use mathematical induction to prove the statement is true for all positive integers n. 6 + 12 + 18 + ... + 6n = 3n(n + 1)​

Answers

Answer 1

Answer:

Step-by-step explanation:

6+12+18+....6n=3n(n+1)

Proof by induction

True for n = 1

6 = 3(1)(1+1)

Assume true for n = k

6+12+18+....6k=3k(k+1)

Then show that

6+12+18+....6(k+1)= 3(k+1)(k+1+1)

We add 6(k+1) to both sides of

6+12+18+....6k=3k(k+1)

6+12+18+....6k +6(k+1) =3k(k+1) + 6(k+1)

= 3(k+1)(k + 2)

= 3(k+1)(k+1+1)

So true for n = k+1

Since true for n=1 it is true for n=2,3,...

Thus true for all natural numbers n by mathematical induction


Related Questions

Find -63+(-208)+(-11) .

Select one:
a. -282
b. 282
c. -134
d. -272

Answers

Answer:

In my calculator it says 156

a. -282

Step-by-step explanation:

I just used a calculator haha

A regular nonagon has an area of 102.4 and one side length measures 7 units long. Find the apothem. Round to the nearest tenth, if necessary.

Answers

Answer:

Apothem = 3.3 units

Step-by-step explanation:

A regular nonagon has an area of 102.4 and one side length measures 7 units long. Find the apothem. Round to the nearest tenth, if necessary.

The formula to find the area of a polygon when given Apothem and Side length =

A = 1/2 × a × p

Where p = no of sides of polygon × side length

In the above question,

We are given a polygon = nonagon = 9 sides

Side length = 7 units

p = 9 × 7 = 63 units

Area = 102.4 square units

Apothem = a = ?

We substitute into the formula

102.4 = 1/2 × a × 63

102.4 = 63a/2

Cross Multiply

102.4 × 2 = 63a

Divide both sides by 63

a = 102.4 × 2/63

a = 3.2507936508 units

Approximately to the nearest tenth = 3.3 units

Martina will make flower arrangements with 3 roses in each arrangement. She will use the equation y = 3x to find the total number of roses she needs. What does x represent in the equation

Answers

X represents each rose and y represents each arrangement

X represents the number of arrangements.

please helpppp! i’ll mark brainliest

Answers

Answer:

from what i see i see thats its D

if not im sorry but i hope i got it right

Step-by-step explanation:

1 1/2 - 2/5 ÷ 4 2/5 × 3/4​

Answers

Answer:

1 19/44 (1.4318182)

Answer:

1 19/44

Step-by-step explanation:

Write each expression in scientific notation. Put your answer for EACH part in the text box. You should have 5 answers for this question.
A) 0.04

B) 0.072

C) 0.0000325

D) 0.003

E) 0.23





please help me

Answers

Answer:

A) 4 × 10^-2

B) 7.2 × 10^-2

C) 3.25 × 10^-5

D) 3 × 10^-3

E) 2.3 × 10^-1

Step-by-step explanation:

plss helppp get a brainliest

Answers

Answer:

Answer is c hope this helps :)

Step-by-step explanation:

find the missing side length labeled with a ? mark.

Answers

Answer: 10

Step-by-step explanation:

Since the lines are parallel, the triangles are congruent. This means their side lengths are an equal ratio!

6 + 6 : 20 = 6 : ?

12:20 = 6:?

12:20 = 6:10

Answer is 10

Which of the following functions best describes this graph?​

Answers

The answer is A, x^2-9x+18

Answer:

I believe the answer is A.

Two airplanes are flying to the same airport. Their positions are shown in the graph. Write a system of linear equations that represents this situation. Solve the system by elimination to justify your answer. Airplane #1 is on (2, 4). Airplane #2 is on (15, 9). The airport is on (6, 12).

Answers

Answer:

Airplane #1 equation: y=5/13x+42/13

Airplane #2 equation: y=1/3x+14

Step-by-step explanation:

So to find the slope of each airplane, you use the formula y2-y1/x2-x1. That means, for airplane#1 the equation will be 9-4/15-2. Simplify this and get 5/13. Then, for airplane#2, the equation will be 12-9/6-15. Simplify this and get 3/-9 and divide each side by 3 to get 1/-3 or -1/3. Next, use point slope formula to find the system of linear equations. Point slope formula is y-y1=m(x-x1). M is the slope. Use any point from the line. In this case, I will use (2,4). Tat means the first airplane's equation would be y-4=5/13(x-2). Then y-4=5/13x-10/13. Then, convert four into a fraction with a denominator of 13. This means, you have to multiply 4 by 13 to get 52/13. Add 52/13 to -10/13 to get 42/13. That means the first equation will be y=5/13x+42/13. The second equation point will be (6,12). This means the equation will be y-12=-1/3(x-6). Simplify this to get y-12=-1/3x+2. Simplify this to get y=1/3x+14. Therefore, Airplane#1 equation will be y=5/13x+42/13 and airplane #2 equation will be  y=1/3x+14.

Hope this helps

Write the equation of the line in fully simplified slope-intercept form

Answers

y=3/5x+5

hope this helps!!

The graph shows a line and two similar triangles. What is the equation of the line? y = 3 x y = one-third x y = one-third x + 2 y = 3 x + 2

Answers

TEMA

Una ecuación es una igualdad matemática entre dos expresiones, denominadas miembros y separadas por el signo igual, en las que aparecen elementos conocidos y datos desconocidos o incógnitas, relacionados mediante operaciones matemáticas

CONCEPTO

Una ecuación es una igualdad matemática entre dos expresiones, denominadas miembros y separadas por el signo igual, en las que aparecen elementos conocidos y datos desconocidos o incógnitas, relacionados mediante operaciones matemáticas

------------------------------------------------------------------------Igualdad entre dos expresiones que contiene una o más variables."ecuación de segundo grado"Igualdad o paralelismo entre dos o más cosas.

In "The Wheel of Woohoo" game, I'm taking a chance on
a spinner with 20 outcomes. If it lands on an even
number, I'll win a prize.
How likely is it to land on an EVEN number?
50-50 chance
highly likely
highly unlikely
unlikely
T

Answers

Answer:

50-50 chance

Step-by-step explanation:

Even: 2 4 6 8 10 12 14 16 18 20

Odd: 1 3 5 7 9 11 13 15 17 19 21

Answer:

50:50 chance

The data below shows the number of hermit crabs that live in each of the nine terrariums that Sunipa owns.

Using this data, create a frequency table.
Number of hermit crabs Number of terrariums
3
4
5

Answers

Answer:

4 for 3, 4 for 5, and 1 for 4

Step-by-step explanation:

khan academy

Answer:

3-4

4-1

5-4

Step-by-step explanation:

Count how many number there are and put them in the table.

Can someone help me pls

Answers

Answer:

maybe 223 degrees

Step-by-step explanation:

4/6-3/8 zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Answers

Answer:

The answer is 7/24 ~hope this helps~

btw, sick pic  B-)

Step-by-step explanation:

Algebra 1

help please!

Answers

Answer:

b

Step-by-step explanation:

Sorry this isn't the answer, I could give it to you but I know a website that would help you better and I don't feel like opening my laptop but desmos would be great for this if you don't already use it

Step-by-step explanation:

But you put the (2,4) in a box and the (-6,5) in another box and the answer will be where they connect like in and x

Sarah drove 420 miles in 6 hours. Jonathan drove the same distance going an average of 60 miles per hour throughout the entire trip.
Who was driving faster and by how much?

Answers

Answer:

Sarah was driving faster by 10 mph.

She was driving 70 miles per hour while Jonathan was only driving 60 miles per hour.

What is 1,198,145 rounded to the nearest ten thousand?

Answers

Answer: 1,200,000

Explanation:

There are 89 students in the sixth grade. Thirty-two percent of the sixth grade students live in Earth . Thirty-six percent of the sixth grade students live in Mars. The remaining students live in Saturn. What fraction of sixth grade students live in Saturn?

Answers

Answer:

32% of the sixth grade students live on Saturn.

(which would be about 29 of them)

solve for x in the equation below, show all work

Answers

Step-by-step explanation:

(3x-1)(x+1)=3(3x-4+x²)

open the brackets

=3x²+3x-x-1=9x-12+3x²

=3x²+2x-1=9x-12+3x²

collecting like terms

=3x²-3x²+2x-9x=-12+1

=-7x=-11

=x=11/7

Jeff as a collection of hockey cards. His brother Steve had 10 more cards than Jeff. Steve gave Jeff all of his cards. Jeff ended up with 992 cards. How many cards did Jeff start with?

Answers

Answer: 491 cards

Step-by-step explanation:

Given

Steve had 10 more cards than Jeff

Suppose Jeff has x cards

So, steve has x+10 cards

Steve handover his cards to Jeff

Now, Jeff has x+x+10=2x+10 cards

It must be equal to 992

[tex]\Rightarrow 2x+10=992\\\Rightarrow 2x=982\\\Rightarrow x=491\ \text{cards}[/tex]

Jeff started with 491 cards

PLZ HELP RN ILL MARK YOU BRAINLIST IF ITS RIGHT PLZZZ IM DESPERATE

Answers

Answer:

y = -14

Step-by-step explanation:

3y = -42

Divide both sides by 3:

y = -14

Answer:

-14

Step-by-step explanation:

-42 divided by 3 =-14

PLEASE HELP!! 100 POINTS!! BRAINLIEST!! What is the GCF of the terms in the numerator and denominator? Rewrite the expression by factoring out any common factors. Write the quadratic expressions in the numerator and the denominator in factored form. Cancel the common factor of the numerator and the denominator to write the expression in simplified form.



4x^2-14x+6/x^3-7x^2+12x

Answers

Answer:

2(2x-1)/x(x-4)

Step-by-step explanation:

4x^2-14x+6/x^3-7x^2+12x

2(2x^2-7x+3)/x(x^2-7x+12)

2(2x^2-6x-x+3)/x(x^2-4x-3x+12)

2(x-3)(2x-1)/x(x-4)(x-3)

100 points this is math help!!!

What is black and white and has lots of problems

9 letters

Answers

Answer:

A math test

Step-by-step explanation:

I just Goggled it lol

The answer is a math book but for some reason at first all I could think of was penguins

Please help with this question... Which expression is equivalent to x^3/2?​

Answers

Answer: D

Step-by-step explanation:

Answer:

Solve (x+2/x-3);(x-2/x-3) Equating the equation to zero and taking out (x-3) as common denominator (x+2)(x-2)/ (x-3)2 Solving using the identities we get => (x2– 4)/(x2 -6x + 9)= 0 => (x2– 4)=(x2-6x + 9) => -4= -6x +9 => -4 -9= -6x => -13= -6x => 13=6x => x= 13/ 6

T=Tails |0|1|2|3|

Probability |1/8|3/8|3/8|1/8|

The table and the relative-frequency histogram show the distribution of the number of tails when 3 coins are tossed. Find the probability P(T=3). Write your answer as a fraction.

Answers

Answer:

did you ever find the answer?

Step-by-step explanation:

answer pls and thank u !

Answers

it would be -3 heehehe

Martha use 1 piece of paper and 1 piece of ribbon to make kites. The paper comes in packs of 3 pieces and the ribbon comes in packs of 4 pieces. What is the least number of kites Martha can make without having supplies left over?
ANSWER QUICKKKKKK

Answers

the answer should be 12 kites



Given that RSTU is a parallelogram and ST is congruent to TU, explain why RSTU must also be a rhombus.

Answers

Given:

RSTU is a parallelogram and ST is congruent to TU.

To find:

Why RSTU must also be a rhombus?

Solution:

We know that the opposite sides of a parallelogram are parallel and congruent.

RSTU is a parallelogram. So,

[tex]RS\parallel TU[/tex] and [tex]ST\parallel RU[/tex]            [Property of parallelogram]            ...(i)    

[tex]RS\cong TU[/tex] and [tex]ST\cong RU[/tex]            [Property of parallelogram]            ...(ii)    

It is given that,

[tex]ST\cong TU[/tex]                ...(iii)

From (ii) and (iii), we get

[tex]RS\cong TU\cong ST\cong RU[/tex]          ...(iv)

From (i) and (iv), we get RSTU is a rhombus because all sides are congruent and appositive sides are parallel.

A parallelogram with each side equal is known as rhombus.

As for the given parallelogram all the sides are equal, therefore it should be rhombus.

What is parallelogram is rhombus?

Parallelogram is a closed shaped quadrilateral polygon in which opposite sides are equal and parallel and opposite angles are equal.

What is rhombus?

Rhombus is a closed shaped quadrilateral polygon in which all the sides are equal and opposites sides are parallel also opposite angles are equal.

Given information-

In the given problem [tex]RSTU[/tex] is a parallelogram.

In the given parallelogram [tex]ST[/tex] is congruent to [tex]TU[/tex].

The image of parallelogram is attached below.

For a parallelogram opposite sides are equal. thus,

[tex]RS=TU\\RU=ST[/tex]

As In the given parallelogram [tex]ST[/tex] is congruent to [tex]TU[/tex]. Thus,

[tex]ST=TU[/tex]

Now the side [tex]ST[/tex] is equal to the side [tex]RU[/tex] and side [tex]RS[/tex] is equal to the side [tex]TU[/tex]. Thus,

[tex]RS=ST=TU=RU[/tex]

All the sides of a rhombus is equal in length. A parallelogram with each side equal is known as rhombus.

As all the sides are equal of the given parallelogram. Thus the given parallelogram is rhombus.

Hence, as for the given parallelogram all the sides are equal, therefore it should be rhombus.

Learn more about the parallelogram and rhombus here;

https://brainly.com/question/20627264

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