the formula 1/2(n^2+n) finds the sum of the first n positive integers. find the sum of the first 5 integers, then use the formula to prove you got the same answer. finally use the formula to find the sum f the first 14 integers. answer asap for brainliest worth 30 points.

Answers

Answer 1

Answer:

Induction is done by demonstrating that if the condition is true for some n then it must also be true for n+1. If you then show that the condition is true for n=0 then it must be true for all n>0. For this problem:

Step 1: n=1

The sum of the first 1 odd numbers is 1. 12=1. Therefore the condition holds for n=1.

Step 2: induction

If the sum of the first n odd numbers is n2 then the sum of the first n+1 integers is n2+(2n+1)=(n+1)(n+1)=(n+1)2

So the condition is also true for n+1.

Step 3: conclusion

Since the we have shown that the condition is true for n=1 and we have shown that if it is true for n then it is also true for n+1 then it follows by induction that it is true for all n≥1.

Step-by-step explanation:

sorry if wrong


Related Questions

Unit 2 Lesson 11 Cool Down Graph


The point (12,5) is on the graph.

What do the coordinates tell you about the water in the bucket?

Answers

Answer: After 5 seconds, there will be 12 gallons of water in the bucket or  in 12 seconds there will be 5 gallons of water in the bucket. Either one of them

Step-by-step explanation:

PLs Help me!
Pls Help me!

Answers

Answer:

It's 90%

Step-by-step explanation:

90% of 60

= 0.9 * 60

= 540

Hope it helps. :)

Answer:

90%

Step-by-step explanation:

Let's set the missing blank value to x. (x% of 600 = 540)

In order to find a percentage of anything, we simply just divide by 100, and then multiply that value to the value we want to find the percentage of. Thus our new equation can be rearranged to this:

0.01x (600) = 540

Now simplify:

6x = 540.

x = 90.

That means 90% of 600 is 540.

what number am i missing please only tell me the one missing!!!

Answers

Answer:

16

Step-by-step explanation:

40 can be multiplied by 5, 8 times. 8 multiplied by 2 is 16.

Soup A has 5 grams of sodium in every 12 cups. Soup B has 8 grams of sodium in every 13 cups. Which soup has more sodium per cup?

Answers

Answer:

Soup B has more sodium per cup.

Step-by-step explanation:

If we're doing sodium per cup, then we have to divide 5 by 12, and 8 by 13.

5÷12=~0.4 grams

8÷13=~0.6 grams

0.6>0.4

So B has more sodium per cup.

Which of the following is a step in simplifying the expression x multiplied by y to the power of 3 over x to the power of negative 4 multiplied by y to the power of 4, the whole to the power of negative 2.?
x to the power of negative 2 multiplied by y to the power of negative 6, the whole over x to the power of 8 multiplied by y to the power of negative 8.
x to the power of negative 2 multiplied by y, the whole over x to the power of negative 6 multiplied by y to the power of 2.
x to the power of negative 2 multiplied by y to the power of negative 6, the whole over x to the power of negative 4 multiplied by y to the power of 4.
x to the power of negative 2 multiplied by y, the whole over x to the power of negative 4 multiplied by y to the power of 4.

Answers

Answer:

Step-by-step explanation:

yea

i need help ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

the correct ans is B.335.1497

33.5 1497
Which is number
A

What the area of the following shape? Please help ASAP.

Answers

The answer is 228 good luck :)

Answer: The answer is 228

Step-by-step explanation: good luck

Miguel Is building a doghouse.He cuts one sheet of wood to make the front wall.he also cuts out a door that is 2 feet by 2 feet.The dimensions, in feet,are shown in the diagram,
Miguel needs to paint the wood.What amid the area he needs to paint?

1.What is the area of the rectangular piece of wood before the square is cut out? Include units with your answer


2. what is the area of the square that was cut out of the wood? Remember to include units


3. What is the area Miguel needs to paint? Explain how you found your answer.

Answers

Answer:

1. 12 ft sq. 2. 4 ft 3. 12 - 4 (door) = 8

Step-by-step explanation:

Which system of equations has an infinite number of solutions?

2x – 6y = 18
x – y = 9
2x – 6y = 18
x + 3y = 9
2x – 6y = 18
x – 3y = 9

Answers

Answer:

I think it's x - y = 9

Step-by-step explanation:

It's the only without a variable with it. Hope this helps :)

Answer:

c on edge

Step-by-step explanation:

Which representation is incorrect?

Answers

Answer:

table

Step-by-step explanation:

The incorrect representation is the table.

3/4+(−3/8)+(−1/4)=(−3/8)+3/4+(−1/4)=−3/8+[3/4+(−1/4)]

Answers

Answer:

The sides aren't equal

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

3/4+(−3/8)+(−1/4)=(−3/8)+3/4+(−1/4)=−3/8+[3/4+(−1/4)]

= 6/8-3/8-2/8=(-3/8)+6/8-2/8=(-3/8)+[6/8-2/8]

= 6/8-3/8-2/8=(-3/8)+6/8-2/8=(-3/8)+[4/8]

=6/8-3/8-2/8=(-3/8)+6/8-2/8=(-3/8)+[4/8]

= 1/8= 1/8 = 1/8

Is Y=-2/7x Proportional or non-proportional?

Answers

Answer:

i think proportional

Step-by-step explanation:

Solve the following equation. Then, explain the steps you took to solve using mathematical reasoning and vocabulary.
7x +3( 8+8x) = -162

Answers

Nah that is not the answer
7x + 24 + 24x = -162
31x + 24 = -162
subtract 24 from both sides
31x = -186
x = -6

Anwser true or false in Order!

Answers

Answer:

true

false

false

true

Step-by-step explanation:

Parentheses before multiplication or division

Cassie has a small cube-shaped box. Its volume is 64 cubic centimeters. What is the area of one face of the box? Enter your answer in the box

Answers

Do length and width it might be 8cm

Simplify the expression using the distributive
property.
9(4y-7)

Answers

Answer:

36y-63

Step-by-step explanation:

9(4y-7)

9*4y + 9*-7

36y-63

Answer:

[tex]\huge\boxed{\sf{36y-63}}[/tex]

Step-by-step explanation:

Hello.

Use the Distributive Property and simplify.

Remember that it states: a(b+c)=ab+ac

Where a, b, and c can be either constants or variables.

Now, simplify the given expression:

[tex]\hookrightarrow\sf{9(4y-7)}=9*4y - 7*9=36y-63[/tex]

I hope it helps.

Have a great day.

[tex]\boxed{imperturbability}[/tex]

In a northwestern U.S. town, the peak temperature is 96° Fahrenheit in August. After the peak, it drops an average of 4° Fahrenheit per week. The graph below models the number of weeks it would take the temperature to drop below freezing, 32° Fahrenheit.
okay so they show a pic of a number line from 10-22 and the 16 number has a ray with a open circle!?

Which of the following is the correct interpretation of the solution?

A. It would take more than 16 weeks to drop below freezing.

B. It would take 16 or less weeks to drop below freezing.

C. It would take less than 16 weeks to drop below freezing.

D. It would take 16 or more weeks to drop below freezing.

Answers

Answer:It would take more than 16 weeks to drop below freezing.

The temperature is dropping from 96°F to 32°F at a rate of 4°F per week, where 32°F is the freezing point.

Hence, 32 = 96 - 4w { Where w week is required to reach 32°F }

⇒ 4w = 64  

⇒ w = 16

Therefore, it would take more than 16 weeks to drop below freezing. ( Answer )

Step-by-step explanation:

The answer is C. It would take less than 16 weeks to drop below freezing.

wich is corect btw this is homework

Answers

Answer:68 with the little two

Step-by-step explanation:

It is a Saturday morning, and Jeremy has discovered he has a leak coming from the water heater in his attic. Since plumbers charge extra to come out on weekends, Jeremy is planning to use buckets to catch the dripping water. He places a bucket under the drip and steps outside to walk the dog. In half an hour, the bucket is 1/3 of the way full.

What is the rate at which the water is leaking per hour? (the unit rate)

Answers

Answer:

the rate is 765

Step-by-step explanation:

IF U GET IT RIGHT YOU GET A BRAINLIEST
Lisa has to spend less than $200.00 on new clothes for spring. She has already spent $125.01 and wants to buy some shirts that are each $20.18. Which of the following inequalities could be used to solve for x, the number of shirts Lisa can buy with the money she has left?

A. $20.18x - $125.01 < $200.00
B. $20.18x < $200.00
C. $20.18x < $125.01
D. $20.18x + $125.01 < $200.00

Answers

Answer:

D.) $20.18x + $125.01 < $200.00

Step-by-step explanation:

The sum of the equation has to be less than $200.00

Answer:I believe it’s d

Step-by-step explanation:

What experience did ramses have that made him a great military leader?

Answers

Answer:

During his reign as pharaoh, Ramses II led the Egyptian army against several enemies including the Hittites, Syrians, Libyans, and Nubians. He expanded the Egyptian empire and secured its borders against attackers. Perhaps the most famous battle during Ramses' rule was the Battle of Kadesh.

Step-by-step explanation:

That's a couple reasons.

PLS HELP DUE SOON!! (retest) will give brainliest <3

Answers

Answer:

B and D

Step-by-step explanation:

Help me pleasee!! If u have questions please dont put an answer tell me down below tyy

Answers

Answer:

D

Step-by-step explanation:

I think the correct answer would be D

Which number line shows 1 to 4 divided into thirds?

Answers

Answer:

Line 1.

Step-by-step explanation:

This is because in order for it to be considered thirds, the third has to equal a whole. Line one goes:

1/3      2/3      3/3

This is split into thirds

The required number line that represents the dividend of the three is the fourth line. Option D is correct.

Given that.
To determine the line that has a dividend of 3.

What is a number line?

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
Line 1 has a dividend of 2,
Line 2 has a dividend of 5
Line 3 has a dividend of 4
Line 4 has a dividend of 3

Thus, the required number line that represents the dividend of the three is the fourth line. Option D is correct.

Learn more about number line here:

brainly.com/question/17683084

#SPJ2


Which of the following is a solution to the inequality below?

-13 < z/2 - 11

A. -56
B. -120
C. 14
D. -116

Answers

I did the math but I got -4 so maybe -14
The only correct option would be C


-13-2-4Since Z is greater than four, it could be any value that is greater than four.

A 222-inch pipe is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.
The shorter piece is __ inches long.

Answers

Is there any options?
The shorter piece is 37 inches long, use the equation 5x+x=222, solve the shorter piece is 37 inches and the longer piece is 185 inches.

Country Carpets charges $22 per square yard for carpeting, and an additional installation fee of $100. City carpets charges $25 per square yard for the same carpeting and an additional installation fee of $70. Write and solve an equation to find the number of square yards of carpeting for which the total cost charged by the two companies will be the same.

Answers

Answer:

10

Step-by-step explanation:

country carpets: y = 22x + 100

City carpets: y = 25x + 70

22x + 100 = 25x + 70

I could be wrong but I hope this helps!

Answer:

10 square yards

Step-by-step explanation:

25x+70= t

22x+100= t

25*10= 250+70= 320

22*10=220+100= 320

what is the answer to
$100 of debt

Answers

Answer:

steal 100 then pay your dept

Put 100 dollars in the bank and boom solved

Quiana has 5 times more text messages from Yolanda than from Pierre. Quiana has 30 text messages from Yolanda. Which equation can be used to find how many text messages Quiana has from Pierre, p?
A. 5 + p = 30
B. 5p = 30
C. 30 + p = 5
D. 30p = 5

Answers

Answer: 30p=5

Step-by-step explanation:

How should the decimal point in 0.937 change to get the correct answer to 0.937 ÷ 10²?

A. move it 2 place to the right

B . move it 2 places to the left

C .move it 3 places to the right

D .move it 3 places to the left

Answers

Answer:

B.

Step-by-step explanation:

When moving a decimal point 2 places to the right you are multiplying. When moving it to the left you are dividing. In this case we are moving 2 places to the left which the exponent 2 is representing. If you were to move 3 places to the right or left you would need to have a three as your exponent.

Other Questions
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