What is the size of the augmented matrix for the linear system?

Answers

Answer 1

The augmented matrix, however, is a two-by-four matrix because it also contains the constants.

What do you meant by  augmented matrix for the linear system?

The augmented matrix will always include one additional column for every additional variable, and the same number of rows as there are equations. An easier technique to write a set of linear equations is to utilize enhanced matrices.

In an augmented matrix, two sides of the matrix are separated by a vertical line that serves as a representation of a succession of equal signs. The collection of linear equations, for instance, would be represented by the matrix. There is only ever one pivot in a column.

For (c): Three rows and four columns make up the augmented matrix of this system. As a result, it only has three pivot points at most. Thus, a pivot column cannot be represented by a single variable.

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Answer 2

Answer:

What is the size of the augmented matrix for the linear system?

B) 2x3

Identify the values for the elements in the augmented matrix:

a11 =  3

a12 =  7

a13 =  20

a21 =  1

a22 =  -4

a23 = 9

Step-by-step explanation:


Related Questions

V=S3

S = 20

Give your answer in simplest form.

Enter

Answers

simplest form of  equation V= 60

Simplifying a fraction means reducing a fraction to its simplest form. A fraction is in its simplest form if its numerator and denominator have no common factors other than 1.

A 'Simplest Form Calculator' is a free online tool that reduces a fraction to its simplest form. In this calculator, you can enter value and find its simplest form within a few seconds.

V=S3

S = 20

Give your answer in simplest form.

V = S3

V = S× 3

S = 20

Therefor

V = 20 × 3

V= 60

simplest form V= 60

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2. Max has two part-time jobs. He makes $12 per hour mowing lawns and $15 per hour tutoring students. Over the weekend he worked for a total of 14 hours and made a total of $192. How many hours did he work for each job?

Answers

Max mowed the lawns for 6 hours and tutored students for 8 hours.

What is equation modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is that Max has two part-time jobs. He makes $12 per hour mowing lawns and $15 per hour tutoring students. Over the weekend he worked for a total of 14 hours and made a total of $192.

We can write the system of equations as -

x + y = 14

12x + 15y = 192

Refer to the graph attached. On solving the equation graphically, we get-

x = 6, y = 8

Therefore, Max mowed the lawns for 6 hours and tutored students for 8 hours.

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If the amount of space between support towers is between 200 and 300 feet, determine the number of towers you will use.

SHOW ALL WORK TO EARN CREDIT.

Answers

So we will do

200+300 500 divided by 2

250 final ans

the swim team trains 4 days every week. Mon, Tues, and Thurs, the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. how many hours per week does the team train?

Answers

The number of hours that the team trains per week is 17 hours.

How to illustrate the fraction?

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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if a flat screen television is a rectangle with a 53-invh diagonal and a width of 45 inches what is the height of the screen?
Draw a picture the in solve for the missing side.​

Answers

The height of the screen will be;

⇒ h = 28 inches

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A flat screen television is a rectangle with a 53-invh diagonal and a width of 45 inches.

Here,

The diagonal of the screen television = 53 inches

And, The width of the screen television = 45 inches

Let the height of the television = h

So, By the Pythagoras theorem, we get;

⇒ AC² = AD² + DC²

Where, AC = Diagonal of television.

AD = Height of the television

DC = Width of the television.

Substitute all the values, we get;

⇒ 53² = h² + 45²

⇒ 2809 = h² + 2025

⇒ 2809 -2025 = h²

⇒ h² = 784

⇒ h = √784

⇒ h = 28 inches

Thus, The height of the screen = 28 inches

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Solve for x.

x2=14


Responses

x=±18
x equals plus or minus 1 eighth

x=±12
x equals plus or minus 1 half

x=±116
x equals plus or minus 1 sixteenth

x=±2

Answers

The solution for x in the equation given as x² = 1/4 is (b) x = ±1/2

How to determine the solution for x

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

An equation

The equation as poorly stated in the question is represented as

x2=14

When written properly

We have the following representation

x² = 1/4

Solving further, we need to take the square root of both sides of the equation

So, we have the following representation

√x² = ±√1/4

Evaluate the exponents on the left-hand side

So, we have the following representation

x = ±√1/4

Evaluate the exponents on the right-hand side

So, we have the following representation

x = ±1/2

Hence, the solution is (b) x = ±1/2

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Can u please help...............

Answers

A graph of ΔABC with vertices A(0, 0), B (3, 3), and C (4, 0) and its image after a 90° rotation about the origin is shown in the image attached below.

What is a rotation?

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle ABC (∆ABC), the coordinates of the vertices of the image (∆A′B′C′) are as follows:

(x, y)                               →            (-y, x)

Ordered pair A  = (0, 0) → Ordered pair A' = (0, 0)

Ordered pair B = (3, 3) → Ordered pair B' = (-3, 3)

Ordered pair C = (4, 0) → Ordered pair C' = (0, 4)

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please assist with helping in the image below!!

Answers

The correct answer is D

Describe a sequence of transformation that maps DOG onto CAT

Answers

Sequence of transformation is first moving 5 unit in y axis than mirror image  with y axis.

What would you say about the order of the transformations?

A particular order of transformational events is referred to as a transformational sequence. This indicates that more than one transformation is handled by a series of transformations, and the order in which they happen is important.

What kind of figure can a series of transformations map onto itself?

The line of reflection must pass through the centre point for the figure to map onto itself. The sides of the figure are cut by two lines of reflection. The vertices of the figure are intersected by two lines of reflection. As a result, there are four potential lines of reflection that pass through the center.

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Write an equation for the nth term of the geometric sequences. Then Find a6


A. 2, 8, 32, 128,.

B. 0. 6, -3, 15, -75,.

C. -1/8, -1/4, -1/2, -1,.

D. 0. 1, 0. 9, 8. 1, 72. 9,

Answers

We want to find an equation and the sixth term of the given geometric sequence.

The equation is: [tex]a_{n} = 4*a_{n}-1[/tex] and the sixth term is equal to 512

What is Geometric sequence?

In a geometric sequence, each term is a constant times the previous term, so the general relation is:

[tex]a_{n} = k*a_{n}-1[/tex]

Here we can use any pair of consecutive terms to find the value of the constant, for example, if we use the first two, we have:

[tex]8 = k*2\\8/2 = 4 = k[/tex]

Now we know the value of the constant, then the general formula is: [tex]a_{n} = 4*a_{n}-1[/tex]

Now we can use this to get the sixth term:

[tex]a_{6} = 4*a_{5}-1=4*128 = 512[/tex]

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100 points + Brainliest Let C represents the cost in dollars and R represents the revenue in dollars. What is the break-even point? Use a table to help if necessary.

C=36x+200
R=76x
Break-even point: (,)

Answers

Answer:

  (x, {C and/or R}) = (5, 380)

Step-by-step explanation:

You want the break-even point when cost (C) and revenue (R) are given by ...

C = 36x +200R = 76x

Profit

Profit is the difference between revenue and cost. The break-even point is the point at which profit is zero:

  P = R -C

  0 = 76x -(36x +200)

  0 = 40x -200 . . . . simplify

  0 = x -5 . . . . . . . . . divide by 40

  x = 5 . . . . . . . . . add 5

The break-even point is at x=5. Revenue and cost are both 380 at that point.

Table

If you prefer to look at these values in a table, you can consider ...

  [tex]\displaystyle \begin{array}{ccc}x&C&R\\\cline{1-3}\vphantom{\^B}3&308&228\\4&344&304\\5&380&380\\6&416&456\end{array}[/tex]

We notice that cost and revenue are the same for x=5. They are both 380 for that value of x.

Graph

Another way to find the break-even point is to use a graph to plot cost and revenue on the same vertical axis. The point at which the lines cross is the break-even point. The break-even point coordinates are (5, 380).

Pls help quickly
Needed as soon as possible thank you in advance

Answers

a) Bearing from A to B is 253°.

b) Bearing from B to A is 287°.

What is a bearing?

A bearing is an angle measured clockwise from north in mathematics. Typically, bearings are expressed as a three-figure bearing.

a)

The bearing of 73° and the co-interior angle formed must total 180°. The counter-clockwise angle from B to A is 107°.

However a bearing must always be measured clockwise from north. 107° is counter-clockwise from north.

The clockwise angle on the other side is needed. Use the angle fact that angles in a full turn add to 360°.

To work the bearing, subtract 107° from 360°.

360° – 107° = 253° and so, the bearing of A from B is 253°.

b)

The bearing of 107° and the co-interior angle formed must total 180°. The counter-clockwise angle from A to B is 73°.

However a bearing must always be measured clockwise from north. 73° is counter-clockwise from north.

The clockwise angle on the other side is needed. Use the angle fact that angles in a full turn add to 360°.

To work the bearing, subtract 73° from 360°.

360° – 73° = 287° and so, the bearing of B from A is 287°.

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Two alien pacehip tart traveling toward each other from pace tation that are 710,000 km apart. The firt pacehip tarted an hour before the econd pacehip and i traveling at 110,000 km/hr. In how many hour will the two pacehip meet if the econd pacehip i traveling at 90. 000 km/hr?

Answers

The two spaceships will meet in 8 hours if the second spaceship is traveling at 90. 000 km/hr.

To calculate the time it will take for the two spaceships to meet, you must use the equation Distance = Rate x Time. Since the first spaceship has a higher rate of speed, it will reach the second spaceship in less time than it would take the second spaceship to reach the first.

This means that the time it takes for the two spaceships to meet will be equal to the time it takes for the first spaceship to travel the distance between the two space stations. We can use the equation to solve for time: Time = Distance/Rate. In this case, the distance is 710,000 km and the rate is 110,000 km/hr, so the time is 6.45 hours.

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What are the different types of algorithms?

Answers

Different types of algorithms are:

Brute Force algorithm Greedy algorithmRecursive algorithmBacktracking algorithm

What is Brute Force algorithm?

As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search—also referred to as generate and test—involves iteratively listing all potential candidates for the solution and determining whether each one satisfies the problem's statement.

A brute-force algorithm would count all integers from 1 to n and determine whether each one divides n without a remainder in order to find the divisors of a natural number n.

For the eight queens puzzle, a brute force method would look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece could engage in mutually exclusive attacks for each configuration.

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Select all the expressions that are equivalent to 16x - 12- 24x+ 4 16 x − 12 − 24 x + 4. Explain or show your reasoning.

1. 4+16x-12(1+2x)4 + 16 x − 12 ( 1 + 2 x )


2. 40x-1640 x − 16


3. 16x-24x-4+1216 x − 24 x − 4 + 12


4. -8x-8- 8 x − 8


5. 10 (1. 6x - 1. 2 - 2. 4x + 4)

Answers

1) 16x - 12(1 + 2x) + 4 is the expression that are equivalent to 16x-12-24x+4.

what is expression?

An expression is a mathematical phrase that can contain numbers, variables, and operators. It can be a combination of these elements and can be evaluated to a specific value or a mathematical function.

An expression can be a simple mathematical statement such as 2x+3, or a more complex one involving multiple operations such as

(3x^2 - 4x + 5) / (2x +1). Expressions are used to represent mathematical operations, equations and relations between variables.

so we need to evaluate option 1 :

16x - 12 -24x +4

=> 16x - 12 -24x +4

the above expression is same as the expression mentioned in the question so option 1 is correct.

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Complete question :

Select all expressions that are equivalent to 16x−12−24x+4. Show or explain your reasoning.

1. 16x - 12(1 + 2x) + 4

2. 40x - 16

3. 4 - 12 + (2x - 3x)

4. -8(x+1)

During a football game the hawks lost 5 yards due to a penalty and lost 6 yards from a quarterback sack. Write and solve an expression that represents the situation.

Answers

An expression that describes the given situation is; Total yards = -6 - 5 and the solution is -11

How to solve basic number problems?

In mathematics, a positive number means we have a plus sign before the number which means if we have +2, it means that there has been a gain of 2 units. In a similar manner, a negative number represents a loss which means that if we have -3, it simply means there is a loss or reduction of 3.

Now, we are told that during a football game, the hawks lost 5 yards due to a penalty and lost 6 yards from a quarterback sack. Thus, using the concept of positive and negative numbers above, we can develop the total number of yards as;

Total yards = -6 - 5

Total yards = - 11 yards

This represents a loss.

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how to subtract 3 1/2 - 1/4 as a fraction (I NEED IT TOMORROW)

Answers

Answer:

13/4 as an improper fraction

3 1/4 as a mixed number fraction

Step-by-step explanation:

Turn 3 1/2 into an improper fraction

7/2 - 1/4

To write 7/2 as a fraction with a common denominator, multiply by 2/2

7/2 x 2/2 = 14/4

14/4 - 1/4 = 13/4

5. QRST is a Rhombus. The diagonals intersect at point 0. mZROS = 7x1, mzSTO= 4x - 22, QT = 4y + 2, ST = 8y-8 R T S X= y = mZTOQ = mzQRS = Perimeter QRST=_​

Answers

The value of x is 18.45°.

The value of y is 2.5 units.

The measure of the angle TOQ is 128.15°.

The measure of the angle QRS is 90°.

The perimeter of QRST is 36 units.

What is a rhombus?

A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

Given,  m∠ROS = 7x - 1, m∠STO= 4x - 22.

We know the sum of linear pair of angles is 180°.

Therefore,

7x - 1 + 4x - 22 = 180.

11x = 203.

x = 203/11.

x = 18.45°.

Also given that line segment QT = 4y + 2 and ST = 8y - 8.

We know the sides of a rhombus are of equal length.

Therefore,

4y + 2 = 8y - 8.

- 4y = - 10.

4y = 10.

y = 10/4.

y = 2.5.

We know vertically opposite angles are equal hence m∠ROS = m∠TOQ.

= 7(18.45) - 1.

= 128.15°.

m∠QRS is 90° as all four interior angles of a rhombus are right angles.

The perimeter of QRST is 4×(QT).

= 4×(10 + 2).

= 4×12.

= 36 units.

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Parker could pay for 45% of his college tuition with his scholarship. The remaining $10,500 he paid for with a student loan. What was the cost of Parker's tuition? Show your work

Answers

The cost of parker's tuition is $19,090.9

How to calculate the cost of parker's tuition?

Parker could pay 45% of his college tuition with his scholarship

He paid for the remaining $10,500 with a student loan

Therefore the cost of parker's tuition can be calculated as follows

100% - 45%

= 55%

let y represent the cost of parker's tuition

55y/100= 10500

0.55y= 10500

y= 10500/0.55

y= 19,090.9

Hence Parker tuition cost is $19,090.9

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The local sports team donated 200 meal vouchers and 24 jerseys for a fundraising event. 125 vouchers and 20 jerseys were part of a raffle . The ratio of tickets sold to raffled items was 8:1; each ticket was sold for $3.50. How much money was raised from the raffle

Answers

On solving the provided question, we can say that by linear equation  $249.67  money was raised from the raffle

What is a linear equation?

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here,

the linear equation that can be formed is

200x + 24 y = 3.50

125 x + 20y = 5

ratio = 8:1

so,  $249.67  money was raised from the raffle

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There are 80 oranges and apples, and 5% of them are apples. William takes out some of the oranges, so apple make up 20% of the remaining pieces of fruit. How many oranges did he take out

Answers

4 out of the 80 are apples. 4 = 20%, 20 = 100% - 16 oranges and 4 apples. 76-16 = 60 oranges that he took out. The answer is 60

What is Y =- 2 on a graph?

Answers

The graph of y is a straight line parallel to the x−axis through the point (0,-2)

Now, According to the question:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The given equation is Y = -2

y = -2 is a line in which all points have the y-value -2. The line has a slope of 0 (horizontal line) since the y-value does not change for any value of x.

The point-intercept form for the equation of a line is:

y = mx + b

We can write y = -2

As y = 0x - 2;

slope = 0, y-intercept = -2

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Jay and kevin are shoveling the snow off a driveway. working together, they can clear the driveway of snow in 14 minutes. working alone, it would take kevin 21 minutes longer to clear the driveway of snow than it would take jay working alone. when j is the number of minutes it would take jay to clear the driveway of snow when working alone, the situation is modeled by this rational equation: how long would it take jay to clear the driveway of snow working alone?
a. 7 minutes
b. 21 minutes
c. 35 minutes
d. 42 minutes

Answers

Therefore, As a result, the answer to the given equation problem is Jay would need to work alone for 21 minutes to remove the snow from the driveway.

Define equation .

A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation. Word illustration The product of 8 and 3 is 11.

Here,

The formula is: 1/j +1/j+ 21 = 11/ 4.

LCM = j+21+j / j(j+21)=1/14

Thus, 2j+21 / j(j+21) = 1/14 is obtained.

14(2j+21) times itself yields j(j+21).

28j+294 expanded to j²+21j

Gather comparable terms

j²+21j-28j-294=0

j²- 7j-294=0

With the use of a graphing calculator, we have:

j = 21 or j= -14

Due to the context,

j's value cannot be negative.

As a result, the answer to the given equation's problem is Jay would need to work alone for 21 minutes to remove the snow from the driveway.

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PLEASE HELP ME I DONT UNDERSTAND

Question 1: The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average of 3/4 foot per year Some students misunderstood question #1 and wrote the following equations in point-slope form:
a) y − 3 = 3/4(x-0)
b) y - 6 = 3/4(x-4)
c) y - 4.5 = 3/4(x-2)
d) y - 12 = 3/4(x-12)
e) y - 15= 3/4(x-15)

Is point slope form okay to use to find the height of the trees in this problem?

There is one equation that is incorrect.... determine which one? why is it incorrect?


Creat two new equations written in point slope form​

Answers

The point slope form is not okay to use to find the height of the trees

The incorrect equation is y - 15= 3/4(x-15) The other equations are y - 3.75 = 3/4(x - 1) and y - 4.5 = 3/4(x - 2)

How to determine if the point slope form is okay?

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

Initial height of purchase = 3 feet tallAverage rate = 3/4 foot per year

The point slope form of a linear equation is represented as

y - y₁ = m(x - x₁)

Where

Slope = m

The point slope form does not show the initial value

So, this form is not okay for the required parameters

How to determine the incorrect equation

The slope-intercept form is given as

y = mx + c

Using the given parameters, we have

y = 3/4x + 3

Subtract 3 from both sides

y - 3 = 3/4x

Rewrite as

y - 3 = 3/4(x - 0)

This equation can be rewritten in any of the following forms

a) y − 3 = 3/4(x-0)b) y - 6 = 3/4(x-4)c) y - 4.5 = 3/4(x-2)d) y - 12 = 3/4(x-12)

Hence, the incorrect equation is y - 15= 3/4(x-15)

Two new equations written in point slope form​

We have the slope-intercept form to be

y = 3/4x + 3

Set x = 1 and 2, and then solve for y

So, we have

y = 3/4 * 1 + 3 = 3.75

y = 3/4 * 2 + 3 = 4.5

So, the equivalent equations are

y - 3.75 = 3/4(x - 1) and y - 4.5 = 3/4(x - 2)

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Jeremy made nine out of twelve basketball shots in P.E. class. What decimal and percent represents the number of shots he made?​

Answers

3/4 shots were made so 75% or .75 of his total shots were made.

How do I solve x-5(x-1=x-(2 x-3)

Answers

Answer:

x = 2/3

Step-by-step explanation:

x - 5(x - 1) = x - (2x - 3)

x - 5x + 5 = x - 2x + 3

-5x + 5 = -2x + 3

-3x = -2

x = 2/3

How do you write log base 10 in Word?

Answers

Log<sub>10</sub> is an expression used to represent logarithmic functions with a base of 10. To write log<sub>10</sub> in Microsoft Word, you can use the “Insert Equation” feature.

To access this, select Insert on the top menu bar, followed by Equation. In the new window that appears, select the Greek and Math Symbols tab. In this tab you will find the log<sub>10</sub> symbol that looks like an upside-down “y”. You can then click on the symbol and it will be added to your document.

If you need to type out the equation, you can type “log<sub>10</sub>” and it will automatically be converted to the log<sub>10</sub> symbol.  You can also use the shortcut CTRL+Alt+L to insert the log<sub>10</sub> symbol directly into your document.

If you are using a Mac, you can use the shortcut Command+Shift+L.  The log<sub>10</sub> symbol is commonly used in mathematics and science, particularly in algebra and calculus. It is used to represent the logarithm of a particular number to the base 10.

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Witch ones do I select

Answers

On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.

What is proportionality?

When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.

Here,

U/5 = 17/11

U = 17/11 X 5

U = 7.72

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OMG PLEASE HELP FAST, Write the equation of the line in fully simplified slope-intercept form.

Answers

The equation of the line in the attached graph in slope intercept form is written as

y = -6x + 2

How to write the equation of the line

The slope, m of the linear function is calculated using the points on the graph (1, -4) and  (2, -10)

m = (y₀ - y₁) / (x₀ - x₁)

plugging in the values and evaluating

m = (-10 + 4) / (2 - 1)

m = (-6) / (1)

m = -6

equation passing through point (2, -10), using the point slope formula

(y - y₁) = m (x - x₁)

y - (-10) = -6(x - 2)

y + 10 = -6x + 12

rearranging the equation

y = -6x + 12 - 10

y = -6x + 2

The equation of the line in slope intercept form is written as y = -6x + 2

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What is dual expression?

Answers

The Dual of Boolean Expression is defined as an expression that is obtained by interchanging the addition and multiplication and interchanging the 0's and 1's .

What is a Boolean Expression ?

The Boolean Expression is defined as an logical statement which results in the Boolean value which can either be True or False.

Sometimes, the synonyms is used to express statement such as ‘Yes’ for ‘True’ and ‘No’ for ‘False’. and also, 1 and 0 are used for digital circuits for True , False .

If in the Boolean expression , the addition and multiplication are interchanged and the binary 0 and 1 are also interchanged then the resulting expression will be called as a Dual Of Boolean Expression .

The given question is incomplete , the complete question is

What is Dual Boolean Expression ?

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