Multiply the number by 4. Add 10 to the product. Divide this sum by 2. Subtract 5 from the quotient. The first number is 1 and the result is 2

The second number is 5 and the result is 10

the third number is 9 and the result is 18

the fourth number is 10 and the result is 20

Write a conjecture that relates the result of the process to the original number selected. part a)

Represent the original number as n.

Answer is 2n

part b Represent the original number as n, and use deductive reasoning to prove the conjecture in part (a). Multiply the number by 4.

Help with part b please.

See Explanation

Step-by-step explanation:

Given the illustration in the question

Required:

Use deductive reasoning to prove (a)

From your question, you need only the (b) part and this is done as follows;

Step 1: Represent the number with: n

Step 2: Multiply n by 4: 4n

Step 3: Add 10 to (2) above: 4n + 10

Step 4: Divide (3) above by 2: (4n + 10)/2 = 4n/2 + 10/2 = 2n + 5

Step 5: Subtract 5 from (4): 2n + 5 - 5 = n

Hence, the end result is proved to be 2n

Test this with any of the given illustration in (a) part, your answer will always be 2n

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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