determine the minimum number of flights that lasted between 3 and 11 days.

Given:

Mean (μ) = 7 days

Standard Deviation (σ) = 2 days

To find the number of flights within the range of 3 to 11 days, we need to calculate how many standard deviations away from the mean these values are.

Lower Bound:

Value = 3 days

Number of standard deviations away from the

\(mean = \frac{(Value - Mean)}{ Standard Deviation}\)

\(mean =\frac{(3 - 7) }{2}\)

\(mean =\frac{-4}{2}\)

\(mean = -2\)

Upper Bound:

Value = 11 days

Number of standard deviations away from the

\(mean = \frac{(Value - Mean)}{Standard Deviation}\)

\(mean = \frac{(11 - 7)}{2}\)

\(mean = \frac{4}{2}\)

\(mean = 2\)

According to Chebyshev's Theorem, the minimum proportion of data values within k standard deviations of the mean is given by \((1- \frac{1}{k^2} )\).

So, we need to determine the proportion of data within 2 standard deviations, which is k = 2.

Proportion within 2 standard deviations = \(1-\frac{1}{2^2}\)

\(=1-\frac{1}{4}\)

\(= 1 - 0.25\)

\(= 0.75\)

Now, we can find the percentage of \(0.75\):

\(= 0.75\times 100\)

\(= 75\%\)

Therefore, at least 75% of the flights (or 15 out of the 20 flights) will last between 3 days and 11 days, according to Chebyshev's Theorem.

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Kikki was walking rate on the way to the store is 0.93.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Kikki walked to the grocery store, which was 2 miles away.

Her walking rate on the way back was 0.75 of her walking rate on the way to the store because she was carrying a bag of groceries.

If it took Kikki 1 hour to make the round trip,

that means,

x + x(0.75) = 1

(1.075)x = 1

x = 1 / 1.075

x = 0.93

Therefore, the rate is 0.93.

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answer:

a function

step-by-step explanation:

hello there!

as you said, there is only able one output ( y ) for each input ( x ) for it able to become a function

here is a little example of a "table" to help me explain this a little better for you!

input ( x ) | output ( y)

      8       |       -3

      3       |       8

      9       |       4

     -2       |       2

since none the inputs have more then one output then that means it is a function

hope this helps you and please let me know if i had made a mistake in the problem, have a wonderful day!! :D

The first step used in the elimination method is to align the coefficients of one chosen variable in both equations.

To solve a system of equations using elimination, the first step is to align the coefficients of one variable in both equations.

This involves multiplying one or both equations by a constant to create equal coefficients for the chosen variable.

This allows for easy elimination when adding or subtracting the equations.

Once the coefficients are aligned, you can proceed to the next step of eliminating one variable by adding or subtracting the equations.

After eliminating one variable, the resulting equation will have only one variable, which can then be solved for its value.

This value can be substituted back into either of the original equations to find the value of the other variable. Finally, the solution to the system of equations is the values of both variables.

In conclusion, the first step used in the elimination method is to align the coefficients of one chosen variable in both equations.

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Answer:

\( \frac{98}{280} \times \frac{100}{1} \)

\(0.35 \times 100 \\ = 35\%\)

Answer:

The answer is y = 6x² + 42x + 60

Step-by-step explanation:

y = 6(x + 2)(x + 5)

y = 6 × (x + 2) × (x + 5)

y = 6 × (x² + 5x + 2x + 10)

y = 6 × (x² + 7x + 10)

y = 6x² + 42x + 60

Thus, The answer is y = 6x² + 42x + 60

-TheUnknownScientist

In the standard form, we will have: \(\sf {6x}^{2}+42x+60\)

We have the function:

\(\sf y = 6(x + 2)(x + 5)\)

First, we must multiply the terms that are in parentheses. Applying distributive property.

\(\sf y = 6(x\cdot x+x\cdot5+2\cdot x+2\cdot5)\)

We will perform the multiplication.

\(\sf y = 6({x}^{2}+5x+2x+10)\)

We will perform the indicated operation.

\(\sf y = 6({x}^{2}+7x+10)\)

Now, we can multiply the number 6 by what is in parentheses. Also applying distributive property.

\(\sf 6{x}^{2}+42+60\)

The answer of this function is:

\(\boxed{\boxed{\sf 6{x}^{2}+42+60}}\)

Answer:

4 months

Step-by-step explanation:

Equation:

y = 55 + 30x

y = gym membership

x = per month

Work:

y = 55 + 30x

175 = 55 + 30x

30x = 175 - 55

30x = 120

x = 4

4 months

Answer:

  $887.50

Step-by-step explanation:

Her gross pay is the sum of the pay amounts for each of the hour amounts:

  pay = 40(12.50) +18(12.50)(1.5) +2(12.50)(2)

  = (12.50)(40 +18(1.5) +2(2)) = 12.50(40 +27 +4) = 12.50(71)

  pay = 887.50

Barbara's gross pay for the week was $887.50.

Step-by-step explanation:

You need to find 37%  of  $ 77.04

  37%   is  .37 in decimal form

.37  * $ 77.04 = $28.50

Making the retail price :  77.04 + 28.50 = $  105.54     Check !

We are given a joint probability density function (PDF) for two random variables, x and y. We need to derive the marginal distributions of x and y and determine whether x and y are independent or not.

1. Marginal distribution of x and y:

To derive the marginal distribution of x, we integrate the joint PDF with respect to y over the entire range of y:

f_x(x) = ∫[0 to 1] (x + y) dy = xy + (1/2)y^2 |[0 to 1] = x + 1/2

Similarly, to derive the marginal distribution of y, we integrate the joint PDF with respect to x over the entire range of x:

f_y(y) = ∫[0 to 1] (x + y) dx = (1/2)x^2 + xy |[0 to 1] = y + 1/2

2. Independence of x and y:

To determine whether x and y are independent, we compare the joint PDF with the product of the marginal distributions. If the joint PDF is equal to the product of the marginal distributions, x and y are independent; otherwise, they are dependent.

Let's calculate the product of the marginal distributions: f_x(x) * f_y(y) = (x + 1/2) * (y + 1/2) = xy + (1/2)x + (1/2)y + 1/4

Comparing this product with the given joint PDF (x + y), we see that they are not equal. Therefore, x and y are dependent.

In summary, the marginal distribution of x is given by f_x(x) = x + 1/2, and the marginal distribution of y is given by f_y(y) = y + 1/2. Additionally, x and y are dependent since the joint PDF is not equal to the product of the marginal distributions.

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Gary will be able to deduct $1,450 in medical expenses on his 2021 tax return.

Based on the information you provided, we can calculate Gary's deductible medical expenses using the following terms:

1. Qualified medical expenses: $5,200
2. AGI (Adjusted Gross Income): $50,000

According to the IRS, taxpayers can deduct qualified medical expenses that exceed 7.5% of their AGI for the tax year 2021. Here's the step-by-step calculation for Gary's deductible medical expenses:

Step 1: Calculate 7.5% of Gary's AGI
7.5% x $50,000 = $3,750

Step 2: Subtract the 7.5% AGI threshold from Gary's qualified medical expenses
$5,200 - $3,750 = $1,450

Gary will be able to deduct $1,450 in medical expenses on his 2021 tax return.

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While playing, they move, but still maintain the sinusoidal function, ... 5.At the end of the performance, the band marches off the field to the ... Asa grabs his camera to takes a picture of the entire football field. At the instant he takes the picture, the first person forming the curve now stands at the 5 yard line.

The initial amount of money Ada have is $9.25 and this can be determined by forming the linear equation.

Given :

The linear equation can be formed in order to determine the initial amount Ada has.

According to the given data, Ada, Betty, Chris, and David have $45 in total. So, let the initial amount Ada have to be 'w', Betty be 'x', Chris be 'y', and David be 'z'.

Then the linear equation that represents the total amount of money all of them have is $45 is given by:

w + x + y + z = 45   --- (1)

It is also given that Ada gets $2 from Betty, Chris triples his money,  and David's money is cut by half, four of them have the same amount. So, let 'a' be the amount that all of them have so, equation (1) becomes:

4a = 45

a = $11.25  

Now, the initial amount of money Ada have is:

a = x + 2

11.25 = x + 2

x = $9.25

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If it is not true, then the relation is not an implicit solution to the differential equation.

You have not provided the given relation and differential equation, so I will provide general steps to determine whether a given relation is an implicit solution to a differential equation using implicit differentiation and assuming that the relation defines y implicitly as a function of x.

1. Differentiate the relation with respect to x using implicit differentiation.

2. Substitute y' for dy/dx.

3. Simplify the resulting expression by collecting like terms.

4. Substitute the original relation into the simplified expression to obtain a statement that must be true if the relation is an implicit solution to the differential equation.

5. Check whether the resulting statement is true for all values of x and y that satisfy the original relation. If it is true, then the relation is an implicit solution to the differential equation.

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Answer:

45

Step-by-step explanation:

Answer:

Plot the points (0,2) and (3,3)

Step-by-step explanation:

(0,2) is the y-intercept and the slope is always rise over run so go up 1 unit and right 3 units, that gets you to (3,3)

you could also plot any point other than (3,3) that is on the same line

After considering the given data we conclude that the work done in pumping all the water out of the tank is approximately 782,376 foot-pounds.

To evaluate the work done in siphoning all the water out of the hemispherical tank, we really want to find the necessary of the power applied by the water as it is siphoned out.

Starting with, we have to decide the constraints of mix. The tank is totally full, so the underlying level of the water level, A, is from the lower part of the tank (the beginning) to the highest point of the half of the globe, which is 10 ft.

The last level of the water level, B, is 2 ft over the highest point of the tank, which is 12 ft.

Presently, we should decide the articulation for the power applied by a little component of water at level y. The power used by a little component of water is equivalent to its weight, which is the product of its mass and the speed increase because of gravity.

The mass of a little component of water can be approximated as the volume of the relating barrel shaped shell. The volume of a barrel shaped shell is given by \(V = \pi r^2h\),

Here,

r = span of the tank

h = level of the round and hollow shell.

For this situation, the span of the tank is 10 ft, and the level of the tube shaped shell is (12 - y) ft.

The power applied by the water at level y is then

\(F(y) = \rho gV\),

Here,

ρ = thickness of water

g = speed increase because of gravity.

To use the work, we really want to incorporate the power capability regarding y:

\(Work = \int(A to B) F(y) dy = \int(0 to 12) \rho g \pi (12 - y) dy\)

Presently, how about we substitute the given qualities:

ρ = thickness of water = 62.4 lb/f  (around)

g = speed increase because of gravity = 32.2 ft/s² (around)

r = 10 ft

\(Work = \int(0 to 12) (62.4)(32.2)(\pi)( )(12 - y) dy\)

Observing this fundamental will give us the work done in foot-pounds. Then, since the vital articulation is intricate, it is prescribed to use mathematical techniques or a PC program to get the exact mathematical worth.

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Answer: b) (-1,-6)

use the slope equation y2-y1 divided by x2-x1

or just use a slope calculator like i did <3

anyways i hope this helps :)

Answer:

8 dollars

Step-by-step explanation:

2s+5m+s+m=207
s=45
2(45)+5m+45+m=207
135+6m=207

subtract 135 from both sides

6m = 72
divide both sides by 6
m=8 dollars per month of gameplay

The numerical solution of Simpson's 1/3 rule for a single segment, according to the given formula, is: ∫[x₁,x₂] f(x) dx ≈ (x₂ - x₁) / 6 * (f(x₁) + 4f((x₁ + x₂) / 2) + f(x₂))

Simpson's 1/3 rule is a numerical integration technique used to approximate the definite integral of a function over a given interval. It is based on approximating the function by a quadratic polynomial within each subinterval and then integrating that polynomial exactly. The formula provided represents the Simpson's 1/3 rule for a single segment.

In this formula, x₁ and x₂ represent the endpoints of the segment over which we want to approximate the integral. f(x₁) and f(x₂) are the function values at these endpoints. The term (x₂ - x₁) / 6 represents the width of the segment divided by 6, which is a constant factor used in the approximation.

The main approximation step in Simpson's 1/3 rule is to evaluate the function at the midpoint of the segment, which is given by (x₁ + x₂) / 2. This is denoted as f((x₁ + x₂) / 2) in the formula. By using this midpoint, we consider the behavior of the function in the middle of the segment as well.

The formula then combines these function values at the endpoints and the midpoint, weighted by specific coefficients (1, 4, 1), to compute an approximation of the integral over the segment. The coefficients are chosen such that they yield an accurate approximation for certain types of functions.

The Simpson's 1/3 rule for a single segment uses the function values at the endpoints and the midpoint, along with appropriate coefficients, to estimate the integral. This approximation provides a reasonable balance between accuracy and simplicity for many functions.

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The absolute minimum value is -18 at the point (7, 0), and the absolute maximum value is 35 at the point (7, 9) within the given triangular region

To find the absolute minimum and absolute maximum of the function f(x, y) = 10 - 4x + 7y on the closed triangular region with vertices (0, 0), (7, 0), and (7, 9), we need to evaluate the function at the critical points inside the region and at the boundary points.

Critical points:

To find the critical points, we need to find the points where the gradient of f(x, y) is equal to zero.

∇f(x, y) = (-4, 7)

Setting -4 = 0 and 7 = 0, we see that there are no critical points in the interior of the triangular region.

Boundary points:

We need to evaluate the function f(x, y) at the vertices of the triangular region.

(a) f(0, 0) = 10 - 4(0) + 7(0) = 10

(b) f(7, 0) = 10 - 4(7) + 7(0) = -18

(c) f(7, 9) = 10 - 4(7) + 7(9) = 35

Therefore, the absolute minimum value is -18 at the point (7, 0), and the absolute maximum value is 35 at the point (7, 9) within the given triangular region.

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Check the picture below.

\(\cfrac{1^3}{12^3}~~ = ~~\cfrac{V}{33764}\implies \cfrac{1}{1728}~~ = ~~\cfrac{V}{33764}\implies \cfrac{(1)(33764)}{1728}=V\implies \boxed{\stackrel{ cm^3 }{19.54}\approx V}\)

The answer that refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time is prevalence.

Prevalence is the total number of cases of a disease or disorder in a population at a given point in time, and does not include cases that have been resolved or previously diagnosed cases. It is an important measure of the health of a population, as it allows researchers to identify patterns in the distribution of a disease or disorder and helps inform public health strategies.

Prevalence is calculated by dividing the total number of cases of a disease or disorder in a population at a given point in time, by the size of the population. For example, if a population of 100,000 people has 500 cases of a particular disease, the prevalence would be 0.005 or 0.5%.

Prevalence is an important metric in epidemiology and public health, and is often used in combination with incidence rates to measure the health of a population. Incidence rates measure the number of new cases of a disease or disorder that occur in a population over a certain time period, whereas prevalence is a snapshot of the total number of cases of a disease or disorder in a population at a given point in time.

Knowing the prevalence of a disease or disorder in a population helps public health practitioners understand the magnitude of a health issue, inform public health strategies, and identify risk factors and trends in the distribution of a disease or disorder.

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The forward Euler discrete scheme is defined by the formula y_n+ h*f(x_n,y_n). The backward Euler discrete scheme is given by y_n+ h*f(x_(n+1),y_(n+1)).

The improved Euler discrete scheme is given by y_n+ (1/2)*(k1+k2) The first-order ODE is given by `y = f(x)`. Below is the forward Euler, backward Euler and improved Euler discrete scheme for this equation: Forward Euler Discrete Scheme - The forward Euler discrete scheme is defined by the formula given below: `y_(n+1)= y_n+ h*f(x_n,y_n)` where `y_(n+1)` is the solution of the ODE at the next step, `y_n` is the solution at the current step, `h` is the step size and `f(x_n,y_n)` is the slope at `(x_n,y_n)`.

Backward Euler Discrete Scheme - The backward Euler discrete scheme is defined by the formula given below: `y_(n+1) = y_n+ h*f(x_(n+1),y_(n+1))`

where `y_(n+1)` is the solution of the ODE at the next step, `y_n` is the solution at the current step, `h` is the step size and `f(x_n+1,y_(n+1))` is the slope at `(x_n+1,y_(n+1))`.

Improved Euler Discrete Scheme - The improved Euler discrete scheme is defined by the formula given below: `k1 = h*f(x_n,y_n)`  `k2 = h*f(x_n+1,y_n+k1)`  `y_(n+1)= y_n+ (1/2)*(k1+k2)`

where `y_(n+1)` is the solution of the ODE at the next step, `y_n` is the solution at the current step, `h` is the step size and `f(x_n,y_n)` and `f(x_n+1,y_n+k1)` are the slopes at `(x_n,y_n)` and `(x_n+1,y_n+k1)` respectively.

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The general form of a quadratic equation is Ax^2 + Bx + C.

For the given expression 2 + 6x^2 - 2x, it is already in general form with A = 6, B = -2, and C = 2.

So the general form of this expression is 6x^2 - 2x + 2.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α, β).

The solution or roots of a quadratic equation are given by the quadratic formula:

(α, β) = [-b ± √(b2 – 4ac)]/2a

Sum and product of roots: If α and β are the roots of a quadratic equation, then

S = α+β= -b/a = -coefficient of x/coefficient of x^2

P = αβ = c/a = constant term/coefficient of x^2

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A. The average number of minutes per day spent moving these products using the static storage policy is 1.33 minutes.

B.  The lowest value of average minutes per day used to move these SKUs with the heap policy is approximately 1.17 minutes per day. The initial placement of the SKUs does make a difference in determining the lowest average movement time, as shown by the difference between Scenario 1 and Scenario 2.

a. Static Storage Policy:

To minimize labor, we can allocate the SKUs to storage locations based on their respective travel times from the receiving area to the storage area. In this case, the travel times are 1 minute for location A, 2 minutes for location B, and 2 minutes for location C.

Given that we maintain a constant inventory of one pallet of SKU x and two pallets of SKU y at all times, we can allocate them as follows:

SKU x: Allocate it to the storage location with the shortest travel time, which is location A (1 minute).

SKU y: Allocate both pallets to the storage location with the next shortest travel time, which is location B or C (both have a travel time of 2 minutes).

By allocating SKU x to location A and both pallets of SKU y to either location B or C, we ensure that the SKUs are stored in the closest available locations, minimizing the travel time needed to move them.

The average number of minutes per day spent moving these products can be calculated by considering the dispatch and receiving schedule:

SKU x: Dispatched every three days. Assuming it takes 1 minute to move a pallet from storage to the receiving area, the average daily movement time for SKU x would be (1/3) minutes per day.

SKU y: Dispatched every two days. Assuming it takes 2 minutes to move a pallet from storage to the receiving area, the average daily movement time for SKU y would be (2/2) minutes per day.

Adding up the average daily movement times for SKU x and SKU y, we get:

Average daily movement time = (1/3) + (2/2) = 1.33 minutes per day.

Therefore, the average number of minutes per day spent moving these products using the static storage policy is 1.33 minutes.

b. Heap Policy:

The heap policy involves storing the most frequently dispatched SKU closest to the receiving area. In this case, SKU y is dispatched every two days, while SKU x is dispatched every three days.

To find the lowest value of average minutes per day used to move these SKUs with the heap policy, we need to consider the different initial placements of the SKUs.

Scenario 1: Initial Placement - Location A for SKU x and Location B for SKU y

SKU x: Travel time from storage to the receiving area = 1 minute

SKU y: Travel time from storage to the receiving area = 2 minutes

Average daily movement time:

SKU x: (1/3) minutes per day

SKU y: (2/2) minutes per day

Total average daily movement time = (1/3) + (2/2) = 1.33 minutes per day

Scenario 2: Initial Placement - Location A for SKU y and Location B for SKU x

SKU y: Travel time from storage to the receiving area = 1 minute

SKU x: Travel time from storage to the receiving area = 2 minutes

Average daily movement time:

SKU y: (1/2) minutes per day

SKU x: (2/3) minutes per day

Total average daily movement time = (1/2) + (2/3) ≈ 1.17 minutes per day

Therefore, the lowest value of average minutes per day used to move these SKUs with the heap policy is approximately 1.17 minutes per day. The initial placement of the SKUs does make a difference in determining the lowest average movement time, as shown by the difference between Scenario 1 and Scenario 2.

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Answer:

$20400

Step-by-step explanation:

8 percent *55000 =

(8:100)*55000 =

(8*55000):100 =

440000:100 = $4400

16000+4400 =$20400

Given :-

To Find :-

Solution :-

As we know that the slope of two parallel lines are same . So , the given equation is ,

\(\sf\longrightarrow\) y = 2x -1

On comparing to the slope intercept form of the line we have ,

\(\sf\longrightarrow\) m = 2

Hence the slope of the parallel line will be 2 .

Now here we can use the point slope form of the line as ,

\(\sf\longrightarrow\) y - (-5) = 2( x - 4)

\(\sf\longrightarrow\) y + 5 = 2x -8

\(\sf\longrightarrow\) 2x - y -8 -5 = 0

\(\sf\longrightarrow\) 2x - y -13 = 0

Hence the required answer is 2x - y -13 = 0.