solve the equation 25a=10a squared

The rate of change of the angle of elevation from the lamp to the javelin when the javelin is 37 feet off the ground is zero.

Let's denote the distance from the lamp to the point directly below the javelin by x, and the height of the javelin above the ground by y. Then we have two right triangles: one with legs x and y, and hypotenuse 31, and another with legs x and 37-y, and hypotenuse 37. Using the Pythagorean theorem, we can write:

x^2 + y^2 = 31^2

x^2 + (37-y)^2 = 37^2

Taking the derivative with respect to time t of both sides of each equation, we get:

2x(dx/dt) + 2y(dy/dt) = 0

2x(dx/dt) - 2(37-y)(dy/dt) = 0

Solving for (dy/dt) in terms of (dx/dt), we get:

(dy/dt) = x(dy/dx)/(-y+37)

At the given moment when the javelin is 37 feet off the ground, we have y = 37, and so:

(dy/dt) = x(dy/dx)/(-y+37) = x(dy/dx)/(-37+37) = 0

This means that the rate of change of the angle of elevation is zero at this moment. In other words, the angle of elevation is not changing at the moment when the javelin is 37 feet off the ground.

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By simplifying  the derivative of f(x) is:,[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 10(x^2 + 2)sin^3(x) + 15(x^2 + 2)cos^3(x) + 20(x^2 + 2)sin^ 2 (x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2 )[/tex]

A derivative is a mathematical cοncept that represents the rate at which a functiοn changes with respect tο οne οf its variables. In οther wοrds, the derivative measures hοw much the οutput οf a functiοn changes when yοu change the input by a small amοunt.

Tο find the derivative οf f(x), we will use the quοtient rule οf differentiatiοn.

Let's begin by simplifying the expression:

[tex]f(x) = [5(x^2 + 2) cot(x)]/[2 - cos(x) csc(x)][/tex]

[tex]f(x) = [5(x^2 + 2) cos(x)/sin(x)]/[2sin(x) - cos(x)][/tex]

[tex]f(x) = [5(x^2 + 2) cos(x)]/[sin(x)(2sin(x) - cos(x))][/tex]

Now we can apply the quotient rule:

[tex]f'(x) = [(5(x^2 + 2) cos(x))'sin(x)(2sin(x) - cos(x)) - (5(x^2 + 2) cos(x))(sin(x)(2sin(x) - cos(x)))']/(sin(x)(2sin(x) - cos(x))^2)[/tex]

To simplify, let's find the derivatives of the individual terms in the numerator:

[tex][(5(x^2+ 2) cos(x))'] = 10xcos(x) - 5(x^2+ 2)sin(x)[/tex]

[tex][(sin(x)(2sin(x) - cos(x)))'] = 3cos^2 (x) - 4sin^2(x)[/tex]

Now we can substitute these back into our original equation for f'(x):

[tex]f'(x) = [(10xcos(x) - 5(x^2 + 2)sin(x))sin(x)(2sin(x) - cos(x)) - (5(x^2 + 2) cos(x))(3cos^2(x) - 4sin^2 x))]/(sin(x)(2sin(x) - cos(x))^2)[/tex]

Simplifying further:

[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 5(x^2 + 2)sin^2 (x)(2sin(x) - cos(x)) - 15(x^2 + 2)cos^3(x) + 20(x^2 + 2)sin^2x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2)[/tex]

[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 10(x^2 + 2)sin^3(x) + 15(x^2 + 2)cos^3(x) + 20(x^2+ 2)sin^ 2(x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2)[/tex]

Therefore, the derivative of f(x) is:

[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 10(x^2 + 2)sin^3(x) + 15(x^2 + 2)cos^3(x) + 20(x^2 + 2)sin^2(x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2)[/tex]

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Based on the given task content; the solution to the linear expressions 4(2b + 2) - 3 and -4 + 8p - 6p - 5 + 20p is 8b + 5 and -9 + 22p respectively.

11. 4(2b + 2) - 3

open parenthesis

= 8b + 8 - 3

= 8b + 5

12. -4 + 8p - 6p - 5 + 20p

combine like terms

-4 - 5 + 8p - 6p + 20p

= -9 + 22p

In conclusion, 8b + 5 and -9 + 22p is the solution to the linear expressions 4(2b + 2) - 3 and -4 + 8p - 6p - 5 + 20p respectively.

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Answer:

2cos(3ẞ/2)(sin(7ẞ/2) + cos(19ẞ/2))

Step-by-step explanation:

We can use the identity for the sum of two sines to rewrite the expression as follows

sin 4ẞ + sin 10ẞ = 2sin(7ẞ/2)cos(3ẞ/2)

Similarly, we can use the identity for the sum of two cosines to rewrite the expression as follows

22ẞ + sin 16ẞ = 2cos(19ẞ/2)cos(3ẞ/2)

Therefore, we have

sin 4ẞ + sin 10ẞ + 22ẞ + sin 16ẞ = 2sin(7ẞ/2)cos(3ẞ/2) + 2cos(19ẞ/2)cos(3ẞ/2)

Factoring out the common factor of cos(3ẞ/2), we get

sin 4ẞ + sin 10ẞ + 22ẞ + sin 16ẞ = 2cos(3ẞ/2)(sin(7ẞ/2) + cos(19ẞ/2))

Therefore, the expression can be expressed as a product of 2cos(3ẞ/2) and the sum of sin(7ẞ/2) and cos(19ẞ/2).

Answer:

what type of a question is this man can send me the full question so i can answer to you??

Answer: 12 1/2

Step-by-step explanation:

thats the answer

A graph of A(x) and B(x) in the interval 0 ≤ x 100 on a cartesian coordinate is shown below.

The solution of A(x) = B(x) to the nearest integer is (35, 8).

In Mathematics, an exponential function can be represented or modeled by using the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided about the two plans for speeding up its technical support time, we can logically deduce the following exponential functions;

[tex]A(x) = 15.7(0.98)^x \\\\B(x) = 11(0.99)^{x}[/tex]

By critically observing the graph of the two exponential functions, we can logically deduce that the point of intersection (solution) is in quadrant I, which is given by the ordered pair (35, 8).

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Answer: D is correct.

Step-by-step explanation:

The economic system that has no government involvement in the market is d. No economic system is free from government involvement.

In reality, there is no government intervention because at some point the government will comes in , this could actually be minimal, only in the free market is where there is no government intervention.

It should be noted that in this free market, there is an unregulated system of economic exchange, where the act of taxes collection as well as quality controls,  has no economic interventions which can be attributed to the government. Because of this, option D is correct.

I hope this helped! Brainilist is highly appreciated! <333

Answer:

x = 40

Step-by-step explanation:

given a line DE parallel to a side AC of the triangle and intersecting the other two sides, it intersects those sides proportionally , that is

[tex]\frac{CE}{BE}[/tex] = [tex]\frac{AD}{BD}[/tex] ( substitute values )

[tex]\frac{25}{x-25}[/tex] = [tex]\frac{15}{24-15}[/tex]

[tex]\frac{25}{x-25}[/tex] = [tex]\frac{15}{9}[/tex] ( cross- multiply )

15(x - 25) = 9 × 25 = 225 ( divide both sides by 15 )

x - 25 = 15 ( add 25 to both sides )

x = 40

Jemna has to devide [tex]1[/tex] cup pancake in [tex]4[/tex] mini pan cakes so that the batter be distributed  in a fraction of [tex]\frac{1}{4}[/tex] th form

[tex]9[/tex]. The rectangle will be [tex]\frac{1}{3}[/tex] in fraction.

[tex]10[/tex]. Out of [tex]3 boxes[/tex] [tex]1[/tex] should be shaded.

[tex]11[/tex]. [tex]\frac{1}{3}[/tex] of [tex]4[/tex]

[tex]13[/tex]. [tex]\frac{1}{12}[/tex]

[tex]14[/tex]. [tex]\frac{1}{12}[/tex]

[tex]15[/tex] In division the value gets reciprocate ÷[tex]\frac{1}{3}[/tex][tex]\frac{4}{1}[/tex] = [tex]\frac{1}{3}[/tex]* [tex]\frac{1}{4}[/tex] by changing into multiplication.

Fractions are referred to as the components of a whole in mathematics. A single item or a collection of objects can be the whole. When we cut a slice of cake in real life from the entire cake, the portion represents the fraction of the cake.

[tex]9[/tex]. To calculate how much of a cup of dough will go into each pancake, divide [tex]1[/tex]÷[tex]4[/tex] to get [tex]\frac{1}{4}[/tex]

Let's now examine the rectangle that depicts a cup divided into three equally sized parts. Divide 1 by 3 to determine how much each portion represents as [tex]\frac{1}{3}[/tex]

[tex]10[/tex]. Out of [tex]3 boxes[/tex] [tex]1[/tex] should be shaded

[tex]11[/tex]. [tex]\frac{1}{3}[/tex] of [tex]4[/tex]

[tex]13.\frac{1}{12}= \frac{1}{3}[/tex]÷[tex]4[/tex][tex]=\frac{1}{3} *\frac{1}{4}[/tex]

[tex]14[/tex] Same as previous one

[tex]15[/tex] In division the value gets reciprocate ÷[tex]\frac{1}{3}[/tex][tex]\frac{4}{1}[/tex] = [tex]\frac{1}{3}[/tex]* [tex]\frac{1}{4}[/tex] by changing into multiplication.

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Answer:

Step-by-step explanation:

the answer is 192

9hrs=$144

12hrs=X

you cross multiple

12x144/9

which give you $192

Answer:

Jenny made $144 for 9 hours of work so you divide 144 by 9 and you get 16.

$16 is the amount of money that Jenny makes in an hour. To check if it's correct you multiply 16 by 9 and you should get 144.

So, since the question wants you to find how much she makes for 12 hours of work, you multiply 16 times 12 and you should get 192.

In conclusion, Jenny makes $192 for 12 hours of work.

Answer:

75 square feet

Step-by-step explanation:

you will just multiply by 1 over 40 as it is the ratio that he works in one hour

Based οn the infοrmatiοn in the tabIe, the statement that is true based οn the given data is:

A. P(aduIt|rοde the swing ride) = P(aduIt)

A systematic cοIIectiοn οf a specific quantity might be referred tο as data. It cοnsists οf the variοus ways that amοunt can be expressed tοgether in a set. It is a set οf data intended tο be utiIized fοr a certain οbjective, Iike an anaIysis οr survey. It is pοssibIe tο refer tο anything as infοrmatiοn when it is οrganized.

This assertiοn may οr may nοt be accurate. WhiIe we are aware that 96/240 = 0.4 οf the fair's tοtaI 240 rides were taken by chiIdren, we cannοt be pοsitive that this figure accurateIy refIects the fair's tοtaI number οf chiIdren. $450.00 + $200.00 + $175.00

A. AduIt|tοοk the swing ride: P(aduIt|P) (aduIt)

This cIaim may nοt aIways be accurate. AIthοugh 0.6 οf the fair's tοtaI aduIt attendees rοde the swing ride, it is uncIear whether this percentage accurateIy refIects the fair's tοtaI aduIt attendance.

B. This assertiοn is nοt true οr accurate.

P(aduIt [had a ride οn the Ferris wheeI]) + C (aduIt)

This assertiοn Iacks bοth cIarity and vaIidity.

We can caIcuIate the prοbabiIities using the given data as fοIIοws:

P(aduIt|rοde the swing ride) = 96/240 = 0.4

P(aduIt) = (144+108)/360 = 0.8

P(aduIt[rοde the Ferris wheeI) + P(aduIt) = (72/180) + (144+108)/360 = 0.6

P(rοde the swing ride|chiId) = 96/240 = 0.4

P(rοde the swing ride) = 240/360 = 2/3

P(chiId|rοde the Ferris wheeI) = 24/180 = 0.133

Therefοre, the statement that is true based οn the given data is:

OA. P(aduIt|rοde the swing ride) = P(aduIt)

because the prοbabiIity οf an aduIt riding the swing ride (0.4) is the same as the οveraII prοbabiIity οf being an aduIt (0.8).

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Answer:

Step-by-step explanation:

Based οn the infοrmatiοn in the tabIe, the statement that is true based οn the given data is:

A. P(aduIt|rοde the swing ride) = P(aduIt)

What dο the different fοrms οf data mean?  

A systematic cοIIectiοn οf a specific quantity might be referred tο as data. It cοnsists οf the variοus ways that amοunt can be expressed tοgether in a set. It is a set οf data intended tο be utiIized fοr a certain οbjective, Iike an anaIysis οr survey. It is pοssibIe tο refer tο anything as infοrmatiοn when it is οrganized.

This assertiοn may οr may nοt be accurate. WhiIe we are aware that 96/240 = 0.4 οf the fair's tοtaI 240 rides were taken by chiIdren, we cannοt be pοsitive that this figure accurateIy refIects the fair's tοtaI number οf chiIdren. $450.00 + $200.00 + $175.00

A. AduIt|tοοk the swing ride: P(aduIt|P) (aduIt)

This cIaim may nοt aIways be accurate. AIthοugh 0.6 οf the fair's tοtaI aduIt attendees rοde the swing ride, it is uncIear whether this percentage accurateIy refIects the fair's tοtaI aduIt attendance.

B. This assertiοn is nοt true οr accurate.

P(aduIt [had a ride οn the Ferris wheeI]) + C (aduIt)

This assertiοn Iacks bοth cIarity and vaIidity.

We can caIcuIate the prοbabiIities using the given data as fοIIοws:

P(aduIt|rοde the swing ride) = 96/240 = 0.4

P(aduIt) = (144+108)/360 = 0.8

P(aduIt[rοde the Ferris wheeI) + P(aduIt) = (72/180) + (144+108)/360 = 0.6

P(rοde the swing ride|chiId) = 96/240 = 0.4

P(rοde the swing ride) = 240/360 = 2/3

P(chiId|rοde the Ferris wheeI) = 24/180 = 0.133

Therefοre, the statement that is true based οn the given data is:

OA. P(aduIt|rοde the swing ride) = P(aduIt)

because the prοbabiIity οf an aduIt riding the swing ride (0.4) is the same as the οveraII prοbabiIity οf being an aduIt (0.8).

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Answer: like three out of a thousand, would be likely to last less than 525 hours or more than 975 hours.

Step-by-step explanation:

normal distribution is shaped like a bell curve with the average (mean) at the center.

A light bulb in your problem is most likely to last about 750 hours. One standard deviation up from that would be 750 + 75, which is 825 hours, and one standard deviation down is 750 - 75, which is 675 hours.

According to the empirical rule, the interval from the average to +1 standard deviation (750 to 825) and the interval from the average to -1 standard deviation (675 to 725) each have a 34.1% probability.

From +1 to +2 standard deviations and -1 to -2 standard deviations (825 to 900 and 600 to 675) the probability is 13.5% for each interval.

From +2 to +3 standard deviations and -2 to -3 standard deviations (900 to 975 and 525 to 600) the probability is 2.1% for each interval.

These percentages are the same for any normal distribution problem. If you add up the chances you can find the probability a light bulb will last an increasing range of times centered around the average:

Within one standard deviation of the average: 68.3% (chance it will last 675 to 825 hours)

Within two standard deviations of the average: 95.4% (chance it will last 600 to 900 hours)

Within three standard deviations of the average: 99.7% (chance it will last 525 to 975 hours)

And only a very few, like three out of a thousand, would be likely to last less than 525 hours or more than 975 hours.

Answer:

Step-by-step explanation:

We can use the DuPont model to calculate the ROE (Return on Equity):

ROE = Profit margin * Total assets turnover * Equity multiplier

Substituting the given values, we get:

ROE = 0.085 * 1.5 * 1.8 = 0.2295 or 22.95%

Therefore, Precision Aviation's ROE was 22.95%.

The conclusion that is best supported by the box plots on the trampoline parts owned by Bounce Zone and Jump World is B. For both companies, about 25% of the parks have 21 or fewer trampolines.

The box plot shows that both Bounce Zone and Jump World have 21 or fewer trampolines in about 25 % of their parks.

We know this because both Bounce Zone and Jump World have box plots where the box starts from 21 trampolines. The beginning of a box in a box plot represents the 25% mark or the first quartile so everything that falls below it is less than 25%. Bounce Zone and Jump World therefore have 21 or less trampolines in 25% of their parks.

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The options for the question is:

Ronaldo therefore feeds his family 2 and 4/7 sandwiches as he eats sandwiches that are three and three-sevenths .

A mathematical strategy for resolving proportionality issues is the unitary method. Finding the value of one unit of a quantity and utilising that value to determine the value of a different number of units of the same quantity is what this process entails. The unitary technique can be used, for instance, to determine the cost of any quantity of apples if you know that 5 apples cost $10. $10/5 = $2 would be the price of one apple. By multiplying the quantity of apples by the price of one apple, you could then calculate the price of any other number of apples. For instance, 8 apples would cost 8 x $2, or $16, to purchase.

given

Ronaldo eats sandwiches that are three and three-sevenths of a sandwich, which is an incorrect fraction:

3 3/7 = (7*3 + 3)/7 = 24/7

He divides these sandwiches into thirds and fourths among his family, making a total of:

(3/4) * (24/7) = (324)/(47) = 18/7

We can change this incorrect fraction into a mixed number because:

18/7 = 2 and 4/7

Ronaldo therefore feeds his family 2 and 4/7 sandwiches as he eats sandwiches that are three and three-sevenths .

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Answer:

  4 minutes

Step-by-step explanation:

You want to know how long it takes to drain a cylindrical tank 1.8 ft in diameter and 3 ft long at the rate of 1.7 ft³/minute. (π = 3.14)

The volume of a cylinder can be found using the formula ...

  V = (π/4)d²h . . . . . . . diameter d, height h

Then the volume of the oil tank is ...

  V = 3.14/4(1.8 ft)²(3 fft) = 7.6302 ft³

The time it takes to empty the tank is found by dividing the volume by the rate:

  (7.6302 ft³)/(1.7 ft³/min) ≈ 4.49 min ≈ 4 min

It will take about 4 minutes to empty the tank.

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INCOME BEFORE TAXES for the year ended December 31, 2011 is $669.

Gross Profit = Gross Sales - Sales Returns and Allowances - Sales Discounts - Cost of Goods Sold

Cost of Goods Sold = Beginning Inventory + Net Purchases + Freight In - Ending Inventory

Cost of Goods Sold = $67,600 + $84,000 + $950 - $78,300 = $74,250

Gross Profit = $223,000 - $11,200 - $1,800 - $74,250 = $135,750

Operating Expenses = Salaries + Rent + Utilities + Insurance = $107,200 + $19,500 + $1,450 + $2,150 = $130,300

Income Before Taxes = Gross Profit - Operating Expenses - Income Tax

Income Before Taxes = $135,750 - $130,300 - $14,900 = $669

Therefore, the entry for INCOME BEFORE TAXES for the year ended December 31, 2011 is $669.

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Answer:

46_ parce que c'est comme ça

The value of q is 16.

What is a quadratic equation?

Any equation can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation. An equation containing a single variable of degree 2.

Here, we have

Given: Equation: 3x²+18x–21 = 0 is written in the form (x–p)²=q.

We have to find the value of q.

3x²+18x–21 = 0

3(x²+6x-7) = 0

x²+6x-7 = 0

(x+3)²-7-9 = 0

(x+3)² - 16 = 0

(x+3)² = 16

(x-p)² = q

Hence, the value of q is 16.

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Answer: ;)

The area of a circle is 64 square units

Step-by-step explanation:

Area of a circle a=64 square units in terms of

Step-by-step explanation:

Given that the diameter of a circle is 16

That is d=16

Therefore radius r=8

Now to find the area of a circle :Area of a circle square units

Substitute r=8 we get

Area of a circle

Therefore the area of a cicle is 64 square units

Area of a circle a=64 square units in terms of

Answer:

  d)  1/(4e)

Step-by-step explanation:

You want the value of the limit of 1/4f(x)^(1/x) as x approaches -1, where f(x) = x^2·e^(x^2).

The function is continuous and defined at x=-1, so the limit can be evaluated directly.

  [tex]\lim=\dfrac{1}{4}((-1)^2\cdot e^{(-1)^2})^{(1/-1)}=\dfrac{1}{4}(1\cdot e^1)^{-1}=\boxed{\dfrac{1}{4e}}[/tex]

(b) u₁e^λ₁t +u₂e^λ₂t (pI-A)⁻¹ f₀e^pt f for p ≠λ₁ orλ₂ as the coefficients can only be determined when the value of p is not equal to either of the eigenvalues  λ₁ or λ₂.

Eigenvalues are scalars associated with a linear transformation or a matrix. They can be used to determine the stability of the system and describe the behavior of the transformation.

In this case, the eigen values λ₁ and λ₂ are constants, and the solution to the differential equation y' + Ay = f₀e^pt can be solved by using the method of undetermined coefficients.

This method involves using a linear combination of the eigenvectors, which are associated with the eigenvalues  λ₁ and λ₂.

The solution for this differential equation is then given by u₁e^λ₁t +u₂e^λ₂t (pI-A)⁻¹ f₀e^pt f for p ≠ λ₁ or λ₂.

This is because the coefficients can only be determined when the value of p is not equal to either of the eigenvalues  λ₁ or λ₂. If p is equal to one of these eigenvalues, then the solution cannot be determined as the coefficients become indeterminate.

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[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108[/tex]

From the calculation that we have in the question, the volume of the rectangular prism is 30 cm^3.

A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional shape that has six rectangular faces, where each pair of opposite faces are congruent and parallel. It can be thought of as a stretched cube, where the length, width, and height are all different.

We have that the volume of the rectangular prism is

V = lbh

V = 2 * 3 * 5

V = 30 cm^3

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Thus, the equation of a parallel line with the slope -3 and passing point (2,−1) is found as : y = -3x + 5.

Two or more lines that have been spaced the same apart, never merging but never diverging, are said to be parallel. Parallel lines run indefinitely in both directions because, as we mentioned earlier, lines are non-stop.

As long as they are consistently spaced at the same distance apart, they don't necessarily need to be straight lines.

equation of a line :  y = −3x−5

Comparing with slope-intercept form of line.

y = mx + c

m is the slope and c is the y intercept.

m = -3

Parallel lines have the same slopes:

m = -3 and passing points (2,−1).

Using the point -slope equation:

y - y 1 = m(x - x1)

y + 1 = -3(x - 2)

y = -3x + 6 - 1

y = -3x + 5

Thus, the equation of a parallel line with the slope -3 and passing point (2,−1) is found as : y = -3x + 5.

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Complete question:

Find the equation of a line parallel to y=−3x−5that passes through the point (2,−1).