How many solutions does the system have? 4x-2y=8 2x+y=2

Answers

Answer 1

Answer:0

Step-by-step explanation:


Related Questions

Somebody help me please

Answers

Answer:

Other dude is correct

Step-by-step explanation:

Solve the system of differential equations s = Ly' - 29x + 42y – 20x + 294 = x(0) = – 15, y(0) = == - 11 The lesser of the two eigenvalues is Its corresponding eigevector is (a, – 2). What is a? a = The greater of the two eigenvalues is Its corresponding eigevector is ( – 7,6). What is b? b = = The solution to the system is x(t) = = y(t) =

Answers

The lesser of the two eigenvalues is λ = -1. Its corresponding eigenvector is [-42 29].

The greater of the two eigenvalues is λ = 1. Its corresponding eigenvector is [42 29].

To solve the system of differential equations:

x' = -29x + 42y

y' = -20x + 29y

We can rewrite it in matrix form as follows:

X' = AX

where X = [x y] is a vector, X' represents the derivative of X with respect to time, and A is the coefficient matrix. In this case, A is given by:

A = [ -29 42 ]

[ -20 29 ]

To find the eigenvalues and eigenvectors, we need to solve the characteristic equation:

det(A - λI) = 0

where λ is the eigenvalue and I is the identity matrix. Solving this equation will give us the eigenvalues, and by substituting these eigenvalues back into the equation (A - λI)V = 0, where V is the corresponding eigenvector, we can find the eigenvectors.

Let's calculate the eigenvalues first. We have:

A - λI = [ -29 42 ]

[ -20 29 ] - λ [ 1 0 ]

[ 0 1 ]

Expanding the determinant, we get:

(-29 - λ)(29 - λ) - (42)(-20) = 0

(λ + 29)(λ - 29) + 840 = 0

λ² - 29² + 840 = 0

λ² - 841 + 840 = 0

λ² = 1

λ = ±1

So the eigenvalues are λ = 1 and λ = -1.

To find the corresponding eigenvectors, we substitute each eigenvalue back into the equation (A - λI)V = 0.

For λ = 1, we have:

[ -29 42 ] [ v₁ ] [ 0 ]

[ -20 29 ] [ v₂ ] = [ 0 ]

This gives us the following system of equations:

-29v₁ + 42v₂ = 0

-20v₁ + 29v₂ = 0

Solving this system, we find that v₁ = 42 and v₂ = 29.

Therefore, the eigenvector corresponding to the eigenvalue λ = 1 is [42 29].

For λ = -1, we have:

[ -29 42 ] [ v₁ ] [ 0 ]

[ -20 29 ] [ v₂ ] = [ 0 ]

This gives us the following system of equations:

-29v₁ + 42v₂ = 0

-20v₁ + 29v₂ = 0

Solving this system, we find that v₁ = -42 and v₂ = 29.

Therefore, the eigenvector corresponding to the eigenvalue λ = -1 is [-42 29].

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Complete Question:

Solve the system of differential equations

x' = -29x + 42y

y' = -20x + 29y

x(0) = -15, y(0) = -11

The lesser of the two eigenvalues is Its corresponding eigenvector is

The greater of the two eigenvalues is Its corresponding eigenvector is

For each of the following rejection regions, what is the probability that a Type I error will be made?
a. t> 2.718, where df = 11
b. t< -1.476, where df = 5
c. t< -2.060 or t > 2.060, where df = 25

a. The probability that a Type I error will be made is _____ (Round to two decimal places as needed.)


Answers

The probability of a Type I error in rejection region a is 0.01.

What is probability?

We must  find  the area under the t-distribution curve outside the rejection region, assuming a two-tailed test in order to to determine the probability of making a Type I error in each rejection region.

for a. t > 2.718, and df = 11:

Using a t-distribution table,  the probability is 0.01.

b. t < -1.476, df = 5:

Using a t-distribution table the probability is 0.05.

c. t < -2.060 or t > 2.060, df = 25:

Using a t-distribution table, the area in each tail is  0.025.

The combined probability of a Type I error in rejection region c is

0.025 + 0.025 = 0.05.

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The total weight of all the students in a class is 3,159 lb. The mean weight of the students is 117 lb. How many students are there in the class?

Answers

Answer:

27

Step-by-step explanation:

You do 3159 ÷ 27

Comes out to 27

I found 27 by just plugging in numbers.

Hope this helps

Answer:

There are 27 students in the class.

Step-by-step explanation:

Since the total weight is 3,159 and the average weight is 117lb, you can just divide 3,159 by 117, which will give you 27.

Factor completely please. 3k^2-19k+20

Answers

3k^2-4k-15k+20
k(3k-4)-5(3k-4) /factor out (3k-4) from it
=> (3k-4)(k-5)

Answer:

3(k*k)-3(3k)-5(2k)+2(5+5)

Step-by-step explanation:

3k²-19k+20

Just find some number that equal the terms when multiplied. ¯\_(ツ)_/¯

DOUBLE CHECK!

3(k*k)-3(3k)-5(2k)+2(5+5)

Multiply what you need to.

3k²-9k-10k+20

Combine like terms.

3k²-19k+20

---

hope it helps

There are 35 green, 22 white, 30 purple and 14 blue gumballs in the gumball machine.
Sharee wants to get a white or green gumball.
What is the probability of getting a white or green gumball?

Answers

Answer:

The probability of getting a white or green gumball is 35.64%.

Step-by-step explanation:

1. calculate the total number of gumballs in the gumball machine

35 + 22 + 30 + 14 = 101 gumballs

2. calculate the number of white and green gumballs combined

22 + 14 = 36 w/g gumballs

3. divide the number of white and green gumballs combined by the total number of gumballs in the gumball machine

36 / 101 = 0.3564

Answer: the probability of getting a white or green gumball is 35.64% (0.3564).

Probability is the chance of occurring an event from the total possible outcomes.

The probability of getting a white or a green gumball is 57/101.

What is probability?

It is the chance of occurring an event from the total possible outcomes.

We have,

Green gumballs = 35

White gumballs = 22

Purple gumballs = 30

Blue gumballs = 14

Total gumballs = 35 + 22 + 30 + 14 = 101

The combination is given by:

= [tex]^nC_{r}[/tex]

= n! / r! (n-r)!

The probability of choosing a white gumball:

= [tex]\frac{^{22}C_{1}}{^{101}C_{1} }[/tex]

= 22 / 101

The probability of choosing a green gumball:

= [tex]\frac{^{35}C_{1}}{^{101}C_{1} }[/tex]

= 35 / 101

The probability of getting a white or a green gumball:

= 22/101 + 35 / 101

= (22 +35) / 101

= 57 / 101

Thus the probability of getting a white or a green gumball is 57/101.

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A triangle has three angles that measure 50 degrees, 28 degrees and 3x. What is the value of x?

Answers

Answer:

57.33

Step-by-step explanation:

50+28+3x=180

78+3x=180-78

3x=172/3

x = 57.33


Evan says that plants get most of the materials they need to
grow from air and water. Use evidence/data to support and
explain his argument.

Answers

The evidence and data support Evan's argument that plants predominantly acquire the materials they need to grow from air and water .

Evan's statement is supported by evidence and data that demonstrate how plants obtain the majority of the materials they need to grow from air and water. Here are some key points to support his argument:

Carbon Dioxide (CO2) from the air: Through the process of photosynthesis, plants take in carbon dioxide from the air. They use the carbon dioxide along with water and sunlight to produce glucose and oxygen. This glucose serves as an essential energy source for plant growth and development.

Water: Plants absorb water from the soil through their root systems. Water plays a critical role in various plant processes, including nutrient uptake, transportation, and the maintenance of cell turgidity. It is a primary component of plant cells and is necessary for photosynthesis to occur.

Essential nutrients from the soil: While air and water provide the primary materials for plant growth, plants also require certain nutrients to thrive. These essential nutrients, such as nitrogen, phosphorus, and potassium, are typically obtained from the soil. However, it's important to note that these nutrients are often dissolved in water and taken up by plant roots.

Experimentation and research: Numerous scientific experiments and studies have been conducted to investigate plant nutrient uptake. These experiments have confirmed that plants can grow and develop using only air, water, and the necessary nutrients found in these sources.

The evidence and data support Evan's argument that plants predominantly acquire the materials they need to grow from air and water. While nutrients from the soil are essential, the primary sources of plant growth materials are carbon dioxide from the air and water, which are crucial for photosynthesis and various physiological processes in plants.

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: A random sample of 850 Democrats included 731 that consider protecting the environment to be a top priority. A random sample of 950 Republicans included 466 that consider protecting the environment to be a top priority. Construct a 95% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment. (Give your answers as percentages, rounded to the nearest tenth of a percent.)

Answers

The 95% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is approximately 37.0% ± 5.0%.

Calculate the proportions for Democrats and Republicans:

Proportion of Democrats prioritizing environment = 731/850 ≈ 0.860

Proportion of Republicans prioritizing environment = 466/950 ≈ 0.490

Next, calculate the standard error (SE) of the difference between the proportions:

SE = √[(p1(1 - p1))/n1 + (p2(1 - p2))/n2]

= √[(0.860(1 - 0.860))/850 + (0.490(1 - 0.490))/950]

≈ √(0.000407 + 0.000245)

≈ √0.000652

≈ 0.0255

Now, calculate the margin of error (ME) using the critical value for a 95% confidence level (z-value):

ME = z × SE

≈ 1.96 × 0.0255

≈ 0.04998

Finally, construct the confidence interval:

Difference in proportions ± Margin of error

(0.860 - 0.490) ± 0.04998

0.370 ± 0.04998

The 95% confidence interval is approximately 37.0% ± 5.0%.

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help me

The two major types of metal electrical cable are:

A.wire and fibre
B.twisted pair and coaxial
C.twisted pair and fibre optic
D.coaxial and fibre optic

2. What are the most common forms of wireless connection?

A.infrared beams
B.microwaves
C.radio waves
D.all of the above

3. Wi-fi connections have limited range of :

A.10 metres
B.600 metres
C.20 metres
D.300 metres​​​

Answers

Answer:

1.The two major types of metal electrical cable are:

A.wire and fibre

2. What are the most common forms of wireless connection?

C.Radio news

3. Wi-fi connections have limited range of :

D.300 metres

A triangular pane of glass has a height of 30 inches and an area of 240 square inches. What is the length of the base of the pane?

Answers

240÷30=8

8×30=240

30 height 8 with

If you have a circle with a central angle of 80 degrees, what is the degrees of its inscribed angle?

Answers

Answer:

The measure of the inscribed angle is [tex]40^{\circ}[/tex]

Step-by-step explanation:

Recall that the measure of the inscribed angle is one-half the measure of the central angle subtended by the same arc.

So, if the measure of the central angle is [tex]80^{\circ}[/tex], so the measure of the corresponding inscribed angle is:

[tex]\frac{1}{2}\times 80^{\circ}=40^{\circ}[/tex]




4. Use polynomial fitting to find the closed form for the sequence 2, 5, 11, 21, 36, ...

Answers

The sequence continues as follows:2, 5, 11, 21, 36, 67, ...

Given sequence2 5 11 21 36...

First differences 3 6 10 15...

Second differences 3 4 5...

Third differences 1 1...

The third differences are constant, which means that we can use a cubic polynomial for the fitting.

The formula for a cubic polynomial is

an³ + b

n² + c

n + d

Let us denote the nth term of the sequence by fn. Then, we have

f1 = 2, f2 = 5, f3 = 11, f4 = 21, f5 = 36...

We can write a system of equations using the first four terms of the sequence.

2 = a + b + c + d

5 = 8a + 4b + 2c + d

11 = 27a + 9b + 3c + d

21 = 64a + 16b + 4c + d

Solving this system, we get a = 1/3, b = 1, c = 11/3, and d = 0.

Thus, the closed-form expression for the nth term of the sequence isf(n) = (1/3)n³ + n² + (11/3)n

The next term in the sequence is f(6) = (1/3)(6)³ + (6)² + (11/3)(6) = 67.

Therefore, the sequence continues as follows:2, 5, 11, 21, 36, 67, ...

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A triangle has a 35° angle, a 55° angle, and a side 6 centimeters in length,
Select True or False for each statement about this type of triangle.
True
False
The triangle might be an isosceles triangle.
The triangle might be an acute triangle.
The triangle must contain an angle measuring 90°.
O

Answers

Answer:

f

f

v

Step-by-step explanation:

find the indicated iq score. the graph depicts iq scores of adults and those scores are normally distributed with a mean of 100 and a standard deviatio of 15 the shaded are under the curve is 0.5675

Answers

The indicated IQ score, corresponding to the shaded area under the curve of 0.5675 in a normal distribution with a mean of 100 and a standard deviation of 15, is approximately 102.55.

To find the indicated IQ score, we need to determine the corresponding z-score using the given information about the normal distribution. Here's how we can calculate it step by step:

Step 1: Identify the shaded area under the curve.

The shaded area under the curve represents the cumulative probability of the IQ scores. In this case, the shaded area is 0.5675 or 56.75%.

Step 2: Convert the cumulative probability to a z-score.

To find the z-score corresponding to the shaded area, we need to find the z-score that gives us a cumulative probability of 56.75%. We can use a standard normal distribution table or a statistical calculator to find the z-score.

Step 3: Find the z-score.

Using a standard normal distribution table, we can search for the closest cumulative probability to 0.5675. The closest cumulative probability we can find in the table is 0.5681, which corresponds to a z-score of approximately 0.17.

Step 4: Convert the z-score to an IQ score.

Now that we have the z-score of 0.17, we can use the formula for transforming z-scores to raw scores:

IQ score = (z-score × standard deviation) + mean

Given that the mean is 100 and the standard deviation is 15, we can calculate the IQ score:

IQ score = (0.17 × 15) + 100

IQ score = 2.55 + 100

IQ score ≈ 102.55

Therefore, the indicated IQ score is approximately 102.55.

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Simplify 4(8x).
A. 8x
B. 4x
C. 32x
D. 8 + 4x

Answers

Answer:

32x

Step-by-step explanation: 4(8x)=32x

Newton has just gone grocery shopping. The mean cost for each item in his bag was $3.38. He bought a total of 6 items, and the prices of 5 of those items are listed below:
$4.09, $4.03, S4.19, $2.24, $4.09
Determine the price of the 6th item in his bag.

Answers

Newton has just gone grocery shopping. The mean cost for each item in his bag was $3.38. The price of the 6th item in his bag is $1.64

To determine the price of the 6th item in Newton's bag, we can use the concept of the mean (average). We know that the mean cost for each item in his bag is $3.38, and he bought a total of 6 items.

To find the sum of all 6 item prices, we can multiply the mean cost by the total number of items:

Sum of all item prices = Mean cost * Total number of items

                                    = $3.38 * 6

                                    = $20.28

We also know the prices of 5 of the items, which are $4.09, $4.03, $4.19, $2.24, and $4.09.

To determine the price of the 6th item, we subtract the sum of the known prices from the sum of all item prices:

Price of the 6th item = Sum of all item prices - Sum of known prices

= $20.28 - ($4.09 + $4.03 + $4.19 + $2.24 + $4.09)

= $20.28 - $18.64

= $1.64

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Write a cosine function that has a midline of y=5, an amplitude of 3, a period of 1, and a horizontal shift of 1/4 to the right

Answers

The graph of this function begins at 5 and moves down to 2 and back to 5 again in a repeated pattern over one period of 1.

A cosine function is a periodic function that fluctuates about its midline and follows a predictable pattern. The formula for a cosine function with a midline of y = c, amplitude of a, and period of b is:y = a cos(bx) + cTo shift the graph of a cosine function,

you can add or subtract a value inside the parentheses of the formula, which results in a horizontal shift.

The shift is to the right if you add, and to the left if you subtract.In this instance,

the cosine function has the following characteristics:Midline = y = 5Amplitude = 3Period = 1Horizontal shift to the right = 1/4We'll have to adjust the formula to include all of these parameters.

First and foremost, let's figure out the function's frequency, which is determined by dividing 2π by the period of the cosine function. In this example, the frequency is 2π/1, which equals 2π.

y = a cos(bx) + c is the formula we'll use. We'll substitute the values given into the formula. The resulting formula is:y = 3cos(2π(x - 1/4)) + 5This is the cosine function with a midline of y = 5, an amplitude of 3, a period of 1, and a horizontal shift of 1/4 to the right.

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identify the slope and y-intercept of the lins given by the equation y=2x 1.

Answers

Answer 2 I took the test

solve the differential equation by variation of parameters. y'' y = csc(x)

Answers

The solution to the differential equation y'' + y = csc(x) using the variation of parameters method is y(x) = cos(x)ln|sin(x)| + Csin(x), where C is a constant.

To solve the differential equation by variation of parameters, we first find the complementary solution (the solution to the homogeneous equation). The homogeneous equation is y'' + y = 0, which has the solution y_c(x) = Acos(x) + Bsin(x), where A and B are constants.

Next, we find the particular solution using the variation of parameters method. We assume the particular solution is of the form y_p(x) = u(x)cos(x) + v(x)sin(x), where u(x) and v(x) are unknown functions.

We differentiate y_p(x) to find y_p' and y_p'' and substitute them into the original differential equation. After simplification, we obtain u'(x)sin(x) - v'(x)cos(x) = csc(x).

To solve this system of equations, we find the derivatives u'(x) and v'(x) and integrate them to obtain u(x) and v(x). Finally, we substitute u(x) and v(x) into the particular solution form y_p(x) = u(x)cos(x) + v(x)sin(x).

The final solution is y(x) = y_c(x) + y_p(x), which simplifies to y(x) = cos(x)ln|sin(x)| + Csin(x), where C is the constant of integration.

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evaluate ∫30(4f(t)−6g(t)) dt given that ∫150f(t) dt=−7, ∫30f(t) dt=−8, ∫150g(t) dt=4, and ∫30g(t) dt=8

Answers

The evaluation of ∫30(4f(t) - 6g(t)) dt given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8 is -80.

Given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8.

Let us evaluate ∫30(4f(t) - 6g(t)) dt.

Therefore,∫30(4f(t) - 6g(t)) dt = ∫30(4f(t) dt - 6g(t) dt) = 4 ∫30f(t) dt - 6 ∫30g(t) dt

Now, using the given values in the question we can say that,∫30(4f(t) - 6g(t)) dt = 4 ∫30f(t) dt - 6 ∫30g(t) dt = 4 (-8) - 6(8) = -32 - 48 = -80

Therefore, the evaluation of ∫30(4f(t) - 6g(t)) dt given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8 is -80.

Note: The given integrals ∫150f(t) dt, ∫30f(t) dt, ∫150g(t) dt, and ∫30g(t) dt are only intermediate steps in order to evaluate the final integral.

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Which graphed function is described by the given intervals? Increasing on (−∞, 0) Decreasing on (0, ∞)
A) A
B) B
C) C
D) D

Answers

The best answer to go with is b

Solve the system with the addition method: - 8x + 5y = -33 +8.x – 4y = 28 Answer: (x, y) Preview 2 Preview y Enter your answers as integers or as reduced fraction(s) in the form A/B.

Answers

The solution to the system -8x + 5y = -33 and 8x - 4y = 28 is (x, y) = (7, -1).

To solve the given system of equations using the addition method, let's eliminate one variable by adding the two equations together. The system of equations is:

-8x + 5y = -33 (Equation 1)

8x - 4y = 28 (Equation 2)

When we add Equation 1 and Equation 2, the x terms cancel out:

(-8x + 5y) + (8x - 4y) = -33 + 28

y = -5

Now that we have the value of y, we can substitute it back into either Equation 1 or Equation 2 to solve for x. Let's use Equation 1:

-8x + 5(-5) = -33

-8x - 25 = -33

-8x = -33 + 25

-8x = -8

x = 1

Therefore, the solution to the system is (x, y) = (1, -5).

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y=Ax^2 + C/x is the general solution of the DEQ: y' + y/x = 39x. Determine A. Is the DEQ separable, exact, 1st-order linear, Bernouli?

Answers

The exact value of A in the general solution is 13

Also, the DEQ is separable

How to determine the value of A in the general solution

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

y = Ax² + C/x

The differential equation is given as

y' + y/x = 39x

When y = Ax² + C/x is differentiated, we have

y' = 2Ax - Cx⁻²

So, we have

2Ax - Cx⁻² + y/x = 39x

Recall that

y = Ax² + C/x

So, we have

2Ax - Cx⁻² + (Ax² + C/x)/x = 39x

Evaluate

2Ax - Cx⁻² + Ax + Cx⁻² = 39x

This gives

2Ax +  Ax  = 39x

So, we have

3Ax = 39x

By comparing both sides of the equation, we have

3A = 39

Divide both sides by 3

A = 13

Hence, the value of A in the general solution is 13

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What is the solution to the following system of equations?
x+y=5
x-y=1

(–2, 7)
(2, 3)
(3, 2)
(7, –2)

Answers

Answer:

x+y=5

×-y=1

2x/2=6/2

x=3

while x+y=5

3+y=5

y=5-3

y=2

Answer:

C

Step-by-step explanation:

(3, 2)

Identify the coefficient in the following expression 6a +7​

Answers

Answer:

The coefficient is 6

Step-by-step explanation:

Find the solution to the initial value problem y' = x² — ½, y(2) = 3.

Answers

The solution to the initial value problem using the method of separation of variables is y = (x³/3) - (1/2)x + 4/3.

To solve the initial value problem y' = x² - 1/2 with the initial condition y(2) = 3, we can use the method of separation of variables. Here are the steps:

Step 1: Separate the variables

Write the given differential equation in the form:

dy/dx = x² - 1/2

Step 2: Integrate both sides

Integrate both sides of the equation with respect to x:

∫dy = ∫(x² - 1/2) dx

Integration yields:

y = (x³/3) - (1/2)x + C

Step 3: Apply the initial condition

To find the constant C, substitute the initial condition y(2) = 3 into the equation obtained in Step 2:

3 = (2³/3) - (1/2)(2) + C

Simplifying the equation:

3 = 8/3 - 1 + C

3 = 8/3 - 3/3 + C

3 = 5/3 + C

Therefore, C = 3 - 5/3 = 9/3 - 5/3 = 4/3.

Step 4: Write the final solution

Substitute the value of C back into the equation obtained in Step 2:

y = (x³/3) - (1/2)x + 4/3

So, the solution to the initial value problem y' = x² - 1/2, y(2) = 3 is y = (x³/3) - (1/2)x + 4/3.

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LA Galaxy have won 35% of there soccer matches, and drawn 9 of them. If they played 40 matches, how many have they lost?

Answers

Answer:17

Step-by-step explanation:

0.35•40=14 to find how many they’ve won

14+9=23 is how many they have won or drawn

40-23=17 is how many they’ve lost

Which angles are neither obtuse angles nor acute angles?

Answers

Answer:

Acute angles are less than 90

obtuse is more than 90

right angles are exactly 90

Step-by-step explanation:

Answer:

First option: 90 degrees

Step-by-step explanation:

Obtuse is greater than 90.

Acute is less than 90.

Right is 90.

For the following exercise, write the equation of the ellipse in standard form. Then identify the center, vertices, and foci. 9x² + 36y²-36x + 72y +36 = 0

Answers

The given equation, 9x² + 36y² - 36x + 72y + 36 = 0, represents an ellipse. In standard form, the equation can be written as (x-1)²/4 + (y+1)²/1 = 1. The center of the ellipse is at (1, -1), the vertices are located at (3, -1) and (-1, -1), and the foci are at (2, -1) and (0, -1).

To write the equation 9x² + 36y² - 36x + 72y + 36 = 0 in standard form, we need to complete the square for both the x and y terms. By rearranging the equation, we have 9x² - 36x + 36 + 36y² + 72y + 36 = 0.

Next, we can factor out a 9 from the x terms and a 36 from the y terms: 9(x² - 4x + 4) + 36(y² + 2y + 1) = 0.

Simplifying further, we have 9(x - 2)² + 36(y + 1)² = 36.

Dividing both sides by 36, we get (x - 2)²/4 + (y + 1)²/1 = 1, which is the standard form of an ellipse.

From the standard form, we can determine that the center of the ellipse is located at (1, -1), the vertices are at (3, -1) and (-1, -1), and the foci are at (2, -1) and (0, -1).

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