Consider the statement n2 + 1 ≥ 2n where n is an integer in [1, 4]. Is the correct proof of the given statement is "For n = 1, 12 + 1 = 2 ≥ 2 = 21; for n = 2, 22 + 1 = 5 ≥ 4 = 22; for n = 3, 32 + 1 = 10 ≥ 8 = 23; and for n = 4, 42 + 1 = 17 ≥ 16 = 24."

Answers

Answer 1

The given statement n² + 1 ≥ 2n is correct for integers n in [1, 4]. The proof uses substitution for each value of n, showing that the inequality holds true for all four cases.

To prove the statement n² + 1 ≥ 2n for integers n in [1, 4], we substitute each value of n and check if the inequality holds true:

1. For n = 1, 1² + 1 = 2 ≥ 2(1) = 2, so the inequality is true.
2. For n = 2, 2² + 1 = 5 ≥ 2(2) = 4, so the inequality is true.
3. For n = 3, 3² + 1 = 10 ≥ 2(3) = 6, so the inequality is true.
4. For n = 4, 4² + 1 = 17 ≥ 2(4) = 8, so the inequality is true.

Since the inequality is true for all n in [1, 4], the statement is proven to be correct.

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Related Questions

in △ABC the measure of angle A is 2x + 3, the measure of angle B is 4x + 2, and the measure of angle C is 2x - 1. what are the measures of the angles?

Answers

All angles in a triangle add to 180. So, we must add all those expressions together and set them equal to 180.

2x+3+4x+2+2x-1=180
Now we combine like terms (2x+4x+3x is 8x, 3+2-1 is 4)
8x+4=180
Now subtract 4 from both sides (4-4 is 0, 180-4 is 176)
8x=176
Now divide both sides by 8.
x=22.

Now substitute 22 wherever you see x in each expression.

2x+3 = 2(22)+3 = 44+ 3 = 47
4x+2 = 4(22)+2 = 88+2 = 90
2x-1 = 2(22)-1 = 44-1 = 43

So the final answer is A=47°, B=90°, C=43°

To check, add these numbers together and see if they equal 180.

90+43+47 is 180, so the answers are correct.

2x +3y = 12

Complete the missing value in the solution to the equation

(__, 8)​

Answers

Answer:

The two solutions of the equation is (0,-4)(6,0).

Please find the solution!!! 4x-3(2x-1)=7x-42​

Answers

Answer:

x = 5

Step-by-step explanation:

4x - 3(2x - 1) = 7x - 42 ← distribute and simplify left side

4x - 6x + 3 = 7x - 42

- 2x + 3 = 7x - 42 ( subtract 7x from both sides )

- 9x + 3 = - 42 ( subtract 3 from both sides )

- 9x = - 45 ( divide both sides by - 9 )

x = 5

Mr.Jessup, an airplane pilot, flies 1,450 miles a day. How many miles will he fly in 8 days? Why?

Answers

Answer: Mr. Jessup will fly 11,600 miles in 8 days. This is because if he flies 1,450 miles a day, and he flies in 8 days, just multiply 1,450 and 8.

Step-by-step explanation:

Do not, I repeat DO NOT ANSWER THIS QUESTION!!!! It is experimental, and I need to answer it with my other account, so please DO NOT ANSWER THIS!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

tfgvftydgxchtfg

Step-by-step explanation:

The length of a rectangle is five times the width the area is 125 cm² what is the length

Answers

Answer:

Length: 25

Step-by-step explanation:

the ratio we use is 5:1

125÷5=25

5 is the width and 25 is the length

to check the answer find the area with those measurements

5x25=125 so its correct

1. A pair of shoes is regularly priced at $52. They are on sale for 15%
off the regular price. What is the sale price of the shoes?

Answers

[tex]52 \times 0.15 = 7.8[/tex]

[tex]52 - 7.8 = 44.20[/tex]

The sale price of the shoes is $44.20

Answer:

52*15/100=7.8$ so u will take away 7.8$ from 52$=44.2$ he has to pay.

How do I graph y=x-3 and y=-2x+6

Answers

Answer:

you can use a graphing calc

Step-by-step explanation:

3. A building stands on level ground. The measure of the angle of elevation of the top of the building, taken at a
point 400 feet from the foot of the building, is 31 degrees. Find, to the nearest tenth of a foot, the height of the
building

Answers

Answer:

12,400

Step-by-step explanation:

so what you are going to first is 400 times 31 which is 12,400

PLEASE HELP ME!!!!!!!

Answers

Step-by-step explanation:

step 1. triangles ABG and ACF are similar.

step 2. triangle ACF is twice the size of triangle ABG.

step 3. if BG = 8 then CF = 16.

I have only 10 points plus give me the right answer this is the last I’m gonna ask but pls help just answer the blank question

Answers

15

I guess so

Hope it is correct

Which of the following is the solution to the compound inequality below?
3x +5>_ -1 or - 2x - 7>_5
A. x>_2 or x >_-6
B. X>_-2 or X<_-6
c. x>_5/3 or x<_-7/2
D. x>_-5/3 or x>_7/2

Answers

Answer:

The answer of the question is b

Which polynomial function has a leading coefficient of 1, roots -2 and 7 with multiplicity 1, and root 5 with multiplicity 2?

Answers

Answer:

(D)

Step-by-step explanation:

If it has a leading coefficient of 1, then it can not (A) or (B) because they have a two in front of it. Next, we can check the roots -2 and 7. -2 goes with (x+2), while 7 goes with (x-7). Therefore, you can already see that the answer is (D). To make sure. let us check the root 5 with multiplicity of 2. 5 goes with (x-5), implying that there must be 2 (x-5)'s. Only (D) satifies that as well, so the answer must be (D).

Answer:

D on edge

Step-by-step explanation:

what is the geometric mean of 2 and 14​

Answers

Answer:

8!

Step-by-step explanation:

add them together to get 16 then divide by 2 (the number of numbers you added) and you get 8!

Hope that helps, please mark me brainliest if it does :)

Answer:

Answer is 5.3

Step-by-step explanation:

I hope it's helpful!

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SHOW THE WORK PLEASEEEE!!!

Answers

Answer:

3x^6y^2/8

Step-by-step explanation:

Simplify the expression.

~Hoped this helped~

~Brainly, please?~

Answer:

3x^6y²/8

Step-by-step explanation:

3²·x^4·y³ / 24x^-2·y = 9x^4y²/24x^-2

9x^6·y²/24 = 3x^6y²/8

Write an integer for this situation 5 feet below sea level

Answers

Answer:

282 feet below sea level.

Step-by-step explanation:

Please help thank you so much

Answers

Answer:

b

Just trust me

Step-by-step explanation:

C

-4 * -5 = 20
-4 * -2 = 8
which would get you 8^20/2^8 which is C

please help, this is really important if you could show work that would be amazing :))

Answers

Step-by-step explanation:

step 1. x = 70° (alternate interior angles)

step 2. y = 90° (same side interior angles).

PLZZZZZZZZZ HELPPPPP

Answers

Answer:

Step-by-step explanation:

(-3,0)

(0,2)

(6,6)

The expression (2x+2x)+(5x+5x)+(1+1) represents the perimeter of a triangle. Select the answer below which shows this expression in simplest form.

HINT: Simplest form means combined 'like' terms.

100 Points
A
14x + 2

B
16x

C
40x + 2

D
16

Answers

Answer:

A) 14x + 2

Step-by-step explanation:

(2x + 2x) + (5x + 5x) + (1 + 1)

= 4x + 10x + 2

= 14x + 2

You can only add 4x and 10x since they both have a variable (x). You cannot add 2 since 2 doesn't have a variable, so the answer in simplest form is 14x + 2

how many fluid ounces of water does sofia use to make the batch of slime?

Answers

Answer:

lo que sea me lo pones en español plis yo te aydo

Step-by-step explanation:

550 + 550 + 650 + 550 + 600 = ?

Answers

Answer:

2,900

Step-by-step explanation:

Find the volume of a cylinder with height = 10ft and the diameter of the base circle is 12ft.

Answers

Answer:

The answer is 1130.97

Step-by-step explanation:

The formula that I used

V=πr2h

Volume = π·62·10 ≈ 1130.97336

Find the value of x and the measure of the angle labeled 3x.
A. x= 14; angle measure is 30°
B. x = 10; angle measure is 42".
C. x = 14; angle measure is 42"
D. x = 10; angle measure is 30°

Answers

Answer:

D

Step-by-step explanation:

3x and 30 are vertically opposite angles and congruent, then

3x = 30 ( divide both sides by 3 )

x = 10 , thus

3x = 3 × 10 = 30°

x = 10 ; angle measure is 30° → D

Answer:

the answer is D, x= 10;angle measure is 30°

Evaluate the expression when a=4 and b=2: 2a + b*

Answers

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

start by substituting. 2(4)+2. use the order of operations to solve left to right. 2 x 4 equals 8. 8 plus 2 equals 10. hope this helps

Which expression has a solution of 27, if r = 3?

Answers

Answer:

rx9

Step-by-step explanation:

9x3=27

Answer:

9r = 27

Step-by-step explanation:

Have a great day <3

A shipping box is in the shape of a rectangular prism. It has a volume of 9,000 in.3, and the dimensions of the base are 20 in. by 30 in. What is the height of the box?

Answers

Answer:

A closed box is to be made in the shape of a cuboid of height h (in cm) with a rectangular base that has sides of length x (in cm) and 2x (in cm). Its volume is required to be `1000 cm^3

The height of the shipping box is 15 inches.

What is volume of rectangular prism?

The volume of a rectangular prism: length x width x height. The volume is expressed in cubic units.

given:

Volume = 9000 cubic inches

Base dimensions = 20 inches by 30 inches

Now, Volume = Base Area * Height

Height = Volume/Base Area

Height = 9000/(20 * 30)

Height = 15 in

Hence, the height of the shipping box in the shape of a rectangular prism is 15 inches.

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1 and 1/3 - 5/6
(ill mark when 2 answers)
(have a good day )
(HELP MEH PLZZ)

Answers

Answer:

1 1/3 - 5/6 = 1/2

Step-by-step explanation:

First we will need to make a common denominator on both sides, so since we have the second side divided in six, we can do the same to the first side as shown;

1/3 = 2/6

now this will help us a lot, now all we have to do is take what we can out of the fraction (2/6) out of the first side so it is equal to 0, NOTE this is not a professional way to do it but it helps me a lot;

5/6 - 2/6 = 3/6

this makes it easy all of a sudden, cause now its in a simpler form, we can tell this because we know that 3/6 is equal to 1/2, so now all we have to do is take 1/2 from our 1 that we are left over with, and VWOLA;

1 - 1/2 = 1/2

GRAND TOTAL;

1 1/3 - 5/6 = 1/2

(note: the space between the 1 and the 1/3 indicates that they are two separate numbers, so you dont have to put the 'and' there)

Round 1.983 to the nearest hundredth

Answers

Answer:

1.98

Step-by-step explanation:

Find the number in the hundredth place 8 and look one place to the right for the rounding digit 3. Round up if this number is greater than or equal to 5 and round down if it is less than 5.

solve 2|x+8|-6<16

Please help thanks!

Answers

Answer: Inequality form : -19<x>3

interval notation:

(--19,3)

Step-by-step explanation:

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