put the steps to proof that the sum t=r+s is irrational if r is a rational in the correct sequence.

Step 1. subtract, writing a as a fraction
step 2. for a contradiction, assume that t is rational, and write r and t as fractions.
step 3 realize a contradiction.
step 4. find a common denominator

A B C or D
A. step 1, step 3, step 2, step 4
B.step 3, step 4, step 2, step 1
C. step 4, step 2, step 1, step 3
D. step 2, step 4, step 1, step 3

9 answers

To prove that the sum \( t = r + s \) is irrational if \( r \) is rational and \( s \) is irrational, the correct sequence of steps is as follows:

  1. Step 2: For a contradiction, assume that \( t \) is rational, and write \( r \) and \( t \) as fractions.
  2. Step 4: Find a common denominator.
  3. Step 1: Subtract, writing \( s \) as a fraction.
  4. Step 3: Realize a contradiction.

Thus, the correct sequence is:

D. step 2, step 4, step 1, step 3

are you sure

Let's clarify the proof that \( t = r + s \) is irrational if \( r \) is rational and \( s \) is irrational.

  1. Step 2: For a contradiction, assume that \( t \) is rational. Write \( r \) and \( t \) as fractions.
  2. Step 4: Find a common denominator in the fractions for \( r \) and \( t \).
  3. Step 1: Subtract \( r \) from \( t \), rewriting it as a fraction (this would give you \( s \)).
  4. Step 3: Realize a contradiction (since \( s \) would then have to be rational, contradicting the assumption that it is irrational).

Given this breakdown, the correct order of steps is indeed:

D. step 2, step 4, step 1, step 3.

I apologize for any confusion in my previous response, but my answer about the correct order is accurate. Thank you for your patience!

what type of number will the product of pie and 3/4 be?

The product of \(\pi\) (which is an irrational number) and \(\frac{3}{4}\) (which is a rational number) will also be an irrational number.

When you multiply an irrational number by a non-zero rational number, the result is always irrational. Therefore, the product \(\frac{3}{4} \times \pi\) is irrational.

consider the expression 47/3+sqrt121 will the sum of the two numbers produce a rational number? explain your reasoning in 1-2 sentences

The expression \( \frac{47}{3} + \sqrt{121} \) will produce a rational number because \( \frac{47}{3} \) is rational and \( \sqrt{121} = 11 \) is also rational. The sum of two rational numbers is always rational, so their total will be rational.

prove that the product of the two rational numbers sqrt 36 and 5/3 is a rational number. Find the product and explain how you know it is a rational number. explain in 1-2 sentences

To prove that the product of the two rational numbers \( \sqrt{36} \) and \( \frac{5}{3} \) is rational, we first calculate the product:

\[ \sqrt{36} = 6 \quad (\text{which is rational}) \] Now, multiplying by \( \frac{5}{3} \):

\[ 6 \times \frac{5}{3} = \frac{30}{3} = 10 \]

The product is \( 10 \), which is a rational number. A number is rational if it can be expressed as a fraction of two integers, and here \( 10 \) can be expressed as \( \frac{10}{1} \). Thus, the product is confirmed to be rational.