Solve using elimination. 9x − 9y = –18 10x − 9y = –13

An eigenvector corresponding to λ₂ = 2 - i is v₂ = [-1, 1].

To find the eigenvalues of matrix A, we need to solve the characteristic equation det(A - λI) = 0, where I is the identity matrix.

Let's compute the determinant:

det(A - λI) = |[2 - λ -1]|

|[ 1 2 - λ]|

Expanding along the first row, we have:

(2 - λ)(2 - λ) - (-1)(1) = (2 - λ)² + 1 = λ² - 4λ + 5 = 0

To solve this quadratic equation, we can use the quadratic formula:

λ = (-(-4) ± √((-4)² - 4(1)(5))) / (2(1))

= (4 ± √(16 - 20)) / 2

= (4 ± √(-4)) / 2

Since we are working over the complex numbers, the square root of -4 is √(-4) = 2i.

λ₁ = (4 + 2i) / 2 = 2 + i

λ₂ = (4 - 2i) / 2 = 2 - i

Now, let's find the eigenvectors corresponding to each eigenvalue.

For λ₁ = 2 + i, we solve the equation (A - (2 + i)I)v = 0:

[2 - (2 + i) -1] [x] [0]

[ 1 2 - (2 + i)] [y] = [0]

Simplifying, we have:

[0 -1 -1] [x] [0]

[ 1 0 - i] [y] = [0]

From the first equation, we have -x - y = 0, which implies x = -y.

Choosing y = 1, we have x = -1.

Therefore, an eigenvector corresponding to λ₁ = 2 + i is v₁ = [-1, 1].

For λ₂ = 2 - i, we solve the equation (A - (2 - i)I)v = 0:

[2 - (2 - i) -1] [x] [0]

[ 1 2 - (2 - i)] [y] = [0]

Simplifying, we have:

[0 -1 -1] [x] [0]

[ 1 0 i] [y] = [0]

From the first equation, we have -x - y = 0, which implies x = -y.

Choosing y = 1, we have x = -1.

In summary:

λ₁ = 2 + i has eigenspace span {[-1, 1]}

λ₂ = 2 - i has eigenspace span {[-1, 1]}

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Answer:

Step-by-step explanation:

Let the calories of a cheeseburger be C, and the calories of a small order of fries be F. Using this notation: Two cheeseburgers and one small order of fries contain a total of 1400 calories. Calories in 2 cheeseburgers + Calories in 1 small order of fries = 14002C + F = 1400. Three cheeseburgers and two small orders of fries contain a total of 2260 calories. Calories in 3 cheeseburgers + Calories in 2 small orders of fries = 22603C + 2F = 2260. We can solve for C and F by solving these two equations for C and F using the method of elimination.

Let's double the first equation and subtract the second equation: 4C + 2F = 2800  -(3C + 2F = 2260). 1C = 540  C = 540. Calories in a cheeseburger = C = 540. Substituting this value of C into either of the two equations and solving for F gives us:2C + F = 14002(540) + F = 1400. F = 320. Calories in a small order of fries = F = 320. Therefore, two cheeseburgers contain 2C = 2(540) = 1080 calories, and one small order of fries contains F = 320 calories. Three cheeseburgers contain 3C = 3(540) = 1620 calories, and two small orders of fries contain 2F = 2(320) = 640 calories.

Answer: Calories in a cheeseburger = C = 540Calories in a small order of fries = F = 320. Calories in two cheeseburgers = 2C = 2(540) = 1080. Calories in three cheeseburgers = 3C = 3(540) = 1620. Calories in one small order of fries = F = 320Calories in two small orders of fries = 2F = 2(320) = 640.

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Answer:

2 < or equal to (t) < or equal to 1000

Step-by-step explanation:

2 is the profit of the (t) amount of t shirts so the amount should be greater than or equal too 1000 because if they have 500 shirts 500 x 2 is 1000

The domain of this function will be given by the set A[1, 500].

The end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

For any function y = f(x), Domain is the set of all possible values of [x] for which [y] exists. Range is the set of all values of [y] that exists for the given domain.

Given is the math club which is selling T-shirts to raise money. Each T-shirt sold represents a profit of $2. The club has a total of 500 T- shirts.

The function representing the profit by selling [x] T - shirts can be written as -

P(x) = 2x

or

y = 2x

Maximum value of y = 2x 500 = $1000

The domain of this function will be given by the set A[1, 500].

Hence, the domain of this function will be given by the set A[1, 500].

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Answer:

Step-by-step explanation:

By apply the cylindrical shells method proved that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h.

Given that,

Consider an upright cone that was generated by rotating the triangular plane region shown in the image about the y-axis. It has a base radius of r and a height of h.

We have to apply the cylindrical shells method to confirm that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h

We know that,

By using the disk method,

V = [tex]\int\limits^b_a {\pi [f(x)]^2} \, dx[/tex]

Differentiating on both the sides,

dV = π[f(x)]² dx

Integrating on both sides with the limits 0 to h

[tex]\int\limits^h_0 { dV }= \int\limits^h_0 {\pi[f(x)]^2 }dx[/tex]

V = [tex]\int\limits^h_0 {\pi \frac{r^2x^2}{h^2} } \, dx[/tex]

V = [tex]\pi \frac{r^2}{h^2}\int\limits^h_0 {x^2 } \, dx[/tex]

V = [tex]\pi \frac{r^2}{h^2}[\frac{x^3}{3}]^h_0[/tex]

V = [tex]\pi \frac{r^2}{h^2}[\frac{h^3}{3}][/tex]

V = [tex]\frac{1}{3}[/tex]πr²h

Therefore, By apply the cylindrical shells method proved that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h.

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The determinant of A is -23 - k.

In case, we have a 3x3 submatrix starting at element (1,1) and ending at element (3,3). Therefore, we can calculate the determinant using cofactor expansion method:

| 1 k 9 |

| 1 2 3 |

| 2 5 7 |

= 1| 2  3 | - k| 1  3 | + 9| 1  2 |

| 5  7 | | 5  7 | | 5  7 |

= 1(2(7) - 3(5)) - k(1(7) - 3(2)) + 9(1(7) - 2(5))

= 1(4) - k(1) + 9(-3)

= -23 - k

Therefore, the determinant of A is -23 - k.

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Answer:

Step-by-step explanation:

x = 5

The value of x in the given angle is 5.

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge.

Labelling the figure,

We have,

Measure of complete angle of circle = 360 degree

∠ABC = 360 - (81 + 74)

          =  205 degree

Now from figure,

∠APE = (205 - 81 )/2

          = 62 degree

Since we know that,

∠APE = 17x - 23

Therefore,

17x - 23 = 62

17x = 85

  x = 5 degree,

Hence,

Required value is 5.

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Answer:

I believe its 60cm squared

I’m not sure

Answer:

i think its 60cm

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Ur welcome

The sample proportion of households without fiber cable can be calculated by subtracting the proportion of households with fiber cable from 1.

In this case, out of the 491 households surveyed, 343 households have internet fiber cable. To find the proportion of households without fiber cable, we subtract the proportion of households with fiber cable (343/491) from 1. The proportion of households without fiber cable is 1 - (343/491). Simplifying this expression, we get (491 - 343)/491 = 148/491.

Therefore, the sample proportion of households without fiber cable is 148/491, which is approximately 0.3012 or 30.12%. This means that in the surveyed sample, around 30.12% of households do not have internet fiber cable. It's important to note that this proportion represents the sample and not the entire population, as it is based on the households surveyed.

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Probability that "sample-proportion" of "households-spending" more than $125 per-week is less than 0.29 is 0.8340.

In order to calculate the probability that the sample-proportion of households spending more than $125 a week is less than 0.29, we use the sampling-distribution of sample-proportions, assuming the sample was selected using simple random sampling.

The Population-proportion (p) is = 0.27

Sample-size (n) is = 467,

Sample-proportion (p') is = 0.29,

To calculate the probability, we find the z-score corresponding to the sample proportion and then find the probability,

The formula to calculate the z-score is:

z = (p' - p)/√((p × (1 - p))/n),

Substituting the values,

We get,

z = (0.29 - 0.27)/√((0.27 × (1 - 0.27))/467),

z = 0.02/√((0.27 × 0.73) / 467),

z ≈ 0.97

We know that the probability associated with a z-score of 0.97 is 0.8340.

Therefore, the required probability is 0.8340.

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Answer:

D

Step-by-step explanation:

if we see on the graph, the point which is scattered is point D !
also took the FLVS test!!

Answer: No

Step-by-step explanation: Because if you substitute the 2 for x and 3 for y it is not equal

Answer:

download discord

Answer:

im confused-

Step-by-step explanation:

Answer:

z = 1.5

Step-by-step explanation:

                               x - mean

standard score = -----------------

                                     6

Substituting 74 for x, 65 for mean, we get:

                               74 - 65

standard score = ----------------- = 9/6 = 1.5

                                     6

The pertinent z-score (standard score) is 1.5.

Answer:

Score = 74 - 65/6

Score = 9/6

Hence

Score is 9/6 or 1.5

[tex] \\ [/tex]

Area of the shaded region = area of big square minus area of little square.

Here is the set up:

Let A_s = area of shaded region.

A_s = (2x + 2)(3x - 4) - [(x - 3)(x - 6)]

Take it from here.

Answer:

B. 5x2 + 7x – 26

Step-by-step explanation:  keeping in mind that the area of a rectangle is simply width * length, if we get the area of the larger rectangle, and then subtract the area of the smaller rectangle, we're in effect making a hole in the larger rectangle's area and thus what's leftover is the shaded area.

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

Answer:

Area = 5x^2 +7x -26

Step-by-step explanation:

The area of the shaded region can be found if you substruct the small rectangle from the big one. The area of any rectangle is calculated if you multiply width and height.

In other words:

A_small = (x-3)(x-6) = x^2-9x +18

A_big = (2x+2)(3x-4) = 6x^2 -2x -8

A_big - A_small = (6x^2 -2x -8) - (x^2-9x +18)

= 6x^2 -2x -8 - x^2 + 9x -18

= 5x^2 +7x -26

Answer:i don’t know yet give me a sec

Step-by-step explanation:

Answer:

12.56 cubic feet (ft^3)

Step-by-step explanation:

Area of the circular face of the cylinder = (pi)r^2, or (3.14)(2)^2.

This ends up being equal to 12.56. Multiply this by the height of the cylinder, 1, and you get 12.56, your final answer.

I would appreciate Brainliest, but no worries.

Answer:

its d

Step-by-step explanation:

The general solution of the differential equation dy/dt + 4/ty = e raised to power of t/t raised to power of 3:

y = C * e raised to power of t * t raised to power of 4

where C is an arbitrary constant.

To find this solution, we can use the following steps:

First, we can factor out e raised to power of t/t raised to power 3 from the right-hand side of the equation. This gives us:

dy/dt + 4/ty = e raised to power t/t raised to power of 3 * (1/t)

Next, we can multiply both sides of the equation by ty to get:

dy + 4 = e raised to power of t/t raised to power of 2

Now, we can integrate both sides of the equation. This gives us:

y + 4t = C * e raised to power of t

Finally, we can solve for y to get the general solution:

y = C * e raised to power of t * t raised to power of 4

where C is an arbitrary constant.

The first step of the solution is to factor out e raised to power t/t raised to power of 3 from the right-hand side of the equation. This is possible because the derivative of e raised to power of t/t raised to power of 3 is e raised to power of t/t raised to power of 3 * (1/t).

The second step of the solution is to multiply both sides of the equation by ty to get dy + 4 = e raised to power of t/t raised to power of 2. This is possible because the derivative of ty is t + y.

The third step of the solution is to integrate both sides of the equation. This gives us y + 4t = C * e raised to power of t. This is possible because the integral of dy is y and the integral of e raised to power t/t raised to power of 2 is -2e raised to power of t/t + C.

The fourth step of the solution is to solve for y to get the general solution y = C * e raised to power t * t raised to power of 4. This is possible by dividing both sides of the equation by C * e raised to power of t.

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If difference scores begin to pile up away from a sample mean difference score of Mp= 0, the null hypothesis will likely be rejected. So, correct option is B.

This suggests that there is a likely effect or relationship between the variables being compared.

Option b. The null hypothesis will likely be rejected is the correct statement in this scenario. When the observed differences are consistently far from zero, it implies that the null hypothesis, which assumes no significant difference or effect, is unlikely to be true.

Thus, based on the evidence provided by the data, we would reject the null hypothesis in favor of an alternative hypothesis that suggests the presence of a difference or effect.

The critical region refers to the region of extreme values that would lead to rejecting the null hypothesis. While the size of the critical region can vary depending on the chosen significance level, it does not directly indicate the likelihood of rejecting the null hypothesis in this context.

Similarly, the sample size (option c) does not provide information about the likelihood of rejecting the null hypothesis in this situation.

So, correct option is B.

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a) SST represents the total sum of squares.

b) SSTr represents the treatment sum of squares.

c) SSE represents the error sum of squares.

d) The true statement is: SST = SSTr + SSE.

e) The average between-group variation is represented by MST (mean square treatment).

a) SST (Total Sum of Squares) represents the total variation in the data. It measures the total deviation of each data point from the overall mean.

b) SSTr (Treatment Sum of Squares) represents the variation attributed to the treatment or factor being studied. It measures the deviation of each group mean from the overall mean.

c) SSE (Error Sum of Squares) represents the residual or unexplained variation in the data. It measures the deviation of each individual data point from its respective group mean.

d) The true statement is: SST = SSTr + SSE. This equation states that the total variation (SST) is equal to the sum of the variation attributed to the treatment (SSTr) and the residual or unexplained variation (SSE).

e) The average between-group variation is represented by MST (mean square treatment). MST is calculated by dividing the treatment sum of squares (SSTr) by the degrees of freedom associated with the treatment. It represents the average variation between the group means and provides information about the treatment effect or the differences between groups.

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Answer:

$7

Step-by-step explanation:

The amount max keeps for spending = 1/2(total allowance - amount he spends on snacks)

total allowance = $17

amount he spends on snacks = $3

Amount he would have for  his college fund and spending money. = $17 - $3 = $14

Since he splits the amount equally between his college fund and spending money, the amount he would have for spending can be determined by dividing 14 by 2

$14/2 = $7

Answer:

11 square units

Step-by-step explanation:

Find the diagram attached

First we need to find the side length of the square with known areas.

Area of a square = L²

L is the side length of the square

For the green square

44 = L²

Lg = √44

For the purple square

Ap = Lp²

33 = Lp²

Lp = √33

Get the length (L) of the unknown square using pythagoras theorem;

Lg² = L²+Lp²

(√44)² = L²+(√33)²

44 = L²+33

L² = 44-33

L² = 11

Since Al = L²

Hence the area of the square adjacent to the third side of the triangle is 11 square units

The equation of the curve as, (y - a) = (b - a) (x - nt) / (a - nt) which is a straight line passing through the two given points, A(nt, a) and B(a, b).

Given: Two points A (e.g., a) and B (a, b) are traversed by the curve whose equation is Sin(x) – y Cos(x) = y (a Solution: (sin x - y cos x) = y Taking y to the left, we get (sin x) = (y y cos x) Again, we can write y as (y) = (sin x) / (1 cos x) Simplifying this even further, we get (y) = (sin x / 2) / (cos x/2) Substituting the values of x = nt A( eg, a) and B( a, b), we get the condition in the structure, y - a = (b - a) (x - ex.)/( a​​​​-ex.)

Tackling the above condition, we get the condition bend which is a straight line going through two given focuses A (eg, a) and B(a, b). As a result, we obtain a curve in the form of an equation (y - a) = (b - a) (x - nt) / (a) - nt), which is a straight line that runs through the two points A(eg, a) and B(a, b) that have been given to us.

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Answer:

x and y are proportional. Two quantities are proportional if there is a constant ratio between them. In this case, the ratio between y and x is always 16:

4/0.25=16

8/0.5=16

12/0.75=16

Since the ratio between y and x is always the same, x and y are proportional.

Step-by-step explanation:

The given statement is true  (i) implies (ii) and (ii) implies (i).

The statement in the question that needs to be proven is :C & F, then X-cef = G is G an open set in C and CnH+ 0 s G for each Hef

We will prove that (i) implies (ii) and (ii) implies (i).

Proof: (i) C & F, then X-cef = G is G an open set in C and CnH+ 0 s G for each Hef

Let X \ {C & F} = U, then U is open, since C & F is closed.

Let H be any point of U.

By hypothesis, there exists an open set G such that CnH+ 0 s G.

Let x in G. If x ∈ C & F, then x ∉ H, so x ∉ U.

Thus, G ⊆ C, and so G ∩ U = ∅.

Hence, U is open(ii) G is G an open set in C and CnH+ 0 s G for each Hef

Let x ∈ X-C & F.

Then x ∉ C & F, so x ∉ C.

Since C is closed, there exists a neighborhood G of x that is disjoint from C.

Let H be any point of X-C & F.

Then H ∈ G and so CnH+ 0 s G.

Thus, C & F is closed.

Therefore, X-C & F is open, since C & F is closed.

Thus, X-C & F = G.

Hence, (ii) implies (i).

Therefore, the statement in the question is proven.

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