what is the slope of the line that contains thenpoints (6,0)(0,3) and (12,-3)?

Answer: 2,3,4

Step-by-step explanation:  Which means that the first number is 2, the second number is 2 + 1 and the third number is 2 + 2. Therefore, three consecutive integers that add up to 9 are 2, 3, and 4.

a) The controllable state space realization is A = [[0, 1], [-8, -6]], B = [[1], [1]], C = [1, 2], and D = 0.

b) The system is controllable.

c) The system is observable.

d) The kernel of the transient matrix [s1-4]' is [0, 0]'.

a) To find the controllable state space realization, we need to express the transfer function in the general state space form:

G(s) = C(sI - A)^(-1)B + D

where A, B, C, and D are matrices.

First, let's factorize the denominator of the transfer function:

s^2 + 6s + 8 = (s + 2)(s + 4)

This gives us the eigenvalues of the system: λ1 = -2 and λ2 = -4.

Now, we can construct the A matrix:

A = [[0, 1],

    [-8, -6]]

Next, we construct the B matrix using the numerator coefficients:

B = [[1],

    [1]]

Then, the C matrix can be obtained from the coefficients of the numerator:

C = [1, 2]

Finally, the D matrix is zero in this case:

D = 0

Therefore, the controllable state space realization is:

A = [[0, 1],

    [-8, -6]]

B = [[1],

    [1]]

C = [1, 2]

D = 0

b) The controllability of the system can be determined by checking the controllability matrix:

Qc = [B, AB]

Qc = [[1, 1],

     [-6, -14]]

The system is controllable if the rank of the controllability matrix is equal to the number of states. In this case, the rank of Qc is 2, and we have 2 states, so the system is controllable.

c) The observability of the system can be determined by checking the observability matrix:

Qo = [[C],

     [CA]]

Qo = [[1, 2],

     [-14, -32]]

The system is observable if the rank of the observability matrix is equal to the number of states. In this case, the rank of Qo is 2, and we have 2 states, so the system is observable.

d) The kernel of the transient matrix is the set of vectors x such that (sI - A)x = 0. Let's solve this equation:

[s - 0   1] [x1] = [0]

[-8  s + 6] [x2]   [0]

From the first row, we have x2 = 0. Substituting this into the second row, we get -8x1 + (s + 6)x2 = 0. Since x2 = 0, we have -8x1 = 0, which implies x1 = 0.

Therefore, the kernel of the transient matrix is [0, 0]'.

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Answer:

2

Step-by-step explanation:

Answer:3

Step-by-step explanation:

The linear relationship between time and distance can be considered proportional. The constant of proportionality in this case is 4.

In a proportional relationship, the ratio between the two quantities remains constant. Here, as time increases by 2 hours, the distance also increases by 8 miles. Let's calculate the ratio of distance to time for each pair of values:

For the first pair (2 hours, 8 miles):

Ratio = distance / time = 8 miles / 2 hours = 4 miles/hour

For the second pair (4 hours, 16 miles):

Ratio = distance / time = 16 miles / 4 hours = 4 miles/hour

For the third pair (6 hours, 24 miles):

Ratio = distance / time = 24 miles / 6 hours = 4 miles/hour

For the fourth pair (8 hours, 32 miles):

Ratio = distance / time = 32 miles / 8 hours = 4 miles/hour

As we can see, the ratio of distance to time remains constant at 4 miles per hour for all the pairs. This indicates a proportional relationship between time and distance.

Therefore, the linear relationship is also proportional, and the constant of proportionality is 4.

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Answer:

the area of the photograph when it is put into the frame is 80 square inches, and the area of the frame is 88 square inches.

Step-by-step explanation:

Answer: 36 inches(2)

Step-by-step explanation:

Answer:

yes

yes

pabrainliest lowdi

sana all

Answer:

pretty sure it's yes for both

Answer: 2

Step-by-step explanation:

The inequality \($uv^2 \leq (uv)^2$\) holds for any vectors u and v in \(R^2\). Equality holds when the vectors u and v are collinear or when one of them is the zero vector.

To prove the inequality \($uv^2 \leq (uv)^2$\), we can start by expressing the dot product of u and v in terms of their components. Let u = (\(u_1, u_2\)) and v = (\(v_1, v_2\)).

Then, the dot product of u and v is given by\(uv = u_1 v_1 + u_2 v_2\).

Now, consider the squared length of the projection of u onto v.

This can be calculated as \((uv)^2\) / \(||v||^2\), where ||v|| represents the length of vector v.

Since ||v||^2 = vv, we have \((uv)^2\) /\(||v||^2\) = \((uv)^2\) / (\($v \cdot v$\)).

On the other hand, the squared length of vector u can be expressed as \(u\cdot u = u1^2 + u2^2\).

Now, we can compare the two expressions: \(uv^2\) and \((uv)^2\) / (vv).

By substituting the expression for uv, we get \(uv^2\) = \((u_1 v_1 + u_2 v_2)^2\), and by substituting the expressions for \(||v||^2\) and uu, we get \((uv)^2\) / (vv) = (\(u_1^2 v_1^2 + u_2^2 v_2^2\)) / (\(v_1^2 + v_2^2\)).

It can be shown that \((u_1 v_1 + u_2 v_2)^2 \geq (u_1^2 v_1^2 + u_2^2 v_2^2)\) for any real numbers \(u_1, u_2, v_1, v_2\). Therefore, \(uv^2\) ≤ \((uv)^2\) / \((vv)\), which implies \(uv^2\) ≤ \((uv)^2\).

Equality holds in the inequality \($uv^2 \leq (uv)^2$\) when the vectors u and v are collinear or when one of them is the zero vector.

Geometrically, this inequality represents the fact that the squared length of the projection of vector u onto vector v is always less than or equal to the squared length of the projection of u onto v.

When the vectors are collinear, their projections coincide and the inequality becomes an equality. Similarly, when one of the vectors is the zero vector, its projection onto any other vector is zero, resulting in equality as well.

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To determine the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.

Although they are connected, confidence level and confidence interval are not the same thing.

Thus, to evaluate the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.

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Answer:

Pretty sure its 20

Step-by-step explanation:

I just did the math

Answer:

5 i think

Step-by-step explanation:

§(*￣▽￣*)§§(*￣▽￣*)§§(*￣▽￣*)§§(*￣▽￣*)§§(*￣▽￣*)§(∪.∪ )...zzz(∪.∪ )...zzz(∪.∪ )...zzz(∪.∪ )...zzz

Answer:

Step-by-step explanation:

If Farmer Cora has a total of 128 onions and wants to place an equal number in each bags then, seeing since he has not decided on the amount of bags, he has the following options

128 onions in 1 Bag

64 onions in 2 Bag

32 onions in 4 Bag

16 onions in 8 Bag

8 onions in 16 Bag

4 onions in 32 Bag

2 onions in 64 Bag

1 onion in 128 Bag

Any of the above options will make each bag have an equal number of onions.

Answer:

12

Step-by-step explanation:

45 total

2/3 * 45 = 30 gave speeches

so 15 remaining

1/5 *15 = 3 gave speeches

remaining 12 didn't

A study showed that 13 of 25 cell phone users with a headset missed their exit, compared with 6 of 25 talking to a passenger. The confidence interval is (0.0581, 0.5019).

The confidence interval is $\hat{p}_1$ and $\hat{p}2$ are the sample proportions, $n_1$ and $n_2$ are the sample sizes, and $z{\alpha/2}$ is the critical value from the standard normal distribution for the desired confidence level.

Here, $\hat{p}1 = \frac{13}{25} = 0.52$, $n_1 = 25$, $\hat{p}2 = \frac{6}{25} = 0.24$, and $n_2 = 25$. The desired confidence level is 98%, so $\alpha = 0.02$ and $z{\alpha/2} = z{0.01} \approx 2.33$.

(0.52−0.24)±2.33

Substituting the values, we get:

Simplifying, we get:

(0.28)±2.33×0.1579

Therefore, the 98% confidence interval is:

(0.0581,0.5019)

Rounding to 4 decimal places, the confidence interval is (0.0581, 0.5019).

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Answer:

m2 = 13

Step-by-step explanation:

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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As per the given data, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

To discover t(zero), we want to alternative 0 for t inside the given feature r(t). This offers us:

\(r(0) = 3e^{(2(0)}), 3e^{(-2(0)}), 3(0)e^{(2(0)})\\\\= 3e^0, 3e^0, 0\\\\= 3(1), 3(1), 0\\\\= 3, 3, 0\)

Therefore, t(0) = (3, 3, 0).

To find r''(0), we need to locate the second one derivative of the given feature r(t). Taking the by-product two times, we get:

\(r''(t) = (3e^{(2t)})'', (3e^{(-2t)})'', (3te^{(2t)})''= 12e^{(2t)}, 12e^{(-2t)}, 12te^{(2t)} + 12e^{(2t)}\)

Substituting 0 for t in r''(t), we have:

\(r''(0) = 12e^{(2(0)}), 12e^{(-2(0)}), 12(0)e^{(2(0)}) + 12e^{(2(0)})\\\\= 12e^0, 12e^0, 12(0)e^0 + 12e^0\\\\= 12(1), 12(1), 0 + 12(1)\\\\= 12, 12, 12\)

Therefore, r''(0) = (12, 12, 12).

Finally, to discover r'(t) · r''(t), we need to calculate the dot made of the first derivative of r(t) and the second spinoff r''(t). The first spinoff of r(t) is given by using:

\(r'(t) = (3e^{(2t)})', (3e^{(-2t)})', (3te^{(2t)})'\\\\= 6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)\)

\(r'(t) · r''(t) = (6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)}) · (12, 12, 12)\\\\= 6e^{(2t)} * 12 + (-6e^{(-2t)}) * 12 + (3e^{(2t)} + 6te^{(2t)}) * 12\\\\= 72e^{(2t)} - 72e^{(-2t)} + 36e^{(2t)} + 72te^{(2t)\)

Thus, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).

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The correct answer is 3.6 because you only divide 18 by 5 and you'll get your answer.

The decimal equivalent of 18/5 is 3.6.

To convert a fraction to a decimal, you divide the top number by the bottom number. In this situation, you take the number 18 and divide it by the number 5.

When you divide, you get 3 as your answer and you have 3 left over. So, the decimal equivalent is 3. 6

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Answer:

A. Hyperbole

Step-by-step explanation:

"I've asked you a million times to please close the back door," said Jade's mother.

A million times is the exaggerated phrase in the sentence. Jade's mother did not really ask her that a million times, but it is used in this sentence as a way to show the reader that she said it a lot.

Hope this helps! : )

\( \frac{4c}{h} - k\)

Step-by-step explanation:

well that is the answer

Answer:

s = (4C/h) - k

Step-by-step explanation:

C = ((s + k)/4)h

multiply by 4/h

4C/h = s + k

subtract k

s = (4C/h) - k

A: -7n

B: 7n - 2

C: \(\frac{n + 4}{12}\)

Hope this helps!

Please give me Brainliest, I need it to level up :)

Answer:

dude that's easy 1,36 2,18 3,12 ,4,9 6,6

Step-by-step explanation:

Answer:

A., B., E., F., G.

Step-by-step explanation:

Hope this helped! Have a nice day!

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\)

Option D is the correct answer.

We have,

In this equation, the variable x represents the number of times the square is cut in half, and y represents the surface area of the square.

As x increases, the exponent of 1/2 decreases, causing the value of y to decrease.

This exponential decay accurately represents the idea that the surface area becomes less and less but never reaches zero units²

Thus,

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\).

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The correct equation that would help model the surface area of a square piece of paper as it is repeatedly cut in half is:  \(\(y=36(\frac{1}{2})^x\)\)

As the square is cut in half, the side length of the square is divided by 2, resulting in the area being divided by \(\(2^2 = 4\)\).

Therefore, the equation \(y=36(\frac{1}{2})^x\)\)accurately represents the decreasing surface area of the square as it is repeatedly cut in half.

and, \(\(y=x^2+4x-16\)\)is a quadratic equation that does not represent the decreasing nature of the surface area.

and, \(\(y=-25x^2\)\) is a quadratic equation with a negative coefficient.

and, \(\(y=9(2)^x\)\)represents exponential growth rather than the decreasing nature of the surface area when the square is cut in half.

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The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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Answer:

90,000 hours

Step-by-step explanation:

Answer:

89/12

Step-by-step explanation:

Answer: The unit rate is 7 stickers per student!

Step-by-step explanation: This can be found by dividing the amount of stickers by the amount of students.

Hope this helps, if not, comment down below please!!!

Answer:

cost of pizza I 5 and using proper cleaning

In the given options, only option C has the form of a second-degree function, y = x², where a=1, b=0, and c=0.

Therefore, the correct answer is C.

What is the polynomial equation?

A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.

The function y = x² is a second-degree function because it contains a variable, x, raised to the second power.

Option A, y = x, is a first-degree function because it contains a variable, x, raised to the first power.

Option B, y = 3x - 7, is a first-degree function because it contains a variable, x, raised to the first power.

Option D, y = 3, is a constant function because it does not contain any variable raised to any power.

Therefore, the answer is option C, y = x² has the form of a second-degree function.

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The number of square inches which make up half of the cookie cake is approximately 100.48 inches².

Given that,

The diameter of a circular cookie cake is 16 inches.

Cookie cake is circular.

We have to find the area of the half of the cookie cake.

Diameter = 16 inches

Radius = 16/2 = 8 inches

Area of a circular figure = πr²

Total area of the cookie cake = π(8)² = 64π

Area of half the cake = 64π /2 = 32π = 100.48 square inches

Hence the area of half of the cookie cake is 100.48 inches².

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