Simplify, and Write answer without parentheses

The product of a rational number and an irrational number is an irrational

number.

The correctly completed proof is presented as follows;

To prove that 4·π is irrational, with the assumption that, 4·π = [tex]\displaystyle \frac{a}{b}[/tex], where b ≠ 0. Which by isolation of π gives π = [tex]\displaystyle \mathbf{ \frac{a}{4 \cdot b}}[/tex].

The right side of the equation is irrational, because the left side of the

equation is irrational, this is a contradiction.

Therefore, the assumption is wrong and the number 4·π is irrational.

Reasons:

The proof is presented as follows;

With the assumption that 4·π is rational, we have;

[tex]\displaystyle 4 \cdot \pi = \mathbf{\frac{a}{b}}[/tex]

Where;

b ≠ 0

Making π the subject of the above formula, by isolating, it, we have;

[tex]\displaystyle \pi = \mathbf{\frac{a}{4 \cdot b}}[/tex]

The right side of the equation is rational, however, the left side of the

equation π is irrational, which results in a contradiction, therefore, the

product 4·π is an irrational number.

Learn more about irrational numbers here:

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Answer:

Answer:

AJ. x<20

Lyla. x> or equal to70

Rook. x>or equal to 6

River. x<8

I hope that this helped

Answer:263/8

Step-by-step explanation:

2^5=32

32= 256/8 | Convert to fraction form

256/8+7/8= 263/8 | Combine fractions

Answer:

Step-by-step explanation:

2^5=32

32= 256/8 | Convert to fraction form

256/8+7/8= 263/8 | Combine fractions

Answer:

m/_a = 8 , m/_b= 3, m/_c = 4

The answer is: J - 3.08 pounds

Option I ) 3.08 pounds

The reason being that it can't round up with the 2 so we just have that number to the hundredth

Step-by-step explanation:

Solution

(s) = 100m

(t) = 72.54s

(v) = ??

We have,

v = s÷t

v = 100 ÷ 72.54

v = 1.37 m/s

Hence, the velocity of the swimmer is 1.37 m/s

[this is how I personally have to do it but not sure about you]

Answer:

what is positive or negative???

Answer:

48

Step-by-step explanation:

25% is 1/4 of the bag. 12x4 = 48.

There are 48 jelly beans in the bag.

Hope that helps

Answer:

The answer is 48.

Step-by-step explanation:

25%= times by 4.

So.. 12 times 4 = 48.

Hope that helps. x

Answer:

This question is straightforward if you find different triangles in the figure itself.

Property of a triangle: All internal angles of a triangle must add up to 180°

Take a look at Triangle DBH.

Method A

Angle BHD = 180°-33°-46° (sum of angles in a triangle)

                   = 101°

Property of angles on a straight line: All angles on a straight line must add up to 180°

Angle x = 180°-101° (supplementary angles)

             = 79°

Method B

Take a look at Triangle DBH.

Property of exterior angle (in this case, angle x): An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.

Angle x = 33°+46°

             = 79°

Answer:

well altogether it is 15 then it would be 3 dollars each

Step-by-step explanation:

:)

Answer:

the variables mean (1)

Step-by-step explanation:

you need to divide

Answer:

equals y<5?

Step-by-step explanation:

i dont think this will help but i hope it does help

Answer:

$8.00

Step-by-step explanation:

20% of 44.85=8.97

thats the closest to 8.00

Answer:

the answer is 9 dollars cuz the real answer is $8.97 and round to the nearest whole the answer is 9

Step-by-step explanation:

Answer:

First pic X= 13.036

Second pic x= 11.23

Step-by-step explanation:

Answer:Multiply X + Y by -6 so you can cancel 6x by -6x. Then you get 3y+24. Then divide by 3 and get Y=8 Then solve for X. Use one of the equations and solve for X. I would do X+8=16. Then minus 8 and get 8. So X=8

Step-by-step explanation:

With that being said the coordinate pair would be (8,8)

Answer:

Slope is -3/5

Slope intercept form: y<-3/5x+2

Step-by-step explanation:

Your going to have a shaded region, with a dashed line

the y intercept will be (2)

the x intercept will be (3.333,0)

Answer:

120

Step-by-step explanation:

To be honest I just looked it up.

Answer:

Step-by-step explanation:

19620 J.

Answer:

length = 5

Step-by-step explanation:

area = length × width

23 = length × 4.6

23 ÷ 4.6 = length

5 = length

Hope This Helped!

Step-by-step explanation:

First off we need to take the whole equation and multiply it so that we can get rid of the fractioned exponent. The number we would use is 12, giving us the new equation: a + 252 = 300. We then can subtract 252 from both sides of the equation, to get the exponent by itself and intentionally create an answer. This would be: a + 252 = 300,-252=48 or a = 48

We are left with A being equal to 48.

[tex]\dfrac 1{12} \cdot a +21 = 25\\\\\\\implies \dfrac a{12} = 25-21\\\\\\\implies \dfrac a{12} =4 \\\\\\\implies a = (12)(4) = 48[/tex]

Answer:

3.27

Step-by-step explanation:

the money he spent in total is 9.53 subtract it to 12.80

The amount of money left after he purchased his lunch is $3.27.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Josh had $12.80 to spend for lunch. For lunch, he purchased two hamburgers that cost $2.75 each, cheese fries that cost $1.85, and a drink that cost $2.18.

The amount of money left will be calculated as,

Money left = 12.80 - [(2 x 2.75 ) + 1.85 + 2.18]

Money left = 12.80 - 9.53

Money left =  $3.27

Therefore, the amount of money left after he purchased his lunch is $3.27.

To know more about an expression follow

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Answers:

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

(2, 10)

Step-by-step explanation:

If you graph the line and all 3 points, you can tell that only (2, 10) lies on the point, therefore, it would make the equation true. You can also figure it out algebraically.

[tex]10 = 7(2) - 4\\\rule{150}{0.5}\\10 = 14 - 4\\\\\boxed{10=10}[/tex]

Hope this helps.

42. 51 $\♤ ●gd rgbdyfurudgdhsuxu

Answer:

........................

The length of x is 3√10 units.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation connecting the lengths of the sides a, b, and the hypotenuse c. Pythagoras, a Greek philosopher who was born around 570 BC, is remembered by the theorem's name. The theorem has likely been proved the most times of any mathematical theorem using a variety of techniques.

As per the given data:

Perpendicular = 9 units

Base = 3 units

Using Pythagoras theorem to find x (hypotenuse):

[tex]x^2 = 9^2 + 3^2\\x^2 = 81 + 9\\x^2 = 90\\x = \sqrt{90}\\x = \sqrt{9\times10}\\x = 3\sqrt{10}[/tex]units

Hence, the length of x is 3√10 units.

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Answer:

A

Step-by-step explanation:

We can solve this by drawing it out

Family B has part of their north-south direction negated by going 1 degree north of east, because they are going south and then going north. Family A does not do this, and as a result, with all else equal, they go further away.

Answer:

Hope I explain it well!

Step-by-step explanation:

k + a/6 = 3k

well, I am not sure if we need to find the a, or the k, so lets find both!

--

First the a:

k + a/6 = 3k (subtract k)

a/6 = 2k (Multiply by 6)

a = 12k

--

Last, the k:

k + a/6 = 3k (Subtract k)

a/6 = 2k (Divide by 2)

a/12 = k

--

There you go, I hope you figure it out <3

Answer:

144°

96+48(further away angles)

Answer:

x = 144°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 48° + 96° = 144°