solve for P assume that none of the denominators are equal to 0
Kl=y(f/p+n + r/u)​

Solve For P Assume That None Of The Denominators Are Equal To 0Kl=y(f/p+n + R/u)

Answers

Answer 1

Step-by-step explanation:

KI=yf/p+n + yr/u

(p+n) KI - yrp/u -yrn/u = yf

pKI - yrp/u = yf - nKI + yrn/u

p(KI - yr/u) = yf - nKI + yrn/u

p = (1/KI-yr/u)(yf-nKI+yrn/u)


Related Questions

Evaluate the function. f(x)=-3x^2 f(x)=−3x 2 \text{Find }f(-2) Find f(−2)

Answers

Answer:

12

Step-by-step explanation:

f(-2) = -3*(-2^2)

f(-2) = -3*-4

f(-2) = 12

Complete the equation describing how
x and y are related.
X
0
1
2
3
5
6
у
5
6
7
8
9
10
y = x + [?]
Enter the answer that belongs in ?).

Answers

Answer:

y= x + 5

Step-by-step explanation:

it is clearly shown

Twice a number increased by the product of the number and fourteen results in forty eight

Answers

Answer:

Let x = the number. Then you have:

2x + 14x = 48 Collect like terms

16x = 48 Divide both sides by 16

x = 3

PLEASE MARK AS BRAINLIEST ANSWER

The number that satisfies the given statement is 3.

We are given that twice a number increased by the product of the number and 14 results in 48.

We will find the value of the number that we used in the given above statement.

Understand the meaning of the keywords used in the statement.

Increased means addition.

Product means multiplication.

Results mean equal to sign.

Let's write the given statement in equation form.

Consider P = the number

Twice a number = 2P

Increased =  +

Products of the number and 14 =  P x 14

Results in 48 = equals 48.

Combining all the above we get,

2P + P x 14 = 48

2P + 14P = 48

16P = 48

P = 48 / 16

P = 3

Thus the number that satisfies the given statement is 3.

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​There are two types of fish in a lake. These are carp and pike.
In a netted area of the lake 120 carp and 16 pike were caught
In the whole lake it is estimated there are 34 000 fish.How​ many pike are there?​​

Answers

Answer:pike are 250 ; from 120+16=136 and 34000/136 is 250

Step-by-step explanation:

Please help me to find out the answer

Answers

Answer:

8.204786801 in

Step-by-step explanation:

cos (79°) = BE/BG= adjacent/hypotenuse

cos ( 79°) = BE/43 in

BE = cos (79°) × 43 in= 8.204786801 in

Clara travels from her home to Stoke.
The distance from her home to Stoke is 100 miles.
She travels at an average speed of 50 miles per hour.
She stops for 20 minutes on the journey. Clara arrives in Stoke at 10:10 am.
At what time did she leave home?​

Answers

Answer:

7:50 am

Step-by-step explanation:

Clara took 2 hours to reach, and she took a 20 min break, so she left at 7:50 and arrived at 10:10.

Answer:

7:50

Step-by-step explanation:

50 miles per hour/50 miles per 60 min.

50 miles + 50 miles = 100 miles.

if 50 miles takes 1 hour, 100 miles would equal to 2 hours.

considering clara took a 20 min break, thats 2 hours and 20 minutes.. subtract that from the time she arrived and you would get 7:50

Help I don’t understand at all

Answers

Answer:

[tex]1)\ \ 4h^2-13h+6\\2)\ \ 7x^3y^2-x^2y+1\\3)\ \ -7n+2\\4)\ \ -8m+4[/tex]

Step-by-step explanation:

1.

Simplify the expression by combining like terms. Remember, like terms have the same variable part, to simplify these terms, one performs operations between the coefficients. Please note that a variable with an exponent is not the same as a variable without the exponent. A term with no variable part is referred to as a constant, constants are like terms.

[tex]2h^2-7h+2h^2-h+6+4h-9h[/tex]

[tex](2h^2+2h^2)+(-7h-h+4h-9h)+(6)[/tex]

[tex]4h^2-13h+6[/tex]

2.

Use a very similar method to solve this problem as used in the first. Please note that all of the rules mentioned in the first problem also apply to this problem; for that matter, the rules mentioned in the first problem generally apply to any pre-algebra problem.

[tex]8x^3y^2-7x^2y+8x-4-x^3y^2+2x^2y+4x^2y-8x+5[/tex]

[tex](8x^3y^2-x^3y^2)+(-7x^2y+2x^2y+4x^2y)+(8x-8x)+(-4+5)[/tex]

[tex]7x^3y^2-x^2y+1[/tex]

3.

Use the same rules as applied in the first problem. Also, keep the distributive property in mind. In simple terms, the distributive property states the following ([tex]a(b+c)=(a)(b)+(a)(c)=ab+ac[/tex]). Also note, a term raised to an exponent is equal to the term times itself the number of times the exponent indicates. In the event that the term raised to an exponent is a constant, one can simplify it. Apply these properties here,

[tex]-2(8n+1)-(5-9n)+3^2[/tex]

[tex]-2(8n+1)-(5-9n)+(3*3)[/tex]

[tex]-2(8n+1)-(5-9n)+9[/tex]

[tex](-2)(8n)+(-2)(1)+(-)(5)+(-)(-9n)+9[/tex]

[tex]-16n-2-5+9n+9[/tex]

[tex](-16n+9n)+(-2-5+9)[/tex]

[tex]-7n+2[/tex]

4.

The same method used to solve problem (3) can be applied to this problem.

[tex]\frac{1}{2}(10-8m+6m^2)-(3m^2+4m-7)-2^3[/tex]

[tex]\frac{1}{2}(10-8m+6m^2)-(3m^2+4m-7)-(2)(2)(2)[/tex]

[tex](\frac{1}{2})(10)+(\frac{1}{2})(-8m)+(\frac{1}{2})(6m^2})+(-)(3m^2)+(-1)(4m)+(-1)(-7)-8[/tex]

[tex]5-4m+3m^2-3m^2-4m+7-8[/tex]

[tex](-3m^2-3m^2)+(-4m-4m)+(5+7-8)[/tex]

[tex]-8m+4[/tex]

6x=1/2(2X +7)
Solve for x

Answers

Answer:

Step-by-step explanation:

6x=1/2(2x +7)            Multiply both sides by 2

2*6x = 1/2(2x + 7)*2

12x = 2x + 7              Subtract 2x from sides

12x-2x =2x-2x+7

10x = 7                      Divide by 10

x = 7/10

x = 0.7

Let's check it

6(0.7) = 4.2

1/2 (2*0.7 + 7)

1/2 (1.4 + 7)

1/2 ( 8.4)

4.2

Both sides check. The answer must be x = 0.7

What is the derivative of 5x^4+4?

Answers

Answer:

[tex]\displaystyle \frac{dy}{dx} = 20x^3[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]  

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = 5x^4 + 4[/tex]

Step 2: Differentiate

Derivative Property [Addition/Subtraction]:                                                 [tex]\displaystyle y' = \frac{d}{dx}[5x^4] + \frac{d}{dx}[4][/tex]Rewrite [Derivative Property - Multiplied Constant]:                                   [tex]\displaystyle y' = 5\frac{d}{dx}[x^4] + \frac{d}{dx}[4][/tex]Basic Power Rule:                                                                                         [tex]\displaystyle y' = 20x^3[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Complete the table y+1=7/8x

Answers

Answer:

y = 7/8x - 1

Step-by-step explanation:

graph shown

Người ta chiếu xạ liều 3000 Rơn ghen vào một quần thể ruồi dấm ở thế hệ F1: Chiếu xạ 1000 con ruồi dấm không cho ăn đường thì có 80 con bị đột biến và chiếu xạ 1000 con ruồi dấm có cho ăn đường thì có 120 con bị đột biến. Cho ăn đường có ảnh hưởng đến tỉ lệ đột biến của ruồi giấm không, với mức ý nghĩa 5%? Giá trị kiểm định là

Answers

Answer:

gggggggggggggggggggggrrrrrrrrrrrttyuuiiiii

Please help me answer this question?

Answers

Answer:

[tex]P'(x)=2.2-0.12x[/tex]

Step-by-step explanation:

start by finding [tex]P(x) = R(x)-C(x)[/tex]

[tex]P(x)=3x-0.06x^2-286-0.8x[/tex]

to find P'(x), you take the derivative of P(x)

[tex]P'(x)=\frac{d}{dx} (2.2x-286-0.06x^2)[/tex]

[tex]\frac{d}{dx} (2.2x-286-0.06x^2)=2.2-0.12x[/tex]

so [tex]P'(x)=2.2-0.12x[/tex]

somone please help asap! i’ll give you points!

Answers

Answer:  Choice B)   [tex]-4 \le x < 2[/tex]

Explanation:

The closed circle at the endpoint -4 means we'll include this value as part of the shaded solution set. In contrast, the endpoint 2 is not included because of the open hole here.

This graph is describing everything between -4 and 2, including -4 but excluding 2.

In other words, we can have x = -4 but can't have x = 2. Then we include everything in between those endpoints. So that's why we go for [tex]-4 \le x < 2[/tex]

Answer:

-4≤x<2

Step-by-step explanation:

-4 has a closed circle which means it is included in the less than or equal to and the 2 is less than x

If x , 2x and 50° are the interior angle of the triangle, find the unknown angle.​

Answers

Answer:

40°

Step-by-step explanation:

x +2x+50=180 [sum of interior angles of a triangle]

or,3x=180-50

or,x=130/3

x=130/3

2x=2×130/3

Which of the following options correctly represents the complete factored
form of the polynomial F(x) = x^3- x2 - 4x-6?
A. F(x) - (x - 3)(x + 1 + I)(x+1- I)
B. F(x) = (x - 3)(x+1+I)(x-1-I)
C. F(x) = (x+3)(x + 1)(x - 1)
D. F(x) - (x+3)(x+1+I)(x +1-I )

Answers

The completely factored form for the given algebraic expression is f(x) = (x-3)(x+1+i)(x+1-i).

What is a completely factored polynomial?

A completely factored polynomial is a polynomial that can no longer be further simplified. A completely factored polynomial can be expressed as a root of its own equation.

Given that:

f(x) = x³ - x² - 4x - 6

To express this as a factored polynomial using the rational:

f(x) = (x-3)(x²+2x+2)

f(x) = (x-3)(x+1+i)(x+1-i)

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What is the common ratio for this geometric sequence?
27, 9, 3, 1, ...

Answers

Answer:

27:9 3:1.................

URGENT PLS HELP! WILL GIVE BRAINLIEST (PICTURE INCLUDED)

Answers

Answer:

1605

Step-by-step explanation:

what is a cell and why it is necessary​

Answers

CELL

Cells are the basic building blocks of living things. The human body is composed of trillions of cells, all with their own specialised function. Cells are the basic structures of all living organisms.

IMPORTANCE

Cells provide structure for the body, take in nutrients from food and carry out important functions.

I HOPE THIS WILL HELP YOU IF NOT THEN SORRY

HAVE A GREAT DAY :)

What number when multiplied by itself is 11 greater than the preceding number when it is multiplied by itself

Answers

Answer: 5 and 6

Step-by-step explanation:

X^2 - 11 = (X-1)^2

X^2 - 11 = X^2-2X+1

X^2 - X^2 + 2X = 11+1

2X = 12

X = 6

The preceding number is 5

(6)(6)=36 and (5)(5)=25

36-25=11

The number required is 6

Let the number required bee x

If the number is multiplied by itself, it becomes x²

If the result is 11 greater than the preceding number when it is multiplied by itself is expressed as:

x² - 11  = (x - 1)²

x² - 11 = x² - 2x + 1

2x = 11 + 1

2x = 12

x = 6

Hence the number required is 6

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helppppp
Find the value of x.
A. 176
B. 128
C. 256
D. 74

Answers

Answer: Choice B) 128

Explanation:

We'll add up the given arc measures and then cut the result in half to get the angle formed by the intersecting chords (that subtend the arcs in question).

chord angle = (arc1+arc2)/2

x = (54+202)/2

x = 256/2

x = 128

Answer:

128

Step-by-step explanation:

Angle Formed by Two Chords = 1/2(SUM of Intercepted Arcs)

x = 1/2 (54+202)

x = 1/2 (256)

x =128

Make mathematical expressions then, simplify ,50 is divided by 2 times one more than the difference of F and 3.​

Answers

Answer:

F = 27

Step-by-step explanation:

50/2 = (F - 3) + 1

25 = F - 2

F = 27

what is 1034÷22 ?
[tex]1034 \div 22 [/tex]

Answers

The answer would be 47

Power Function:
Consider the following graphs (1 and 2), and answer the questions FOR EACH GRAPH:

A) In what interval of the graph is it increasing, decreasing and constant? This answer must be justified by means of the definition
B) What is the domain and range?
C) Is it an odd or even function? This answer must be justified by means of the definition

Answers

Graph 1

Part (a)

The function is increasing when x > 0. The function is decreasing when x < 0.

The function is never constant

An increasing portion is when the graph goes uphill when moving left to right. A decreasing portion goes in the opposite direction: it goes downhill when moving left to right.

The reason why the function is never constant is because there aren't any flat horizontal sections. Such sections are when x changes but y does not. No such sections occur.

------------------------

Graph 1

Part (b)

Domain = set of all real numbers

Range = set of y values such that [tex]y \ge 0[/tex]

The domain is the set of all real numbers because we can plug in any value for x without any restriction. There are no division by zero errors to worry about, or square roots of negative numbers to worry about either.

The range is the set of nonnegative numbers as the graph indicates. The lowest y gets is y = 0.

------------------------

Graph 1

Part (c)

The function is even

The function f(x) = 1.6x^12 is an even function due to the even number exponent. For any polynomial, as long as the exponents are all even, then the function itself is even. If all the exponents were odd, then the function would be odd. This applies to polynomials only. A power function is a specific type of polynomial.

Note in the graph, we have y axis symmetry. The mirror line is vertical and placed along the y axis. This is a visual trait of any even function.

We could use algebra to show that f(-x) = f(x) like so

f(x) = 1.6x^12

f(-x) = 1.6(-x)^12

f(-x) = 1.6x^12

The third step is possible because (-x)^12 = x^12 for all real numbers x. It's similar to how (-x)^2 = x^2. You could think of it like (-1)^2 = (1)^2

============================================================

Graph 2

Part (a)

The function is decreasing when x < 0 and when x > 0

The function is never increasing

The function is never constant

In other words, the function is decreasing over the entire domain (see part b). The only time it's not decreasing is when x = 0.

The function is decreasing because the curve is going downhill when moving to the right. You can think of it like a roller coaster of sorts.

At no point of this curve goes uphill when moving to the right. Therefore, it is never increasing. The same idea applies to flat horizontal sections, so there are no constant intervals either.

------------------------

Graph 2

Part (b)

Domain: x is any real number but [tex]x \ne 0[/tex]

Range: y is any real number but [tex]y \ne 0[/tex]

Explanation: If we tried plugging x = 0 into the function, we get a division by zero error. This doesn't happen with any other number. Therefore, the set of allowed inputs is any number but 0.

The range is a similar story. There's no way to get y = 0 as an output.

If we plugged y = 0 into the equation, then we'd get this

y = 17x^(-3)

0 = 17/(x^3)

There's no way to have the right hand side turn into 0. The numerator is 17 and won't change. Only the denominator changes. We can't have the denominator be 0.  

------------------------

Graph 2

Part (c)

The function is odd

We can prove this by showing that f(-x) = -f(x)

f(x) = 17x^(-3)

f(-x) = 17(-x)^(-3)

f(-x) = 17* ( -(x)^(-3) )

f(-x) = -17x^(-3)

f(-x) = -f(x)

This is true for nearly all real numbers x, except we can't have x = 0.

Graphic 1:

(A) If f(x) = 1.6x ¹², then f '(x) = 19.2x ¹¹. Both f '(x) and x have the same sign, which means

• for -∞ < x < 0, we have f '(x) < 0, so that f(x) is decreasing on this interval

• for 0 < x < ∞, we have f '(x) > 0, so f(x) is increasing on this interval

f(x) is not constant anywhere on its domain.

(B) Speaking of domain, since f(x) is a polynomial (albeit only one term), it has

• a domain of all real numbers

• a range of {y ∈ ℝ : y = f(x) and y ≥ 0} (in other words, all real numbers y such that y = 1.6x ¹² and y is non-negative)

(C) This function is even, since

f(-x) = 1.6 (-x)¹² = (-1)¹² × 1.6x ¹² = 1.6x ¹² = f(x)

Graphic 2:

(A) Now if f(x) = 17/x ³, then f '(x) = -51/x ⁴. Because x ⁴ ≥ 0 for all x, this means f '(x) < 0 everywhere, except at x = 0. So f(x) is decreasing for (-∞ < x < 0) U (0 < x < ∞).

(B) f(x) has

• a domain of {x ∈ ℝ : x ≠ 0} (or all non-zero real numbers)

• a range of {y ∈ ℝ : y = f(x) and y ≠ 0} (also all non-zero reals)

(C) This function is odd:

f(-x) = 17/(-x)³ = 1/(-1)³ × 17/x ³ = -17/x ³ = -f(x)

it takes Bert 30 minutes longer to mow a rectangular lawn that measures 30 feet by 25 feet than it takes him to mow a rectangular lawn that measures 20 feet by 15 feet. if he mows the two lawns at the same rate per square foot, how long does it take him to mow both lawns ?

A)50min
B)60min
C)70min
D)80min

Answers

Answer:

C: 70 Mins

Step-by-step explanation:

1, 20ft*15ft=300ft^2

2, 30ft*25ft=750ft^2

3, 750ft-350ft=450ft^2

4, 450 ft^2 = 30 mins

5, 350ft=750ft=1050ft^2

6, 1050/450=2.3333

7, 30*2.3333=70

8, 70 mins

At the same rate per square foot , Bert will take 80 minutes to mow the both lawns.

What is rate?

Rate is the ratio between two related quantities in different units.

Area of the rectangular lawn = lw

where

l = lengthw = width

area of the lawn1  = 30 × 25 = 750 ft²

area of the lawn2 = 20 × 15 = 300 ft²

Therefore,

He mow the firts lawn 30 minutes longer than the second lawn. Therefore,

let

x = time to mow the second lawn

x + 30 = time to mow the first lawn

rate for the first lawn = 30 + x / 750

rate for the second lawn = x / 300

Hence,

30 + x / 750 = x / 300

cross multiply

9000 + 300x = 750x

9000 = 750x - 300x

9000 =  450x

x = 9000 / 450

x = 20

it will take him 30 + 20 + 20 = 80 minutes to mow the both lawns.

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plz help brainliest to correct answer

Answers

Answer:

-2 would be right next to -3 because its negative and -1 would be right next to -2, 2 would be two points away from 0 bc its a whole number

Each mark on the line is one unit. 0 is the starting point. For a positive number, move one unit at a time for the number you have. For example, to graph 2, start at 0 and move to the right 2 units. Just make a dot there and write 2 above it. For negative numbers, you go to the left. So start at 0, and go one to the left and that’s -1. Go one more to the left and that’s -2.

A state lottery sells instant-lottery scratch tickets. 12% of the tickets have prizes. Neil goes to the store and buys 10 tickets. What is the probability that exactly three of Neil's tickets will have prizes? ​

Answers

Answer:

The probability of success is .12

The probability of failure is .88

According to the binomial theorem the probability of 3 success is

10! / (3! * 7!) * .12^3 * .88^7 = .085

Câu 99: Cho hàm số f x  xác định trên ℝ , bảng biến thiên của hàm số f x   như sau.
x  1 1 3 
f x    |  0  | 
f x  
 
0 0
4
Mệnh đề nào dưới đây đúng?
A. Hàm số f x  đồng biến trên 1;.
B. Hàm số f x  đồng biến trên  ; 1 và 3;.
C. Hàm số f x  nghịch biến trên  ; 1.
D. Hàm số f x  đồng biến trên     ; 1 3;   .

Answers

Answer:

i doesn,t understand this language

It is known that 10% of adults can pass a fitness test. What is the probability at most 12 adults in a
sample of 100 adults pass this fitness test?

Answers

Using the normal distribution, there is a 0.7967 = 79.67% probability that at most 12 adults in a sample of 100 adults pass this fitness test.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].

The parameters of the binomial distribution are given by:

p = 0.1, n = 100.

Hence the mean and the standard deviation for the approximation are given by:

[tex]\mu = np = 100 \times 0.1 = 10[/tex][tex]\sigma = \sqrt{np(1-p)} = \sqrt{100 \times 0.1 \times 0.9} = 3[/tex]

The probability at most 12 adults in a sample of 100 adults pass this fitness test, using continuity correction, is P(X < 12.5), which is the p-value of Z when X = 12.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{12.5 - 10}{3}[/tex]

Z = 0.83

Z = 0.83 has a p-value of 0.7967.

0.7967 = 79.67% probability that at most 12 adults in a sample of 100 adults pass this fitness test.

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Which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x2 – 4 into the quadratic
formula?
Quadratic formula: x =
-bb2-4ac
2 a
Ox=
-(-1){V - 1)2 - 4(1)(-4)
2(1)
O x=-11/12-46- 1)( - 4)
2(-1)
O x= -13V (1)? - 4( - 1)(-2)
2(-1)
O x=-(-1)+7(-1)2 - 4(1)(-2)
2(1)

Answers

The values of a, b, c are obtained from the given equation, by equation

in the form in which it is equal to 0.

The correct substitution of the values a, b, and c from the equation -2 = -x + x² - 4 is the option;

[tex]\underline{x = \dfrac{-1 \pm \sqrt{1^2 - 4 \cdot (-1) \cdot (-2)} }{2 \cdot (-1)}}[/tex]

Which is the method by which the values of a, b, and c are substituted?

Given:

The quadratic formula is presented as follows;

[tex]x = \mathbf{ \dfrac{-b \pm \sqrt{b^2 - 4 \cdot a \cdot c} }{2 \cdot a}}[/tex]

The given equation is presented as follows;

-2 = -x + x² - 4

Which gives;

0 = -x + x² - 4 + 2 = -x + x² - 2

-x + x² - 2 = 0

Therefore, we have;

[tex]x = \mathbf{ \dfrac{-1 \pm \sqrt{1^2 - 4 \times (-1) \times (-2)} }{2 \times (-1)}}[/tex]

The correct option is therefore;

[tex]x = \dfrac{-1 \pm \sqrt{1^2 - 4 \cdot (-1) \cdot (-2)} }{2 \cdot (-1)}[/tex]

Learn more about the quadratic formula here:

https://brainly.com/question/1630251

22. The ratio in which (4, 5) divides the join of (2, 3)
and (7, 8) is :
(a) 4 : 3
(c) 3 : 2
(b) 5:2
(d) 2:3

Answers

Let the ratio be m:n

(x,y)=(4,5)Points be (x1,y1)=(2,3)(x2,y2)=(7,8)

We know

[tex]\boxed{\sf (x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]

[tex]\\ \sf\longmapsto (4,5)=\left(\dfrac{7m+2n}{m+n},\dfrac{8m+3n}{m+n}\right)[/tex]

Now

.[tex]\\ \sf\longmapsto \dfrac{7m+2n}{m+n}=4\dots(1)[/tex]

[tex]\\ \sf\longmapsto \dfrac{8m+3n}{m+n}=5\dots(2)[/tex]

Adding both

[tex]\\ \sf\longmapsto \dfrac{7m+2n+8m+3n}{m+n}=4+5[/tex]

[tex]\\ \sf\longmapsto \dfrac{7m+8m+2n+3n}{m+n}=9[/tex]

[tex]\\ \sf\longmapsto \dfrac{15m+5n}{m+n}=9[/tex]

[tex]\\ \sf\longmapsto 15m+5n=9(m+n)[/tex]

[tex]\\ \sf\longmapsto 15m+5n=9m+9n[/tex]

[tex]\\ \sf\longmapsto 15m-9m=9n-5n[/tex]

[tex]\\ \sf\longmapsto 6m=4n[/tex]

[tex]\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{6}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{3}{2}[/tex]

[tex]\\ \sf\longmapsto m:n=3:2[/tex]

Option B is correct

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