-3a + 6b = a + 4b what does b equal???​

The elements of the matrix are: A² – 2A + I = | 0 0 -1 | | 0 25 0 | | 2 0 -1 |. To compute A² – 2A + I, we need to first find A², then multiply A by 2, and finally add the identity matrix I to the result.

The identity matrix I is a matrix with 1s on the main diagonal and 0s elsewhere.

A² = A * A = | 1 0 -1| * | 1 0 -1| = | 1*1+0*0+(-1)*2  1*0+0*(-4)+(-1)*0  1*(-1)+0*0+(-1)*2 |
             | 0 -4 0|   | 0 -4 0|   | 0*1+(-4)*0+0*2  0*0+(-4)*(-4)+0*0  0*(-1)+(-4)*0+0*2 |
             | 2 0 2|    | 2 0 2|    | 2*1+0*0+2*2  2*0+0*(-4)+2*0  2*(-1)+0*0+2*2 |

      = | 1 0 -3 |
        | 0 16 0 |
        | 6 0 2 |

2A = 2 * | 1 0 -1| = | 2 0 -2|
        | 0 -4 0|   | 0 -8 0|
        | 2 0 2|    | 4 0 4|

I = | 1 0 0 |
   | 0 1 0 |
   | 0 0 1 |

A² – 2A + I = | 1 0 -3 | - | 2 0 -2 | + | 1 0 0 | = | 1-2+1  0-0+0  -3-(-2)+0 |
             | 0 16 0 |   | 0 -8 0 |   | 0 1 0 |   | 0-0+0  16-(-8)+1  0-0+0 |
             | 6 0 2 |    | 4 0 4 |    | 0 0 1 |   | 6-4+0  0-0+0  2-4+1 |

         = | 0 0 -1 |
           | 0 25 0 |
           | 2 0 -1 |

Therefore, A² – 2A + I = | 0 0 -1 |
                        | 0 25 0 |
                        | 2 0 -1 |

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The differences and examples of liabilities and assets have been detailed below.

The things that your business has and can potentially provide future financial gain are called assets. What you owe other people is the liability. In essence, assets increase your financial situation while obligations decrease it.

A. A company's assets are things it has that will be useful to it in the future, whereas its liabilities are things it must pay.

Unlike liabilities, which are not depreciable, assets are subject to depreciation over time.

B. Cash, receivables, goodwill, investments, buildings, etc. are a few examples of assets.

Liabilities include things like Accounts payable, Interest payable, and Deferred Revenue, among others.

Hence, the differences and examples of liabilities and assets have been provided.

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Answer:

1 year.

Step-by-step explanation:
First set up the equation for each tree

Tree A = 6 + 18x

Tree B = 3 + 21x

Since we want to find how long it would take the tree to be same height just set the equation equal to each other.

6+18x = 3+21x

Now you can just solve it by isolating x.

First, subtract 18x from both sides so that we can have just one x and coefficient.

6 = 3 + 3x

Then, subtract 3 from both sides to isolate the x.

3 = 3x

Next, divide both sides by 3.

1 = x

X means the years and so that means it would take just 1 year for the trees to be same height.

(a) The joint PMF of X, Y, and N can be found by multiplying the two independent PMFs of X and Y. The joint PMF is: P(X=x, Y=y, N=n) = P(X=x) * P(Y=y) = (1-p)^x * p * (1-p)^y * p = (1-p)^(x+y) * p^2.
(b) The joint PMF of X and N can be found by marginalizing over Y. The joint PMF is: P(X=x, N=n) = P(X=x, Y=n-x) = (1-p)^(x+(n-x)) * p^2 = (1-p)^n * p^2.

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Answer:

Let's call the weight of the book that was removed "x".

The total weight of the twelve books can be represented as 12 times the average weight of 2.75 pounds:

12(2.75) = 33

After the book is removed, there are only 11 books left, and their total weight can be represented as 11 times the new average weight of 2.70 pounds:

11(2.70) = 29.7

We can set up an equation using these two expressions and the weight of the book that was removed:

33 - x = 29.7

Solving for x, we get:

x = 33 - 29.7

x = 3.3

Therefore, the weight of the book that was removed was 3.3 pounds.

The area of rectangular field is   [tex]\frac{9}{20} \ \text{miles}^2[/tex].

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

Here the given rectangle , length= [tex]\frac{9}{10}[/tex]miles and Breadth = [tex]\frac{1}{2}[/tex]miles

Now using area of rectangle formula,

=> A = length× breadth square unit.

=> A = [tex]\frac{9}{10}\times\frac{1}{2}[/tex]

=> A =   [tex]\frac{9}{20} \ \text{miles}^2[/tex]

Hence the area of rectangular field is  [tex]\frac{9}{20} \ \text{miles}^2[/tex].

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Answer:

I believe that no, it is not a rectangle because we don't know if the other 2 sides equal each other. In a rectangle 2 sets of sides are equal so no. it is not a rectangle.

thanks for coming to my ted talk

Step-by-step explanation:

The binomial 121y8z2 - 256x6 can be factored using the difference of two squares rule.

To factor the binomial 121y8z2 - 256x6, use the special factoring methods. Notice that the binomial has a difference of two squares, where the first term is a perfect square and the second term is the square of a binomial. This means that you can factor this binomial using the difference of two squares rule:

[tex]121y8z^2 - 256x^6 = (11y4z^2 - 16x^3) * (11y4z^2 + 16x^3)[/tex]

Therefore, the binomial 121y8z2 - 256x6 can be factored using the difference of two squares rule.

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Answer: i think -22/3 and 6/17

Step-by-step explanation:

Answer:

free

Step-by-step explanation:

28-28=0

Answer:

12 of them

Step-by-step explanation:

5x5 cube so

25*48%

Answer:

its 12 squares

Step-by-step explanation:

First you take all the squqres as 100 percent then you divide both sides by 100 to find how much squares is 1 percent, then multiply the 1 percent answers by the percentage you need which is 48 to get the squares

Answer:

0.26x

Step-by-step explanation:

If x is decreased by 74% then new value of x

= x - 74% of x

74% as decimal = 74/100 = 0.74

New value of x
= x - 0.74x

=x(1 - 0.74)

=0.26x

The correlation of the rates return between stock A and B for the given covariance and standard deviation is given by option B. -0.53.

Covariance between stock A and B = -0.112

Standard deviation of the rates return for stock A = 0.26

Standard deviation of the rates return for stock B = 0.81

Formula for correlation in terms of covariance and standard deviations is

Correlation = covariance / (standard deviation of A x standard deviation of B)

Here correlation of the rates of return between A and B.

Substitute the given values we get,

⇒ Correlation = (-0.112) / (0.26 x 0.81)

⇒ Correlation ≈ -0.430769 / 0.81

⇒ Correlation ≈ -0.5318

⇒ Correlation ≈ -0.53

Therefore, the correlation of the rates of return between A and B is is equal to option B. -0.53.

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Answer:

8) the ordered pair (-1,-1) is a solution

9)the ordered pair (-8,-2) is a solution

Step-by-step explanation:

8) 3x-5y≥2

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

2=2

9)-x-6y>12

-(-8)-6(2)=-4

-4>12

Answer: -2x = 16

Step-by-step explanation:

The answer is -2x = 16.

We start by isolating the -2x on one side of the equation. To do this, we must subtract 3x from both sides of the equation. This gives us -2x = 4 - 3x. We then add 3x to both sides of the equation to give us -2x + 3x = 4. Since 3x + (-3x) = 0, we are left with -2x = 16.

Answer:

x=8

Step-by-step explanation:

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

12-3x=4-2x add 12 to both sides

-3x=-2x-8 add 2x to both sides

-x=-8 divide both sides by 1

x=8

let me know if this helped :)

Answer: This is a classic problem in mathematics known as the arithmetic series or the Gauss sum.

To find out how many days the person can donate with a total of Rs. 210, we need to sum the sequence of donations until we reach the total amount of Rs. 210. The sequence of donations is:

1 + 2 + 3 + 4 + 5 + ... + n

The sum of the sequence can be expressed as:

n(n+1)/2

So we need to solve the equation:

n(n+1)/2 = 210

n(n+1) = 420

n^2 + n - 420 = 0

We can solve this quadratic equation using the quadratic formula:

n = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -420.

n = (-1 ± sqrt(1^2 - 4(1)(-420))) / 2(1)

n = (-1 ± sqrt(1 + 1680)) / 2

n = (-1 ± sqrt(1681)) / 2

n = (-1 ± 41) / 2

Since we are looking for a positive integer value of n, we can discard the negative solution:

n = (41 - 1) / 2

n = 40 / 2

n = 20

Therefore, the person can donate for a maximum of 20 days with a total donation of Rs. 210, starting with Rs. 1 on the first day and increasing by Rs. 1 each day.

Step-by-step explanation:

For  [tex]4x + 2x^2(3x-5)[/tex] : degree = 3, number of terms = 3, so the answer is 3 and 3.

For [tex](-3x^4 + 5x^3 - 12) + (7x^3 - x^5 + 6)[/tex]: degree = 5, number of terms = 4, so the answer is 5 and 4.

For [tex](3x^2 - 3)(3x^2 + 3)[/tex] : degree = 4, number of terms = 1, so the answer is 4 and 1.

What is expression ?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, ×, ÷, etc.) that represents a mathematical relationship or quantity.

Expressions can be simple, such as 2 + 3, or more complex, such as [tex](4x^2 - 2x + 5)/(x - 1).[/tex] They can also include variables, which are symbols that represent unknown or changing values.

For the expression [tex]4x + 2x^2(3x-5):[/tex]

Simplified form:[tex]6x^3 - 10x^2 + 4x[/tex]

Degree: 3

Number of terms: 3

For the expression [tex](-3x^4 + 5x^3 - 12) + (7x^3 - x^5 + 6):[/tex]

Simplified form: [tex]-x^5 - 3x^4 + 12x^3 - 6[/tex]

Degree: 5

Number of terms: 4

For the expression[tex](3x^2 - 3)(3x^2 + 3):[/tex]

Simplified form: [tex]9x^4 - 9[/tex]

Degree: 4

Number of terms: 1

Therefore, the correct options are:

For [tex]4x + 2x^2(3x-5)[/tex] : degree = 3, number of terms = 3, so the answer is 3 and 3.

For [tex](-3x^4 + 5x^3 - 12) + (7x^3 - x^5 + 6)[/tex] : degree = 5, number of terms = 4, so the answer is 5 and 4.

For [tex](3x^2 - 3)(3x^2 + 3):[/tex] degree = 4, number of terms = 1, so the answer is 4 and 1.

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The investor should invest $32,500 in the lowest-yielding, least-risky account, $20,000 in the medium-yielding, medium-risk account, and $17,500 in the highest-yielding, highest-risk account.

To solve this problem, we can use a system of linear equations.

We have three equations and three unknowns: x, y, and z.

The equations are: x + y + z = 50,0000.03x + 0.055y + 0.09z = 2540

We can use substitution or elimination to solve for one of the variables and then plug that value back into the other equations to find the remaining variables.

For example, we can solve for x in the first equation:

x = 50,000 - y - z

Then we can substitute this value of x into the second equation:

0.03(50,000 - y - z) + 0.055y + 0.09z = 2540

Simplifying this equation gives us:

1500 - 0.03y - 0.03z + 0.055y + 0.09z = 25400.025y + 0.06z = 1040

Now we can solve for one of the remaining variables, such as y:

y = (1040 - 0.06z) / 0.025

And we can substitute this value of y back into the first equation to find z:

50,000 - (1040 - 0.06z) / 0.025 - z = 50,000

Solving for z gives us:

z = 17,500

Finally, we can plug this value of z back into the equations for x and y to find the remaining variables:

x = 50,000 - y - 17,500 = 32,500 - y

y = (1040 - 0.06(17,500)) / 0.025 = 20,000

So the solution is x = 32,500, y = 20,000, and z = 17,500.

This means that the investor should invest $32,500 in the lowest-yielding, least-risky account, $20,000 in the medium-yielding, medium-risk account, and $17,500 in the highest-yielding, highest-risk account.

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The person had died approximately 5 hours and 10 minutes before the coroner's examination.

Using the formula, t=−10 log10(T-R/95.6-R), we can calculate the elapsed time since death.

Given that T = 83.5°F, R = 75°F and t is the elapsed time since death in hours, we can calculate the elapsed time.

t = -10 log10(83.5-75/95.6-75)

t = -10 log10(8.5/20.6)

t = -10 * 0.517 = -5.17 hours

Therefore, the person had died approximately 5 hours and 10 minutes before the coroner's examination.

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The concepts that we use are

1. circumcenter of the circle.

b. Area of the circle  

c. Area of the circle

d. Circumference of the circle.

The circumference of a circle is the distance around its outer boundary, while the area of a circle is the total space enclosed within its boundary.  

The formula we use in a given problem depends on the context of the problem the following situations can be understood as follows

Here we have 5 situations

a. The distance around a circular track.

Here to find the distance around the circular track we need to calculate the perimeter of the circular track i.e circumcenter of the circle.

b. The total number of equally-sized tiles on a circular floor.

The total size of tiles on the circular floor represents the area of the circle. Hence we need to use the area of the circle  

c. The amount of oil it takes to cover the bottom of a frying pan.

The amount of oil that spread on the bottom of the pan will equal the area of the circular surface of the pan

Hence, we need to use the Area of the circle

d. The distance your car will go with one turn of the wheels.

The distance will cover by the wheel will equal to boundary line around the wheel hence, we need to use the circumference of the circle.

Therefore,

The concepts that we use are

1. circumcenter of the circle.

b. Area of the circle  

c. Area of the circle

d. Circumference of the circle.

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Complete Question:

For each quantity, decide whether circumference or area would be needed to calculate it. Explain or show your reasoning.

a. The distance around a circular track.

b. The total number of equally-sized tiles on a circular floor.

c. The amount of oil it takes to cover the bottom of a frying pan.

d. The distance your car will go with one turn of the wheels.

Quantitative, discrete, ratio

(i) Quantitative, discrete, interval
(ii) Qualitative, nominal
(iii) Qualitative, ordinal
(iv) Quantitative, discrete, ratio

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The value of b that makes the area between the two functions equal to 50.5 on the interval [-6.2, 6.2] is 29.64355.

To find the value of b that makes the area between the two functions equal to 50.5 on the interval [-6.2, 6.2], we need to set up an integral and solve for b.

First, we need to find the difference between the two functions:
x2 - x1 = b - y^2

Next, we need to integrate this difference over the given interval:
∫[-6.2, 6.2] (b - y^2) dy

Using the power rule for integration, we get:
[b*y - (y^3)/3] from -6.2 to 6.2

Plugging in the values for the interval and simplifying, we get:
(6.2b - 158.488) - (-6.2b - 158.488)

Simplifying further, we get:
12.4b - 316.976

Now, we can set this equal to the given area and solve for b:
12.4b - 316.976 = 50.5

12.4b = 367.476

b = 367.476/12.4

b = 29.64354839

Rounding to five decimal places, we get:
b = 29.64355

So, the value of b that makes the area between the two functions equal to 50.5 on the interval [-6.2, 6.2] is 29.64355.

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The distance from the point [tex]$(1,2)$[/tex] to the line [tex]$y=\frac{1}{2}x-3$[/tex] is approximately 3.7 units.

In mathematics, an expression is a combination of numbers, variables, and operators, which when evaluated, produces a value. An expression can contain constants, variables, functions, and mathematical operations such as addition, subtraction, multiplication, and division.

To find the distance from a point to a line, we need to find the length of the perpendicular segment from the point to the line.

The line [tex]$y=\frac{1}{2}x-3$[/tex]  can be rewritten in slope-intercept form as [tex]$y = \frac{1}{2}x - 3$[/tex], so its slope is [tex]\frac{1}{2}$.[/tex]

A line perpendicular to this line will have a slope that is the negative reciprocal of [tex]\frac{1}{2}$[/tex], which is [tex]-2$.[/tex]

We can then use the point-slope form of a line to find the equation of the perpendicular line that passes through the point [tex]$(1,2)$[/tex]:

[tex]$y - 2 = -2(x - 1)$[/tex]

Simplifying, we get:

[tex]$y = -2x + 4$[/tex]

Now we need to find the point where the two lines intersect, which will be the point on the line [tex]$y = \frac{1}{2}x-3$[/tex] that is closest to [tex]$(1,2)$[/tex]. We can do this by setting the equations of the two lines equal to each other and solving for [tex]$x$[/tex]:

[tex]$\frac{1}{2}x - 3 = -2x + 4$[/tex]

Solving for [tex]$x$[/tex], we get:

[tex]$x = \frac{14}{5}$[/tex]

To find the corresponding [tex]$y$[/tex] value, we can substitute this value of [tex]$x$[/tex] into either of the two line equations. Using [tex]$y = \frac{1}{2}x-3$[/tex], we get:

[tex]$y = \frac{1}{2} \cdot \frac{14}{5} - 3 = -\frac{7}{5}$[/tex]

Therefore, the point on the line [tex]$y = \frac{1}{2}x-3$[/tex] that is closest to [tex]$(1,2)$[/tex] is [tex]$\left(\frac{14}{5}, -\frac{7}{5}\right)$[/tex].

Finally, we can use the distance formula to find the distance between [tex]$(1,2)$[/tex] and [tex]$\left(\frac{14}{5}, -\frac{7}{5}\right)$[/tex]:

[tex]$\sqrt{\left(\frac{14}{5} - 1\right)^2 + \left(-\frac{7}{5} - 2\right)^2} \approx 3.7$[/tex]

Rounding to the nearest tenth, the distance from the point [tex]$(1,2)$[/tex] to the line [tex]$y=\frac{1}{2}x-3$[/tex] is approximately 3.7 units.

Therefore, the distance from the point [tex]$(1,2)$[/tex] to the line [tex]$y=\frac{1}{2}x-3$[/tex] is approximately 3.7 units.

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3 a. The function w satisfies the equation (ex+2y)wy​−2xwx​=0.

3 b. The value of wxy​ is -2x(ex+2y)cos(ex+2xy) - 2ysin(ex+2xy)

4 . The material derivative of fatP is 0.

3. (a) To verify that the function w satisfies the equation (ex+2y)wy​−2xwx​=0, we can take the partial derivatives of w with respect to x and y, and then substitute them into the equation.

First, let's find the partial derivatives of w:

∂w/∂x = f'(ex+2xy)(ex+2y)
∂w/∂y = f'(ex+2xy)(2x)

Now, we can substitute these partial derivatives into the equation:

(ex+2y)(f'(ex+2xy)(2x)) - 2x(f'(ex+2xy)(ex+2y)) = 0

Simplifying this equation, we get:

2exf'(ex+2xy) + 4xyf'(ex+2xy) - 2exf'(ex+2xy) - 4xyf'(ex+2xy) = 0

This simplifies to 0 = 0, which is true. Therefore, the function w satisfies the equation (ex+2y)wy​−2xwx​=0.

(b) If f(u) = cosu, then we can find wxy​ by taking the partial derivative of w with respect to x and y, and then substituting f(u) = cosu:

∂w/∂x = f'(ex+2xy)(ex+2y) = -sin(ex+2xy)(ex+2y)
∂w/∂y = f'(ex+2xy)(2x) = -sin(ex+2xy)(2x)

Now, we can find wxy​ by taking the partial derivative of ∂w/∂x with respect to y:

wxy​ = ∂(∂w/∂x)/∂y = ∂(-sin(ex+2xy)(ex+2y))/∂y = -2x(ex+2y)cos(ex+2xy) - 2ysin(ex+2xy)

4. To find the material derivative of fatP, we can use the formula:

Df/Dt = ∂f/∂t + ∂f/∂x(dx/dt) + ∂f/∂y(dy/dt) + ∂f/∂z(dz/dt)

First, let's find the partial derivatives of f:

∂f/∂t = ysinx + ez
∂f/∂x = ty*cosx
∂f/∂y = tsinx
∂f/∂z = tez

Now, we can find the material derivative of fatP by substituting the point P = (π,1,0) and the derivatives of x, y, and z with respect to t:

Df/Dt = (1*sinπ + e^0) + (π*1*cosπ)(dx/dt) + (π*sinπ)(dy/dt) + (π*e^0)(dz/dt) = 0 + 0 + 0 + 0 = 0

Therefore, the material derivative of fatP is 0.

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The value of the given segments are EC = 6, AC = 12, EB = 4, and BD = 8.

A quadrilateral with opposing sides that are parallel and equal is known as a parallelogram. Due to the opposite sides' alignment and equality, they have equal angles on them. The lines that link the parallelogram's opposing corners are known as its diagonals.

Given that,

EA = 6

For a parallelogram the diagonals of the quadrilateral bisect each other.

Thus,

EC = 6

AC = EA + EC = 6 + 6 = 12

Similarly, ED = 4

EB = 4

and the value of BD = ED + EB = 8

Hence, the value of the given segments are EC = 6, AC = 12, EB = 4, and BD = 8.

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Answer: None of the statements are true.

The expression has only two terms: 17 and (5)(9 + 14y).

No term in the expression equals 23.

The expression has three factors: 17, 5, and (9 + 14y).

The constant in the factor 9 + 14y is 9.

The factors in the expression are 17, 5, 9, and (9 + 14y).

Step-by-step explanation:

Answer:

x = 0

Step-by-step explanation:

3(3x+5) - 8 =7

9x + 15 - 8 = 7

9x + 7 = 7

9x = 0

x = 0

Let's check

3(3(0) + 5) - 8 = 7

3(0 + 5) - 8 = 7

3(5) - 8 = 7

15 - 8 = 7

7 = 7

So, x = 0 is the correct answer.

The probability of at least one part being defective is 21 or more when 14 parts are produced. So, the correct answer is D: 14.

Let X be the number of defective parts among n parts produced. Since each part can either be defective or non-defective, X follows a binomial distribution with parameters n and p, where p = 0.05.

We want to find the smallest value of n such that P(X ≥ 1) ≥ 0.21. We can use the complement rule to rewrite this as P(X < 1) ≤ 0.79.

P(X < 1) = P(X = 0) = (1 - p)^n

= (0.95)^n

We need to find n such that (0.95)^n ≤ 0.79. Taking logarithms of both sides, we get:

n log(0.95) ≤ log(0.79)

n ≥ log(0.79) / log(0.95)

n ≥ 13.65

Since we need n to be an integer, we round up to the nearest integer and get n = 14.

Therefore, the answer is option D: 14.

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For the inequality  x > y > 0 and a > b > 0 the expression ( x /y)> (x +b)/ (y+ a) > b/a is true if x/b > y/a.

For  x > y > 0 and a > b > 0

The inequality x/b > y/a

Simplify by cross-multiplication we get,

⇒xa > yb

Adding xy to both sides,

⇒xy + xa > xy + yb

Factoring the left-hand side,

⇒ x(y + a) > y(x + b)

Dividing both sides by (y + a)(x + b), as x > y > 0 and a > b > 0,

⇒ x/(x + b) > y/(y + a)

Multiplying both sides by x/y  we get the expression,

⇒x/y > (x + b)/(y + a) __(1)

It proves the half part of the expression, x/y > (x + b)/(y + a)

Now second part x/y > (x + b)/(y + a) > b/a.

Using inequality x/b > y/a to get:

a/b > y/x

Multiplying both sides by (x + b)/(y + a),

⇒(a/b) × (x + b)/(y + a) >(y/x) × (x + b)/(y + a)

Expand both sides and simplifying,

⇒ ( ax + ab ) / (by + ab ) > ( xy + by ) / ( xy + ax )

⇒( ax + ab )( xy + ax ) > ( xy + by ) (by + ab )

⇒ ax²y + a²x² + abxy + a²bx > by²x + abxy + b²y² + ab²y

⇒ (ax -by )( x + b )( y + z) > 0

⇒ax - by > 0 or ( x + b )> 0 or ( y + z) > 0

⇒ ax > by

⇒ x /y > b /a

As a > b > 0

⇒ (x +b)/ (y+ a) > b/a  __(2)

From (1) and (2) we have,

( x /y)> (x +b)/ (y+ a) > b/a

Therefore , the expression ( x /y)> (x +b)/ (y+ a) > b/a is true for the given condition.

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The above question is incomplete, the complete question is:

Suppose x > y > 0 and a > b > 0. Is it true that x/b > y/a then expression

( x /y)> (x +b)/ (y+ a) > b/a.