Answer:
The rule for number 20 is plus 1/6, and the unknown term is 5/6.
Step-by-step explanation:1. If you skip the first two fractions and move to 1, 1/6 you will notice that it has an increase of 1/6.
2. Now, to make sure that 1/6 is the correct rule, we do have to go back to the first two fractions and give them common denominators: 1/2 turns into 3/6, and 2/3 turns into 4/6.
3. No once you look at your fractions, you can see that 1/6 is the true rule.
4. Now that we know t he rule we can turn to completing the unknown term. Since we are only moving by 1/6 it makes it very easy to add that 1/6 to your 4/6 to get 5/6. You can't simplify 5/6, so your final answer for the unknown term is 5/6.
Hope this helps :)
You can use the Pythagorean theorem
Answer: The factor form of the function F(x) is 
, where 
gives two complex roots.
Explanation:
The given function is,
According to the rational root theorem 1 and -1 are the possible roots of each polynomial.
Put x=-1
Since the value of F(x) is 0 at x=-1 therefore the -1 is a root of given polynomial and (x+1) is a factor of F(x).
Use synthetic division method to divide the polynomial by (x+1).
The last row of the synthetic division shows the coefficient of remaining polynomial.
At x=2 the value of F(x) is 0, therefore (x-2) is a factor of F(x).
Use synthetic division method to divide the polynomial by (x-2).
Therefore the roots of F(x) are,
Where 
factors with real root and 
are factors with complex roots.
It’s an arithmetic sequence with a common difference of 12
