Prove: The difference of the reciprocals
of two successive integers equals the
product of their reciprocals.
1
1
-
n
n + 1
[?]
n(n + 1)
[ ].[
n n+1

Answers

Answer 1

Step-by-step explanation:

let two successive integers n, n+1

difference of the reciprocals:

[tex]\frac{1}{n}-\frac{1}{n+1} \\=\frac{(n+1)-n}{(n)(n+1)}\\=\frac{1}{(n)(n+1)}\\=\frac{1}{(n)}\frac{1}{(n+1)}\\[/tex]


Related Questions

10 ft
8 ft
Help Resources
Skip
6 ft
Find the outer perimeter of this figure.
Round your answer to the nearest
hundredth. Use 3.14 to approximate a.
P = [?] ft
Notice that only half of the circle is included in the figure!
Enter

Answers

Answer:

P=28.56 ft

Step-by-step explanation:

P= Side1 +Side2 + 0.5 circle

P=10+6+ πDiam/2=16+4π=28.56 ft

Answer:

28.56ft

Step-by-step explanation:

The side lengths of a triangle are 9, 12, and 15. Is this a right triangle?

Answers

Answer:

Step-by-step explanation:

Those are the side lengths not the angles so I'm not sure, also are you sure that's right? I believe there has to be a hypotenuse and the hypotenuse is the sum of the two shorter sides added together.

Do you have any more information? I can try to help :)

Answer:

Yes, because 9^2+12^2>15^2

Step-by-step explanation:

Ap3x

What is the angle of AHM?

Answers

154 degrees; when you add up the two angles you get 154 subtract that from 180 which is the sum of a triangle. You should get 26 for the third angle of the triangle. when you extend the segment if MH you form an X the acute angle of the X are 26 to find H you subtract 26 from 180 since a straight line is 180 and you get 154 for the abtuse angles which is also H
154 degrees i had this question before

When simplifying radical expressions, what combination of factors are you looking for and why?​

Answers

Before we can simplify a radical expression, we must know the important ... The idea here is to find a perfect square factor of the radicand, write the radicand as a ... Sometimes we need to use a combination of steps.

there are 3 consecutive even integers. three times the smallest is twice the largest. what are the integers

100 poi's SOLVE FAST PLZ AND I WILL GIVE BRAINLEITS I PORMISE

Answers

Answer:

8,10,12

Step-by-step explanation:

Answer:

integer 1 = 8

integer 2 = x+2 = 8+2 = 10

integer 3 = x+4 = 8+4 = 12

Step-by-step explanation:

integer 1 = x , smallest

integer 2 = y , x+12

integer 3 = z , largest, x+4

three times the smallest is twice the largest.

3 (x) = 2 (x+4)

solve for x:

3x = 2x + 8

3x-2x = 8

x = 8

Replacing:

integer 1 = 8

integer 2 = x+2 = 8+2 = 10

integer 3 = x+4 = 8+4 = 12

What is the least common denominator of 11/14 and 11/15

Answers

Answer:

210

Step-by-step explanation:

210 is the least common multiple of 14 and 15

Find the area of sector TOP in
O using the information given below.
r=9m, mTP=189

Answers

Answer:

I believe that the answer is 1701 m² sorry if don't get it right

PLEASE HELP I WILL GIVE BRAINLIEST!!

Answers

Answer:

43.96

Step-by-step explanation:

To find Circumference the formula is

2*3.14*R=C

replace R with your radious which is 7

2*3.14*7=43.96

Two years ago, the average number of customers in your all of your company's stores per week was 3173 customers. This figure had increased 6% over the previous two years. Assume that you are doing a current study to test the claim that the mean weekly number of customers is different than it was two years ago. Assume a population standard deviation of 1,550 customers. Suppose you look at a random sample of 73 stores and find an average weekly customer total of 3,391. You wish to test the claim stated above at the 0.10 level. Run the appropriate hypothesis test.

Required:
Write ONLY the conclusion to your hypothesis test.

Answers

Answer:

Accept the null hypothesis

Step-by-step explanation:

Two years ago, the average number of customers in your all of your company's stores per week was 3173 customers. Assume that you are doing a current study to test the claim that the mean weekly number of customers is different than it was two years ago.

The null hypothesis is:

[tex]H_{0} = 3173[/tex]

The alternate hypothesis is:

[tex]H_{A} \neq 3173[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

Due to our test, we have that [tex]\mu = 3173[/tex]

Assume a population standard deviation of 1,550 customers.

This means that [tex]\sigma = 1550[/tex]

Suppose you look at a random sample of 73 stores and find an average weekly customer total of 3,391.

This means that [tex]n = 73, X = 3391[/tex]

Test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{3391 - 3173}{\frac{1550}{\sqrt{73}}}[/tex]

[tex]z = 1.24[/tex]

p-value:

Since we are testing if the mean is different of a value, and the z-score is positive, the pvalue is 2 multiplied by 1 subtracted by the pvalue of z = 1.24.

z = 1.24 has a pvalue of 0.9251

2*(1 - 0.9251) = 2*0.0749 = 0.1498

0.1498 > 0.1, which means that we accept the null hypothesis, that is, that the mean weekly number of customers is equal to what it was two years ago at the 0.1 level of significance.

Find the value of x.
(Do not include the degree symbol in your answer. Round to the nearest degree as needed)

Answers

Answer:

X = 49.4

Step-by-step explanation:

Tan x = 7/6

Tan x = 1.1667

X = 49.4 degrees

Given the same figure as in the previous question, what is BC?

Answers

Answer:

using Thales theorem, we have:

[tex] \frac{17}{bc} = \frac{12}{12 + 8} \\ < = > \frac{17}{bc} = \frac{12}{20} = \frac{3}{5} \\ \\ < = > bc = \frac{17 \times 5}{3} = \frac{85}{3} = 28.3[/tex]

=> BC = 28 feet 4 inches

A single person earns a gross biweekly salary of $780 and claims 6 exemptions. How does their net pay change due to the federal income tax withheld?

Answers

No federal income taxes are withheld.

You do not have any pay any federal income tax withheld. If your biweekly income is $780 then I'm assuming your monthly income should be doubled which is $1560, so in this income, you to pay only FICA tax worth $119.

What is federal income tax?

The federal income tax is a tax on annual earnings. All wages like salaries, cash gifts from employers, business income, even tips, income from gambling, bonuses and unemployment benefits are subjected to a federal income tax.

What is FICA tax?

FICA is a payroll tax that stands for Federal Insurance Contributions Act and is deducted from each paycheck.

Learn more about Income Tax here

https://brainly.com/question/1775528

#SPJ2

someone please help on this homework question

Answers

Answer:

25%, 40 trees, 50%, 36 trees

What is the distance between the points (2, 3) and (5, -4)?
7.6 units
6.3 units
3.7 units
10 units

Answers

Answer:

7.6 units

Step-by-step explanation:

d=(5−2)2+(−4−3)2−−−−−−−−−−−−−−−−√

d=(3)2+(−7)2−−−−−−−−−−√

d=9+49−−−−−√

d=5–√8

d=7.615773

Write an expression to describe the sequence below. Use n to represent the position of a
term in the sequence, where n = 1 for the first term.
11, 12, 13, 14, ...

Answers

Answer:

n+10

Step-by-step explanation:

This is applicable because if you plug in the numbers it will work for example. -

what sequence is 12 in, it is the second number so n=2

so add 10 to 2 which is 12

So as seen the answer is n+10

thanks and mark me brainliest


please i will mark you brill help me

Answers

Answer:

2n + 20

Step-by-step explanation:

2n + 20

2 times anything doubles it, then you are adding 20. An expression doesn’t have an equal sign (equations do)

39. Find the circumference of a circle with radius of 18 in. Leave your answer in terms of pi
324pi In.
54pi in
36pi in.
18pi in.

Answers

Answer:

36pi

Step-by-step explanation:

multiply the radius by 2 to get 36 but dont multiply by pi just put 16π

Answer:

36pi in

Step-by-step explanation:

I figured out what was wrong thanks to the comment up top.

they just want the diameter why didnt they say that :/

Find the equation of the line with slope m=−12 that contains the point (2,−4).

Answers

Answer:

y=-12x+20

Step-by-step explanation:

-4=-12(2) +b

-4=24+b

(add 24 both sides)

20=b

slope: -12

y intercept: (0,20)

Answer:

y + 4 = -12(x - 2)

Step-by-step explanation:

Use the point-slope formula for the equation of a straight line:

y - k = m(x - h)

Here m = -12, h = 2 and k = -4, and so we have:

y + 4 = -12(x - 2)

If represents 14 people, how many people would be represented by ? 21 people 14 people 7 people 28 people

Answers

Answer:

Answer is 28

Step-by-step explanation:

14+14=28

Answer:

Your answer is 28. I'm sure of it =D

Step-by-step explanation:

Each unit on the grid below represents 1 cm. Find the height of the arrow on a rescaled drawing using the scale 1cm= 0.5 m.

Answers

Answer:

8

Step-by-step explanation:

add them duh

One has $1000 in his bank account to use for education after high school he spends 3% of this amount every month how much money does he have in his account every month

Answers

Answer:

Every month, he will spend $30 of his $1000.

Step-by-step explanation:

The first thing I did was found out 3% of 1000. To do this, you need to move the decimal point in 3% over twice. Like this:

3 → .03

Then, multiply 1000 by .03.

1000 * .03 = 30

So, this means that he will spend $30 of his money each month.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Hope this helped, and good luck on your school !! Also, can ya please mark me brainliest, cause I spent 2 hours last night (At like 11:00pm) working on these questions to get the expert title. Now, all I need is one more brainliest title. If you don't do that, it's fine! Hope you have a wonderful day~ !

I need help pls and sorry there is an answer marked it’s because by accident I press it but pls help me

Answers

Answer:

2

Step-by-step explanation:

because the outer line is one line and the triangle in other line

Answer:

3

Step-by-step explanation:

There is a line of symmetry from each vertex of the triangle through the square opposite it. I can't draw it out here but there's one going straight down the middle, another going from the triangles leftmost point through the right hand square and another from the triangles rightmost point through the left hand square.

0.5 divided by 0.05 plz show work

Answers

Answer:

Step-by-step explanation:

Answer: 10

working below!

The function f(3) = 50.000(0.975)", where x represents the underwater
depth in meters, models the intensity of light below the water's surface in lumens per
square meter. What is the intensity of light 200 meters below the surface

Answers

9514 1404 393

Answer:

  316 lumens/m²

Step-by-step explanation:

We assume your intensity function is ...

  f(x) = 50,000(0.975^x) . . . . x meters below the surface

__

Use 200 for x and do the arithmetic.

  f(200) = 50,000(0.975^200) ≈ 316 . . . . lumens/m²

The student council starts the year with a balance of $-15 (they were in debt). It comes up with the idea to sell tickets to a student versus teacher mud fight. The student council fund is now growing by $15 a minute.

1. After 9 minutes of mud fight ticket sales, what was the balance?
2. How many minutes did it take before the student council was able to pay off their debt?

Answers

Answer:

sorry di ko din po knows

Step-by-step explanation:

sorry tagala

Answer:

1. Is 12

Step-by-step explanation:

start -15

tickets $15

min 9

remember you started -15 so the first 15 got you into positive so that one doesnt count wich means you now have to miltiply 15*8=120


Rewrite the equation by completing the square.
x2 + 7x + 12 = 0

Answers

Answer:

9x²+12=0

Step-by-step explanation:

Which number equals 9x 100+9* 10+0+1+0
A.900.937
B.909.307
C990.0037
D9090.0037​

Answers

Answer:

pretty sure its c

Step-by-step explanation:

What is the mean absolute value of the data set below? pls answer ASAP

Answers

The mean is 17.
U put the values in order which they already are and then u add them all up and divide by home many numbers there are in the data set
10+12+15+18+30/5

What is the solution set for (2x-7)^2=25

Answers

The solution set for the quadratic equation (2x - 7)² = 25 is 6 and 1.

What is a quadratic equaton?

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

The solution set for a quadratic equation is the roots of the quadratic equation.

Given, (2x - 7)² = 25.

2x - 7 = ± 5.

2x = ± 5 + 7.

x = (± 5 + 7)/2.

x = 12/2 Or 2/2.

x = 6 or 1.

learn more about quadratic equations here :

https://brainly.com/question/11589380

#SPJ2

Am bad at math I don’t get this

Answers

Answer:

x=35 y=18

Step-by-step explanation:

We have two triangles. These triangles are Similar as stated in the statement. Since they are similar, there side length will be in proportion.

To find x and y we need to set up a proportion of the corresponding sides of the triangles.

Let find the corresponding sides of both triangle.

JK corresponds with NM

KL corresponds with ML

JL corresponds with NL

To find side x we can use this proportion

JK/KL=NM/ML

Plug in the lengths

[tex] \frac{40}{kl} = \frac{16}{14} [/tex]

Cross multiply

[tex]560 = 16kl[/tex]

Divide by 16

[tex]kl = 35[/tex]

so x=35

Now to find y use this proportion

JL/JK=LN/NM

[tex] \frac{45}{40} = \frac{y}{16} [/tex]

Cross multiply

[tex]720 = 40y[/tex]

[tex]y = 18[/tex]

Answer:

X = 35

Y = 18

Step-by-step explanation:

The triangles are similar meaning that they are scaled up and down differently. ( and in this case rotated) Notice the shape of the triangles. The side measuring 40 in the larger triangle correlates to the side measuring 16 in the smaller triangle. We can use this to find the scale difference between the two triangles. 40/16 = 2.5. The larger triangle is scaled up 2.5 times the smaller triangle. X correlates to the side measuring 14. Scale 14 up 2.5 times. 14* 2.5 = 35, so x= 35.

Y correlates to the side measuring 45. Scale 45 down 2.5 times. 45/2.5 = 18. Y = 18

Other Questions
A drawer contains 4 $20 bills, 2 $10 bills, 6 $5 bills, and 13 one- dollar bills. If one bill is selected at random, what is the probability that it is a $20 bill? Round to 4 decimal places. Which statement shows the associative property of addition? (+7)+ 13 = U+ (7 + 13) 21+2y=2y+21 if m+ 3 = 18 then 18 = m + 3 what is commercial bank? in your own words. points on why public schools is better than private school Why does Sam want to be cremated in The Cremation of Sam McGee? Check up 1 write an expression for the area of the gym. Write an expression for the area of the cafeteria. Write an expression for the total area of the gym and cafeteria. Write an expression for the total perimeter of the gym and cafeteria. A car travels a distance of 150 m in the direction of a constant force of 50 N. The work done on the car is In 2-3 complete sentences, explainhow Alice Walker's SETTING influenced herwriting. Which of the following examples demonstrates heat transfer through radiation?A.Boiling water on a stove.B.IAA heater blowing air into a room.C.IAA hamburger cooking on a grill.D.The sun heating up a pool. can you help please I have a lot more questions like this. In hockey, Ed makes 7 goals for every 10 shots. If he takes 6 shots, what is the probability that he will make at least 5 goals? hi please help me with this angles work for math class find the arc length semicircle 10 What factors led to the decline of villages across Europe during the Middle Ages?a. bird flu and locustsb. the plaguec. the Great Famined. the Great Famine and the plague giving brainliest *easy* A squirrel runs at a steady rate of 0.51 m/s in a circular path around a tree. If the squirrel's centripetal acceleration is 0.43 m/s 2 , what is the radius of the circle? A farmer had 90 black sheep and 10 white ones. What fraction of the flock is black? It is paragraph: It is urgent plz help!!In 2011, the population of the world reached seven billion people. The UN Population Division (2015) predicts the number could be as high as 9.7 billion by 2050; that is an extra two billion peoplethe same number of people who currently reside in the African and American continents combined-living on Earth using its resources to survive. This is hard to conceive. 2 Although families are getting smaller, people are living longer because medical and technical advances have lessened the impact of infectious disease. As a result, the UN's worst case scenario for 2100 is that the world population will reach almost 16 billion (UN, 2011). That is more than twice the number of people we have today. And yet already we are placing undue pressure on the Earth. The kind of pressure that, if increased, could have a profound and irreparable effect on our planet.The first fundamental issue is water. Just 2.5% of the world's water is fresh, with much of that caught up in polar ice caps (University of Michigan, 2000). Drought and poor infrastructure mean that already today water is a scarce resource. Over seven hundred million people lack access to clean water (WHO, 2013) and one in three people in every continent do not have enough water to satisfy their daily needs (WHO, 2009). Without clean drinking water, there will be an exponential increase in the incidence of diseases such as cholera and typhoid, which will undoubtedly place an excessive strain on healthcare systems. Without water for agriculture and industry, our food and manufacturing industries will be unable to satisfy demand. Already today, 10% of people consume foods which have been irrigated using waste water full of chemicals or disease (WHO, 2009). Should water become even scarcer, this is likely to grow further.The second critical issue is land. Current agricultural practices and the impact of pollution both contribute to soil erosion and a decreased level of soil fertility. It is estimated such poor quality land affects 1.5 billion people around the world (UNCCD, 2011). Deforestation and mining have had a devastating impact on our ecosystem and the biodiversity on which it thrives. The WWF (n.d.) estimates that we may be losing 10,000 species a year. All of this affects the number of crops that can be grown and produces greater food insecurity. How can we allow such environmental degradation to occur under our noses? 5 Another prime concern is energy. Governments, such as those in Denmark and Germany, are investing in renewable energy to eliminate their reliance on oil and to tap into resources with greater sustainability. However, the number of road vehicles reached one billion in 2010 (WardsAuto, 2011), an increase of 20 million from the previous year, and is continuing to increase due to the growing wealth in developing countries. It is therefore likely that there will be an unprecedented demand for oil over the next 50 years, pushing prices to exorbitant levels. This will make it more difficult for people to afford food, heating, and other manufactured goods, placing more people into poverty.Overpopulation is not a problem for one country or continent; it is a problem for all of us. The UN (2012) estimates that by 2030 the world will need 50% more food, 30% more water, and 45% more energy than it does today. We must stop burying our heads in the sand and make a sustained effort to reduce population growth. We must develop a coherent strategy that will increase access to education for all. Not only is education a fundamental human right, it also facilitates a reduction in population growth. Large families tend to be prevalent in developing countries and yet when men, women, and children in these areas receive education, family sizes shrink. The UN estimates that in less developed countries where women are not educated, they have twice as many children as in those countries where they are educated. It is therefore this area in which we should invest time and money. Who can argue with free and equal education for all?It is true that the world's population is growing, but this is not the cause of our current and future global problems. Believing this will give rise to ignorance of the real problem and the resulting irreparable damage to our planet. 2 Let me start by explaining why overpopulation is a myth. The UN Population Division regularly predicts population growth, but provides a low variant, medium variant, and high variant to factor in various likelihoods. In the 2010 revision, their high variant suggested that the world population will be almost 16 billion in 2100, but the low variant predicted it will peak at 8 billion and decrease to just over 6 billion by 2100. In most cases, it is the low variant that has come true in the past, suggesting the same will be true of their future population predictions. Which is breaking down information into parts? analysis point of view perspective synthesis