approximate the area under the curve y=x^3 from x=3 to x=6

Answers

Answer 1

To approximate the area under the curve y=x^3 from x=3 to x=6, we can use the midpoint rule with four subintervals.First, we need to find the width of each subinterval:delta x = (6 - 3) / 4 = 0.75Next, we can find the midpoint of each subinterval:x1 = 3 + 0.5 * delta x = 3.375

x2 = x1 + delta x = 4.125

x3 = x2 + delta x = 4.875

x4 = x3 + delta x = 5.625Now, we can evaluate the function at each midpoint:y1 = x1^3 = 40.39

y2 = x2^3 = 71.25

y3 = x3^3 = 106.29

y4 = x4^3 = 146.48Finally, we can use the midpoint rule formula to approximate the area:A ≈ delta x * (y1 + y2 + y3 + y4)

= 0.75 * (40.39 + 71.25 + 106.29 + 146.48)

= 267.98Therefore, the approximate area under the curve y=x^3 from x=3 to x=6 is 267.98 square units.


Related Questions

A noodles factory gives 10% commission to a wholesaler for selling its produtcs. After giving the commission to the wholesaler, the company recieves Rs 315000 in baishakh. Find the total sales of noodles by the wholesaler in baisakh.

Answers

To find the total sales of noodles by the wholesaler in Baishakh, we need to calculate the original amount before the commission was deducted.

Let's assume the total sales by the wholesaler in Baishakh is represented by 'x'.

The commission given to the wholesaler is 10% of the total sales, which can be expressed as 0.10x.

The amount received by the company after deducting the commission is Rs 315,000.

So, the equation becomes:
x - 0.10x = Rs 315,000

Simplifying the equation:
0.90x = Rs 315,000

Dividing both sides by 0.90:
x = Rs 350,000

Therefore, the total sales of noodles by the wholesaler in Baishakh is Rs 350,000.

Answer: 350000

Step-by-step explanation: Let the total sale of noodles by the wholesaler be x.

Given: Commission for the wholesaler is 10%

After receiving a 10% commission the company got rupees 315000.

x-10% of x =315000

x - 10\100 = 315000

x-x\10 = 315000

10x - 10\10 =315000

9x = 3150000

x= 3150000\9

x= 350000

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.

Answers

Applying the angle of intersecting secant-tangent theorem, the measure of arc VT is calculated as: m(VT) = 116°.

How to Find the Measure of Arc Using the Angle of Intersecting Secant-Tangent Theorem?

Given that the lines appear tangent, the measure of the arc VT indicated above can be calculated using the angle of intersecting secant-tangent theorem which states that:

m<U = 1/2(m(WT) - m(VT))

Given the following:

measure of angle U = 37 degrees.

measure of arc WT = 190 degrees.

Plug in the values:

37 = 1/2(190 - m(VT))

74 = 190 - m(VT)

m(VT) = 190 - 74

m(VT) = 116°

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I will give brainliest and ratings if you get this correct ​

Answers

The output levels that will maximize profits are Q1 = 52.5 and Q2 = 52.5.

How to determine the output level that maximize profits

To maximize profits, we need to find the output levels of the two goods that will maximize the difference between total revenue and total cost (i.e., profit).

The profit function can be expressed as:

π = TR - TC

  = 15Q1 + 18Q1^2 + 15Q2 + 18Q2^2 - 20 - 2Q1.Q2 - 393

Taking the partial derivative of the profit function with respect to Q1 and setting it equal to zero, we get:

∂π/∂Q1 = 15 + 36Q1 - 2Q2 = 0

Taking the partial derivative of the profit function with respect to Q2 and setting it equal to zero, we get:

∂π/∂Q2 = 15 + 36Q2 - 2Q1 = 0

Using Cramer's rule, we can solve for Q1 and Q2:

Q1 = (2(15) - (15)(36))/(-4) = 52.5

Q2 = (2(15) - (15)(36))/(-4) = 52.5

Therefore, the output levels that will maximize profits are Q1 = 52.5 and Q2 = 52.5.

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Because you loved Professor Salaam’s class so much, you go to the market and decide to trade your car for 2 magical doubling beans. After 1 day, you notice that your 2 magical beans have turned into 4 magical beans. After 2 days you look and there are 8 magical beans. On the third day you notice there are now 16 beans. Since you are a brilliant mathematician, you decide to estimate how many beans you will have after 15 days.

Part A

How many beans will you have?




Part B

If each magical bean is worth $0.50, and your car was worth $65,000, did your trade make sense (after 15 days)?



(b)
A
YES
B
NO
C
MAYBE?
D
Not enough information
(c)


Part C

Estimate how many days you would need to have doubled your beans for the trade to make sense.

Answers

Part A: After 15 days will have 32,768 magical beans.

Part B: As the value of the magical beans is less than the value of the car the trade does not make sense at least not from a financial perspective. B NO.

Part C: We would need at least 17 days for the number of magical beans to exceed the value of the car. C MAYBE?.

Based on the given information can observe that the number of beans doubles every day.

So, after 15 days will have 2¹⁵ = 32,768 magical beans.

The value of the 32,768 magical beans would be:

32,768 beans × $0.50/bean

= $16,384

Part C:

Let us assume that after 'n' days, the number of beans would be equal to or greater than the value of the car.

Value of the car in terms of magical beans = $65,000/$0.5 per bean

= 130,000 beans

Now, we can set up an equation based on the doubling of beans:

2ⁿ >= 130,000

Taking the logarithm base 2 on both sides, we get:

n × log2(2) >= log2(130,000)

n >= log2(130,000)

n >= 16.98

We would need at least 17 days for the number of magical beans to exceed the value of the car.

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Is this correct? Or what do you think the answer is please

Answers

The partial fraction of the given rational expression is [tex]\frac{25}{(x+1(x+2)} =\frac{25A}{3(x-1)} -\frac{25B}{3(x+2)}[/tex]

Solving partial fractions

Given the following equation below:

[tex]\frac{25}{(x+1(x+2)}[/tex]

We are expression as the sum of partial fractions

Let the numerator of both partial expressions be A and B to have:

[tex]\frac{25}{(x+1(x+2)} =\frac{A}{x-1} +\frac{B}{x+2}[/tex]

Simplifying the expression, we will have;

[tex]\frac{25}{(x+1(x+2)} =\frac{A(x+2)+B(x-1)}{x-1(x+2)}[/tex]

Cancelling the denominator:

25 = A(x+2) + B(x-1)


If x - 1 = 0, then x = 1. Substitute to have:

25 = A(1+2)

3A = 25
A = 25/3

If x + 2 = 0, x = -2

25 = B(-3)
B = -25/3

Substitute into the function to have:

[tex]\frac{25}{(x+1(x+2)} =\frac{25A}{3(x-1)} -\frac{25B}{3(x+2)}[/tex]

This gives the partial fraction of the given rational expression.

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You rent an apartment that costs $1700 per month during the first year, but the rent is set to go up 11% per year. What would be the rent of the apartment during the 10th year of living in the apartment? Round to the nearest tenth (if necessary).​

Answers

The required amount of rent be $4,850.19.

The original rent of apartment per month = $1700

And the interest = 11%

Time = 10 years.

To determine the apartment's rent during the tenth year:

Rent is calculated as Initial = Rent x [tex](1 + Increase Rate )^{year}[/tex] .

We plug the values and compute the rent for the tenth year using the provided data,

Rent = $1700 x (1 + 0.11)¹⁰

Rent = $1700 x 2.85

Rent = $4,850.19

Thus,

The apartment's rent in the tenth year would be about $4,850.2 per month.

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Can someone help me with this pls its due td pls

Answers

The measures are given as follows:

x = 2.m < A = 110º.m < ABD = 34º.

How to obtain the measures?

On a parallelogram, the opposite sides are congruent, hence the value of x is obtained as follows:

2x = 4

x = 2.

Opposite angles are congruent, meaning that they have the same measure, hence the measure of angle A is given as follows:

m < A = m < C = 110º.

Consecutive angles are supplementary, meaning that the sum of their measures is of 180º, hence the measure of angle B is given as follows:

m<B = 180º - 110º = 70º.

Considering the angle addition postulate, the measure of angle ABD is given as follows:

m < ABD = 70 - 36

m < ABD = 34º.

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A pentagonal pyramid.
There are
faces on the solid.

There are
edges on the solid.

There are
vertices on the solid.

Answers

Answer:

A pentagonal pyramid. There are 6 faces on the solid. There are 10 edges and there are 6 vertices on the solid.

What is a pentagonal pyramid?

A pentagonal pyramid is defined as a type of pyramid that has a base with the shape of a regular polygon.

The properties of a pentagonal pyramid include the following:

It has 6 faces. It has 5 triangles as lateral sides. It also has a pentagon at the base.

It has 6 vertices.

It also has 10 edges.

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Determine the equation of the given conic xy-coordinates when the aces are rostered through the given angle
x^2-y^2=2y , o/ = cos^-1 3/5
Precalc helppp

Answers

The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

The equation of the conic in xy-coordinates when the axes are rotated through the given angle can be determined by using a rotation matrix. Given that the conic is represented by the equation:

x^2 - y^2 = 2y

And the rotation angle is θ = arccos(3/5), we can proceed as follows:

1. Rewrite the given equation in matrix form:

[x, y] * [1  0] * [x]  = [2y]

        [-1 0]   [y]      [0]

2. Define the rotation matrix using the given angle θ:

R(θ) = [cos(θ)  -sin(θ)]

          [sin(θ)   cos(θ)]

3. Apply the rotation matrix to the equation:

[x, y] * R(θ)^T * R(θ) * [x] = [2y]

        [1  0]     [-1 0]   [y]     [0]

[x, y] * R(θ)^T * [1  0] * R(θ) * [x] = [2y]

                              [-1 0]   [y]     [0]

[x, y] * [cos(θ) sin(θ)] * [1  0] * [cos(θ)  -sin(θ)] * [x] = [2y]

        [-sin(θ) cos(θ)]   [-1 0]     [sin(θ)   cos(θ)]   [y]     [0]

Simplifying the expression:

[x * cos(θ) + y * sin(θ)] * [x * cos(θ) - y * sin(θ)] - [x * sin(θ) - y * cos(θ)] * [x * sin(θ) + y * cos(θ)] = 2y

Expanding and rearranging terms:

x^2 * cos^2(θ) - y^2 * sin^2(θ) - x^2 * sin^2(θ) + y^2 * cos^2(θ) = 2y

Combining like terms:

x^2 * (cos^2(θ) - sin^2(θ)) + y^2 * (cos^2(θ) - sin^2(θ)) = 2y

Using the trigonometric identity cos^2(θ) - sin^2(θ) = cos(2θ):

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

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4x+4=4x-4 what dose x equal

Answers

The value of the variable is equal to 0

What are algebraic expressions?

Algebraic expressions are described as those mathematical expressions that are known to consist of terms, coefficients, constants, variables and factors.

These algebraic expressions are also composed of arithmetic operations, such as;

AdditionBracketParenthesesMultiplicationDivisionSubtraction

From the information given, we have that;

4x+4=4x-4

To determine the value of x, take the steps;

collect the like terms, we have;

4x - 4x = -4 - 4

subtract the values, we have;

0 = -8

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PLEASE HELP! I WILL GIVE BRAINLIEST!! A worker at an animal shelter recorded data about the adoption of cats in the table shown below.


Based on the table, which of these statements are true? Choose all that are correct.


a

Of all the cats adopted, 34.9% are between 6 months and 1 year old

b

Of the cats 1 year or older, about 58% took more than 1 month to be adopted.

c

Of all the cats adopted, about 66% were adopted in a month or less.

d

Of the cats that took more than a month to adopt, 12.5% were younger than 6 months

e

Of the cats who took 1 to 7 days to be adopted, 25% were between 6 months and 1 year old.

Answers

C because if the animal is adopted then other people adopted in a month

PLEASE HELP I WILL MARK YOU BRAINLIEST!!

Answers

Answer:

96π

Step-by-step explanation:

the shape is made up of a cylinder and a cone.

Volume of cylinder = π r ² h

= π (3)² (9)

= 81π.

Volume of cone = (1/3) X vertical height X π r ²

= (1/3) (5) π (3)²

= 15π

volume of composite solid = 81π + 15π = 96π

14. Which is NOT a part of your budget? (1 point) fixed expenses Ogross pay Odiscretionary expenses Orealized income​

Answers

Realized income is NOT part of your budget.

Income that has really been received or generated within a certain period is referred to as realized income. It stands for the money that has been made or acquired through a variety of sources, including work, investments, or commercial ventures.

Realized income is a crucial part of a budget since it shows the actual cash that a person or organization has available for budgeting and financial planning.

The income is what may be used for a variety of costs, savings, investments, or other financial objectives.

In order to appropriately reflect the financial resources available for controlling spending and making financial decisions, realized income is often included as part of a budget.

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What is m∠1?

A. 22

B. 46

C. 76

D. 27

Answers

Answer:

Step-by-step explanation:

B

Za kingdom charges according to this table. how much does Za Kingdom charge for each pizza

Answers

The amount that Za Kingdom charges for each pizza is $8.

How to determine the amount charged by Za kingdom

To determine the amount charged by Za Kingdom, we first note that the cost of each pizza plus the delivery fee is $21.

Assuming the basic price to be $8 and the delivery fee of $13, we have the sum of $21. So, for 3 pizzas, we will have 8 times 3 = 24 + 13 = 37

Also, the amount for 10 pizzas will be 8 times 10 = 80 + 13 = 93. So, the price of each pizza is $8.

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Find absolute and relative change as a percentage.
The U.S. per person consumption of beef decreased from 67.8 pounds in 2000 to 57.7 pounds in 2020.

Answers

The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.

How to determine the absolute and relative change as a percentage.

To find the absolute and relative change as a percentage in the U.S. per person consumption of beef from 2000 to 2020, we can follow these steps:

Calculating the absolute change:

Absolute change = Final value - Initial value

= 57.7 pounds - 67.8 pounds

= -10.1 pounds

Step 2: Calculate the relative change:

Relative change = (Absolute change / Initial value) * 100

= (-10.1 pounds / 67.8 pounds) * 100

≈ -14.9%

The absolute change is -10.1 pounds, indicating a decrease in per person consumption of beef.

The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.

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18.3% of the animals in the local shelter are neither cats nor dogs. 2% of those animals that are not cats or dogs are rabbits. If there are 267 animals in the shelter, approximately how many of them are rabbits? Do not round any numbers until you finish the problem

Answers

Let's start by finding the percentage of animals in the shelter that are cats or dogs:

100% - 18.3% = 81.7%

Let's convert this percentage to a decimal:

81.7% = 0.817

Now, let's find the total number of animals that are cats or dogs:

0.817 x 267 = 218.139

We know that 2% of the animals that are not cats or dogs are rabbits. Let's find the percentage of animals in the shelter that are not cats or dogs:

100% - 81.7% = 18.3%

Let's convert this percentage to a decimal:

18.3% = 0.183

Now, let's find the total number of animals that are not cats or dogs:

0.183 x 267 = 48.951

We can now find the number of rabbits in the shelter:

2% of 48.951 = 0.02 x 48.951 = 0.97902

Therefore, approximately 0.97902 animals in the shelter are rabbits.

We should round this number to the nearest whole number, which is 1.

So approximately 1 animal in the shelter is a rabbit.

Answer the question by comparing the equation,
f
(
x
)
=
2
cos
(
2
π
6
(
x
+
4
)
)
+
3
to the equation,
f
(
x
)
=
acos
(
2
π
b
(
x
+
c
)
)
+
d
.


What is the period of the function?

Answers

The calculated value of the period of the function is 6

Calculating the period of the function?

From the question, we have the following parameters that can be used in our computation:

The equation, f(x) = 2cos(2π/6(x + 4)) +3

A sinusoidal function is represented as

f(x) = acos(2π/b(x + c)) + d

Where the period is B

When the equations are compared, we have

2π/b = 2π/6

This gives

b = 6

Hence, the period of the function is 6

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Complete question

Answer the question by comparing the equation,f(x)=2cos(2π6(x+4))+3 to the equation,f(x)=acos(2πb(x+c))+d.What is the period of the function?

If you have a system of two equations with two unknowns, and the graphs of
the two equations do not intersect, the system must have
A. at least 1 solution
B. exactly 1 solution.
C. no solution
D. more than 1 solution

Answers

If you have a system of two equations with two unknowns, and the graphs of the two equations do not intersect, the system must have no solution.

option C.

What is the solution of the two equations?

When we have a system of two linear equations in two variables, it can be represented graphically as two lines in a plane. The solution to the system corresponds to the point of intersection of these lines.

If the two lines do not intersect, then they are parallel. In this case, there is no point that satisfies both equations, which means that there is no solution to the system of equations.

In other words, if the two graphs do not intersect, it means that there are no values of the two unknowns that can simultaneously satisfy both equations.

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dentify the radius and the center of a circle whose equation is (x – 5)² + y² = 81.
The radius of the circle is units.
The center of the circle is at (, ).

Answers

Answer:

Step-by-step explanation:

General formula

(x-h)^2 + (y-k)^2 = r^2

where (h,k) center of circle whose radius r

applying the formula to our Q

(x – 5)² + y² = 81

(x – 5)² + (y-0)² = 9^2

---> center of circle (5,0)

---> radius is 9

Helppppp pleaseeeeeeee

Answers

To achieve a 1 in row 1, column 1, divide row 1 by 4 in the given matrix, resulting in the updated matrix. This row operation preserves the system of linear equations represented by the matrix.

To get a 1 in row 1, column 1 of the given matrix, you can perform the following valid row operation:

R1 = (1/4) * R1

This operation scales row 1 by a factor of 1/4, resulting in the new matrix:

1 , -3/4 , -43/4

3 , -2 , -30

By dividing each element in row 1 by 4, the value in row 1, column 1 becomes 1. This row operation maintains the equivalence of the system of linear equations represented by the matrix.

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How many quarts are equivalent to 5 pints

Answers

Answer: 3 quarts is equivalent to 5 pints

Problem 1-26
Jerrod and Sonia were working with their team on
problem 1-2 to put the function machines in order.
These functions are reprinted for you below.
f(x) = √x
g(x) = (x - 2)²
h(x) = 2*-7
k(x) = − − 1
Jerrod first put an input of 6 into the function g(x) and
got an output of -16. He wanted to try f(x) as his next
function in the order, but he thinks there might be a
problem using -16 as an input. Is there a problem?
Explain.

Answers

There is a problem with the input -16 in the function f(x) = √x

How to determine if there is a problem with the input

From the question, we have the following parameters that can be used in our computation:

f(x) = √x

g(x) = (x - 2)²

h(x) = 2x - 7

k(x) = -x -1

Also, we understand that

He puts the functions in the machine in order

So, we have

f(x) = √x

The input is -16

So, we have

f(-16) = √-16

The square root of -16 is not a real number

Hence, there is a problem with the input

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What time is shown on the clock?

Answers

Answer:

3:55

Step-by-step explanation:

3:55

3:55 since the short hand doesn’t yet reach 4 and the the long hand is on the 11

a baseball diamond is a square with sides of 90 feet. what is the shortest distance ,to the nearest tenth of a foot, between first base and third base?

Answers

Answer:

The distance from first base to third base is 127.3 ft,

Find the volume of a cylinder with a diameter of 20 km and a height of 5 km in terms of pie.

what is the volume of the cylinder?

Answers

Answer:

The volume of the cylinder is 500 π cubic kilometers.

Step-by-step explanation:

Formula: V = πr²h

r = d/2

r = 20km/2

r = 10 km

h = 5km

Solve for the volume using the formula.

Substitute the given

V = π(10km)²(5km)

V = 500π km³

I hope this helps you

Combine like terms to simplify the expression:
Enter any coefficients as simplified proper or improper fractions or integers.
2|5k-3/5+1/10k

Answers

The simplified expression of 2|5k - 3/5 + 1/10k| is |51/5k - 6/5|

How to simplify the expression

From the question, we have the following parameters that can be used in our computation:

2|5k-3/5+1/10k

Express properly

So, we have

2|5k - 3/5 + 1/10k|

Collect the like terms in the expression

So, we have the following representation

2|5k - 3/5 + 1/10k| = 2|5k  + 1/10k - 3/5|

Evaluate the like terms

This gives

2|5k - 3/5 + 1/10k| = 2|51/10k - 3/5|

Expand the brackets

2|5k - 3/5 + 1/10k| = |51/5k - 6/5|

Hence, the simplified expression of 2|5k - 3/5 + 1/10k| is |51/5k - 6/5|

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Maliha has 4 gallons of lemonade.
Jazmine has 5 times as much lemonade
as Maliha. How many quarts does
Jazmine have?

1 gallon = 4 quarts

Answers

Jazmine has 80 quarts of lemonade, which is 5 times the amount Maliha has (16 quarts).

We are given that Maliha has 4 gallons of lemonade. To find out how much lemonade Jazmine has, we need to calculate 5 times the amount Maliha has.

To convert the gallons to quarts, we know that 1 gallon is equal to 4 quarts.

Therefore, Maliha has 4 x 4 = 16 quarts of lemonade.

Now, since Jazmine has 5 times as much lemonade as Maliha, we can calculate Jazmine's amount by multiplying Maliha's amount (16 quarts) by 5.

Jazmine's lemonade = 16 quarts x 5 = 80 quarts.

Hence, Jazmine has 80 quarts of lemonade.

This can be understood as follows:

Maliha's 4 gallons of lemonade can be converted to 16 quarts (4 gallons x 4 quarts/gallon). Jazmine, on the other hand, has 5 times as much lemonade as Maliha.

Therefore, we multiply Maliha's amount (16 quarts) by 5 to find Jazmine's amount, which equals 80 quarts.

It's important to note that 1 gallon is equal to 4 quarts, which is a conversion factor used to convert between the two units of measurement.

By applying this conversion factor, we can determine the amount of lemonade in quarts for both Maliha and Jazmine.

In conclusion, Jazmine has 80 quarts of lemonade, which is 5 times the amount of lemonade Maliha has (16 quarts).

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does anyone knows the solution of this

Answers

The complete solution to the system is 25/17, 61/17, 2/17 respectively.

How to find solution to a matrix system?

Using the Gauss-Jordan elimination method to find the solution of the system of linear equations represented by the given augmented matrix:

Starting matrix:

[1 -2/3 -1/3 | 1]

[1 -2 6 | -17]

[-3 -7 3 | -43]

Add Row 1 to Row 2 and Row 3:

[1 -2/3 -1/3 | 1]

[0 -4/3 17/3 | -18]

[0 -1 0 | -40]

Multiply Row 2 by -3/4:

[1 -2/3 -1/3 | 1]

[0 1 -17/4 | 27/2]

[0 -1 0 | -40]

Add Row 1 to Row 2 and Row 3:

[1 0 -7/4 | 19/2]

[0 1 -17/4 | 27/2]

[0 0 -17/4 | -13/2]

Multiply row 3 by -4/17:

[1 0 -7/4 | 19/2]

[0 1 -17/4 | 27/2]

[0 0 1 | 2/17]

Add Row 3 to Row 1 and Row 2:

[1 0 0 | 25/17]

[0 1 0 | 61/17]

[0 0 1 | 2/17]

Therefore, the solution of the system of linear equations is:

x = 25/17

y = 61/17

z = 2/17

So the solution is [25/17, 61/17, 2/17].

Thus the completed augmented matrix is:

[1 0 0 | 25/17]

[0 1 0 | 61/17]

[0 0 1 | 2/17]

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quadrilateral a'b'c'd' is the image of quadrilateral abcd under a rotation about the origin (0 0) A) -45 degrees B) -15 degrees C) 15 degrees D) 45 degrees

Answers

The rotation's angle is -45 degrees.

Quadrilateral A'B'C'D' is the representation of quadrilateral ABCD rotated around (0,0).

Consider D and D's coordinates.

D(2,3) and D'(-2,-3)

Now, Join D and D' then

<DOD = 45

Here, the actual rotation is  -45 degree rotation can be visualized as a reflection across the y-axis followed by a 45 degree rotation in the clockwise direction.

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