Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: A = 1 with eigenvector = [] and generalized eigenvector - [1-3]. Write the solution to the linear system' = Ar in the following forms. A. In eigenvalue/eigenvector form: [x(t)] = C1 [8] 248-89 + e B. In fundamental matrix form: [x(t)] [y(t)] [188 C. As two equations: (write "c1" and "c2" for c₁ and c₂) x(t) = y(t) = Note: if you are feeling adventurous you could use other eigenvectors like 47 and other generalized eigenvectors like - 37. Just remember that if you change , you must also change for its fundamental solution!

The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer:

c. -20x and 20x

Step-by-step explanation:

x² is the square of x.

100 is the square of 10 and of -10.

The middle term of (a + b)² is 2ab.

For b = 10:

2ab = 20x

for b = -10:

2ab = -20x

Answer: c. -20x and 20x

Answer:(2,-3)

Step-by-step explanation:

Answer:

A. 3.4.5

Step-by-step explanation:

I looked it up and it forms a right angle.

The required equation is g(x) = 10(3)x which is the correct answer would be an option (A).

The graph of g(x) is obtained by stretching the graph of f(x) vertically by a factor of 2.

Since the vertical stretch of a graph multiplies the y-coordinates of each point on the graph by a constant factor, the equation of g(x) must be obtained by multiplying the y-coordinate of each point on the graph of f(x) by 2.

In the given equation f(x) = 5(3)x, the y-coordinate of each point on the graph of f(x) is 5(3)x.

Thus, to stretch the graph of f(x) vertically by a factor of 2, we need to multiply this y-coordinate by 2 to get the y-coordinate of the corresponding point on the graph of g(x). This gives us the following equation for g(x):

⇒ g(x) = 2 × 5(3)x = 10(3)x

Therefore, the required equation is g(x) = 10(3)x.

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It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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Answer:

The formula looks like this:

where SA = surface area, l = length, w = width, and h = height. In the rectangular prism net above, l = 8 inches, w = 5 inches, and h = 3 inches. Simply put these numbers into the formula and solve for surface area.

Answer:

y = 5x

where

y = number of fence posts that Edwin installs
x = number of hours that Edwin takes to install y posts

Step-by-step explanation:

Let y = number of fence posts that Edwin installs in x hours

We have the relation:

y ∝ x where ∝ is the symbol for is-proportional-to

We can rewrite this as an equation using the constant of proportionality,k:

y =kx

Given y = 40 fences, x = 8 hours we get

40 = k(8) = 8k

or, switching sides

8k = 40

k = 40/8 = 5

So Edwin can install 5 fences per hour

Plugging this into the equation of proportionality

y = 5x

Given:

The terminal side contains the point (-6, -8).

To find:

Here, x= -6 and y= -8.

Using the formula,

Hence, the answer is,

Answer:

Step-by-step explanation:

Two washing machines are offered at $480, with one marked down 50% and the other marked down 30% and another 20% off. You want to know why the first machine has a better price, and what that price is.

The price after a 50% markdown is ...

  $480 × (1 -50%) = $480 × 0.50 = $240 . . . first machine sale price

The price after a 30% markdown is ...

  $480 × (1 -30%) = $480 × 0.70

After the additional 20% markdown, the price is ...

  ($480×0.70) × (1 -20%) = $480 × 0.70 × 0.80

  = $480 × 0.56 ≈ $269

The first machine is a better deal, because The 50% markdown is off the original price.

The 30% markdown on the second machine is off the original price, but the additional 20% is off the reduced price. Hence the total markdown is not as great as on the first machine.

Answer:

Step-by-step explanation:

This is a parallelogram. It's a quadrilateral. All quadrilaterals interior (inside) angles add up to 360 degrees.

Because it's a parallelogram, we know that the opposite angles are equal.

So x is equal to that angle in the opposite corner (diagonal), and 122 is the measure of the other opposite corner angle, too.

So add up those angles:

x + x + 122 + 122 = 360

Combine like terms

2x + 244 = 360

Solve for x

2x = 116

x = 58

Double check that it's correct:

58+58+122+122 = 360.

Answer:

x=58°

Step-by-step explanation:

The sum of the interior angles of a rhombus is 360 degrees. Therefore, if angle A of a rhombus is 122 degrees, then the opposite angle (angle C) is also 122 degrees. The adjacent angles (angle B and angle D) are supplementary to angle A and angle C, meaning that they add up to 180 degrees. So, angle B and angle D are each 180 - 122 = 58 degrees. To summarize, the angles of the rhombus are:

There are 2518 sets of five marbles that include either the lavender one or exactly one yellow one, but not both.

To solve this problem, we need to find the number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both colors. Here's one way to approach the problem:

Number of sets of five marbles that include the lavender one: There is only one lavender marble, so we can choose any 4 other marbles to go with it.

There are a total of 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 7 x 6 x 5 x 4 = 840 possible sets of five marbles that include the lavender one.

Number of sets of five marbles that include exactly one yellow one: There are two yellow marbles,

So there are 2 possible choices for the yellow marble. For each choice, we can choose any 4 other marbles to go with it.

As before, there are 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 2 x (7 x 6 x 5 x 4) = 1680 possible sets of five marbles that include exactly one yellow one.

Number of sets of five marbles that include both the lavender one and exactly one yellow one:

We need to subtract these sets from the total number of sets that include either the lavender one or exactly one yellow one.

We have already found that there are 840 sets of five marbles that include the lavender one, and 1680 that include exactly one yellow one.

To find the number of sets that include both, we can choose any one yellow marble and the lavender one.

There are 2 choices for the yellow marble and 1 choice for the lavender one,

So there are 2 x 1 = 2 possible sets of five marbles that include both the lavender one and exactly one yellow one.

Number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both:

Finally, we need to subtract the number of sets that include both the lavender one and exactly one yellow one from the total number of sets that include either the lavender one or exactly one yellow one.

The total number of sets that include either the lavender one or exactly one yellow one is 840 + 1680 = 2520. The number of sets that include both is 2,

So the number of sets that include either the lavender one or exactly one yellow one, but not both, is 2520 - 2 = 2518.

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The 95% confidence interval to estimate the proportion of students on financial aid = (0.522, 0.658)

In this question we have been given a university dean is interested in determining the proportion of students who receive some sort of financial aid.

Let p be the population proportion of students who receive some financial aid.

The dean randomly selects 200 students and finds that 118 of them are receiving financial aid.

i.e. n= 200

p{hat} = 118/200 = 0.59

We know that the critical value for 95% confidence interval : z = 1.96

The standard deviation would be,

σ = √[p{hat}(1 - p{hat})/N]

σ = √0.59(1 - 0.59)/200

σ = √(0.0012095)

σ = 0.0348

The 95% confidence interval for population proportion would be,

(0.59 ± (1.96 * 0.0348))

= (0.59 - (1.96 * 0.0348), 0.59 + (1.96 * 0.0348))

= (0.5218, 0.6582)

Therefore, the 95% confidence interval : (0.522, 0.658)

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Answer:

\(2k - 9\)

Step-by-step explanation:

jsjsjsjsjjsjsksksksksksksksksksjskkwjwjwjwkw

Answer:

Anticlockwise 60°

Step-by-step explanation:

Let my starting point be 0°

Turning to the right(clockwise)40° = 0° + 40° = 40°

I am now at 40° to the right of my starting point.

Turning to the left(anticlockwise) 70° = 40° - 70° = -30°

I am now 30° to the left of my starting point.

Turning to the right 90° = -30° + 90° = 60°

I am 60° to the right of my starting point.

To go back to the startoing point(0°), I should go to the left(anticlockwise) by 60°

This is a change of -60°

-Chetan K

Answer:

210

Step-by-step explanation:

210 students attend the school. if 60 students are taking art, and there are 2 art students in every 7 students, that means there are 30 groups of 7 because 30×2=60 so since the other 5 do not take art, you would multiply 30×5 and get 150. Then you would add 60 and you would get 210

The number of tiles is 96

From the question, we have

The width of the room is 16 feet, 8 inches and the client has chosen a square tile that measures 4 inches on each side.

16 feet = 192 inches

Number of tiles = (192*8)/(4*4)

= 96 tiles

The number of tiles is 96.

Multiplication:

The product of two or more numbers is computed by mathematicians using multiplication. In everyday life, it is a basic mathematical operation that is frequently used. We employ multiplication when we must combine groups of like sizes. The operation of multiplication serves as a representation of the fundamental idea of adding the same number repeatedly. The product of two or more numbers is what is obtained when those numbers are multiplied, and the factors are the quantities that are multiplied. Multiplying the numbers simplifies the process of adding the same number repeated.

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Answer:

n=1

Step-by-step explanation:

2n+1-1=3-1

2n=2 divide both sides by two

n=1

 can i get brainliest please???

it would be very much appreciated

have a nice day :)

A:

The function d(x) = |x| -4 would be graphed on the number line with the point (0, -4) as the starting point. The function would then continue in either direction from that point, depending on the value of x.

B:

To graph this function, start by finding the points where x = 0 and x = -4. These will be your y-intercepts. So, plot those points on a graph first. Then, for every other value of x, determine whether it is positive or negative. For positive values of x, plot a point above the y-axis; for negative values of x, plot a point below the y-axis. Connect all these points with a smooth curve to get your final graph!

The graph of | x | - 4 , this function will be similar to | x | but will shift 4 units down along the y-axis.

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

Given, d(x) = | x | - 4.

So, at x = 0 d(x) = - 4.

So, the coordinate points are (0, - 4).

Now, to graph, this function will be similar to | x | but will shift 4 units down along the y-axis.

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Answer:

H

Step-by-step explanation:

Sum of angles in a triangle is 180 degrees

That means

180= 25 + 45+ unknown angle

180= 70 + unknown angle

180 - 70 = unknown angle

110 = unknown angle

B. x^9

just simplify

The value of f(g(1) from the table of functions is given as 1.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

when x = 1

g(x) = 3

or f(g(1) = f(3) = 1

The value of f(g(1) from the table of functions is given as 1.

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All of the equations that are true include the following:

B. 56 + 70 = 14(4 + 5).

C. 28 + 49 = 7(4 + 7).

In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

In order to determine the true equation, we would apply the distributive property of multiplication and then check whether or not the right-hand side is equal to the left-hand side.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

32 + 96 = 8(4 + 14)

32 + 96 = 32 + 112 (False).

56 + 70 = 14(4 + 5).

56 + 70 = 56 + 70 (True).

28 + 49 = 7(4 + 7).

28 + 49 = 28 + 49 (True).

27 + 36 = 3(9 + 13)

27 + 36 = 27 + 39 (False).

25 + 35 = 5(5 + 6)

25 + 35 = 25 + 30 (False).

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Answer:

Sorry that this is a bit late but the answer is I believe D

Answer:

D

Step-by-step explanation:

I did the prep

Answer:

Lowering the level of significance, α increases the probability of making a Type II error, β.

Step-by-step explanation:

Lowering the level of significance, α increases the probability of making a Type II error, β.

This is because the region of acceptance becomes bigger, and it makes it less likely for one to reject a null hypothesis, when it is false, the type II error.

Answer:

Step-by-step explanation:

The vertex is at (-3, -1)  and the leading coefficient is negative ( because  the curve is inverted)

y = -a(x + 3)^2 - 1

One point on the curve is (-2, -3) so

-3 = -a(-2+3)^2 - 1

-3 = -a - 1

-a = -2

So we have

y = -2(x + 3)^2 -  1

y = -2(x^2 + 6x + 9) - 1

y = -2x^2 - 12x - 19.

Answer:

x = -7

Step-by-step explanation:

it’s right!

Answer:

57

Step-by-step explanation:

Given:

x = 4

y = 5

w = -3

Work:

3xy + w

3(4)(5) + (-3)

12(5) - 3

60 - 3

57

Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

Answer:

40.62

Step-by-step explanation:

that's the answer I got