For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. 15.log(z19x1319​)16.ln(b−40a−2​)17.log(x3y−4​)18.ln(y1−yy​​)

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

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 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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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: i think -22/3 and 6/17

Step-by-step explanation:

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 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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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.

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.

By answering the above question, we may state that This expression's equation evaluation results in: r = 8.5 ft

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A formal statement that proves the equality of two calculations is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two phrases that are inscribed on opposite sides of a letter. Frequently, the logo and indeed the particular software are identical. like in 2x - 4 = 2, for example.

The following is the formula for a circle's circumference:

C = 2πr

where is a mathematical constant that is roughly equivalent to 3.14159, C is the circumference, r is the radius, and.

The circle's circumference is stated to be 17 feet. In order to find r, we may put this equal to the circumference formula as follows:

17π = 2πr

When we divide both sides by 2, we obtain:

r = 17π / (2π)

Units cancel out, leaving:

r = 17 / 2

This expression's evaluation results in:

r = 8.5 ft

As a result, the circle's radius is 8.5 feet.

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The expanded form of the given expression is x^2 - 64.

The distributive property states that for any two numbers a and b, a(b+c) = ab + ac. This means that you can multiply a number by the sum of two numbers and get the same result as when you multiply that number by each of the two numbers separately and then add the two products together.

To expand the given expression, we need to use the distributive property. The distributive property states that a(b + c) = ab + ac. Applying this property to the given expression, we get:

(x + 8)(x - 8) = x(x - 8) + 8(x - 8)

Next, we need to distribute the x and 8 to the terms inside the parentheses:

x(x - 8) + 8(x - 8) = x^2 - 8x + 8x - 64

Finally, we can simplify the expression by combining like terms:

x^2 - 8x + 8x - 64 = x^2 - 64

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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 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 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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Answer:

a) When we say "like terms", we mean terms that have the same variables and/or exponents.

b) When we say "combining like terms", we mean adding or subtracting terms with the same variables, so that the two terms become one term.

c) An example of combining like terms is: 6x + 3x = 9x.

Answer:

Step-by-step explanation:

Ok, I hate point-slope form but I can help!

I'm going to answer slope-intercept first, then point slope.

2. y = 1/4x - 1 ; y+2 = 1/4(x+4)

3. y = -3/2x + 1 ; y+2 = -3/2(x-2)

4. y = x - 2 ; y-1 = 1(x-3)

Hope this helps!

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 :)

In the first production method, the company produces approximately 4,996 books.

Let's represent the number of books produced as x.

Total cost of method 1 = One-time fixed cost + Variable cost * Number of books produced

= $82,363 + $9.25x

Total cost of method 2 = One-time fixed cost + Variable cost * Number of books produced

= $21,162 + $21.50x

Setting the two equations equal to each other, we get:

$82,363 + $9.25x = $21,162 + $21.50x

Simplifying this equation, we get:

$61,201 = $12.25x

Dividing both sides by $12.25, we get:

x = 4,995.92

This means that the costs from the two methods will be the same when the company produces approximately 4,996 books.

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The value of fy(1,1) is 5.5 with one decimal digit on the right side of the decimal point.

To find the value of fy(1,1), we need to first find the partial derivative of f(x,y) with respect to y. This is done by treating x as a constant and taking the derivative with respect to y.

The partial derivative of f(x,y) with respect to y is:
fy(x,y) = (1/2)(4x2 - 2y + 7x4y5)-1/2 (-2 + 35x4y4)

Now we can plug in the values of x=1 and y=1 into the partial derivative to find the value of fy(1,1):
fy(1,1) = (1/2)(4(1)2 - 2(1) + 7(1)4(1)5)-1/2 (-2 + 35(1)4(1)4)
fy(1,1) = (1/2)(4 - 2 + 7)-1/2 (-2 + 35)
fy(1,1) = (1/2)(9)-1/2 (33)
fy(1,1) = (1/2)(1/3)(33)
fy(1,1) = 5.5

Therefore, the value of fy(1,1) is 5.5 with one decimal digit on the right side of the decimal point.

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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:

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.

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 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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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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If W is a subspace, then

1. Geometric description of W is a line passing through the origin with a slope of 2.

2. W is not a subspace of R ^ 2.

3. Here, W is the union of two lines passing through the origin with slopes of 1 and -1.

4. In this case, W is not a subspace of R ^ 2.

5. Geometrically, W is a line passing through the origin with a slope of 0.

6. Here, Geometrically, W is a single point at the origin.

1. W = \{x / x_{1} = 2x_{2}\} is a subspace of R^2 because it satisfies the three conditions of being a subspace: it contains the zero vector (0,0), it is closed under addition, and it is closed under scalar multiplication. Geometrically, W is a line passing through the origin with a slope of 2.

2. W = \{x / x_{1} - x_{2} = 2\} is not a subspace of R^2 because it does not contain the zero vector (0,0). Geometrically, W is a line that does not pass through the origin.

3. W=\ x / x_{1} = x_{2} or x_{1} = - x_{2} is a subspace of R^2 because it satisfies the three conditions of being a subspace. Geometrically, W is the union of two lines passing through the origin with slopes of 1 and -1.

4. W = {x: x₁ and x_{2} are rational numbers} is not a subspace of R^2 because it is not closed under scalar multiplication. For example, if we multiply the vector (1/2, 1/3) by the scalar √2, we get the vector (√2/2, √2/3), which is not in W. Geometrically, W is the set of all points with rational coordinates.

5. W = \{x / x_{1} = 0\} is a subspace of R^2 because it satisfies the three conditions of being a subspace. Geometrically, W is a line passing through the origin with a slope of 0 (the x-axis).

6. W = \{x / |x_{1}| + |x_{2}| = 0\} is a subspace of R^2 because it contains only the zero vector (0,0), which satisfies the three conditions of being a subspace. Geometrically, W is a single point at the origin.

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Step-by-step explanation:

Refer to pic..........

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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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.