What is the solution to the system X-3y=-9 and -3x+9y=12

To find the equation of the tangent line to the curve y = 7sin(x) at x = π, we first need to find the slope of the tangent line.

We can use the derivative of y with respect to x to find the slope:

dy/dx = 7cos(x)

At x = π, the value of the derivative is:

dy/dx = 7cos(π) = -7

So the slope of the tangent line at x = π is -7.

To find the equation of the tangent line, we also need to know the y-coordinate of the point on the curve where x = π.

y = 7sin(π) = 0

So the point on the curve where x = π is (π, 0).

Now we can use the point slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

Plugging in the values we found, we get:

y - 0 = -7(x - π)

Simplifying, we get:

y = -7x + 7π

So the equation of the tangent line to y = 7sin(x) at x = π is y = -7x + 7π.

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Answer: 2x+y=1

3x-y=-6

==>5x=-5

==>x=-1 and y=1-2*(-1)=3

Sol={(-1,3)}

Answer A

When using supervised learning, the fit() technique requires two arrays of training data, but unsupervised learning only requires one array.

After the model is initialised, the "fit" method runs the algorithm on the training data. That is all it does, in essence. Thus, the machine learning model is trained using the training data by the sklearn fit approach. In the manufacturing industry, the term "form-fit-function" (FFF) refers to a part's distinguishing features (a single component that goes into the final build of your product, typically kept on an item master).

model.fit(): fit practise data This accepts the data X and the labels y as two arguments for supervised learning applications (e.g., model. fit(X, y)). Function at Cost. The cost function for linear regression is the Sum of Squares of Errors with the lowest value. Calculate the squared error sum for each and every available line.

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The number of hours worked by Anthony , Josh and Dominic is 2 hours , 0 hours and 5 hours respectively

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of hours worked by Anthony = A

Let the number of hours worked by Josh = J

Let the number of hours worked by Dominic = D

Total number of hours worked by Anthony , Josh and Dominic = 7 hours

So , A + J + D = 7   be equation (1)

Now ,

Dominic worked twice as many hours as Anthony did with an extra hour

So , D = 2A + 1   be equation (2)

And ,

Dominic worked 5 more hours than Josh did

So , D = 5 + J   be equation (3)

Simplifying be equation (2) and be equation (3) , we get

2A + 1 = 5 + J

Subtracting 5 on both sides , we get

J = 2A - 4   be equation (4)

Now ,

Substituting the values of equation (2) , equation (3) and equation (4) in equation (1) , we get

A + 2A - 4 + 2A + 1 = 7

5A - 3 = 7

Adding 3 on both sides , we get

5A = 10

Divide by 5 on both sides , we get

A = 2

Therefore , the number of hours Anthony worked is 2 hours

Now , Substituting the value of A in equation (4) , we get

J = 4 - 4

J = 0 hours

Therefore , the number of hours Josh worked is 0 hours

Now , Substituting the value of A in equation (2) , we get

D = 4 + 1

D = 5 hours

Therefore , the number of hours Dominic worked is 5 hours

Hence , The number of hours worked by Anthony , Josh and Dominic is 2 hours , 0 hours and 5 hours respectively

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Answer:

272/49

Step-by-step explanation:

hope this helps :)

Answer:

\( \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{:}\ \)

Linear function :The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input. Linear functions are related to linear equations.

Step-by-step explanation:

We have

y=mx+c

for 1st

not satisfied.

for

2nd

not satisfied

3rd

3rd satisfied

4th

[note : substitute value of x to get value of y from table]

so

third table represents a linear function.

Answer:

The third option is the answer

Step-by-step explanation:

its like the only one which fits the question

Answer:

6

Step-by-step explanation:

Answer:

The coefficient would be 6

Step-by-step explanation:

3x2x is just multiplying 3x and 2x (assuming). If that is the case, then when you multiply the two together, your coefficient is 6.

Take the difference in y coordinates and divide that by the difference in the x coordinates. That's the slope, sometimes called the "rise over run"  For a straight line or a linear function the slope is a constant

(6-10)(7,10) = 2/3 = slope

the line is

y-h = m(x-k) where m=2/3 and (k,h) = (10,10) or either point

to get y-10 = (2/3)(x-10)

3y -30 = 2x-20

2x-3y = -10

or use (k,h) as (7,8)

y-8 = (2/3)(x-7)

3y-24 = 2x-14

2x-3y = -10

or if you write it in y=mx + b form

it's y=(2/3)x + 10/3  where 10/3 is the y-intercept and 2/3 = slope

In this form, take the derivative of (2/3)x + 10/3

to get y' = 2/3,  the derivative is the slope

Answer:

840

Step-by-step explanation:

7000×2×6 ÷ 100. since it is 2%

= 840

Answer:

\(\frac{(x -7)(x-1)}{y}\)

Step-by-step explanation:

\(x^{2}\) / x - 1 - 6x - 7/ x - 1

(it's the equation shown in the picture, you might have typed it wrong on your question)

The equation has the same denominator so, it will become:

\(\frac{x^{2} - 6x - 7}{y}\)

Which factors into:

\(\frac{(x -7)(x-1)}{y}\)

Answer:

x=19/5

Step-by-step explanation:

x*2+8x=38

10x  =38

Step-by-step explanation:

5(1+x)

= 5 + 5x

= 5x + 5

.......

Answer:

(−∞,∞)

Step-by-step explanation:

5(1+x)=5x+5

5*1=5

(5+x)=5x+5

5*x=5x

5+5x=5x+5

5-5=0

5x-5x=0

Answer:

\(\dfrac{1}{12}$ gallons\)

Step-by-step explanation:

\(M$arie bought $ \dfrac{1}{2}$ gallon of milk\)

She exhausted the half gallon in 6 days.

Since she takes equal amount of milk per day

Her Unit Rate of Milk Consumption

\(=\dfrac{1}{2}\div 6\\ =\dfrac{1}{12}$ gallons per day\)

Marie drinks \(\dfrac{1}{12}\) gallons of milk per day.

Answer: 1/12

Step-by-step explanation:

Answer:

60.1 feet

Step-by-step explanation:

x= length of ladder

48/sin53 = x/sin90

x=48*sin90/sin53

x=60.1

Answer: (14 , 15/2)

Step-by-step explanation:

...

Answer:

No, K isn't the midpoint of JL

Answer:  y=-7x + 37

Step-by-step explanation:

Parallel lines will have the same slope but different y-intercepts  so again we can  use the coordinates to determine the y intercept of the new equation.

So we know that the slope intercept formula is y=mx + b where m is the slope and b is the y-intercept so we will input the x and y coordinates to solve for b.

9 = -7(4) + b

9 = -28 + b

+28  +28

b = 37  

The equation will be y= -7x + 37

The equation of line passes through the point (4, 9) will be;

⇒ y = - 7x + 37

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (4, 9).

And, The parallel line is,

⇒ y = - 7x - 9

Now,

Since, The equation of line passes through the point (4, 9).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

y = - 7x - 9

m = dy/dx = - 7

m = - 7

Thus, The equation of line with slope - 7 is,

⇒ y - 9 = -7 (x - 4)

⇒ y - 9 = - 7x + 28

⇒ y = - 7x + 28 + 9

⇒ y = - 7x + 37

Therefore, The equation of line passes through the point (4, 9) is,

⇒ y = - 7x + 37

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Main Answer: The most general antiderivative of the function g(v) = 9 cos(v) − 6 / (1 − v²) is given by G(v) = 6ln|1 − v²| + 9 sin(v) + C where C is a constant of the antiderivative.

Supporting Explanation: The given function is g(v) = 9 cos(v) − 6 / (1 − v²). We can observe that the function is of the form f(v)/g(v), where f(v) = 9 cos(v) and g(v) = 1 − v². We know that the antiderivative of f(v)/g(v) is given by log |g(v)| + C1, where C1 is a constant of integration. Hence, the antiderivative of 9 cos(v) / (1 − v²) can be obtained as 9 times the antiderivative of cos(v) / (1 − v²).We know that antiderivative of cos(x) is sin(x). Using this and partial fractions, we can simplify the given function g(v) as shown below: g(v) = 9 cos(v) − 6 / (1 − v²)= 9 cos(v) / (1 − v²) − 6 / (1 − v²)= 9 [(1 − v² + 1)/(1 − v²)] + 6ln|1 − v²|= 9 + 9 / (1 − v²) + 6ln|1 − v²|. Thus, the most general antiderivative of the function g(v) = 9 cos(v) − 6 / (1 − v²) is given by G(v) = 6ln|1 − v²| + 9 sin(v) + C where C is a constant of the antiderivative.

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Answer:

it cannot be converted to radical form

Step-by-step explanation:

Answer:

i dont see the graph

Step-by-step explanation:

i could do this with a graph lol

Answer:

4.29

Step-by-step explanation:

In a Linear Programming problem, the objective function line is moved in the direction that reduces cost.

Linear Programming (LP) is an operation research approach used to determine the best outcomes, such as optimum profit, minimum cost, or maximum yield, given a set of constraints represented as linear relationships. Linear programming's fundamental idea is to find the best value of a linear objective function that takes into account a variety of constraints that are linear inequalities or equations. The goal of the constraints is to restrict the values of the decision variables. A linear programming problem consists of a linear objective function and linear inequality constraints, as well as decision variables. In a Linear Programming problem, we try to maximize or minimize a linear objective function, which represents our target. This objective function is expressed as a linear equation consisting of decision variables, each of which has a coefficient. Linear programming's ultimate goal is to find values of the decision variables that maximize or minimize the objective function while still satisfying the system of constraints we're working with. In this case, the objective function line is moved in the direction that reduces cost, which means we are minimizing the cost. We do this by moving the objective function line down towards the minimum point. This is the point where the objective function has the smallest possible value that meets all of the constraints.

Thus, in a Linear Programming problem, the objective function line is moved in the direction that reduces cost.

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Answer:

Step-by-step explanation:

Joshua wants to buy a flat-screen TV that costs $625. He saves $62.50 each week to buy the TV. In how many weeks will he have enough money to make his purchase?

A. 8

B. 9

C. 10

D. 11

cost of television divided by weekly savings = number of weeks

625 : 62.50 = 10 weeks

The expected value of the cash prize at the fundraiser is $2.

The expected value can be calculated by multiplying the probability of each outcome by its corresponding monetary value, and then summing up these values. In this case, the probability is determined by the number of tickets sold, and the monetary value is the cash prize.

To find the expected value, we need to calculate the product of the probability and the cash prize for each possible outcome. Since there are 1700 tickets sold, each with a $9 price, the probability of winning the cash prize is 1/1700. Therefore, the expected value can be calculated as:

Expected Value = (Probability of winning) * (Cash prize)

= (1/1700) * $3400

= $2

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Answer:

1. V≈1244.07

2. V≈54286.72

3.V≈23816.41

4. V≈254.47

5. V≈4247.43

6. V≈21714.69

7. V≈4712.39

Step-by-step explanation:

use the formula V=πr^2h

The volume of the given cylinders is 1. V≈1244.07 2. V≈54286.72 3. V≈23816.41 4. V≈254.47 5. V≈4247.43 6. V≈21714.69 7. V≈4712.39.

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = \(\pi r^{2} h\)

A.

a) The height of the cylinder is given as 11 in and the radius is 6 in.

So, The volume of the cylinder = \(\pi r^{2} h\)

                                                    = 3.14 x 6^2 x 11

                                                    = 1244.07cubics in

b)  The height of the cylinder is given as 30 in and the radius is 24 in.

So, The volume of the cylinder = \(\pi r^{2} h\)

                                                    = 3.14 x 24^2 x 30

                                                    = 54286.72 cubics in

c) The height of the cylinder is given as 21 in.

The radius of the base of the cylinder is given as 19 in.

So, The volume of the cylinder = \(\pi r^{2} h\)

                                                    = 3.14 x 19^2 x 21

                                                    = 23816.41 cubics in

B.

d) The height of the cylinder is 9ft the radius is 3 ft.

So, The volume of the cylinder = \(\pi r^{2} h\)

                                                    = 3.14 x 3^2 x 9

                                                    = 254.47 cubics ft

e) The height of the cylinder is 8 ft the radius is 13 ft.

So, The volume of the cylinder = \(\pi r^{2} h\)

                                                    = 3.14 x 13^2 x 8

                                                    = 4247.43 cubics ft

f) The height of the cylinder is 27 ft the radius is 16 ft.

So, The volume of the cylinder = \(\pi r^{2} h\)

                                                    = 3.14 x 16^2 x 27

                                                    = 21714.69 cubics ft

g) The height of the cylinder is 15 ft the radius is 10 ft.

So, The volume of the cylinder = \(\pi r^{2} h\)

                                                    = 3.14 x 10^2 x 15

                                                    = 4712.39 cubics ft

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The solution to the equation 2(x + 6) = 3(x - 4) + 5 is x = 19.

To solve the equation 2(x + 6) = 3(x - 4) + 5, the first step is to simplify both sides of the equation by distributing the coefficients. Distributing the coefficient 2 on the left side gives us 2x + 12, while distributing the coefficient 3 on the right side gives us 3x - 12. The equation now becomes 2x + 12 = 3x - 12 + 5.

Next, we can combine like terms on both sides of the equation. On the right side, we have 3x - 12 + 5, which simplifies to 3x - 7. So the equation becomes 2x + 12 = 3x - 7.

To isolate the variable x, we can move all the terms with x to one side of the equation and all the constant terms to the other side. In this case, we can subtract 2x from both sides to get rid of the 2x term on the left side. This gives us 12 = x - 7.

Finally, we can add 7 to both sides to isolate x. This gives us x = 12 + 7, which simplifies to x = 19.

So the solution to the equation 2(x + 6) = 3(x - 4) + 5 is x = 19.

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Answer:

x = 1/4

Step-by-step explanation:

-6x –(-9 – 4x) = -2(3x – 5)

-6x + 9 + 4x = -6x + 10

-2x + 9 = -6x + 10

-2x + 6x = 10 - 9

4x = 1

x = 1/4

Answer:

30,000 meters squared.

The length of the shortest path that the gecko can take to reach the fly is \($2 \sqrt{29}$\) feet.

Here's how to solve the problem: We can start by sketching out a diagram of the room and labeling the positions of the gecko and the fly. We'll use the corner where the gecko is as the origin, and label the coordinates of the gecko as (0,1,1) and the coordinates of the fly as (12,1,7). The distance between these two points is the shortest path that the gecko can take to reach the fly.

Now we can use the distance formula to calculate this distance:

\($$\sqrt{(12-0)^2 + (1-1)^2 + (7-1)^2}=\sqrt{144+36}=2\sqrt{29}$$\)

Therefore, the length of the shortest path the gecko can take to reach the fly is \($2\sqrt{29}$\) feet.

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Answer:

To find the unit rate, we need to express the rate as a quantity of 1. In this case, we can express the rate as the number of miles traveled per hour.

The unit rate is 55 miles per hour.

We can find the unit rate by dividing the total distance traveled by the time it took to travel that distance:

165 miles / 3 hours = 55 miles per hour

Answer:

55 mph

Step-by-step explanation:

You are given     miles      and     hours   and want to find  miles/hour

   165 miles / 3 hours = 55 miles per hour