Consider the following system of linear equations given by:
3,5x12 +23 3x1 +102 +53 3x1+3x2+7, 25x3 0: = 4; (1)
(a) Verify that the system described by Eq. (1) admits a unique solution.
(b) Determine the solution using Gaussian elimination.
(c) Determine an approximation to the solution, with 3 iterations x
(5), using the Methods of
Gauss-Jacobi and Gauss-Seidel with x(0) = [x1(0)1, x2(0), x3(0)]>= [d1, d2, d3]>, where d1 is the first digit of your code. person, d2 is the second digit of your code. of person and d3 is the third digit of your code. of person.
(d) What is the maximum error made in each of the methods? Use the estimate calculation of the
error (absolute or relative) to compose the analysis.
(e) Analyze the results found in (b) and (c), commenting on the differences.
(f) What strategy would you recommend to reduce the maximum error obtained? Justify the recommendation.
(g) Considering the results found, which method do you consider more efficient in solving of the problem?

The ∆ABC is an isosceles triangle and have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.

An isosceles triangle have the measure of its base angles to be equal, and the sum of the interior angles sum up to 180°.

Given that sides AB ≅ BC, then the triangle ∆ABC has two sides with similar length and base angles so;

angles m∠A and m∠C are the base angles are both equal to 51°

m∠B = 180° - (51 + 51)° {sum of interior angles of a triangle}

m∠B = 180° - 102°

m∠B = 78°

Therefore, the isosceles triangle ∆ABC have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.

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If T: R³ -> R³ is a one-to-one linear operator and B = {v1, v2, v3} is a linearly independent set of vectors in R³, then [T]B may or may not be an invertible matrix. The invertibility of [T]B depends on whether the vectors T(v1), T(v2), T(v3) form a linearly independent set in R³.

The matrix [T]B represents the transformation T with respect to the basis B. To determine if [T]B is invertible, we need to consider the linear independence of the images T(v1), T(v2), and T(v3) under T.

If T(v1), T(v2), and T(v3) form a linearly independent set in R³, then the matrix [T]B will be invertible. This is because the columns of an invertible matrix are linearly independent, and the columns of [T]B correspond to T(v1), T(v2), and T(v3).

However, if T(v1), T(v2), and T(v3) are linearly dependent, then [T]B will not be invertible. In this case, the columns of [T]B will be linearly dependent, leading to a singular matrix.

Therefore, whether [T]B is invertible or not depends on the linear independence of the images of the vectors v1, v2, and v3 under T. If T(v1), T(v2), and T(v3) are linearly independent, [T]B will be invertible; otherwise, it will not be invertible.

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Answer:

The polynomials can be identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The non-polynomial expressions will be the expressions which contain other operations. Explain why the non-polynomial expressions are not polynomials.

Answer:

See below

Step-by-step explanation:

Each person donates $10 plus the $70 he got must be at least $250.

10x + 70 \(\geq\) 250

10x \(\geq\) 180

x \(\geq\) 18. To get at least $250, 18 people need to contribute.

On the other side:

10x + 70 \(\leq\) 350

10x \(\leq\)  280

x \(\leq\) 28 To get $350, 28 people need to contribute.

Write the entire inequality as 250 \(\leq\) 10x + 70 \(\leq\) 350

Answer:

47

Step-by-step explanation:

^

To find the value of x + 2 that ensures the given model is a valid probability model, we need to check if the given conditions for a probability model are satisfied:

1. The sum of all probabilities should be equal to 1.

2. Each probability should be between 0 and 1.

Let's check these conditions for the given model. P(x) = x! for x = 0, 1, 2, …Here, x! denotes the factorial of x. So, P(x) is the factorial of x divided by itself multiplied by all smaller positive integers than x. Therefore, P(x) is always positive. Also, P(0) = 1/1 = 1.

Hence, the probability P(x) satisfies the second condition. Now, let's find the sum of all probabilities.

P(0) + P(1) + P(2) + … = 1/1 + 1/1 + 2/2 + 6/6 + 24/24 + …= 1 + 1 + 1 + 1 + 1 + …This is an infinite series of 1s. The sum of infinite 1s is infinite, and not equal to 1. Therefore, the sum of all probabilities is not equal to 1. Hence, the given model is not a valid probability model. To make the given model a valid probability model, we need to modify the probabilities such that they satisfy both the conditions.

We can modify P(x) to P(x) = x! / (x + 2)! for x = 0, 1, 2, …Now, let's check the conditions again. P(x) = x! / (x + 2)! is always positive.

Also, P(0) = 0! / 2! = 1/2.

Hence, the probability P(x) satisfies the second condition. Now, let's find the sum of all probabilities.

P(0) + P(1) + P(2) + … = 1/2 + 1/6 + 1/24 + …= ∑ (x = 0 to infinity) x! / (x + 2)!= ∑ (x = 0 to infinity) 1 / [(x + 1)(x + 2)]= ∑ (x = 0 to infinity) [1 / (x + 1) - 1 / (x + 2)]= [1/1 - 1/2] + [1/2 - 1/3] + [1/3 - 1/4] + …= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...= 1

This is a converging infinite series. The sum of the series is 1. Therefore, the given modified model is a valid probability model. Now, we need to find the value of x + 2 that ensures the modified model is a valid probability model.

P(x) = x! / (x + 2)! => P(x) = 1 / [(x + 1)(x + 2)]

For P(x) to be valid, it should be positive. So, [(x + 1)(x + 2)] should be positive. This means x should be greater than -2. Hence, the smallest value of x is -1. Therefore, the value of x + 2 is 1.

The modified model is P(x) = x! / (x + 2)! for x = -1, 0, 1, 2, …The probability distribution table is: x P(x)-1 1/2 0 1/6 1 1/3 2 1/12...The value of x + 2 that ensures the modified model is a valid probability model is 1.

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in a large population, 68 % of the people have been vaccinated. if 3 people are randomly selected, 0.968 is the probability that at least one of them has been vaccinated.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being represented as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.

The probability is a measure of how likely an event is to occur. It gauges the event's degree of certainty. P(E) = Number of Favorable Outcomes/Number of All Outcomes is the formula for probability.

Given that,

In a large population, 68% of the people have been vaccinated.

Among them 3 people are randomly selected.

probability that at least one of them is vaccinated:

= 1 - P (none of the 3 has been vaccinated)

= 1 - (1 - 0.68)³

=0.968

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The value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. The fraction is defined as the division of the whole part into an equal number of parts.

The given fractions 34/9, 43/9, and 32/5 can be written in the form of the mixed fraction as below:-

To write the fractions in the form of the mixed fraction first divide the fraction by the complete number and put the remainder on the numerator.

34/9 = 3(⁷/₉)

43/9 = 4(⁷/₉)

32/5 = 6(²/₅)

Therefore, the value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

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Answer:

15

Step-by-step explanation:

x = 2

-4x+8+2x+3 = ?

-4 (-2) + 8 + 2 (-2) + 3 =

= 8 + 8 - 4 + 3

= 16 - 4 + 3

= 12 + 3

= 15

hopefully this helped you :)

There are 18 different triples of natural numbers with a sum of 10, considering (1,8,1) and (8,1) as the same triple as (1,1,8).

To find the number of different triples of natural numbers with a sum of 10, we can consider different cases based on the value of the first number in the triple.

Case 1: The first number is 1.

In this case, we need to find the number of ways to represent 10 as a sum of the remaining two numbers. Since we have already considered (1,8,1) and (8,1) as the same triple as (1,1,8), we only need to find the ways to represent 10 using two numbers, excluding 1. The possible pairs are:

(2,8), (3,7), (4,6), (5,5)

Case 2: The first number is 2.

In this case, we need to find the number of ways to represent 8 as a sum of the remaining two numbers. The possible pairs are:

(1,7), (3,5), (4,4)

Case 3: The first number is 3.

In this case, we need to find the number of ways to represent 7 as a sum of the remaining two numbers. The possible pairs are:

(1,6), (2,5), (4,3)

Case 4: The first number is 4.

In this case, we need to find the number of ways to represent 6 as a sum of the remaining two numbers. The possible pairs are:

(1,5), (2,4), (3,3)

Case 5: The first number is 5.

In this case, we need to find the number of ways to represent 5 as a sum of the remaining two numbers. The possible pair is:

(1,4)

Case 6: The first number is 6.

In this case, we need to find the number of ways to represent 4 as a sum of the remaining two numbers. The possible pairs are:

(1,3), (2,2)

Case 7: The first number is 7.

In this case, we need to find the number of ways to represent 3 as a sum of the remaining two numbers. The possible pair is:

(1,2)

Case 8: The first number is 8.

In this case, we need to find the number of ways to represent 2 as a sum of the remaining two numbers. The only possible pair is:

(1,1)

Adding up the counts from each case, we get:

4 + 3 + 3 + 3 + 1 + 2 + 1 + 1 = 18

Therefore, there are 18 different triples of natural numbers with a sum of 10, considering (1,8,1) and (8,1) as the same triple as (1,1,8).

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Answer:

The fraction in simplest form is: 25/3

Answer:

A polynomial is a combination of terms separated by

+

or

−

signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms.

Polynomial

Step-by-step explanation:

The generalized 9th degree polynomial is given below \(a_1x^9+a_2x^8+a_3x^7+a_4x^6+a_5x^5+a_6x^4+a_7x^3+a_8x^2+a_9x+a_{10}=0\) where \(a_1,a_2,....a_9\) are the coefficients and \(a_{10}\) is constant. The polynomial \(x^9\) is known as the nonic equation.

Given :

Polynomial  -- \(x^9\)

The following steps can be used in order to classify the given polynomial:

Step 1 - The generalized polynomial equation is given below:

\(a_1x+a_2x^2 + a_3x^3+a_4x^4+a_5x^5+.............+a_nx^n=0\)

where \(a_1,a_2,....,a_n\) are the coefficients.

Step 2 - The generalized quadratic equation is given below:

\(ax^2+bx+c=0\)

where a, b are the coefficients and c is the constant.

Step 3 - So the generalized 9th degree polynomial is given by:

\(a_1x^9+a_2x^8+a_3x^7+a_4x^6+a_5x^5+a_6x^4+a_7x^3+a_8x^2+a_9x+a_{10}=0\)

where \(a_1,a_2,....a_9\) are the coefficients and \(a_{10}\) is constant.

The polynomial \(x^9\) is known as the nonic equation.

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Answer:

The petrol used was 0.1 litre for every 1 kilometre.

The coordinates of the point where the artist should support the triangle for balance are approximately (6, 5.83).

To find the balancing point, we need to locate the centroid of the triangle. The centroid is determined by averaging the x-coordinates and the y-coordinates of the three vertices. Let's calculate the coordinates step by step:

x-coordinate of centroid = (0 + 6 + 12) / 3 = 6

y-coordinate of centroid = (4 + 11.5 + 1) / 3 ≈ 5.83

Therefore, the coordinates of the balancing point are approximately (6, 5.83). By placing the support at this point, the triangle will balance because the centroid represents the center of mass of the triangle. This ensures an even distribution of weight among the three vertices. To achieve balance, the artist should support the triangle at the coordinates (6, 5.83), which corresponds to the centroid.

By doing so, the weight will be evenly distributed, allowing the triangle to balance effectively.

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If you go twice as fast, your stopping distance will increase by four times (option C).

This relationship is based on the laws of physics and the principles of motion.

When an object is in motion, its stopping distance is influenced by its initial speed, reaction time, and braking capabilities. The stopping distance consists of two components: the thinking distance (the distance traveled during the reaction time) and the braking distance (the distance needed to bring the object to a complete stop).

According to the laws of physics, the braking distance is directly proportional to the square of the initial speed. This means that if you double your speed, the braking distance will increase by a factor of four. In other words, going twice as fast will require four times the distance to come to a stop.

It is important to note that this relationship assumes other factors, such as road conditions and braking efficiency, remain constant. However, in real-world scenarios, these factors may vary and can affect the stopping distance to some extent.

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To cover a floor with an area of 10 square foot, 5 tiles is needed.

Area is the amount of space enclosed by a two-dimensional figure.

If the tile is 2 feet long and twice as long as they are wide, suppose that the tile is a rectangle, then the area of each tile will be:

Area of tile = l x w

where l = 2 feet

w = 1 foot

Area of tile = 2feet(1 foot)

Area of tile = 2 ft^2

To determine how many tiles are needed to cover a 10 foot square floor, divide the area of the floor with the area of each tile.

# of tiles = Area of floor/Area of each tile

# of tiles = 10 ft^2/2ft^2

# of tiles = 5

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The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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Answer:

-30-45k

Step-by-step explanation:

-5*6=-30

-5*9k=-45k

Answer:

-30 -45k

Step-by-step explanation:

-5(6+9k)

Distribute

-5*6 -5*9k

-30 -45k

Steps to solve:

m - 2/6 < -1

~Add 2/6 to both sides

m < -4/6

Best of Luck!

Answer:

Wheres the question?????

Answer:

BRUV WHERE THE QUESTION

Step-by-step explanation:

The volume of the fully inflated balloon is \(\frac{19652}{3}\)π inch³ and volume of half inflated balloon is  \(\frac{19652\pi }{6}\).

Volume of a three dimensional shape is the space occupied by the shape.

Given that,

Diameter of a fully inflated balloon = 34 inch

Radius is half the diameter.

Radius of fully inflated balloon = 34 / 2 = 17 inches

Volume of a sphere = \(\frac{4}{3}\) π r³, where r is the radius.

(a) Volume of fully inflated balloon = \(\frac{4}{3}\) π (17)³

                                                    = \(\frac{19652}{3}\)π inch³

(b) Volume of the half inflated balloon = Half of the fully inflated volume

                                                          = (\(\frac{19652}{3}\)π / 2) inch³

                                                          = \(\frac{19652\pi }{6}\) inch³

(c) Volume of half inflated balloon = \(\frac{19652\pi }{6}\)

\(\frac{4}{3}\) π r³ = \(\frac{19652\pi }{6}\)

\(\frac{4}{3}\) r³ = \(\frac{19652}{6}\)

r³ = \(\frac{19652}{8}\)

r = 13.49 inch

Hence the volume and radius are found.

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Answer:

2430kg

Step-by-step explanation:

3 tonnes is 3000kg so 3 tonnes 335kg is 3335kg. Take 3335 - 905 you get 2430

Lydia earns $52.5 more than Gabrielle after 3 years.

percentage, a relative value indicating hundredth parts of any quantity.

we can use the formula for compound interest:

\(A = P(1 + r/n)^n^t\)

where A is the final amount,

P is the principal (initial investment),

r is the annual interest rate (as a decimal),

n is the number of times the interest is compounded per year, and

t is the number of years.

For Lydia (n=365)

A=1000(1+0.0525/365)¹⁰⁹⁵

A=1115.7

For Gabrille, we use the same formula but with n = 2 (compounded semi-annually):

A = 1000(1 + 0.0525/2)⁶

A = 1000(1.0265625)⁶

A = 1168.2

To find the difference in the amounts earned, we subtract Gabrielle's amount from Lydia's:

1168.2- 1115.7 = 52.5

Hence, Lydia earns $52.5 more than Gabrielle after 3 years.

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Answer:D

Step-by-step explanation:

the -1 means down one

x+5=0 subtract 5 so x= -5 means 5 to the left from the orgin (0 0) from point (-5,-1) you move up 4 and right 1 that's the 4 on the

Answer:

1. 53

2. 20

3. 37

4. 29

Step-by-step explanation:

Since your trying to find the hypotenuse you equation is...

1. 28^2 + 45^2 = C^2

    784 + 2025 = C^2

      Square Root 2809= C^2

    C=53

So after you square root 2809 you get 53.

2. 12^2 + 16^2 = C^2

     144 + 256 = C^2

      Square Root 400 = C^2

    C=20

So after you square root 400 you get 40.

3.  12^2 + 35^2 = C^2

    144 + 1225 = C^2

    Square Root 1369 = C^2

   C=37

So after you square root 1359 you get 37.

4. 20^2 + 21^2 = C^2

   400 + 441 = C^2

  Square root 841 = C^2

  C=20

So after you square root 841 you get 29.

Answer:

b

Step-by-step explanation:

u just have to think about it

The radius of Deimos to one significant digit in meters is approximately 9.4 m

.

Given the ratio of the Sun-from-Mars distance to Deimos-from-Mars distance is 365,000, the distance between Mars and Deimos can be found to bedeimos distance = Sun-Mars distance / 365,000

Next, we can find the diameter of Deimos by noting that 550 of its diameters is equal to the distance it takes to transit the shadow of Mars during a lunar eclipse.

Let's call the diameter of Deimos "d", so we can

diameter = 1/550 * deimos distance

Finally, the Sun appears about 8.4 times as large as Deimos in the Martian sky. If we call the radius of Deimos "r", then the radius of the Sun is 8.4r.

Using the information given, we can set up the following equation:

deimos distance / (3,000,000 + r) = 8.4r / (3,000,000)Simplifying and solving for r,

we get:r = 9.39 m (rounded to one significant digit)

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Answer:

67 1/2 cm

Step-by-step explanation:

v=lxwxh

v=4 1/2x 6x 2 1/2

v=67 1/2 cm^3

Volume of rectangular prism is given by:

‎ㅤ‎ㅤ‎ㅤ➙ V = l × b × h

Here, we have :

Therefore, volume:

\( \implies\quad \tt {V =l\times b\times h }\)

\( \implies\quad \tt { V =6\times 2\dfrac{1}{2}\times 4\dfrac{1}{2}}\)

\( \implies\quad \small{\tt { V = 6\times \dfrac{(2\times 2)+1}{2}\times \dfrac{(4\times 2)+1}{2}}}\)

\( \implies\quad \tt {V = 6\times \dfrac{4+1}{2}\times \dfrac{8+1}{2} }\)

\( \implies\quad \tt {V =6\times \dfrac{5}{2}\times\dfrac{9}{2} }\)

\( \implies\quad \tt {V =\dfrac{6\times 5\times 9}{2\times 2} }\)

\( \implies\quad \tt { V =\cancel{\dfrac{270}{4}}}\)

\( \implies\quad \tt { V = \dfrac{135}{2}}\)

\( \implies\quad \underline{\underline{\pmb{\tt { V = 67\dfrac{1}{2}\:cm^2}}}}\)