Repeat the following procedure for the four given numbers.
Multiply the number by 8 . Add 12 to the product. Divide this sum by 2 . Subtract 6 from the quotient.
The 1 st number is 2 . The result is 8 .
The 2 nd number is 5 . The result is 20 .
The 3rd number is 9 . The result is 36 .
The 4 th number is 11 . The rult is 44 .
a. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as .
The result is . (Simplify your answer.)
b. Represent the original number as , and use deductive reasoning to prove the conjecture in part (a).
Multiply the number by 8 .

Question

Repeat the following procedure for the four given numbers.
Multiply the number by 8 . Add 12 to the product. Divide this sum by 2 . Subtract 6 from the quotient.
The 1 st number is 2 . The result is 8 .
The 2 nd number is 5 . The result is 20 .
The 3rd number is 9 . The result is 36 .
The 4 th number is 11 . The rult is 44 .
a. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as

.
The result is

. (Simplify your answer.)
b. Represent the original number as

, and use deductive reasoning to prove the conjecture in part (a).
Multiply the number by 8 .

UpStudy AI · Accepted Answer

### a. Conjecture

The result of the process is $$4n$$.

### b. Proof of the Conjecture

Let $$ n $$ be the original number selected. We'll follow the given procedure step by step to prove that the final result is $$4n$$.

1. **Multiply the number by 8**:
   $$
   8n
   $$

2. **Add 12 to the product**:
   $$
   8n + 12
   $$

3. **Divide this sum by 2**:
   $$
   \frac{8n + 12}{2} = 4n + 6
   $$
   
4. **Subtract 6 from the quotient**:
   $$
   (4n + 6) - 6 = 4n
   $$
   
**Conclusion**:

After performing all the steps, the final result is $$4n$$. This confirms that for any original number $$n$$, the outcome of the process will always be four times the original number.

$$
\boxed{4n}
$$
The final result is $$4n$$.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions