19. The numerator of a fraction is 1 less than the denominator.
When both numerator and denominator are increased by 2,
the fraction is increased by 1/12Find the original fraction.

Answers

Answer 1

Let the original fraction be

[tex]\dfrac{n-1}{n}[/tex]

Now let's increase both numerator and denominator by 2:

[tex]\dfrac{n+1}{n+2}[/tex]

This produces a 1/12 increase:

[tex]\dfrac{n+1}{n+2}-\dfrac{n-1}{n}=\dfrac{1}{12}[/tex]

The left hand side can be rearranged as

[tex]\dfrac{2}{n^2+2n}=\dfrac{1}{12}[/tex]

Invert both sides:

[tex]\dfrac{n^2+2n}{2}=12 \iff n^2+2n=24[/tex]

Solve the quadratic equation:

[tex]n^2+2n-24=0 \iff n=-6 \lor n=4[/tex]

So, in the first case, the original fraction is

[tex]\dfrac{n-1}{n}=\dfrac{-6-1}{-6}=\dfrac{7}{6}[/tex]

In the second case, we have

[tex]\dfrac{n-1}{n}=\dfrac{4-1}{4}=\dfrac{3}{4}[/tex]


Related Questions

Write an expression to describe a number x increased by 10

Answers

Answer:

x+10

Step-by-step explanation:

increased = + so x+10

HOpe this helps plz hit the crown :D

answer please !!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!

Answers

Answer:

x = 67

Step-by-step explanation:

180 - 113 = 67

Answer:

x=67 degrees

Step-by-step explanation:

113+x=180--->linear pair

x=67--->subtractioin property

15 – (3 + 4) + 7 x 2 – 3 2

Answers

Answer:

-10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Step-by-step explanation:

Step 1: Define

15 - (3 + 4) + 7 × 2 - 32

Step 2: Evaluate

(Parenthesis) Add:                    15 - 7 + 7 × 2 - 32Multiply:                                     15 - 7 + 14 - 32Subtract:                                    8 + 14 - 32Add:                                           22 - 32Subtract:                                    -10

someone help me please

Answers

Answer:

The answer is B

Step-by-step explanation:

The solution is -3 by the way

Can somebody please help me with this question

Answers

Answer:

B

Step-by-step explanation:

triangle RST is translated 6 units to the left and 4 units up to create triangle R'S'T'.

Answers

Answer: (x,y) —> (x-6, y+4)

Step-by-step explanation:

Answer:

(x,y) —> (x-6, y+4)

Step-by-step explanation:

:)

Blockbuster Video charges $3 to a rent a video, plus an additional $2 for every day that the video is late. Which equation can be used to represent the fee that a customer pays for the video based on the number of days that the video is late?
y = 3 + 2
y = 3x + 2x
y = 2x + 3
y = 3x + 2
y = 3(2x)

Answers

Answer:

y=2x+3

Step-by-step explanation:

the normal charge is 3 + 2 x number of days so this equation is the correct one.

12x + 10x what is the awnser

Answers

Answer:

22x?

Step-by-step explanation:

is there more to this question? if not its just simple addition and then add "x" at the end

Madeline drives 15 miles in 12 minutes. If she drove three hours in total at the same rate, how far did she go?
Before you try that problem, answer the question below.
How many minutes did Madeline drive in total?

Answers

Answer:

225 miles in total

Step-by-step explanation:

At Irtaza's Deli he is selling 7 oranges for $5.99 and Brianna's Food Mart is selling them 10 for $8.99. Where would you go shopping and why?

Answers

Answer:

At Irtaza's Deli

Step-by-step explanation:

For this you should find the unit price and whichever is less is where you should go.

(1) Irtaza Deli:

First I would round the 5.99 to 6 then we'll do 6 divided by 7.

[tex]\frac{6}{7}=.8571428571=.86[/tex]

(2) Brianna's Food Mart:

First I would round the 8.99 to 9 then we'll do 9 divided by 10.

[tex]\frac{9}{10}=.9[/tex]

Now let's compare:

So the first store sells oranges for $.86 and the second store sells them for $.90. I don't know about you but I would go to the first store they would be much more cheaper.

A term without a variable is called what?

Answers

Answer:

constants

are the term

Answer:

Constants

Step-by-step explanation:

I hope this is correct and have a great day

Avril wrote the expression 4(x + 3) to represent the area of a rectangle. Which expression is an equivalent representation of the area?
А
4x + 3
B
x(4+3)
С
4x + 12
D
3(x + 4)

Answers

Answer:

It is 4x + 12

4x + 12

expand the bracket :
4 * x = 4x
4*3= 12
4x+12

a rectangular prism is 5 in Long 8 inch wide and 10 inches tall what is the length of its longest diagonal ​

Answers

480
Step-by-step explanation:
If you take length times width times height so it'll be 8 times 10 = 80 times 6 =480


I hope this helps!

In comparison to 2/3 where would 4/6 on number line

Answers

The answer is the same place. I have the same answer as the one above

The fraction numbers 2/3 and 4/6 will lie on the same point on the number line.

What is a number line?

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The fraction numbers are given below.

2/3 and 4/6

Convert the fraction into the simplest fraction, then we have

4 / 6 = 2 / 3

The fraction numbers 2/3 and 4/6 will lie on the same point on the number line.

More about the number line link is given below.

https://brainly.com/question/13189025

#SPJ5

The point-slope form of a line that has a slope of 3 and passes through point (6, 0) is shown below. ​

Answers

Answer:

Step-by-step explanation:

its the second one

u gotta add zero to the other side to isolate the y which would give you

y = [tex]\frac{2}{3}[/tex]x - 6

I hope this helps :)

Lavinia is standing at point A(4,8, 2). This is the starting point of a mountain hike. The end of the hike is at point B(6, 12, 10). There is a rest stop half way between A and B.

1. Find the coordinates of the rest stop.
2. Find the total distance from A to B.

Answers

Answer:

Question 1: b) Find the total distance from A to B

Distance formula:

d=Square root of (x2-x1)^2+(y2-y1)^2+(z2-z1)^2

d=Square root of (6-4)^2+(12-8)^2+(10-2)^2

d= 9.165 = 9.17 units

Answer:

1 a

Use the midpoint formula:

m=x1+x2/2, y1+y2/2, z1+z2/2

m= 4+6/2 ,8+12/2, 2+10/2

m= (5 ,10, 6)

Step-by-step explanation:

A rectangular sandbox is surrounded on all sides by a strip of grass that is 5 ft wide on all sides. The length of the sandbox is 4 ft more then width, and the total area for the sandbox and the grass is 189 square feet. Find the dimensions of the sandbox.

Answers

Answer:

Dimensions:

Length = 13.256m

width = 9.256m

Step-by-step explanation:

Let the length of the sandbox be = l and its width be = w

The length of the sandbox is 4 ft more than the width.

This means that  [tex]l = 4 + w[/tex] ----- equation 1

For the next step, we will be assuming that the strip of grass is a perfect rectangle. The length of the grass strip will be equals to the length of the sandbox.

Area of the grass =  length X width = [tex](4 +w) \times 5= 5(4+w)[/tex]------ equation 2

The total area for the sandbox and the grass is 189 square feet.

This means that

[tex](w \times (4+w)) + 5(4+w)=189\\w^2+4w+20+5w=189\\w^2+9w-169=0\\w=9.256m[/tex]

(Kindly note that the positive value for the width was chosen as length cannot be negative).

Now that we have our width, we can put this into equation 1 to get the length.

[tex]l=9.256+4=13.256m[/tex]

PLS HELP WILL GIVE BRANLIEST PLUS 15 POINTS

Answers

The answer is B since he bought 4 in all it is x+y =4 . x=dvd y= blue ray discs .

so 2x + 5y =11
2x since dvds are $2
5y since blue ray discs are $5
11 since that’s the total

Two more than 16 times a number is the same as 21
less than the product of -7 and the number.
Please show your work thank you

Answers

Answer:

2*16n = 21 -7n

Step-by-step explanation:

hope this helps :)

what are the like terms in this exspression 9a-3b + 4ab

Answers

Answer:

none of these terms are like terms

Answer:

there is  no like terms in this expression

Step-by-step explanation:

there is "a", "b" and "ab"

you cant combine anything because they are all different

Hope this helps!!

PLZ HELP ITS URGENTTTT FIRST TO ANSWER WILL BE BRAINLIEST
3x³y²/9xypower 5

Answers

The answer is x^2/3y^3 hopefully this is correct
Uhhhh I never learned this

Approximately 60 percent of municipal solid waste in the United States is composed of some form of organic matter that could be composted. Every American generates approximately 2 kg of waste every day. The amount of compostable waste that could be generated by one individual in a week would be closest to

Answers

Answer:

8.4 kg

Step-by-step explanation:

First, find how much waste is created in a week:

Multiply 2 by 7, since they create 2 kg of waste each day:

2(7)

= 14 kg

Then, find 60% of this:

Multiply 14 by 0.6:

14(0.6)

= 8.4

So, the amount of compostable waste created by 1 person in a week is approximately 8.4 kg

The amount of compostable waste that could be generated by one individual in a week would be closest to 8.4kg.

Amount of compostable waste:

Using this formula
Compostable waste amount=Kg of waste× Number of days in a week× Municipal solid waste percentage

Where:
Kg of waste=2kg

Number of days in a week=7 days

Municipal solid waste percentage=60% or 0.60

Let plug in the formula

Compostable waste amount=2kg×7 days×0.60

Compostable waste amount=8.4 kg

Inconclusion the amount of compostable waste that could be generated by one individual in a week would be closest to 8.4kg.

Learn more about compostable waste here:https://brainly.com/question/25342752

Marin spends 28% of her monthly income for a Loan payment. her loan payment is rupees 1,736. What is her monthly income?

Answers

Answer:

6200 rupees

Step-by-step explanation:

Think the monthly income x

According to the question

The equation is

x×28%=1736

x×28/100=1736

x=1736÷28/100

x=1736×100/28

x=62×100

x=6200

So monthly income is 6200 rupees

Answer:

[tex]6200\ Rupees[/tex]

Step-by-step explanation:

[tex]We\ are\ given\ that,\\Percent\ of\ salary\ Marin\ spends\ for\ her\ loans=28 \% \\Amount\ of\ total\ payment\ on\ the\ loans= 1736\ rupees\\Hence,\\Let\ her\ monthly\ income\ be\ x\\Hence,\\The\ question\ also\ tells\ us\ that:\\28 \%\ of\ Marin's\ Monthly\ Income= Loan\ Payment\\Or,\\28 \%\ of\ x=1736\\Hence\ as\ 28 \%\ can\ also\ be\ represented\ as: \frac{28}{100},\\\frac{28}{100}*x=1736\\Hence\ by\ multiplying\ the\ LHS\ and\ RHS\ with\ \frac{100}{28},\\[/tex]

[tex]\frac{28}{100}*\frac{100}{28}*x=1736*\frac{100}{28}\\Hence,\\x=62*100\\x=6200\\[/tex]

Tollowing:
a)
3x + 4 = 9.5
7 + 2x =
b)
= 5

Answers

See attachment for math work and answer.

*BRAINIEST & 25 POINTS*

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

m<R = 65

Step-by-step explanation:

m<R + m<S + m<T = 180° (sum of interior angles in a triangle)

(5x - 11) + (3x - 3) + (3x + 18) = 180°

Solve for x.

5x - 11 + 3x - 3 + 3x + 18 = 180

Add like terms

11x + 4 = 180

11x = 180 - 4

11x = 176

x = 16

m<R = (5x - 11)

Plug in the value of x

m<R = 5(13) - 11

m<R = 65

a= -3i
g=2i - 1lj
Find: -a - g

Answers

Answer:

Step-by-step explanation:

Given:

a= -3i

g=2i - 1lj

Solve:

-a - g

If l is an L then

-(-3i) - (2i-1lj)

i + lj

If I is an i then

-(-3i) - (2i-1ij)

i + ji

A building has 17 floors of offices above ground and 5 floors below ground. Kaylea parks on the 4th floor below ground and has an office on the 15th floor. The ground floor is zero. How many floors must she go up from her car to her office?

Answers

Answer:

19 floors

Step-by-step explanation:

Let us consider the ground floor as 0 and the floors above it as positive and the floors below the ground floor as negative.

So, the floor in which she parked is -4 and the floor where her office is at +15.

The number of floors she has to climb is the absolute value of the difference of the two floors.

The number of floors she has to go up is [tex]|-4-15|=19[/tex].

Find the measure of each exterior angle of the regular polygon.

Answers

Answer:

30°

Step-by-step explanation:

Sum of exterior angles of the regular polygon is 360°

The pictured is 12-gon

Each exterior angle measures:

360°/12 = 30°

Answer:

30 degrees

Step-by-step explanation:

(Sum=360)

360/12=30

(We got 12 because there are 12 sides in the polygon!)

Three bakers can each bake three
cakes in three hours. How many cakes can
8 bakers bake working at the same rate in
20 hours? Use the solve a simpler problem
strategy.

Answers

Answer:

i think its 20 cakes

Step-by-step explanation:

1 cake per hour

Solve x−5≥1. please help me quick

Answers

Answer:

x greater than or equal to 6

[6, infinity)

Step-by-step explanation:

x-5+5 greater than or equal to 1+5

Step-by-step explanation:

x=6

[tex]x - 5 \geqslant 1[/tex]

[tex]x - 5 + 5 \geqslant 1 + 5 [/tex]

[tex]x \geqslant 6[/tex]

Other Questions
(3.5x10^5)x(4x10^-3)=exponent form From top to bottom, what is the correct order of the social structure of ancient Egypt?Pharaoh, Scribes, Priests, Merchants, FarmersPharaoh, Priests, Scribes, Merchants, Farmers plz help me this is due and thank you1. Jordan loves creating short films using his phone camera and small posable figures. He has learned how to edit the videos so that it looks as if the figures are alive and moving! What possible career paths might Jordan want to consider for his future? Explain.2. What important services do journalists and broadcasters perform for our community? Give one example of a situation where journalists or broadcasters are helpful.3. What quality might be important for someone who works in the Performing Arts pathway of the Arts, A/V Technology, and Communication career cluster? List three specific careers in that pathway and explain how the quality you chose would be important to have in order to succeed in each career.4. Josh began his career as the front desk clerk of a large hotel. He enjoys working in the Lodging pathway of the Hospitality and Tourism career cluster and plans to take more classes in hospitality and business. After finishing his education, what positions might be available to Josh along his career path?5. Kylie lives near a beautiful beach and has grown up surfing the waves. Many families come to visit her area and Kylie has noticed that visiting children are rarely successful when they try to surf. Taking advantage of her location and experience, what kind of service in the Hospitality and Tourism career cluster might Kylie think of offering, and why? All of the points in the picture are on the same line Describe how to find the inverse of the function.To find the inverse of the function, change f(x) to y, switch and y, and solve for . The resulting function can be written as , where . A rectangular lawn measures 6m by 10m. Angela is planning a mulch walkway of width "x" around the entire edge of the lawn. Write a function that represents the area of the lawn combined with the area of the walkway. How do you pay for stuff and what do you pay for? (What is the basis for your economy?) (Bartering & trade, coins/commerce, taxes, free market, command, etc.) Enter the coordinates of the pointon the unit circle at the given angle.45 [?]22 How original were Newtons contributions to science? (In what ways did Newton depend on the mechanical view?) Question 6In which of the following lists of mixed economies does the free market system dominate?CubaGreece, China, United StatesNorth Korea, France, South AfricaUnited States United Kingdom, Singapore, CanadaRussia, Peru, France, Canada Techniques used to rank individuals according to social class are a. reputational. c. objective. b. subjective. d. all of the above Please select the best answer from the choices provided A B C D Question 2 (1 point) These allow electricity to flow easily through them (think copper and aluminum). (Lessons 5.01-5.03) Electric Currents Resistors Conductors Insulators Which of the tables represents a function?Table AInput Output5 35 24 1Table BInput Output1 23 25 3Table CInput Output0 01 21 3Table DInput Output4 24 34 4(5 points)Table ATable BTable C neon, a monatomic gas, that starts out at conditions of standard temperature and pressure (273.15 K, 105 Pa). Alice heats the gas at constant volume until its pressure is doubled, then Bob further heats the gas at constant pressure until its volume is doubled. If Alice and Bob assume that neon behaves as an ideal gas, then how much heat have they added to the gas for the entire process. Decide whether the meaning is correct or incorrect as written.nosotros = wecorrectincorrect On average, Americans have lived in 4 places by the time they are 18 years old. Is this average a different number for college students? The 50 randomly selected college students who answered the survey question had lived in an average of 3.79 places by the time they were 18 years old. The standard deviation for the survey group was 1.2. What can be concluded at the = 0.10 level of significance? substitute =3in the following equation to find y5y - 2x=9 What did the Inca believe about their rulers?they could turn common elements into goldthey were descended from the Maya in Mesoamericathey were descended from the gods and never truly diedthey could not be defeated in battle with their enemies Which of the following verbs has an irregular yo form?A. ComerB. ConducirC. VivirD. Hablar Which of the following is an extended definition of shenanigans?