Let's try to find some primes that divide this number.
The number is not divisible by 2, because it is odd.
The number is divisible by 3 though, because the sum of its digits is:
So, we can divide the number by 3 and keep going with the factorization:
This number is again divisible by 3, because
We have
This number is no longer divisible by 3. Let's go on looking for primes that divide it: 5 doesn't because the number doesn't end in 0 nor 5. This number is not divisible by 7 or 11 either (just try). It is divisible by 13 though: we have
And 557 is prime, so we're done. This means that the prime factorization of 65169 is
Answer:
x≥2.56
Step-by-step explanation:
first we can write the inequality
2+9x≥25
we can now solve this with algebra
9x≥23
x≥2.56
Answer:
1. Technically 2, but might be 0 in your teacher's opinion.
2. 1
Step-by-step explanation:
Solving problem one.
So I don't know if you have learned about imaginary numbers, but if you have, then you would end up with two answers if you plugged in the quadratic formula.
If you haven't learned about imaginary numbers, then I would say your best option would be to write 'No real solution' since there are technically 2 solutions.
Solving problem two.
Turns out this quadratic has a special property and it's actually a square of one equation. You can find out by just factoring the equation.
It's (3x-2)^2. Since it's squared, that means that only 2/3 would work as x in this equation.
Essentially, we are trying to find the missing constant term of 
(remember that we are subtracting 
due to the negative sign in front of the second term). Let's expand this to see what we can work with:
Now, we know the second term is 
, so let's set the second term in the polynomial we just found equal to :
- Divide both sides of the equation by
- Divide both sides of the equation by 2
We have found . We know the missing constant term is 
, according to the polynomial we found earlier. Thus, the missing term is:
The missing constant term is 36.
