The denominator of a fraction is 8 more than its numerator. If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction becomes 1/2. Find the fraction

pleases help as soon as possible..thank you so much

Answers

Answer 1

Answer:

The fraction is 13/21.

Step-by-step explanation:

The denominator of a fraction is 8 more than its numerator.

Let x be the numerator: x

So the denominator is: x + 8

[tex]\frac{x}{x + 8}[/tex]

If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction becomes 1/2.

It will become:

[tex]\frac{x - 1}{x + 8 + 3} = \frac{1}{2}[/tex]

[tex]\frac{x - 1}{x + 11} = \frac{1}{2}[/tex]

Now, by using cross multiplication, multiply (x - 1) by 2 and (x+11) by 1.

It will become:

2x - 2 = x + 11

Now transpose and combine the same values. Make sure to change the integer sign. If the integer is positive, change it to negative when you transpose it.

2x - x = 11 + 2

x = 13

So the value of x is 13. Now to check if it is correct. Go back to the equation([tex]\frac{x - 1}{x + 11} = \frac{1}{2}[/tex])

Put the value of x in it.

[tex]\frac{13-1}{13+11} = \frac{1}{2}[/tex]

[tex]\frac{12}{24} = \frac{1}{2}[/tex]

12/24 is equivalent to 1/2 so that is correct.

Now, to find the main fraction. Go back to the original equation which is;

([tex]\frac{x}{x + 8}[/tex])

Put the value of x.

[tex]\frac{13}{8 + 13}[/tex]

= 13/21

Not a verified expert but I put much effort to answer your question. Hope it helps:)


Related Questions

can somebody tell me if these answers are correct?​

Answers

I think the a is right
I would handle b) like this: 8.50:12~0,7
1,55-0.7=$0,85

Is 1/3 greater than, less than, or equal to 1?​

Answers

Answer:

1/3 is less than 1

Step-by-step explanation:

3/3=1

1/3<1

Given: AB is perpendicular to BD. Find m<1
See picture for full problem. Please and thank you!

Answers

Step-by-step explanation:

angle 5 = supplementary to 89 = 180-89 = 91°

the sum of all angles in a triangle is always 180°.

so,

angle 3 = 180 - 51 - 91 = 38°

angle 2 = complementary to 38 = 90-38 = 52°

therefore,

angle 1 = 180 - 38 - 52 = 90°

I'M GIVING BRAINLIEST!!!!!!!!!!!

Answers

Answer:

i dont know

Step-by-step explanation:

MEEEEEEEEEE please

According to the scatterplot, what would you predict would be the crime index for a city with a population of 220,000? A. 450 B. 465 C. 500 D. 550

Answers

Answer:

Step-by-step explanation:

500

ANSWER ASAP PLEASE!!!!!
What is the domain of the square root function graphed below?
A. x is greater than 1
B x is greater or equal to 1
C. x is greater than 3
D. x is greater or equal to 3

Answers

Answer: the answer is D hope it helps.

Just took the test. Edge

If represents the number of entry tickets sold and the hours of space rental, which inequality represents the constraints in the situation

Answers

2000000000017827272626728182

Answer:

no question or any number or question available

plz help will mark as brainliest​

Answers

Step-by-step explanation:

18 cm is the correct answer

a break on the earth crust that is a result of movement or shaking refers to​

Answers

Answer:

A fault

Step-by-step explanation:

A fault is a crack in the Earth's crust that allows chunks of the crust to move relative to one another along its length.

Find the slope of the line that passes through each pair of points (8,2) (8, -1)

Answers

Answer:

Undefined

Step-by-step explanation:

Use the following formula to solve for slope:

[tex]\frac{y_2-y_1}{x_2-x_1} =m[/tex]

[tex]m=\frac{(-1)-2}{8-8}[/tex]

[tex]m=\frac{-3}{0}[/tex]

The equation is not a function and therefore the slope is undefined because there are multiple y values for a single x value.

Give coordinates for three possible pairs of points for the other two verticies...

Answers

Answer:

A) (-1,3) and (4,3)

B) (-1,-7) and (4,-7)

C) (1.5, .5) and (1.5, -4.5)

Step-by-step explanation:

For 1 and 2, because the y-values of the points are the same, the length of the square can be found by subtracting the x-coordinates.

4-(-1)=4+1=5

The length of the side of the square is 5.

1. For the first set of points, the square is above the two given points so just add 5 to the y-values

-2+5=3

This gives you the points:

(-1,3) and (4,3)

2. For the second set of points, the square is below the two given points so subtract 5 from the y-values.

-2-5=-7

This give you the points:

(-1,-7) and (4,-7)

3. The third answer is when the two given points are on opposite corners

of the square.

Here the diagonal is equal to 5 since they are on opposite corners of the square.

The diagonal of a square can be found with the pythagorean theorem

Since we have the diagonal we can find the side lengths we need.

[tex]2s^2=25[/tex]

s=[tex]\sqrt{\frac{25}{2} }[/tex]

s=3.5355

We want the new vertices to be in the middle of the other vertices x-coordinates

[tex]\frac{4-(-1)}{2} =\frac{5}{2} =2.5[/tex]

The new vertices will be 2.5 units away from the other vertices

-1+2.5=1.5

The new vertices will be at x=1.5

Now we need the pythagorean theorem again to find the y-values

[tex](2.5)^2+h^2=(3.5355)^2[/tex]

[tex]6.25+h^2=\frac{25}{2}[/tex]

[tex]h=\sqrt{\frac{25}{2} -6.25}[/tex]

h=2.5

The new vertices will be:

(1.5, -2+2.5)=(1., .5)

(1.5, -2-2.5)=(1.5, -4.5)

Martin charges $10 for every 5 bags of leaves he rakes. Last weekend, he raked 28 bags of leaves. How much money did he earn?

Answers

Answer:

$48

Explanation:

24 Divided by 5 = 4.8 times 10 =48

Answer:

$56

Step-by-step explanation:

$10 divided 5=$2

one bag $2

28bags=$2 multiply 28=$56

please help me with this. I will give brainliest to whoever gets the question right. attachment below.

Answers

Answer:

22100

Step-by-step explanation:

First you would add the truckloads of concrete for both playgrounds (3 5/8 + 3 5/8 + 1 9/10). Then you would divide that by 1/2. Finally multiply that number by 2000. (Pls mark me the brainliest)

Graph the line with the equation y = 6/5x-2

Answers

Answer:

Step-by-step explanation:

The graph of equation is shown in figure.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of line is,

⇒ y = 6/5x - 2

Now,

Since, The equation of line is,

⇒ y = 6/5x - 2

Clearly, The slope = 6/5

And, The y - intercept = - 2

Thus, The graph of equation is shown in figure.

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ2

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Answers

The answer is A plot the points

An arithmetic sequence is given below.
15, 19, 23 ,27 …
Write an explicit formula for the nth term an

Answers

Step-by-step explanation:

arithmetic sequence means every new term is the previous term plus a certain constant.

as we can see, this constant is +4 in our case.

15 + 4 = 19

19 + 4 = 23

23 + 4 = 27

...

so, we have

a1 = 15

a2 = a1 + 4 = 15 + 4 = 19

a3 = a2 + 4 = a1 + 4 + 4 = a1 + 2×4 = 15 + 8 = 23

...

an = an-1 + 4 = a1 + (n-1)×4 = 15 + (n-1)×4

Conor earns $9 an hour for yard work. He raked leaves one afternoon and earned $29.25.
How much does Conor earn for each minute he does yard work?
Hint: There are 60 minutes in 1 hour.

Answers

29.25 divided by 9 is 3.25. You have to take the total amount of money he made $29.25 and divide it by the amount he gets every hour $9. So 29.25 divided by 9 is 3.25 or 3 hours and 15 minutes.

Answer:

15 cents a minute

Step-by-step explanation:

9 ÷ 60 = $0.15

kate has $2.95 in quarters and nickels and the total number of ocins is 23 how many quarters and how many nickels does kat have

Answers

Answer: 9 quarters and 14 nickels

Step-by-step explanation:

9*25=225

14*5=70

225+70=295

The total number of nickels is 14 and the total number of quarters is 9 and this can be determined by forming the linear equation.

Given :

kate has $2.95 in quarters and nickels and the total number of coins is 23.

The following steps can be used in order to determine the total number of quarters and nickels Kat have:

Step 1 - Let the total number of quarters be 'x' and the total number of nickels be 'y'.

Step 2 - Remember one quarter is equal to $0.25 and one nickel is $0.05.

Step 3 - The total amount of money Kat has:

0.25x + 0.05y = 2.95  --- (1)

Step 4 - Total number of coins is given by:

x + y = 23

x = 23 - y    --- (2)

Step 5 - Substitute the value of 'x' in equation (1).

0.25(23 - y) + 0.05y = 2.95

5.75 - 0.25y + 0.05y = 2.95

2.8 = 0.20y

y = 14

Step 6 - Now, substitute the value of 'y' in equation (2).

x = 23 - 14

x = 9

So, the total number of nickels is 14 and the total number of quarters is 9.

For more information, refer to the link given below:

https://brainly.com/question/11897796

Solve for Z:

4 > 5Z + 34
help me so hard

Answers

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:  

Z  < − 6

Interval Notation:

( − ∞ , − 6 )

Step-by-step explanation:

Answer:

z<-6

Step-by-step explanation:

4-5Z>34

-5z>34-4

-5z>30

z<-6

please I need immediate help ​

Answers

Answer:

sorry what? the photo is not clear

Step-by-step explanation:

dude the photo

plz brainliest

Whos gonna help you in the exam?

I’ll give brainliest, thanks and 5 stars.

Answers

Answer:

First, you can break 6 into 3 * 2.

[tex]\frac{6^4*15^3}{3^3*2^4} =\frac{3^4*2^4*15^3}{3^3*2^4}[/tex]

Then, cancel out the common factor of [tex]3^3[/tex]:

[tex]\frac{3^4*2^4*15^3}{3^3*2^4} =\frac{3*2^4*15^3}{2^4}[/tex]

Next, cancel out the common factor of [tex]2^4[/tex].

[tex]\frac{3*2^4*15^3}{2^4} =3*15^3[/tex]

You can evaluate it as 10125 if you'd like.

Describe the steps you used to solve the equation and
find the amount of Carrie's allowance.
Linear
equation: 1/4 a + 1/3 a+ 8 = 22

Answers

Answer: 22

Step-by-step explanation: 1/4a + 1/3a + 8 = 22

Answer:

Sample Response: First, the like terms had to be combined using the lowest common denominator (LCD). Then the subtraction property of equality was used to isolate the variable term. Finally, both sides of the equation were multiplied by the reciprocal of the coefficient to solve for a.

Step-by-step explanation:

Find the inverse function in slope-intercept form (mx+b):
f(x) = -x - 5

Answers

Answer:

In order to find the inverse of a function, we flip it over the line y=x, or we switch the x and y values in the equation and solve it for y. So let's do the latter:

m(x) = 5x - 5

y = 5x - 5

x = 5y - 5

5y = x + 5

y = (x + 5)/5

Step-by-step explanation:

hope this is helpful

Answer: f ^−1(x)=x+5

The (least common multiple, greatest common factor) of 5 and 10 is 5.

Answers

Answer:

the Greatest common factor is 5

Zach goes on holiday. The ratio of the costsflights: hotels = 3 : 8. The cost of the flightsis $861. Workout the total cost of flightsand hotels.

Answers

total cost of the hotels is 2,296

Answer:

hahshdbdndjksosondndndud

I need help with my Geometry. Can you help?
Thanks.​

Answers

Answer:

  1.  32 units

  2.  C(-15, -4) and D(17, -4)

Step-by-step explanation:

1.

The midpoint divides CD into two segments that are the same length:

  CM = MD

  8(x -2) = 4(5x -16)

  8x -16 = 20x -64 . . . eliminate parentheses

  48 = 12x . . . . . . . . . add 64 -8x

  x = 4 . . . . . . . . . . . divide by 12

Then the length of CD is ...

  CD = 2·CM = 2(8(x -2)) = 2(8(4-2))

  CD = 32

__

2.

If we put C and D on the same horizontal line as M, their coordinates are ...

  C = M -(16, 0) = (1,-4) -(16, 0) = (-15, -4)

  D = M +(16, 0) = (1, -4) +(16, 0) = (17, -4)

Coordinates C and D that have M(1, -4) as a midpoint are ...

  C(-15, -4) and D(17, -4).

Please help me!!!!!!

Answers

Answer:

do you know what the question is asking?

Step-by-step explanation:

7+(4x8)-9
i need help this is weird

Answers

Answer:

30

Step-by-step explanation:

7+(4*8)-9

Multiply first inside the parentheses

7+(32)-9

Then add and subtract from left to right

39 - 9

30

Answer:

If x is a variable then the answer is 4x⁸ - 2

If x is a multiplication representation then the answer is 30

Step-by-step explanation:

If x is a variable:

1) Eliminate redundant parentheses

[tex]7+(4x^{8} )-9\\7+4x^{8} -9[/tex]

2) Subtract the numbers

[tex]7+4x^{8} -9\\-2+4x^{8}[/tex]

3) Rearrange Terms

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

PLEASE HELP IT’S DUE TMR!!

Answers

4856

1.07

12.9

7.00

0.00199 (199)

0.000660 (660)

:)

the distance between town A and town B is 123 km. Two buses begin their journey and move directly toward each other. From town A, the bus is moving at a speed of 45 km/hr and from town B, the bus is moving at a speed of 67 km/hr. Assuming the buses started at the same time, find how far is their meeting point from town A? ​

Answers

Answer:

Speed of slower bus = 50mph and

speed of faster bus = 60 mph

Step-by-step explanation:

Let speed of first bus be x mph

Then speed of second bus = x+10 mph.

Let A and B have a distance d.

Then given that faster bus reached in 3.5 hours.

i.e.  ... i

THe other bus was away from B by 1/6 times d.

Distance travelled by slower bus = 1-1/6 = 5d/6  

Time taken = 3.5 hours

i.e.  ... ii

Divide i by ii to eliminate d.

ie Speed of slower bus = 50mph and

speed of faster bus = 60 mph

Use ii equation

miles

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