Find the least common denominator for these
two rational expressions,

Answer:

The correct option is D.

Step-by-step explanation:

Given information: △ABC≅△ECD.

The corresponding parts of congruent triangles are congruent.

The congruent angles are :

[tex]\angle A\cong \angle E[/tex]

[tex]\angle B\cong \angle C[/tex]

[tex]\angle C\cong \angle D[/tex]

[tex]\triangle BCA\cong \triangle CDE[/tex]

Option A is incorrect.

[tex]\triangle CAB\cong \triangle DEC[/tex]

Option B is incorrect.

The congruent sides are :

[tex]BC\cong CD[/tex]

Option C is incorrect.

[tex]AC\cong ED[/tex]

[tex]AB\cong EC[/tex]

It can also written as

[tex]AB\cong CE[/tex]             [tex][\because EC=CE,\text{Reflective Property}][/tex]

Therefore the correct option is D.

The correct statement is BC ≅ ED.

The correct statement is BC ≅ ED.

Since △ABC ≅ △ECD, the corresponding sides and angles of the triangles are congruent.

Therefore, we can conclude that BC ≅ ED.

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Answer:

29 square root 5.

Step-by-step explanation:

You must simplify the surds to subtract them.

ANSWER

[tex]29 \sqrt{5} [/tex]

EXPLANATION

The given radical expression is

[tex]11 \sqrt{45} - 4 \sqrt{5} [/tex]

We remove the perfect squares to get:

[tex]11 \sqrt{9 \times 5} - 4 \sqrt{5} [/tex]

Split the square root sign to obtain:

[tex]11 \sqrt{9} \times \sqrt{5} - 4 \sqrt{5} [/tex]

We simplify further to get:

[tex]11 \times 3 \sqrt{5} - 4 \sqrt{5} [/tex]

[tex]33 \sqrt{5} - 4 \sqrt{5}[/tex]

This simplifies to

[tex]29 \sqrt{5} [/tex]

Answer:

x=5

Step-by-step explanation:

Factoring  x2 - 2x – 15 we get

(x+3)(x-5) so x+3=0 and x-5=0 or x=-3 and x=5

Answer:

x=5

Step-by-step explanation:

x^2 - 2x – 15 = 0

Factor

What 2 numbers multiply to -15 and add to -2

-5*3 = -15

-5+3 = -2

(x-5) (x+3) = 0

Using the zero product property

(x-5) =0   x+3 =0

x-5+5 =0+5      x+3-3 = 0-3

x=5                  x=-3

Answer:

The amount of her commission= 150

Step-by-step explanation:

Sale price = 2000

Rate of commission = 7.5%

Amount of commission =?

Formula:

Commission_amount = sale price * commission_percentage / 100

Now put the values in the formula.

Commission_amount=2000*7.5/100

Commission_amount=150.

Thus the amount of her commission is 150....

Answer:all real number greater than 0

Step-by-step explanation:

Firstly if you input any number equal to 0 or less than 0 you will not find the defined range...

You cant use o or any negetive number as domain in the term of log or ln type math..

But if u put any value more than 0 you can find all real number as range

Such as, log(0.001)=-3

log(1)=0

log(120)=2.07

So the domain is all real number above o...but the range is all real number including 0 and negetive number..

The domain of y=logx is all real numbers greater than 0.

Hence, option b is the correct answer.

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Answer:

In general, quadratic equations have two x-intercepts. But sometimes it happens that a quadratic eqution has one x-intercept or no interepts. That's why we should fully analyze this equation:

Given the following equation: y=3x^2 + 7 + m

If y=0, then:

3x^2 + 7 + m = 0 ⇒ x^2 = (-m-7)/3

Then [tex]x =[/tex]± [tex]\sqrt{\frac{-m-7}{3}}[/tex]

Given that we can take the square root of a negative number, the only way this equation has two x-intercepts is if m<-7.

Summarizing:

The equation: y=3x^2 + 7 + m has two x-intercepts only if m is less than -7. If m equals -7, the equation has only one x-intercept, and finally, if m is greater than -7, the equation has NO x-intercepts.

Answer:

3/50 or 0.06

Step-by-step explanation:

6/100=3/50

6/100=0.06

Answer:

0.06

Step-by-step explanation:

Answer:

-14

Step-by-step explanation:

Follow PEMDAS, then the left -> right rule.

PEMDAS =

Parenthesis

Exponent (& roots)

Multiplication

Division

Addition

Subtraction

First, multiply 6 with -2:

6 x -2 = -12

Next, add 1, then subtract 3.

-12 + 1 = -11

-11 - 3 = -14

-14 is your answer.

~

Answer:

-14

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

Do parenthesis first.

6*(-2)=-12

-12+1-3

Add and subtract the numbers from left to right to find the answer.

-12+1-3

-12+1=-11

-11-3=-14

-14 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

y = x -1

Step-by-step explanation:

x - y = 7

We need to put this in slope intercept form to find the  slope.

Add y to each side

x-y+y =7+y

x = y+7

Subtract 7 from each side

x-7 = y+7-7

x-7 = y

The slope is 1  since it is in the form y = mx+b

We have a slope 1 and an point (1,0)

We can use point slope form to make an equation

y-y1 = m(x-x1)

y-0 = 1(x-1)

y = x -1

This is in slope intercept form

For this case we must indicate an expression equivalent to:

[tex]x + 2 + [4x- \frac {x ^ 2 + 6x + 8} {x + 4}][/tex]

If we factor the quadratic expression, we must find two numbers that when multiplied give as result 8, and when summed give as result 6. These numbers are 4 and 2. Then:

[tex]x ^ 2 + 6x + 8 = (x + 2) (x + 4)[/tex]

Rewriting the expression:

[tex]x + 2 + [4x- \frac {(x + 2) (x + 4)} {(x + 4)}] =[/tex]

Simplifying common terms we have:

[tex]x + 2 + [4x- (x + 2)] =[/tex]

Taking into account that:

[tex]- * + = -\\x + 2 + 4x-x-2 =\\x-x + 2-2 + 4x =\\4x[/tex]

ANswer:

4x

Answer: y= -3/2x

Explanation:

3x+ 2y- 6

→ 2y= -3x+ 6

→ y= -3/2x+ 3

Parallel to y= ax+ b is to have the same slope (ax) and have a different y- intercept.

For this equation, y= -3/2x + 3, it is y= -3/2x because the line has to pass through point (0,0).

Answer:

The answer is D: -1.00

Step-by-step explanation:

I just took the test on edg 2020 and got it correct

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The required value of the given trigonometric ratio is - 1.

Hence option D is correct.

Use the concept of trigonometric ratio defined as:

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain all trigonometric functions' values.

The trigonometric ratios of an acute angle supplied are the ratios of the sides of a right-angled triangle with respect to that angle.

The given trigonometric ratio is,

[tex]\text{sin}(\dfrac{7\pi}{2})[/tex]

Since we can write the expression of radian as,

[tex]\dfrac{7\pi}{2} = 3\pi + \dfrac{\pi}{2}[/tex]

Then,

[tex]\text{sin}(\dfrac{7\pi}{2}) = \text{sin}(3\pi + \dfrac{\pi}{2})[/tex]

Since we know that,

sin(3π + θ) = -sinθ

Therefore,

[tex]\text{sin}(3\pi + \dfrac{\pi}{2}) = -\text{sin}(\dfrac{\pi}{2})[/tex]

Ans we also know sin(π/2) = 1

So,

[tex]\text{sin}(\dfrac{7\pi}{2}) = -1.00[/tex]

Hence, the required value of the given trigonometric ratio is - 1 which is option D.

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The growth of y = 3x is identical to itself as it's the same function. The growth in y = 3x represents consistent linear growth, with a steady increase of the dependent variable as the independent variable increases. In an exponential function, the growth rate increases over time, unlike the consistent slope of a linear function.

The question seems to contain a typo and asks how the growth of y = 3x compares to the growth of itself, y = 3x. Since this is the same function, their growth rates are identical. To provide a meaningful comparison, let's consider an inverse relationship such as y = k/x versus an exponential relationship such as y = 3x. In the case of the inverse relationship, as x increases, y decreases; the growth rate is negative. In contrast, for the exponential function y = 3x, as the independent variable x increases, the dependent variable y increases exponentially, and the rate at which y grows also increases over time. For example, if x represents time and y represents a population, in exponential growth like that of bacteria under ideal conditions, the population increases significantly with each generation.

Graphs are an essential tool in displaying data and unveiling patterns. In a graph of y = 3x, also referred to as a line graph, you would find that the slope, which describes the growth rate, is consistent along the entire line. Here, the slope of the line is 3, indicating a consistent growth rate, where y increases by 3 units for every 1 unit increase in x. This consistent slope is representative of linear growth, differing from exponential growth where the growth rate increases as the value rises.

Final answer:

The original question likely contains a typo, comparing y = 3x to itself. Assuming the comparison was intended to be between a linear and an exponential function, a linear growth rate is constant as seen in y = 3x, whereas an exponential growth rate increases over time and is proportional to the value of the variable, as would be seen in y = [tex]3^x.[/tex]

Explanation:

The question seems to have a typo since it compares y = 3x to the same expression y = 3x. Assuming the comparison should be between two different types of functions, such as linear and exponential, we can provide a general explanation of how growth rates differ between linear and exponential functions.

For a linear function like y = 3x, the growth is consistent. That means for every unit increase in x, y increases by 3 units. This represents a constant rate of change. In contrast, with an exponential function, such as y =[tex]3^x[/tex], the rate of growth is proportional to the current value. In other words, as x increases, the value of y grows at an ever-increasing rate, which is characteristic of exponential growth.

A good example is in the growth of bacteria which can reproduce at an exponential rate, leading to a much faster increase compared to linear growth, as more bacteria contribute to the population each generation. Similarly, economies can grow exponentially, with the growth applied to an also growing base value, resulting in a curve that steepens over time.

Answer:

[tex]\large\boxed{y=\dfrac{1}{2}x}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]

[tex]\text{We have the equation:}\ y=-2x+4\to m_1=-2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{We have the equation:}\ y=\dfrac{1}{2}x+b.\\\\\text{Put the coordinate of the point (4, 2) to the equation:}\\\\2=\dfrac{1}{2}(4)+b\\\\2=2+b\qquad\text{subtract 2 from both sides}\\\\0=b\to b=0.\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x[/tex]

Answer: C

Step-by-step explanation:

Binomial have only two terms.

A) 3x²-6x²-+x has three terms

B) 6x³-6x²+x-1 has four terms

C) 3x³-6x has two terms

D) 6x³ has only one term

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}5y=3x+15&\text{subtract 3x from both sides}\\6x=10y-30&\text{subtract 10y from both sides}\end{array}\right\\\left\{\begin{array}{ccc}-3x+5y=15\\6x-10y=-30&\text{divide both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-3x+5y=15\\3x-5y=-15\end{array}\right}\\.\qquad0=0\qquad\bold{TRUE}\\\\\bold{Infinitely\ many\ solutions}\\\\5y=3x+15\qquad\text{divide both sides by 5}\\\\y=\dfrac{3}{5}x+3\qquad(*)\\\\\text{Put the coordinates of the points to the equation (*)}[/tex]

[tex]A.\ (5,\ 6)\\\\6=\dfrac{3}{5}(5)+3\\\\6=3+3\\\\6=6\qquad\bold{CORRECT}\\\\B.\ (-15,\ 12)\\\\12=\dfrac{3}{5}(-15)+3\\\\12=(3)(-3)+3\\\\12=-9+3\\\\12=-6\qquad\bold{FALSE}\\\\C.\ (0,\ 3)\\\\3=\dfrac{3}{5}(0)+3\\\\3=0+3\\\\3=3\qquad\bold{CORRECT}\\\\D.\ (-10,\ -3)\\\\-3=\dfrac{3}{5}(-10)+3\\\\-3=(3)(-2)+3\\\\-3=-6+3\\\\-3=-3\qquad\bold{CORRECT}[/tex]

Answer:

The total surface area of the solid is 702 cm² ⇒ answer B

The true statements are m∠WYX = 46° and  m∠YWX = 63° ⇒ 1st and 2nd answers

Step-by-step explanation:

* Lets explain the solid figure

- It has one rectangular base of dimensions 10 cm and 14 cm

- It has 4 rectangular side faces , two of dimensions 6 cm and 10 cm

 and another two of dimensions 6 cm and 14 cm

- It has 4 triangular faces , two of base 10 cm and height 12 cm and

 another two of base 14 cm and height 11 cm

- The total surface area of the solid is the sum of the area of the 9 faces

* Lets find the area of all the faces

# Area of the base

∵ The base is a rectangle

∵ Area of the rectangle = length × width

∵ Length = 14 cm and width = 10 cm

∴ Area of the base = 14 × 10 = 140 cm²

# Area of the four rectangular faces

∵ Length = 10 cm  and width = 6 cm

∴ The area of the face with dimensions 10 , 6 = 10 × 6 = 60 cm²

∵ Length = 14 cm  and width = 6 cm

∴ The area of the face with dimensions 14 , 6 = 14 × 6 = 84 cm²

# Area of the four triangular faces

∵ Area of a triangle = 1/2 × base × height

∵ The base = 10 cm and the height = 12 cm

∴ The area of the face = 1/2 × 10 × 12 = 60 cm²

∵ The base = 14 cm and the height = 11 cm

∴ The area of the face = 1/2 × 14 × 11 = 77 cm²

∵ The total surface area of the solid = the sum of the areas of 9 faces

∴ TSA = 140 + 2 × 60 + 2 × 84 + 2 × 60 + 2 × 77

∴ TSA = 140 + 120 + 168 + 120 + 154 = 702 cm²

* The total surface area of the solid is 702 cm²

* Lets solve the 2nd part

- WXY is a scalene triangle

- m∠WXY is 71°

- The two sides of the triangle WY and XY exceeded

- The ray WY and the ray XY intersect each other at point Y and

  formed vertically opposite angles with measure 46°

∵ Ray WY intersect ray XY at point Y

∴ m∠WYX = 46°

- In Δ WYX

∵ m∠WXY = 71° ⇒ given

∵ m∠WYX = 46° ⇒ proved

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠YWX + m∠WXY + m∠WYX = 180°

∴ m∠YWX + 71° + 46° = 180

∴ m∠YWX + 117° = 180° ⇒ subtract 117 from both sides

∴ m∠YWX = 63°

Lets check the true statements

# m∠WYX = 46° ⇒ true

# m∠YWX = 63° ⇒ true

# m∠WXY = 46° ⇒ not true

# m∠YWX = 46° ⇒ not true

# m∠WYX = 134° ⇒ not true

* The true statements are m∠WYX = 46° and  m∠YWX = 63°

Answer:

Option C is correct.

Step-by-step explanation:

y = x^2-x-3     eq(1)

y = -3x + 5      eq(2)

We can solve by substituting the value of y in eq(2) in the eq(1)

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

x^2-x+3x-3-5=0

x^2+2x-8=0

Now factorizing the above equation

x^2+4x-2x-8=0

x(x+4)-2(x+4)=0

(x-2)(x+4)=0

(x-2)=0 and (x+4)=0

x=2 and x=-4

Now finding the value of y by placing value of x in the above eq(2)

put x =2

y = -3x + 5

y = -3(2) + 5

y = -6+5

y = -1

Now, put x = -4

y = -3x + 5

y = -3(-4) + 5

y = 12+5

y =17

so, when x=2, y =-1 and x=-4 y=17

(2,-1) and (-4,17) is the solution.

So, Option C is correct.

Answer: Third Option

(2, -1) and (-4, 17)

Step-by-step explanation:

We have the following system of equations:

[tex]y = x^2 - x-3[/tex]

[tex]y=-3x + 5[/tex]

We have the first three steps to solve the system.

[tex]x^2- x-3 = -3x +5[/tex]   equal both equations

[tex]0 = x^2 + 2x - 8[/tex]      Simplify and equalize to zero

[tex]0 = (x-2)(x+4)[/tex]     Factorize

Then note that the equation is equal to zero when [tex]x = 2[/tex] or [tex]x = -4[/tex]

Now substitute the values of x in either of the two situations to obtain the value of the variable y.

[tex]y=-3(2) + 5[/tex]

[tex]y=-6 + 5[/tex]

[tex]y=-1[/tex]

First solution: (2, -1)

[tex]y=-3(-4) + 5[/tex]

[tex]y=12 + 5[/tex]

[tex]y=17[/tex]

Second solution: (-4, 17)

The answer is the third option

Answer:

x = - 7

Step-by-step explanation:

Given

3(x - 4) = 5x + 2 ← distribute left side

3x - 12 = 5x + 2 ( subtract 5x from both sides )

- 2x - 12 = 2 ( add 12 to both sides )

- 2x = 14 ( divide both sides by - 2 )

x = - 7

Step-by-step explanation:

Each day it splits in half. You wouldn't multiply by 2, for you would have to go, day 1 = 1 amoeba

day 2 = 3 amoebas (because you have the previous amoeba plus the starting one)

You would continue like this until you get day 8 and 16.

Amoebas reproduce by splitting in half every 24 hours. To calculate the number of amoebas after a certain period of time, use the exponential growth formula. After 8 days, there will be 256 amoebas, and after 16 days, there will be 65,536 amoebas.

To determine the number of amoebas after a certain period of time, we need to use the exponential growth formula. In this case, amoebas reproduce by splitting in half every 24 hours. So, if we start with one amoeba, after 24 hours, there will be two amoebae (2¹). After 48 hours, there will be four amoebas (2²) and so on.

For (a) 8 days, we need to calculate the number of 24-hour periods in 8 days. There are 8 days x 24 hours/day = 192 hours. So, we divide 192 by 24 to get the number of 24-hour periods, which is 8. Therefore, after 8 days, there will be 2⁸ = 256 amoebas.

For (b) 16 days, we repeat the same calculations. There are 16 days x 24 hours/day = 384 hours. Dividing 384 by 24 gives us 16 24-hour periods. Therefore, after 16 days, there will be 2¹⁶ = 65,536 amoebas.

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We can either convert to standard form first or convert to a common multiplier, kinda like a common denominator.  The latter makes more sense if they wanted the result in scientific notation, but let's do it that way anyway.

a)

4.5 × 10⁴ + 3.8  × 10³ = 45 × 10³ + 3.8  × 10³ = 48.8× 10³ = 48,800

Answer:  48,800

b)

4.5 × 10⁴ - 3.8  × 10³ = 45 × 10³ - 3.8  × 10³ = 41.2× 10³ = 41,200

Answer:  41,200

c)

7.2 × 10⁻³ + 6.3  × 10⁻² = 7.2 × 10⁻³ + 63  × 10⁻³ = 70.2 × 10⁻³

       = 7.02 × 10⁻² = 0.0702

Answer: 0.0702

Answer:

In graph

Step-by-step explanation:

First put it in Slope -Intercept form.

then graph the y- intercept first.

After that it's rise over run so think 1/1

up 1 over one.

Answer:

CCCCCCCCCCCCC

Step-by-step explanation:

Answer:

The Greatest Common factor is 1.

Step-by-step explanation:

You can't reduce the numbers anymore.

The greatest common factor of 37 and 88 is 1 .

The greatest common factor of two or more integers, which are not all zero, is the largest positive integer that equally divides each of the integers. The greatest common factor of two numbers say x and y is represented as gcf(x,y) .

The two numbers given are 37 and 88 .

There is no common divisors of 37 and 88 except 1 .

Thus the greatest common factor, of numbers -

gcf(37,88) = 1

Therefore, the greatest common factor of 37 and 88 is 1 .

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Answer:  C

Step-by-step explanation:

20 people have a dog: 8 are yes dog/yes cat & 12 are yes dog/no cat

17 people have no dog: 10 are no dog/yes cat & 7 are no dog/no cat

[tex]\begin{array}{c|c|c|c}\underline{\qquad \qquad}&\underline{Cat}&\underline{No\ Cat}&\underline{TOTAL}\\Dog&8&12&20\\\underline{\ No\ Dog\ }&\underline{\ 10\ }&\underline{\quad 7\quad }&\underline{\quad 17\quad }\\TOTAL&18&19&37\end{array}[/tex]

Answer:

19

Step-by-step explanation:

Plug in x = 3 into the function

f(x)=2x^2+1

f(x)=2(3)^2+1

f(x)=18+1

f(x)=19

The answer is:

f(3) = 19

Work/explanation:

To evaluate this function, plug in 3 for x:

[tex]\sf{f(x)=2x^2+1}[/tex]

[tex]\sf{f(3)=2(3)^2+1}[/tex]

[tex]\sf{f(3)=2\times9+1}[/tex]

Then, according to PEMDAS, we multiply:

[tex]\sf{f(3)=18+1}[/tex]

[tex]\sf{f(3)=19}[/tex]

Therefore, when x = 3, the function evaluates to 19.

Answer:

f(x) = |x|

Step-by-step explanation:

Only f(x) = |x| is an even function.  If you evaluate this function at x = 3, for example, the result is 3; if at x = -3, the result is still 3.  That's a hallmark of even functions.

Answer:

f(x) = |x|

Step-by-step explanation:

If we keep -x in place of x and it does not effect the given function, then it is even function. i.e. f(-x) = f(x).

and, If we put -x in place of x then the resultant function will get negative of the first function, then it is odd function. i.e. f(-x) = -f(x).

1. f(x) = |x|

Put x = -x ,then

f(-x) = |-x| = |x| = f(x)

Hence, f(x) is even function.

2.f(x) = x³ - 1

Put x = -x, then

f(-x) = (-x)³ - 1

      = -x³ - 1 = -f(x)

Hence, this function is odd.

3. f(x) = -3x

Put x = -x

then, f(-x) = -3(-x)

                = 3x = -f(x)

Hence, the given function is odd function.

Thus, only f(x) = |x| is even function.

A matching side of Polygon A measures 5 inches if it is 4 times smaller than a side of Polygon B that measures 20 inches.

If Polygon A is 4 times smaller than Polygon B, and a side of Polygon B measures 20 inches, then the matching side of Polygon A measures 5 inches. This is because when an object is said to be 'x times smaller' than another, you divide the original size by 'x' to find the new size. Therefore, the matching side length of Polygon A would be 20 inches ÷ 4 = 5 inches.

Example related to area comparison between two squares: Marta has a square with a side length of 4 inches. She has another square with side lengths that are twice as long. The side length of the larger square would be 4 inches x 2 = 8 inches. Since the area of a square is the side length squared, the area of the larger square would be 8 inches x 8 inches = 64 square inches, which is 4 times the area of the smaller square (16 square inches).

The inequality 3y - 9x ≥ 9, you can start by rearranging it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Now, you can graph the line y = 3x + 3. When graphing the inequality, you will shade the region above the line, which represents the solutions to the inequality 3y - 9x ≥ 9.

To graph the inequality 3y - 9x ≥ 9, you can start by rearranging it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

3y - 9x ≥ 9

3y ≥ 9x + 9

y ≥ 3x + 3

Now, you can graph the line y = 3x + 3.

When graphing the inequality, you will shade the region above the line. The shading represents the solutions to the inequality 3y - 9x ≥ 9.

Here's how you can graph it:

Step-by-step explanation:

(1)

Let the numerator be x and denominator be y. A/Q x + y = 4 + 2x → - x + y = 4

(2)

multiplying each term by 2, 2x-2y= -8

(3)

Also, (x+3) / (y+3) = 2 / 3 → 3x - 2y = -3

Subtracting (2) from (3) → x = 5 and by putting this in (1) we can get y=9. Hence, the fraction is 5 / 9

Answer:

[tex]\frac{5}{9}[/tex]

Step-by-step explanation:

let the fraction be [tex]\frac{x}{y}[/tex], then

x + y = 2x + 4 ( subtract x from both sides )

y = x + 4 → (1)

If 3 is added to numerator and denominator, then

[tex]\frac{x+3}{y+3}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

3(x + 3) = 2(y + 3) ← distribute both sides

3x + 9 = 2y + 6 ← substitute y = x + 4

3x + 9 = 2(x + 4) + 6

3x + 9 = 2x + 8 + 6 = 2x + 14 ( subtract 2x from both sides )

x + 9 = 14 ( subtract 9 from both sides )

x = 5

Substitute x = 5 into (1)

y = 5 + 4 = 9

Hence the original fraction is [tex]\frac{5}{9}[/tex]