1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nataly_w [17]
3 years ago
12

(show the supposition, proof and conclusion)

Mathematics
1 answer:
larisa86 [58]3 years ago
5 0

Answer:

Step-by-step explanation:

We are given that a and b are rational numbers where b\neq0 and x is irrational number .

We have to prove a+bx is irrational number by contradiction.

Supposition:let  a+bx is a rational number then it can be written in \frac{p}{q} form

a+bx=\frac{p}{q} where q\neq0 where p and q are integers.

Proof:a+bx=\frac{p}{q}

After dividing p and q by common factor except 1 then we get

a+bx=\frac{r}{s}

r and s are coprime therefore, there is no common factor of r and s except 1.

a+bx=\frac{r}{s} where r and s are integers.

bx=\frac{r}{s}-a

x=\frac{\frac{r}{s}-a}{b}

When we subtract one rational from other rational number then we get again a rational number and we divide one rational by other rational number then we get quotient number which is also rational.

Therefore, the number on the right hand of equal to is rational number but x is a irrational number .A rational number is not equal to an irrational number .Therefore, it is contradict by taking a+bx is a rational number .Hence, a+bx is an irrational number.

Conclusion: a+bx is an irrational number.

You might be interested in
Solve 9/10=z/8 . Round to the nearest tenth.
kompoz [17]
\boxed {Question}
\frac{9}{10} =  \frac{z}{8}

\boxed {Cross \  multiply}
10z = 8 \times 9

\boxed {Evaluate}
10z = 72
z = 72 \div 10
z = 7.2

\Longrightarrow \bf \ Answer \ : \ z = 7.2

4 0
3 years ago
Please help, as soon as possible...
vodomira [7]

Answer:

1. a) Square

2. c) Rectangle

Step-by-step explanation:

1. If you cut this rectangular prism in way to be PERPENDICULAR to the base, that means you're cutting it straight down, from the top to the bottom, in a vertical line.  The cross-section obtained will be just like an end of the prism, which in this case is a square.  Because it's a regular rectangular prism, no matter where you cut it, as long as it's vertical, perpendicular to the base, you'll get a square due to this particular form.  Technically, the answer could also be a rectangle, since a square is a rectangle.

2.  you cut this rectangular prism in way to be PARALLEL to the base, that means you're cutting it straight, from the front to the back, in an horizontal line. The cross-section obtained will be just like an top of the prism, which in this case is a rectangle.  Because it's a regular rectangular prism, no matter where you cut it, as long as it's an horizontal line, parallel to the base, you'll get a rectangle due to this particular form.

6 0
3 years ago
Find the area of the sector.
Rasek [7]

Answer:

104.72 m^2.

Step-by-step explanation

I'm taking the angle to be 30 degrees.

Area of sector = area of the circle * 30/360

= pi*20^2 * 30/360

= 400pi * 1/12

= 104.72 m^2.

7 0
3 years ago
Read 2 more answers
A certain forest covers an area of 2100 km². Suppose that each year this area decreases by 3.5%. What will the area be after 5 y
Blizzard [7]

Answer:

\large\boxed{\sf \ \ \ 1757 \ km^2 \ \ \  }

Step-by-step explanation:

Hello,

<em>I would recommend that you checked the answers I have already provided as this is the same method for all these questions, and maybe try to solve this one before you check the solution.</em>

<u>At the beginning the area is 2100</u>

<u>After one year</u> the area will be

   2100*(1-3.5%)=2100*0.965

<u>After n years</u> the area will be

   2100\cdot0.965^n

So after 5 years the area will be

   2100\cdot0.965^5=1757.34027...

So rounded to the nearest square kilometer is 1757

Hope this helps

8 0
3 years ago
Read 2 more answers
Which equation described a line parallel to the line that connects points (-8 ,9) and (3, -4)?
musickatia [10]

Answer:

y = (-13/11)x - 5/11

Step-by-step explanation:

Where's the list of equations from which you're to choose?

The line that connects points (-8 ,9) and (3, -4) has the following slope:

          9 - (-4)

m = ----------------- = -13/11

          -8 - 3

Then the new line with this slope is y = (-13/11)x + c

and because (-8, 9) satisfies this equation, 9 = (-13/11)(-8) + c, and we need to calculate c from this.                                 9 = 104/11 + c, or

                                                                        -c = 104/11 - 99/11, or - 5/11

Then the desired equation is y = (-13/11)x - 5/11

8 0
1 year ago
Other questions:
  • PLEASE HELP I WILL MARK BRAINLEST PLEASE!!!!! 11 bounus points if u get it correct
    9·2 answers
  • What is the volume of a cone with a height of 9.5 inches and a radius of 8 inches? Cone V = 1 3 Bh 1. Rewrite the formula for th
    9·2 answers
  • X = 5<br> y = -3 What is the solution to the system of equations?
    15·1 answer
  • X over 3/4 =7/8<br> put answer in fraction form<br> first answer get brainliest
    11·1 answer
  • What slope passes through the points (2,7) and (-1,4) ?<br><br> A. -1 <br> B. 1<br> C. 3
    6·1 answer
  • Equation through the point (5,9) with a slope of -4
    11·2 answers
  • 2.John is playing a video game in which he needs to catch balls. He earns 20 points for each of the first 25 balls that
    8·1 answer
  • Which of these is a unit rate?
    6·1 answer
  • What is the value of 135,620 written in scientific notation ​
    9·1 answer
  • There are two cylinders.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!