Prove that √2 is an irrational number and hence show that 3+5√3 is also irrational​

Answer:

look at the photo

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

Step-by-step explanation:

area of a rectangle is

length × width

so, in our case

2 2/5 km² = 1 2/5 × width (or length, it does not matter)

12/5 km² = 7/5 × width

width = 12/5 / 7/5 = 12×5 / 7×5 = 12/7 = 1 5/7 km

The length of the rope Kurt started with is 13 1/3 inches

From the question, we are to determine the total length of the rope

From the given information,

The first piece was 4 4/5 inches long

and

The second piece was 8 1/2 inches long

Then,

The length of the rope Kurt started with will be

4 4/5 + 8 1/2

[tex]4\frac{4}{5} + 8\frac{1}{2}[/tex]

First, convert the fractions into improper fractions

[tex]\frac{24}{5} + \frac{17}{2}[/tex]

The Lowest common multiple (LCM) of the denominators is 10.

Then, we get

[tex]\frac{(2\times 24) + (5 \times 17)}{10}[/tex]

= [tex]\frac{48 + 85}{10}[/tex]

= [tex]\frac{133}{10}[/tex]

= [tex]13 \frac{1}{3}[/tex]

Hence, the length of the rope Kurt started with is 13 1/3 inches.

Learn more on Calculating lengths here: https://brainly.com/question/26496891

#SPJ1

Answer:

x= -2, x= +11

Step-by-step explanation:

I hope this is right!

To factorise, we need two numbers that add to make -9 and multiply together to make -22.

2 - 11 works, so we put it in the brackets in this order.

(x + 2) (x - 11)

so x + 2 = 0 and x - 11 =0

but we could also simplify this to say that x could be either -2 or + 11.

I hope this helps.

Have a lovely day.

Answer: 3

Step-by-step explanation:

      First, we will write a mathematical equation for the phrase given.

-> Let n be "a number"

             four subtracted from twice a number is two

             four subtracted from twice a number = 2

             (twice a number) - 4 = 2

             2n - 4 = 2

      Now, we will solve this equation by isolating the variable.

             2n - 4 = 2

             2n = 6

             n = 3

Read more about algebraic equations here:

https://brainly.com/question/27791850

The value of the annual premium will be $1134.40

From the information given, the annual base premium will be:

= Liability premium + Collision premium + Comprehensive premium

= $383 + $240 + $86

= $709

The annual premium will be:

= Annual base premium × Driver eating factors

= $709 × 1.60

= $1134.40

Learn more about premium on:

brainly.com/question/25280754

#SPJ1

Answer:

$18

Step-by-step explanation:

One book=$6

Two books=$12

6(price of one book)x4(four books)=24

So then it says find it for three books

So then you do $6x3 books which is $18 :)

The type of statistical technique that is employed in future predictions of outcomes based on presented data is: C. linear regression.

Linear regression can be described as a statistical technique that is used to make future predictions using the regression equation of a line of best fit that models the relationship between variables Y and X.

Through the regression equation, outcomes of the future can be predicted. This statistical technique is known as: C. linear regression

Learn more about the linear regression on:

https://brainly.com/question/25987747

#SPJ4

Answer:

Step-by-step explanation:

Limits exist for:

[tex]\lim_{x \to4 \4} \frac{x^2 -x-12}{4-x}[/tex] = [tex]\frac{(x-4)(x+3)}{4-x}[/tex] = ( - 1 )( x + 3 ) = - 7

[tex]\lim_{x \to \ 2} \frac{x^2 +2x-8}{2-x}[/tex] = [tex]\frac{(x+4)(x-2)}{2-x}[/tex] = ( - 1 )( x + 4 ) = - 6

[tex]\lim_{x \to2 } \frac{x^2 +3x - 10}{x^2 -4}[/tex] = [tex]\frac{(x+5)(x-2)}{(x+2)(x-2)}[/tex] = [tex]\frac{x+5}{x+2}[/tex] = [tex]\frac{7}{4}[/tex]

Answer:

1/7

Step-by-step explanation:

Answer:

  0, for q ≠ 0 and q ≠ 1

Step-by-step explanation:

Assuming q ≠ 0, you want to find the value of x such that ...

  q^x = 1

This is solved using logarithms.

__

  x·log(q) = log(1) = 0

The zero product rule tells us this will have two solutions:

  x = 0

  log(q) = 0   ⇒   q = 1

If q is not 0 or 1, then its value is 1 when raised to the 0 power. If q is 1, then its value will be 1 when raised to any power.

_____

Additional comment

The applicable rule of logarithms is ...

  log(a^b) = b·log(a)

Answer:

21 316/729

Key rules to solve:

Step-by-step explanation:

[tex]\left(\frac{2-1}{2\cdot \:7\frac{1}{3}}\right)^6[/tex]

[tex]=\left(\frac{2-1}{2\cdot \frac{22}{3}}\right)^6[/tex]

[tex]=\frac{\left(2-1\right)^6}{\left(2\cdot \frac{22}{3}\right)^6}[/tex]

[tex]=\frac{1}{\left(2\cdot \frac{22}{3}\right)^6}[/tex]

[tex]=\frac{1}{\frac{7256313856}{729}}[/tex]

[tex]\rightarrow 21 \frac{316}{729}[/tex]

Teniendo en cuenta la definición de sistema de ecuaciones lineales, cada medida tiene una capacidad de A= 8 L, B= 4 L y C= 12 L.

Un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones de primer grado, en el cual se relacionan dos o más incógnitas.

Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema. Es decir, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en ambas ecuaciones.

En este caso, se dispone de un recipiente de 24 litros de capacidad y de tres medidas, A, B y C.

Se sabe que el volumen de A es el doble del de B → A=2B

Las tres medidas llenan el depósito → A+ B +C= 24 L

Las dos primeras medidas llenan hasta la mitad del recipiente → A +B= 24 L÷2 → A +B= 12 L

Entonces, el sistema de ecuaciones a resolver es el formado por las tres ecuaciones anteriormente mencionadas.

Existiendo diversos métodos para resolver un sistema de ecuaciones, se decide resolver mediante el método de sustitución, que consiste en despejar una de las dos variables en una de las ecuaciones del sistema y sustituir su valor en la otra ecuación.

En este caso, reemplazando la primer ecuación en la tercera ecuación se obtiene:

2B +B= 12 L

3B= 12 L

B= 12 L÷3

B= 4 L

Reemplazando este valor en la primer ecuación se obtiene:

A=2B

A=2×4 L

A= 8 L

Finalmente, para obtener el valor de C se reemplaza el valor de A y B en la segunda ecuación:

A + B + C= 24 L

8 L + 4 L + C= 24 L

12 L + C= 24 L

C= 24 L - 12 L

C= 12 L

Finalmente, cada medida tiene una capacidad de A= 8 L, B= 4 L y C= 12 L.

Aprende más sobre sistemas de ecuaciones lineales:

brainly.com/question/15924499

brainly.com/question/17411423

#SPJ1

Answer:

P(AUB)=P(A)+P(B)

Step-by-step explanation:

I found it somewhereI don't know?Trust me:)

Answer:

14 Minutes

Step-by-step explanation:

1.68 divided by 0.12 is 14 or Multiply 0.12 by 14 and you get 1.68.

Answers:

======================================================

Explanation:

Skip to the "Work Shown" section below to see the steps for each part.

Each variable is a place holder for some unknown number. We can think of it like a box that holds a number. Luckily the letter x is found in the word "box" to help cement this line of thinking.

1x = 1 box

2x = 2 boxes

3x = 3 boxes

and so on

This shorthand notation allows us to quickly add boxes

2 boxes + 3 boxes = 5 boxes

So 2x+3x = 5x

And we can subtract boxes as well

7 boxes - 3 boxes = 7x - 3x = 4x = 4 boxes

The same number must go in box x for this to work out.

When it comes to dealing with negative numbers, it might help to use a vertical number line. I like to think of it like going up and down an elevator on a skyscraper. Negative integers represent basement levels.

It's possible to have boxes within boxes. The box A has the three boxes x-y+z inside it. So wherever we see an "A", replace it with x-y+z. Unfortunately we don't know what numbers go in the boxes for x, -y and z. Use the same type of thinking for B and C.

Don't forget to use the distributive property to distribute the negative through to each term.

Example: (x+y)-(w+z) = x+y-w-z

Many students make the mistake in saying that (x+y)-(w+z) = x+y-w+z which is not true. The +z should be -z at the very end.

Let me know if you have any other questions.

The next section below shows the steps needed to get the three answers.

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

Work Shown:

Part (I)

A+B+C = (x-y+z)+(2x-3y+4z)+(4x-5y-6z)

A+B+C = (x+2x+4x)+(-y-3y-5y)+(z+4z-6z)

A+B+C = 7x - 9y - z

Part (II)

A-B+C = (x-y+z)-(2x-3y+4z)+(4x-5y-6z)

A-B+C = x-y+z-2x+3y-4z+4x-5y-6z

A-B+C = (x-2x+4x)+(-y+3y-5y)+(z-4z-6z)

A-B+C = 3x - 3y - 9z

Part (III)

A+B-C =  (x-y+z)+(2x-3y+4z)-(4x-5y-6z)

A+B-C =  x-y+z+2x-3y+4z-4x+5y+6z

A+B-C = (x+2x-4x)+(-y-3y+5y)+(z+4z+6z)

A+B-C = -x + y + 11z

there you go hope it helps :)

For this problem, we need to use our integral knowledge to set up the problem:

The bounds will be from 2 to 6, cutting tiny horizontal bars into the graph, to approximate the area

Now for the function inside the integral:

 ⇒ it is the top function minus the bottom function

       ⇒ function within integral = x² - 0

Let's put it all together and solve:

   [tex]Area=\int\limits^6_2 {x^2-0} \, dx =\int\limits^6_2 {x^2} \, dx=\frac{6^3}{3} -\frac{2^3}{3} \\Area=\frac{6^3-2^3}{3} =\frac{216-8}{3} =\frac{208}{3}[/tex]

Answer: 208/3 ≈ 69.333

Hope that helps!

The appropriate domain of the population function is 0 ≤ t ≤ 14

The function is given as:

P(t) = 3(2)^t

From the question, we understand that the maximum time is 2 weeks.

2 weeks in days is 14 days

This means that the function is valid for 14 days i.e. t = 0 to 14

Hence, the appropriate domain of the population function is 0 ≤ t ≤ 14

Read more about domain at:

https://brainly.com/question/1770447

#SPJ1

The diagram shows that the triangles on the graph had similar ratios, as such their vertical heights to their horizontal are equivalent.

Option D is correct.

The slope of a graph determines the steepness of the graph and it is the difference between two points on the y-coordinate(rise) and the difference between two points on the x-coordinate(run).

[tex]\mathbf{slope = \dfrac{rise}{run}}[/tex]

[tex]\mathbf{slope = \dfrac{\Delta y}{\Delta x}}[/tex]

[tex]\mathbf{slope = \dfrac{ y_2-y_1}{x_2-x_1}}[/tex]

From the diagram attached, we can see that the triangles on the graph had similar ratios, as such their vertical heights(y-coordinates) to their horizontal (x-coordinates) are equivalent.

Learn more about the slope of a graph here:

https://brainly.com/question/19376563

#SPJ1

choice (A) is correct

hope it helps

Answer:

252 in^3

Step-by-step explanation:

give brainliest, please!

hope this helps :)

to figure out the volume we have to multiply the base, and height together.

the base is 18 and the height is 14.

18 times 14 = 252

252 in^3

Answer:

3,024 in. 3

Step-by-step explanation:

1 foot = 12 inches

18x12x14= 3024

I just did this assignment

Answer: you can use .5 yards of ribbon

Step-by-step explanation: this equals 18inches or 1.5 feet hope this helps

Answer:

Zero

Step-by-step explanation:

the line is not going up or down therefore there is no slope

Answer:

Point A

Step-by-step explanation:

Please Mark me as brainliest

Answer: point A

Step-by-step explanation:

You move two to the right and up one because the two is the x-coordinate so on the x-axis you start from (0,0) and move to the right since it’s positive. If it was negative it would be to the left. Same as when dealing with y. The y coordinate is one so you move up on the y-axis(always start from the origin which is (0,0)). If it was negative you move down. Rise/run in this case 1/2.

Answer:

she should get ready by 11:10

Step-by-step explanation:

Add All the time up 75(1 hour 15min=60+75)+40+25+30=170minutes

170minutes/60= 2 hour 50minutes

subtract 2 hour 50minutes from 2:00

= 11:10

Answer:

Step-by-step explanation:

The total number of bags in the bottle = 20 + 15 = 35

Then

the probability that the first bag is blue = 20/35

If we replace the first bag :

the probability that the second (picked) bag is blue = 15/35

Conclusion:

If two bags are picked at random one after the other with replacement

Then

the probability that the first bag is blue and then red is :

(20÷35)×(15÷35)

= (4÷7)×(3÷7)

= 12÷49

= 0.244897959184

The crane is 139.8cm tall.

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Using Trigonometry

tan 30 = h/y

1/√3 = h/y

y= h√3

and, tan 25= h/y+62

         0.96= h/(h√3 +62)

             h= 0..96 (h√3 +62)

             h= 0.96*h*1.732+0.96*62

             h=0.796h +28.52

             0.2404h= 28.52

                  h= 139.8 cm

Hence, whooping crane is 139.8 cm.

Learn more about angle of elevation here:

https://brainly.com/question/21137209

#SPJ1