Show that √2 is an irrational numbe.​

Answers

Answer 1

Answer:

[tex] \sqrt{2} =1.41421356237...[/tex]

Answer 2

Answer:

The proof that √2 is indeed irrational is usually found in college level math texts, but it isn't that difficult to follow. It does not rely on computers at all, but instead is a "proof by contradiction": if √2 WERE a rational number, we'd get a contradiction.

...

A proof that the square root of 2 is irrational.

2 = (2k)2/b2

b2 = 2k2


Related Questions

Consider the graph of the function f(x)=2x.
Which statement describes a key feature of
function g if g(x) = 2f(x)? Answers:
A. y-intercept at (0,2)
B. y-intercept at (2,0)
C. horizontal asymptote of y = -2
D. horizontal asymptote of y = 2

Answers

Given:

The parent function is:

[tex]f(x)=2^x[/tex]

The other function is:

[tex]g(x)=2f(x)[/tex]

To find:

The statement that describes a key feature of function g.

Solution:

We have,

[tex]f(x)=2^x[/tex]

[tex]g(x)=2f(x)[/tex]

Using these two functions, we get

[tex]g(x)=2(2)^x[/tex]

Putting [tex]x=0[/tex], we get

[tex]g(x)=2(2)^{(0)}[/tex]

[tex]g(x)=2(1)[/tex]

[tex]g(x)=2[/tex]

The y-intercept of the function g at (0,2). So, option A is correct and option B is incorrect.

We know that [tex]g(x)\to 0[/tex] as [tex]x\to -\infty[/tex] and it will never intersect the line [tex]y=0[/tex]. It means the horizontal asymptote of the function g is

Therefore, the correct option is A.

Answer:

A

Step-by-step explanation:

*Brainliest* What is the value of X?

or how do I solve this equation?

Answers

Answer:

x = 6

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360

69+111+12x-3 +111 = 360

Combine like terms

12x+288=360

Subtract 288 from each side

12x+288-288 = 360-288

12x = 72

Divide by 12

12x/12 = 72/12

x = 6

Answer:

x = 6

Step-by-step explanation:

All angles together equal 360

Us this to set up your formula

360 = 111 + 111 + 69 + 12x-3

360 = 288 + 12 x

360 - 288 = 12x

72 = 12x

72/12 = x

6 = x

You could also use the fact that angle t and r are equal to set your formula up as

69 = 12x-3

69+3=12x

72=12x

72/12=x

6=x

The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system?

Answers

The question is incomplete, the complete question is:

The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system?

x + 3y = 42

2x − y = 14

A: Multiply the second equation by -3. The solution is x = 12, y = 9.

B: Multiply the second equation by -2. The solution is x = 12, y = 10.

C: Multiply the second equation by 2. The solution is x = 15, y = 9

D: Multiply the second equation by 3. The solution is x = 12, y = 10

Answer: The correct option is D.

Step-by-step explanation:

The elimination method is a technique wherein we eliminate the coefficient of any one variable.

The given equations are:

x + 3y = 42

2x − y = 14

We multiply the second equation by (3) and the equations formed are:

x + 3y = 42

6x − 3y = 42

The final equation after eliminating the y-term becomes:

7x = 84

x = 12

Putting value of 'x' in any of the original equation, we get:

⇒ 12 + 3y = 42

⇒ 3y = 30

⇒ y = 10

Hence, the correct option is D.

the graphs of f(x) =-2x and g(x)=(1/2)^z are shown

Answers

Answer:

f(x)-3x+5 and g(x)=4+5 is it true ?Step-by-step explanation:

Cameron is making trail mix. The ratio of peanuts to raisins to walnuts is 3:2:1. If there are 224 raisins, how many total peanuts and walnuts are there?

Answers

Answer:

336 Peanuts

112 Walnuts

Step-by-step explanation:

So first, you can not change the order of the items in a ratio. So the 224 raisins will be in the middle.

It will look like _ : 224 : _

Next, divide 224 by 2 to get the number of walnuts, the number on the right.

So the number on the right will be 112.

Next, multiply 112 by 3 to get 336.

What is the range of the given function? To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by the equation u = 748g, where g is the total number of gallons of water used and u is the number of units.

Answers

The question is incomplete. The complete question is :

To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by the equation g = 748u, where g is the total number of gallons of water used and u is the number of units. Determine which statements about the relationship are true. Check all that apply.

g is the dependent variable.

u is the dependent variable.

g is the independent variable.

u is the independent variable.

The variables cannot be labeled without a table of values.

The variables cannot be labeled since any value can be selected for either

Solution :

Given equation :

g = 748 u

Here, g = total number of gallons of water used

         u = number of units

Customers uses the number of units of water.

The unit of water is independent of the total number of gallons of water used.

So the number of units u is an independent variable.

But the value of gallons of water depends on the number of units that is used.

Therefore, number of gallons of water g is a dependent variable.

Thus, we can say that :

g is dependent variableu is independent variable

Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each. They spent $26.38 total and bought 35 items total. How many candy bars did they buy?

Answers

Answer:

22

Step-by-step explanation:

number of gum = x

number of candy bar = y

0.54x + 0.88y = 26.38

x + y = 35

         0.54x + 0.88y = 26.38

(+)      -0.54x - 0.54y = -18.9

-----------------------------------------

                       0.34y = 7.48

y = 7.48/0.34

y = 22

Answer: 22

The number of the gum is 13 and the number of the candy will be 22.

What is linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each.

They spent $26.38 total and bought 35 items total.

Let x be the number of the gum and y be the number of the candy.

Then the equation will be

x + y = 35 ...1

0.54x + 0.88y = 26.38 ...2

By solving the equations 1 and 2, then we have

x = 13 and y = 22

Then the number of the gum is 13 and the number of the candy will be 22.

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ2

Anyone.....................​

Answers

Answer:

[tex] \frac{1}{p - q} [/tex]

Step-by-step explanation:

[tex] \frac{ {p}^{2} + 2pq + q}{ {p}^{3} - p {q}^{2} + {p}^{2} q - {q}^{3} } [/tex][tex] \frac{ {p}^{2} +2 \times p \times q+ {q}^{2} }{p^2−pq^2+p^2q−q^3} [/tex][tex] \frac{(p + q {)}^{2} }{p^3−pq^2+p^2q−q^3} [/tex][tex] \frac{( p+ q {)}^{2} }{p(p^2−1q^2)+q(p^2−q^2)} [/tex][tex] \frac{ (p + q {)}^{2} }{ {p}^{3} - p {q}^{2} + {p}^{2} q - {q}^{3} } [/tex][tex] \frac{(p+q {)}^{2} }{(p+q)(p−q)(p+q)} [/tex]

[tex] \frac{(p + q {)}^{2} }{(p + q {)}^{2}(p - q) } [/tex] ( cancel common factors)

[tex] \frac{1}{p - q} [/tex]Hope it is helpful...

What is the solution to the inequality 5.25 - b 2 6.52
+
+→
5
-5 -4 -3 -2 -1 0
1
2
3
4
OH ++
-5 -4 -3 -2 -1 0 1 2
+
3
+
4
5
OA
-5 -4 -3 -2 -1 0 1
2
3 4 5
-5 -4 -3 -2 -1 0 1 2 3 3 4 4 5

Answers

Answer:

1st option

Step-by-step explanation:

Solving the inequality

5.25 - b ≥ 6.5 ( subtract 5.25 from both sides )

- b ≥ 1.25

Divide both sides by - 1, reversing the symbol as a result of dividing by a negative quantity.

b ≤ - 1.25

Since less than or equal to the number line will have a solid circle at - 1.25 and the arrow pointing left.

The solution is represented on the first diagram

In 6 seconds, a total of 3 waves crash into a cliff. The distance between 2 adjacent wave crests on the water is 8 meters.

Answers

Answer:

Wavelength = 16 m

Step-by-step explanation:

Given that,

In 6 seconds, a total of 3 waves crash into a cliff.

The distance between 2 adjacent wave crests on the water is 8 meters.

We need to find the wavelength of the wave.

We know that, the distance between two consecutive wave is called wavelength of a wave.

We can understand that, total of 3 wave crests, the distance between first and second wave crest is 8 meters.

Hence, the wavelength is 8 m + 8 m = 16 m

Which of the following functions best describes this graph?
A. Y = (x-3)(x + 4)
B. y = x^2-5x +6
C. y = x^2 -9x+18
D. y - (x+3)(x +6)

Answers

Answer:

(A). y = ( x - 3 ) ( x + 4 )

Step-by-step explanation:

Question 8 of 10
Which property of polynomial multiplication says that the product of two
polynomials is always a polynomial?
A. Distributive
B. Addition property of equality
C. Commutative
D. Closure

Answers

Answer:

D. Closure

Step-by-step explanation:

D. Closure

the answer would be b

Duncan is putting icing on the top of a rectangular cake if the top of the cake is 6 inches wide by 10 inches long what is the area of the top of the cake

A. 80 square inches

B.60 square inches

C.30 square inches

D. 120 square inches

Answers

Duncan is putting icing on the top of a rectangular cake if the top of the cake is 6 inches wide by 10 inches long what is the area of the top of the cake

A. 80 square inches

B.60 square inches

C.30 square inches

D. 120 square inches

Answer:

B- 60 square inches

Ellus
Find the range of the data.
The ages of people eating
chocolate ice cream at a park.
12, 2, 8, 5, 3, 2,5
Range: [? ]
Enter the number that belongs in the green box.

Answers

Answer:

range = 10

Step-by-step explanation:

The range is the difference between the largest and smallest values in the data set.

largest value = 12

smallest value = 2

range = 12 - 2 = 10

Below are two parallel lines with a third line intersecting them.

Answers

Answer:

56

Step-by-step explanation:

they are same side interior angles so both add up to 180 so just subtract 124 from 180 to get 56

I think the answer is 56 because a line=180 and 124-180 is 56

Write the equation of the line in slope-intercept form

Answers

Answer:

y = 4/1 + 0

Step-by-step explanation:

we rise 4 units up and move 1 unit to the right

and the y intercept is 0 because its exactly in the center of x and y axis

what is a kite? what are its properties? what is its use in our daily life?

Answers

Answer:

Well, in geometry, the properties would be that the angles produced by the intersection of the diagonals are right angles. A kite is basically entertainment, made by cloth and string

A kite is a four sided shape. Like an elongated rectangle.a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite to each other instead of being adjacent. Kite quadrilaterals are named for the wind-blown, flying kites, which often have this shape and which are in turn named for a bird. Kites are also known as deltoids, but the word "deltoid" may also refer to a deltoid curve, an unrelated geometric object.Kites have been used for human flight, military applications, science and meteorology, photography, lifting radio antennas, generating power, aerodynamics experiments, and much more.

Select the correct answer. What is -16 + 49 written as a complex number in the form ? A. 7 + 4i B.7 - 4i C.-4+7i D.4+7i

Answers

Answer:

A. 7 + 4i

Step-by-step explanation:

Select the correct answer. What is -16 + 49 written as a complex number in the form ? A. 7 + 4i B.7 - 4i C.-4+7i D.4+7i

Writing as a complex number, we find the square root of -16 + 49

Hence:

√ -16 + 49 = √-16 + √49

= 4i + 7

Rearranging

= 7 + 4i

Therefore, the correct option is A. 7 + 4i

Use the following list of balances for Paul's Guitar Shop to answer the following question. Guitar Sales 24,800, Depreciation expense 2,000, Wage expense 10,950, Rent 500, Music Lesson Revenue 3,000, Interest expense 500, Supplies expense 500, Utilities expense 400. What is the TOTAL value of EXPENSES? *

Answers

Answer:

The Total Value of Expenses is $14,350

Step-by-step explanation:

AMOUNT

Depreciation Expense $ 2,000

Wage Expense $ 10,950

Interest Expense $ 500

Supplies Expense $ 500

Utility Expense $ 400

TOTAL $ 14,350

How do I do this ? no links please

Answers

Ask your teacher. It’s the best help you can get because this doesn’t make any sense. To get your teachers help a quick email would do

Hey there!


ASSUMING….
-14.4 = -1.2m

-1.2m = -14.4

DIVIDE -1.2 to BOTH SIDES

-1.2m/-1.2 = -14.4/-1.2

SIMPLIFY IT!

m = -14.4/-1.2

m = 12


Therefore, the answer should be:

m = 12


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

PLEASE I NEED THE ANSWER DON'T IGNORE MY QUESTION!!! Solve for X for the following

Answers

Answer:

Fig. 1 :- 7.6

Fig. 2 :- 15

Step-by-step explanation:

We can use Pythagoras theorem to solve for x

[tex]c^{2} =a^{2} +b^{2}[/tex]

Figure 1:

[tex]c^{2} =7^{2} +3^{2}[/tex]

[tex]c^{2} =49+9[/tex]

[tex]c^{2} =58[/tex]

[tex]c=\sqrt{58}[/tex]

[tex]c=7.615773106[/tex]

You can now round your answer:

[tex]c=7.6[/tex]

Figure 2:

[tex]c^{2} =12^{2} +9^{2}[/tex]

[tex]c^{2} =144+81[/tex]

[tex]c^{2} =225[/tex]

[tex]c=\sqrt{225}[/tex]

[tex]c=15[/tex]

I hope this helps :)

Step-by-step explanation:

fig(1)

h=x

p=3

b=7

now,

h^2=p^2+b^2. (by Pythagoras theory)

or, x^2=3^2+7^2

or, x^2=9+49

or, x^2=58

or, x=√58

fig(2)

h=x

p=12

b=9

now,

h^2=p^2+b^2

or, x^2=12^2+9^2

or, x^2=144+81

or, x^2=225

or, x=15

Find k if (x+1) 2x^3+kx^2+1

Answers

Question:

Find k if (x+1) is a factor of 2x³ + kx² + 1

Answer:

k = 1

Step-by-step explanation:

The factor of a polynomial F(x) is another polynomial that divides evenly into F(x). For example, x + 3 is a factor of the polynomial x² - 9.

This is because;

i. x² - 9 can be written as (x - 3)(x + 3) which shows that both (x - 3) and (x + 3) are factors.

ii. If x = -3 is substituted into the polynomial x² - 9, the result gives zero. i.e

=> (-3)² - 9

=> (9) - 9 = 0

Therefore, if (x + a) is a factor of a polynomial, substituting x = -a into the polynomial should result to zero. This also means that, if x - a is a factor of a polynomial, substituting x = a into the polynomial should give zero.

From the question

Given polynomial: 2x³ + kx² + 1

Given factor: x + 1.

Since x + 1 is a factor of the polynomial, substituting x = -1 into the polynomial should give zero and from there we can calculate the value of k. i.e

2(-1)³ + k(-1)² + 1 = 0

2(-1) + k(1) + 1 = 0

-2 + k + 1 = 0

k - 1 = 0

k = 1

Therefore the value of k is 1.

Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth.

Answers

Answer:37.68

Step-by-step explanation:

Do yk the anwser to my question?

I need help i'm struggling with this work!

Answers

Answer:

Domain: x is greater than or equal to 0

Range: y is greater than or equal to -5

So the answer for domain is e.

And the answer for range is a.


While attempting to multiply the expression (3x + 7)" a student made mistakes. Explain and write the correct way.

Answers

Answer:

9x²+42x+49

Step-by-step explanation:

that is not the correct way to foil.

the correct way would be (3x+7)²= (3x+7)(3x+7)

simplifying that would give us 9x²+42x+49

his mistake was multiplying wrong because he did not foil

HURRRYYYY I NEED AND ANSWER ***
What percentage of the data values falls between the values of 3 and 24 in the data set shown?
0
5
10
15
20
25
25%
050%
оооо
75%
О 100%

Answers

Answer:

I think that's 25 though I have no assurance

i think 50 because it looks to be 14/25 and that’s almost 50%

Help?,?,?,?.!.??.?.?.?.?.?.

Answers

Answer:

Step-by-step explanation:

b(a + 1) + a = b*a + b + a = ab + b + a

1) b(2a +1 ) = b*2a + b*1 = 2ab + b  Not equivalent.

2)a + (a +1)*b = a + ab+ b     Equivalent

3) (a +1)(b+ a) = a*(b +a) + 1*(b+a) = ab+ a² +b + a  Not equivalent.

4) (a + 1)b + a = ab+ b + a   Equivalent

5) a + b(a+1) = a +ab + b Equivalent

6) a + (a +1) + b = a + a + 1 + b = 2a + 1 +b  Not equivalent.

7) a(b +1) + b = ab + a + b  Equivalent

two hundred minus the number two

Answers

Answer:

200-2 = 198

Step-by-step explanation:

If you have 200 apples and you eat two you have 198 apples

Solve for x in the triangle round your answer to the nearest tenth
PLZ HELP ASAP I WILL MARK BRAINLIEST

Answers

Answer:

Step-by-step explanation:

Answer:

x = 9.32

Step-by-step explanation:

For a right angles triangles , we can use trigonometry equations :-

In this case , we need to use sine equation in perpendicular :

sin θ = opposite side / hypotenuse

sin 58° = x / 11

x = sin 58 ° × 11

x = 0.84 × 11

x = 9.32852906

Round nearest tenth = 9.32

Given that (1,4) is on the graph f(x), find the corresponding points of a function 1/4f(x)

Answers

Answer:

(1,1)

Step-by-step explanation:

In the equation f(x), you are plugging in the x coordinate which in this case is one. That means in 1/4f(x), x will remain the same, because you are still plugging in the same thing. What will change is the y coordinate. 1/4f(x) is saying that the y coordinate will be a fourth of the original y coordinate(4). 4 times 1/4 is equal to one.

If the x coordinate stays the same, and the y coordinate is a fourth of 4, the corresponding points in the function f(x) will be (1,1)

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