what are remainder theorem

Gauss-Seidel Method:
Iteration 1:
Starting with x(0) = [0, 0], we can substitute the initial values into the system of equations:
3(0) + 1(0) + 3x₂(1) + 6x₂(0) + 2x₂(0) = 0 -> 3x₂ = 0
3(0) + 3x₂(1) + 7x₂(0) = 4 -> 3x₂ = 4

Solving these equations, we find x(1) = [0, 4/3].

Iteration 2:
Using the updated values from the previous iteration, we have:
3x₁(1) + x₂(0) + 3x₂(1) + 6x₂(4/3) + 2x₂(4/3) = 0 -> 3x₁ + 16x₂ = -16/3
3x₁(1) + 3x₂(1) + 7x₂(4/3) = 4 -> 3x₁ + 19x₂ = 16/3

Solving these equations simultaneously, we obtain x(2) ≈ [-16/15, 8/15].

Iteration 3:
Using the updated values from the previous iteration:
3x₁(-16/15) + x₂(8/15) + 3x₂(-16/15) + 6x₂(8/15) + 2x₂(8/15) = 0 -> 3x₁ + 32x₂ = -16/5
3x₁(-16/15) + 3x₂(8/15) + 7x₂(8/15) = 4 -> 3x₁ + 19x₂ = 16/3

Solving these equations, we find x(3) ≈ [-16/35, 16/35].

After three iterations of the Gauss-Seidel method using the given initial value x(0) = [0, 0], we obtain an approximate solution of x(3) ≈ [-16/35, 16/35].

Jacobi's Method:

Iteration 1:
Starting with x(0) = [0, 0], we can update each component separately:
x₁(1) = (0 - (1(0) + 3x₂(0)) / 3 -> x₁ = 0
x₂(1) = (4 - (3x₁(0) + 7x₂(0))) / 3 -> x₂ = 4/3

Hence, x(1) = [0, 4/3].

Iteration 2:
Using the updated values from the previous iteration:
x₁(2) = (0 - (1(0) + 3x₂(4/3)) / 3 -> x₁ ≈ -16/15
x₂(2) = (4 - (3x₁(0) + 7x₂(4/3))) / 3 -> x₂ ≈ 8/15

Therefore, x(2) ≈ [-16/15, 8/15].

Iteration 3:
Using the updated values from the previous iteration:
x₁(3) = (0 - (1(-16/15) + 3x₂(8/15)) / 3 -> x₁ ≈ -16/35
x

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Answer:

45cm

Step-by-step explanation:

3 x 5 x 3 x 1/2

(if im wrong im sorry)

Answer:

16.1, 16, 16

Step-by-step explanation:

1) we are going to do the mean :)

you add all the number together and divide by the same number

you should get 354/22 which is 16.0909....... since its round to tenth place, we place it at 16.1.

2)  median, for this one, you have to lay out the numbers and see which one is in the middle, in 14,15,16,17,19, 16 is the median.

3)  the number that appear the most is the mode, so right now we have

three 17s and six 16s, don't worry about the others because its not in the answer choice, so its 16.

Hope this helps :D

Answer:

19/21

Step-by-step explanation:

1×7+4×3/21

19/21

During the change-of-shift report, you would provide an SBAR (Situation, Background, Assessment, Recommendation) framework report to the oncoming nurse for A.B., a 68-year-old man admitted with pleural effusion and pneumonia.

In the Situation section, you would start by stating that A.B., a 68-year-old man, was admitted with pleural effusion and pneumonia. You would mention his presenting symptoms of shortness of breath, chest pain, weakness, and a dry, irritating cough. Provide the vital signs: blood pressure 142/82 mmHg, heart rate 118 beats per minute, respirations 38 breaths per minute (labored and shallow), temperature 102.1°F (38.9°C), and Spo2 of 85% on room air.

In the Background section, you would mention that a thoracentesis was performed, draining 1500 mL of fluid, and a specimen for culture and sensitivity (C&S) was sent to the lab. Explain that A.B. was started on ceftriaxone 500 mg IV every 12 hours, but the pleural C&S results showed a large amount of Klebsiella organism growth that is not sensitive to ceftriaxone.

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Answer: Its spring break relax PLS

Step-by-step explanation:

Explanation: Its really similar to solving an equation, so all I did was add 2 to both sides :)

Answer:

P = P (1 + r / n) ^ rt

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

3 x ((5) + 4)

3 x 9 =27

Answer:

9) (68 + 160)/2 = 114°

10) 80/2 = 40°

11) 105 x 2 = 210°

12) 80 x 2 = 160°

13) (360 - 180 - 108)/2 = 36°

14) (360 - 69 - 95)/2 = 98°

Answer:

I answered it on the second time you asked this question check it out

Here are the solutions to the given problems:

1. To find the sum of cells A1 and C3, we simply write the formula as: =SUM(A1,C3)

2. To find the sum of all rows from A5 to A27 using the range operator, we use the formula: =SUM(A5:A27)

3. To determine the largest value in cells D2 and D3, we use the formula: =MAX(D2,D3)

4. To find the number of numeric values from rows F5 to F21, cell G12, and cell H9, we use the formula: =COUNT(F5:F21,G12,H9)

The above formulas are used in Microsoft Excel for performing calculations.

Microsoft Excel is a popular spreadsheet program developed by Microsoft. It is a part of the Microsoft Office suite of productivity software, which also includes programs like Word, PowerPoint, and Outlook.

Excel provides a grid-based interface where users can organize and analyze data. The program uses a collection of cells arranged in rows and columns, forming a worksheet. Each cell can hold various types of data, such as numbers, text, dates, and formulas.

Excel offers a wide range of features and tools to perform calculations, create charts and graphs, manipulate data, and automate tasks. Users can enter data manually or import it from external sources, perform mathematical and statistical calculations, create formulas to link and manipulate data across cells, and use functions for various purposes.

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Answer:

S

=

{

(

−

2

,

5

)

}

Step-by-step explanation:

Answer:

this would be the answer 4.66666667 but when rounded it would be 5 or 4.7

Step-by-step explanation:

brainliest ???

Answer:

739.47

Step-by-step explanation:

height - h, radius -r

V=hπ²r=5×3.14²×15=739.47

Answer:

312

Step-by-step explanation:

a) the value of the expression is 29.

b) the value of the expression is -3.

d) the value of the expression is 270.

a) To calculate the expression 4x2 + 3 + 6 - 2 + 7 X 2, follow the order of operations (PEMDAS/BODMAS):

4x2 = 8
7 X 2 = 14

Now we can substitute these values into the expression:

8 + 3 + 6 - 2 + 14

Performing the addition and subtraction from left to right:

= 11 + 6 - 2 + 14
= 17 - 2 + 14
= 15 + 14
= 29

Therefore, the value of the expression is 29.

b) To calculate the expression 4+2-6-1 - 7+ 12, again use the order of operations:

4 + 2 = 6
-7 + 12 = 5

Now we can substitute these values into the expression:

6 - 6 - 1 - 7 + 5

Performing the subtraction and addition from left to right:

= 0 - 1 - 7 + 5
= -1 - 7 + 5
= -8 + 5
= -3

Therefore, the value of the expression is -3.

c) To calculate the expression (-48 - 12) = (-3 + 11), perform the subtraction and addition:

-48 - 12 = -60
-3 + 11 = 8

Now we can substitute these values into the equation:

-60 = 8

The equation is not true since -60 is not equal to 8. Therefore, there is no solution to this equation.

d) To calculate the expression (-5)(6)(-9), perform the multiplication:

(-5)(6)(-9) = -30(-9)
= 270

Therefore, the value of the expression is 270.

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Answer:

1/2

Step-by-step explanation:

Hope it helps :)

Answer: 3x-x+2=4

Step-by-step explanation:

12/X=3/6 CROSS MULTIPLY.

3X=12*6

3X=72 X=72/3 X= 24 FEET TALL.

Answer:

D. the average difference in height between each player and the mean height

Answer:

The answer is x is greater than or equal to -2

Step-by-step explanation:

I just did the math by hand

Answer:  x ≤ -5

Step-by-step explanation:

3x - 11 ≥ 7x + 9

3x ≥ 7x + 20

-4x ≥ 20  when dividing negative numbers, change the sign to the opposite.

x ≤ -5

The correct answer is B. Permutations should be used because no item may be selected more than once, and the order matters. There are 720 different executive committees possible.

To determine the appropriate counting technique, we need to consider two factors: whether repetition is allowed and whether the order matters.

In this scenario, each position in the executive committee is distinct (mayor, deputy mayor, secretary, administrator, treasurer), and no member can hold multiple positions. Therefore, repetition is not allowed.

Additionally, the order of the positions in the committee matters. The committee will be different depending on who holds each position.

Based on these considerations, the correct answer is:

B. Permutations should be used because no item may be selected more than once, and the order matters.

To calculate the number of different committees possible, we can use the concept of permutations. Since there are six members in the city council and we need to select five for the committee, the calculation would be:

6P5 = 6! / (6-5)! = 6! / 1! = 6 * 5 * 4 * 3 * 2 * 1 / 1 = 720

Therefore, there are 720 different executive committees possible.

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Answer:

No a triangle CAN’T have 2 obtuse angles. I dont know about the drop down menus since I can’t see the choices but there can’t be 2 obtuse angles in a triangle. I can guess two of them anyway

The second drop down one is “greater”

The last option is 180

Im not sure about he first since dropdowns aren’t presented

The probability of selecting a green baseball cap from the order of 64 caps is 0.25 or 25%.

To calculate the probability of selecting a green baseball cap from the order of 64 caps, we can use the concept of probability.

Given:

Total number of caps (n) = 64

Number of green caps (k) = 16

The probability (P) of selecting a green cap can be calculated as the ratio of the number of green caps to the total number of caps:

P(green cap) = k / n

Substituting the values:

P(green cap) = 16 / 64

P(green cap) = 0.25

Therefore, the probability of selecting a green baseball cap from the order of 64 caps is 0.25 or 25%.

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If a is a 7×9 matrix, the smallest possible dimension of nul A is 2. The correct option is a.

The smallest possible dimension of the null space (also known as the kernel) of matrix A depends on the rank of the matrix.

The rank of a matrix represents the maximum number of linearly independent rows or columns it contains.

In this case, we have a 7×9 matrix.

According to the rank-nullity theorem,

the dimension of the null space is given by the difference between the number of columns and the rank of the matrix.

The smallest possible dimension of the null space would be:

Dimension of null space = Number of columns - Rank of matrix

Since the matrix A has 9 columns, the smallest possible dimension of the null space would be:

Dimension of null space = 9 - Rank of matrix

The rank of the matrix can vary. It can range from 0 (if the matrix is a zero matrix) to a maximum of 7 (if all rows are linearly independent). So, depending on the rank, the smallest possible dimension of the null space can be any value between 9 and 2.

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The complete sequence is:

20, 0.6, 41.6667, 69.4444, 12, 500.

To find the missing numbers in the given sequence, let's analyze the pattern and fill in the gaps.

Looking at the sequence, we can observe that there is an exponential pattern occurring.

Let's break it down step by step:

Starting with the first number, 20, we can see that each subsequent number is decreasing or increasing exponentially.

If we divide the second number by the first number, we get 12/20 = 0.6. Similarly, dividing the third number by the second number gives us 500/12 = 41.6667.

We can see that there is a decreasing exponential pattern from the first to the third number.

Let's continue this pattern:

If we divide the fourth number by the third number, we get an approximate value of 41.6667/0.6 = 69.4444.

So, we can deduce that the missing numbers in the sequence are approximately 0.6, 41.6667, and 69.4444.

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Answer:

c.32/3π units ³

Step-by-step explanation:

V= 4/3πr³

r=4/2=2units

V= 4/3π(2)³

V= 4/3π *8

V= 32/3π units ³

Answer:

V≈32/3

Step-by-step explanation:

V=4 /3πr3=4 /3·π·23≈33.51032

33.5/3.14=10.6

32/3=10.6

Please brainliest! I worked so hard!