find all missing angles​

X(t) = Pexp(Dt)P⁻¹X(0),where X(0) is the initial Condition.

9.1 To find the eigenvalues of a matrix A is equivalent to finding the solutions to the equation det(A- λI) = 0. λ is an eigenvalue of A if and only if λ is a solution of the characteristic equation det(A- λI) = 0.

We have A = [2 9; 1 2]

The characteristic equation is given by|2- λ 9| = (2- λ)(2- λ) - 9 = λ² - 4λ - 5 = 0Therefore, the eigenvalues are given byλ₁ = -1 and λ₂ = 5.9.2

The eigenspace of a matrix A associated with an eigenvalue λ is the set E of all eigenvectors of λ, together with the zero vector E = ker(A - λI).

Thus we must solve the equations(A - λ₁I)x = 0 and (A - λ₂I)x = 0.For λ₁ = -1, we have A + I = [3 9; 1 3],

giving(A + I)x = 0 ⇒ x₁ + 3x₂ = 0 ⇒ x₁ = - 3x₂.So the eigenspace E₁ = Span{(-3, 1)}.For λ₂ = 5, we have A - 5I = [-3 9; 1 -3], giving(A - 5I)x = 0 ⇒ - 3x₁ + 9x₂ = 0 ⇒ x₁ = 3x₂.So the eigenspace E₂ = Span{(3, 1)}.9.3

If there exists a basis of eigenvectors for A, then A is diagonalizable. A is diagonalizable if and only if the eigenspaces Ei are such that dim(Ei) = multiplicity of λi, where λi is the ith eigenvalue of A. If so, then A is similar to a diagonal matrix .

The dimensions of E₁ and E₂ are both 1, and so dim(E₁) + dim(E₂) = 2 = n, where n is the order of the matrix.

So A is diagonalizable.9.4 Let P = [x y] be a matrix whose columns are the eigenvectors of A.

Then P-¹AP is a diagonal matrix whose diagonal entries are the eigenvalues of A.

So, we have P = [-3 3; 1 1], with P⁻¹ = [-⅓ ⅓; ⅓ ⅓] andP⁻¹AP = [-1 0; 0 5].Therefore, A = P[P⁻¹AP]P⁻¹ = [-3 3; 1 1][1 0; 0 5][-⅓ ⅓; ⅓ ⅓] = [-2 -9; 1 2].9.5 We have already found that A = PDP⁻¹ whereD = diag(-1, 5) andP = [-3 3; 1 1].

Therefore,A² = PDP⁻¹PDP⁻¹ = PD²P⁻¹= [-3 3; 1 1][1 0; 0 25][-⅓ ⅓; ⅓ ⅓] = [7 -27; 5 -19].A³ = A²A = [7 -27; 5 -19][-2 -9; 1 2] = [-187 297; -131 207].9.6

The differential equations are 3/₁ = ₁ + 2x₂ and 3/₂ = 21₁ + 1₂. We can write these asa vector equationX' = AX,where X = [x₁ x₂]ᵀ, X' = [3/₁ 3/₂]ᵀand A = [1 2; 21 1].We have already diagonalised A as A = PDP⁻¹, whereD = diag(-1, 5) andP = [-3 3; 1 1].Therefore,X' = AX ⇒ P⁻¹X' = P⁻¹AX ⇒ Y' = DY,where Y = P⁻¹X = [-1/3 2/3; 1/3 1/3]X and Y' = P⁻¹X'.SoY' = DY = [-1 -5; 2 10]Y.

The solution is given byY(t) = exp(Dt)Y(0),where exp(Dt) is the matrix exponential exp(Dt) = [e⁻ᵗ e⁻5ᵗ; -2e⁻ᵗ + 2e⁻5ᵗ 2e⁻ᵗ - e⁻5ᵗ].

Therefore,X(t) = Pexp(Dt)P⁻¹X(0),where X(0) is the initial condition.

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Answer:

x=28/3

Step-by-step explanation:

Answer:

x=9 and 1/3

Step-by-step explanation:

x/8+5/6=2

Common denominator will be 48. So:

6x/48+40/48=2

That means that (6x+40)/48=2

(since they both have the same denominator)

Now, multiply 2 by 48. You get 96.

6x+40=96

Subtract 40

6x=56

x=9 and 1/3

Answer:

t = -3

Step-by-step explanation:

Answer: (-3,-7)

Step-by-step explanation: I had to get it wrong on delta to give u this answer, ur welcome.

Answer:

you have to provide the questions

Step-by-step explanation:

What were some major changes that took place in the art world following the Reformation?

The answer is C because they do not repeat.

Answer:

......................

Step-by-step explanation:

you are welcome

a)  Yes, the result is significant at the 5% level.

b)  No, the result is not significant at the 5% level.

c)The difference in significance between the two results can be explained by the slight increase in the sample mean from 541.4 to 541.5.

(a)To test the hypotheses, we will use a one-sample t-test since we have the sample mean (xbar = 541.4) and the population standard deviation (σ = 100) is known. The sample size is 100.

The test statistic (t-score) is calculated using the formula:

t = (xbar - μ) / (σ / √n)

where xbar is the sample mean, μ is the population mean under the null hypothesis, σ is the population standard deviation, and n is the sample size.

In this case:

xbar = 541.4, μ = 525, σ = 100, and n = 100.

t = (541.4 - 525) / (100 / √100)

t = 16.4 / 10

t = 1.64

Using a significance level of 0.05 (5%), we compare the t-score to the critical value from the t-distribution table. For a one-tailed test, the critical value at the 5% level with degrees of freedom (df) = n - 1 = 99 is approximately 1.66.

Since the calculated t-score (1.64) is smaller than the critical value (1.66), we fail to reject the null hypothesis. The result is not statistically significant at the 5% level.

(b)Using the same calculations as in part a), the t-score is calculated as follows:

t = (541.5 - 525) / (100 / √100)

t = 16.5 / 10

t = 1.65

The critical value at the 5% level with df = 99 is still approximately 1.66.

Since the calculated t-score (1.65) is still smaller than the critical value (1.66), we still fail to reject the null hypothesis. The result is not statistically significant at the 5% level.

c)While the increase is minimal, it leads to a slightly higher t-score (1.65) in part b) compared to part a) (1.64).

Considering that any increase greater than 15 points is considered a success, it's important to note that neither result (541.4 or 541.5) meets this criterion. Therefore, the training program does not appear to have a statistically significant impact on GMAT scores based on the given data and significance level.

It's worth considering a larger sample size or conducting further studies to gather more data and assess the training program's effectiveness with a higher degree of certainty.

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Answer:

g(x + 3) = -5x -38

Step-by-step explanation:

Given g(v) = -5v -23

We are to find g(x + 3)

What we shall simply do here is substitute (x + 3) for v in the g(v) equation

That would be;

g(x + 3) = -5(x + 3) -23

g(x + 3) = -5x -15 -23

g(x + 3) = -5x -38

Answers:

128 subsets

127 proper subsets

=========================================================

If we have a set A = {x is some integer such that 7 < x < 15}

Then set A can be written as A = {8, 9, 10, 11, 12, 13, 14}. This is called roster notation. We write every integer between 7 and 15, excluding both 7 and 15.

There are 7 items in set A. So n = 7

This means there are 2^n = 2^7 = 128 different subsets possible

And there are (2^n) - 1 = (2^7) - 1 = 128-1 = 127 different proper subsets. A proper subset is a subset that is smaller than the original set

Answer: B.

Step-by-step explanation: Negatives are smaller than positive numbers

Answer:

That would be B

Step-by-step explanation:

because -3 is way behind 0 following by 0.9 being greater than -3 while 45 is greater and way ahead of the others

Answer:

8 hours

Step-by-step explanation:

57 + 9h = 129

9h = 72

h = 8

Heidi needs to babysit for 8 hours to afford the new bike.

The linear equation is the algebraic form of equation whose variable has the exponent of one. It is the combination of two variables and a constant value present in them.

For the given situation,

Heidi's savings = $57

Amount for babysitting per hour = $9

Total cost of the bike = $129

Let us consider 'x' for hours she needs to babysit.

This can be represented as linear equation as

[tex]57 +9h=129[/tex]

⇒ [tex]9h=129-57[/tex]

⇒ [tex]9h=72[/tex]

⇒ [tex]h=8[/tex]

Hence we can conclude that Heidi needs to babysit for 8 hours to afford the new bike.

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The area of sector KLM is approximately 24.0196 square units when rounded to two decimal places.

The area of sector KLM is to be found in circle L, which has a measure of 58 degrees and a length of 14.

The formula for determining the area of a sector is given below:Area of sector = (angle measure/360°) x πr²

The angle measure is 58°. The radius is half of the length of KL, which is 14 units. So, r = 14/2 = 7.Substituting the values in the formula,

Area of sector = (58/360) x π x 7²Area of sector = (0.1611) x (49π)Area of sector = 7.6379π

The final answer needs to be rounded off to two decimal places, which is achieved by multiplying it by 100, rounding to the nearest integer, and then dividing by 100.Area of sector ≈ 7.64 x π units²

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Answer:

(-5,4)

Step-by-step explanation:

If you look at A and then at AB midpoint you will see that A is 5 down from M and 4 right from M. So, if you minus 4 from -1 you get -5, and if you add 5 from -1 you get 4. Therefor the answer is (-5,4)

Advanced math : shes correct

Answer:

67.5

Step-by-step explanation:

Answer:

4n + 16

Step-by-step explanation:

Difference = +4 each time

20 - 4(1) = 16

Therefore nth term = 4n + 16

Proof:

4(2) + 16 = 24

4(3) + 16 = 28

Answer:

  (0, -26)

Step-by-step explanation:

We can use the 2-point form of the equation for a line to write its equation:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (1 -(-8))/(36 -24)(x -24) -8

  y = 9/12(x -24) -8

  y = 3/4x -26

Comparing this to slope-intercept form:

  y = mx + b

we see that the y-intercept, b, is -26.

The y-intercept of the line is (0, -26).

A representative sample based on the hospital scenario is option A

A subset of a larger population that accurately reflects the traits, diversity, and distribution of the total population is referred to as a representative sample.

Due to time, financial, or logistical limitations, it is frequently not possible or practical to investigate an entire population when conducting research or gathering data. In these situations, researchers choose a representative sample from which to deduce generalizations about the total population.

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Answer:

B

Step-by-step explanation:

y=kx+m

k=y2+y1 / x2+x1

(3,5) and (7,9)

k=(9-5)/(7-3)=4/4=1

Now we want to find out what m is. This is by inserting a point in the equation of the line y=kx+m.

so I'll pick (3,5)

5=1×3+m

m= 2

To check if it's correct we could try it with the other point, (7,9).

9=1×7+m

m=2

Therefor the equation would be. y=1x+2

Answer:

x=1

Step-by-step explanation:

-16+x=-15

-16+x+16=-15+16   Add the terms to both sides of the equation.

After that you simplify.

Answer:

Step-by-step explanation:

3x+y=4

First this is not really have a soluction

So a list 2 soluction right here

solve for x

3x+y=4

-y     -y

3x=4-y

x= -y+4/3

Or solve for y

3x+y=4

-3x

y=-3x+4

Or maby you want a another soluction...

Answer:

Slope Intercept form: y = -3x + 4

Slope: -3

Step-by-step explanation:

For slope intercept:

Subtract 3x from both sides:

3x + y - 3x = 4 - 3x

Simplify:

y = -3x + 4

For slope:

If the equation is y = -3x + 4 then using the formula y = mx + b:

Slope = -3

False.

For a square matrix A, the vectors in the column space of A (col(A)) are not necessarily orthogonal to the vectors in the null space of A (nul(A)). The column space consists of all possible linear combinations of the columns of A, while the null space consists of all vectors that satisfy the equation Ax = 0.

Orthogonality between col(A) and nul(A) would imply that any vector in col(A) is perpendicular to any vector in nul(A), which is generally not the case. There may exist some specific scenarios where col(A) and nul(A) have orthogonal vectors, but it is not a general property.

Therefore, the statement that vectors in the column space of a square matrix A are orthogonal to vectors in the null space of A is false.

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The value of the external part of the secant segment d is 3.

The secant-tangent power theorem states that "if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment."

It is expressed as:

( tangent segment )² = External part of the secant segment × Secant segment.

From the diagram:

Tangent segment = 6

External part of the secant segment = d

Secant segment = ( d + 9 )

Plug these values into the above formula:

( tangent segment )² = External part of the secant segment × Secant segment.

6² = d( d + 9 )

Solve for d

36 = d² + 9d

d² + 9d - 36 = 0

Factor usng method:

( d - 3 )( d + 12 ) = 0

d = 3 and d = -12

Since we are dealing with dimension, we take the positive value.

Therefore, the value of d is 3.

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The exponential function f(x) can be written in the form f(x) = -4×(2)⁻¹×2ˣ

The exponential function f(x) = -4×2¹⁻ˣ in the form f(x) = abˣ, we can simplify it as follows:

f(x) = -4×2¹⁻ˣ

Using the property of exponents that aᵇ⁻ⁿ = aᵇ / aⁿ, we can rewrite the function as:

f(x) = -4×(2¹ / 2ˣ)

Simplifying further:

f(x) = -4×(2 / 2ˣ)

Since 2 can be written as 2¹, we can rewrite the function as:

f(x) = -4×(2¹ / 2ˣ) = -4×(2¹×2⁻ˣ) = -4×2¹⁻ˣ

Now we can see that a = -4 and b = 2⁻¹. Therefore, the exponential function f(x) can be written in the form f(x) = abˣ as:

f(x) = -4×(2)⁻¹×2ˣ

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Answer:

leg = √7 units (approximately 2.65 units)

Step-by-step explanation:

Given a right isoceles triangle with a hypotenuse of 14 units, the two other legs must be congruent in length. Because this is a right triangle, the pythagorean theorem a^2 + b^2 = c^2, can be used.

Since the two legs are congruent, side a = side b. This means that

2leg^2 = hypotenuse.

_____________

2leg^2 = 14 units

÷ 2. ÷2

_____________

leg^2 = 7 units

√ √

____________

leg = √7 units

Answer:

both are 2cnd play

Step-by-step explanation:

Answer:

x = 3.8

Step-by-step explanation:

Perimeter is all the side lengths added up.

Step 1: Set up equation

x + 2(8.3) + 3.8 = 24.2

Step 2: Solve for x

Answer:

[tex]\Large \boxed{\sf 3.8}[/tex]

Step-by-step explanation:

Perimeter of a shape is the sum of all sides.

Opposite sides in a parallelogram are of equal length.

Answer:

-2.

Step-by-step explanation:

(2/9)^4 * (2/9)^-7 = (2/9)^-3   so

(2/9)^-3 = (2/9)^(2m+1)

So -3 = 2m + 1  ( as the base 2/9 is common to both sides of the equation)

2m = -4

m = -2.

Answer: isn’t it 1.6 because you multiply 5 x 5 x 5 = 125 and then you divide 200\125 =1.6