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DaniilM [7]
3 years ago
13

How, Let a = a rational number. Let b = an irrational number. Assume a + b = c and c is rational (attempting to disprove the con

jecture). a + b = c b = c - a Explain how Alfred's argument contradicts his initial assumption proving that the sum cannot be rational?
Mathematics
2 answers:
alisha [4.7K]3 years ago
7 0
If a and c are rational then a can be written as x/y and c  can be w/z  where w,x,y and z are integers

so as alfred said  if  b = c - a = x/y - w/z  =  (zx - wy) / yz  which is  rational.
So b cannot be irrational..
laiz [17]3 years ago
6 0
If 'a' is a rational number and c is rational, then 
a = p/q
c = r/s
where p,q,r,s are integers (q and s can't be zero)

Subtracting c-a gives
b = c-a
b = (p/q) - (r/s)
b = (ps/qs) - (qr/qs)
b = (ps - qr)/(qs)

The quantity pq - qr is an integer. The reason why is because ps and qr are both integers (multiplying any two integers leads to another integer). Subtracting any two integers results in another integer.

So we have (ps - qr)/(qs) in the form (integer)/(integer) = rational number

Therefore, b is a rational number, but this contradicts the given info that b is irrational. If b is irrational, then we CANNOT write it as a ratio of integers.

This contradiction proves the assumption "a+b = c and c is rational" is incorrect
The sum is irrational.

Therefore, if a+b = c, where 'a' is rational and b is irrational, then c is irrational.
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vaieri [72.5K]
Weekly compact: 18
Weekly standard: 25
Weekly full size: 36
Total weekly: 18 + 25 + 36 = 79

standard weekly as percent of total weekly:

25/79 * 100 = 31.6455...%

Answer: 32%
8 0
3 years ago
What is the answer to this?
Dmitry [639]

Answer:

  (c)  III

Step-by-step explanation:

If you simplify the equations and the left side is identical to the right side, then there are an infinite number of solutions: the equation is true for all values of x.

Another way to simplify the equation is to subtract the right side from both sides. If that simplifies to 0 = 0, then there are an infinite number of solutions.

__

<h3>I. </h3>

  2x -6 -6x = 2 -4x . . . . eliminate parentheses

  -4x -6 = -4x +2 . . . . no solutions (no value of x makes this true)

__

<h3>II.</h3>

  x +2 = 15x +10 +2x . . . . eliminate parentheses

  x +2 = 17x +10 . . . . one solution (x=-1/2)

__

<h3>III.</h3>

  4 +6x = 6x +4 . . . . eliminate parentheses

  6x +4 = 6x +4 . . . . infinite solutions

__

<h3>IV.</h3>

  6x +24 = 2x -4 . . . . eliminate parentheses; one solution (x=-7)

8 0
2 years ago
A square blanket has a diagonal stripe. The diagonal stripe is 66 inches long. How long is each side of the square blanket?
user100 [1]

9514 1404 393

Answer:

  33√2 in ≈ 46.7 inches

Step-by-step explanation:

The diagonal of a square is √2 times the side length, so for side length s we have ...

  s√2 = 66 in

  s = (66 in)/√2

  x = 33√2 in ≈ 46.7 in . . . . length of each side of the blanket

6 0
3 years ago
4. Tell whether the systems have one solution,
hjlf

Answer:

x= 2,

,y = 5

Step-by-step explanation:

Solve by Substitution :

// Solve equation [1] for the variable y

[1] y = 5x - 5

// Plug this in for variable y in equation [2]

[2] -4x + 2•(5x-5) = 2

[2] 6x = 12

// Solve equation [2] for the variable x

[2] 6x = 12

[2] x = 2

// By now we know this much :

x = 2

y = 5x-5

// Use the x value to solve for y

y = 5(2)-5 = 5

Solution :

{x,y} = {2,5}

5 0
2 years ago
10. Solve for z: 2 + 8 - z = -24
iVinArrow [24]

Answer:

The answer is z = 34.

Step-by-step explanation:

1) Simplify 2 + 8 - z to 10 - z.

10 - z =  - 24

2) Subtract 10 from both sides.

- z =  - 24 - 10

3) Simplify - 24 - 10 to -34.

- z =  - 34

4) Multiply both sides by -1.

z = 34

<u>Therefor</u><u>,</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>is</u><u> </u><u>z</u><u> </u><u>=</u><u> </u><u>34</u><u>.</u>

7 0
2 years ago
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