Answer:
B
Step-by-step explanation:
OHXOKXSOIXSOIIZ OIZOKJOZLKZLKZLKZLKSALK
Answer:
Step-by-step explanation:
A standard polynomial in factored form is given by:
Where <em>p</em> and <em>q</em> are the zeros.
We want to find a third-degree polynomial with zeros <em>x</em> = 2 and <em>x </em>= -8i and equals 320 when <em>x </em>= 4.
First, by the Complex Root Theorem, if <em>x</em> = -8i is a root, then <em>x </em>= 8i must also be a root.
Therefore, we acquire:
Simplify:
Expand the second and third factors:
Hence, our function is now:
It equals 320 when <em>x</em> = 4. Therefore:
Solve for <em>a</em>. Evaluate:
So:
Our third-degree polynomial equation is:
Problem: find 0 ≤ x ≤ 28 such that x^85 ≡ 6 modulo 35.
By Fermat-Euler theorem:
If a and n are coprime, i.e. (a,n)=1, then
a^phi(n) ≡ 1 mod n
where phi(n)=totient function, the number of positive integers less than n that is coprime with n.
for n=35, phi(35)=24 calculated as follows:
There are 10 positive integers from 1 to 34 which are NOT coprime with 35, namely {5,7,10,14,15,20,21,25,28,30}.Therefore phi(35)=34-10=24
From Fermat-Euler theorem,
x^(phi(35) = x^24 ≡ 1 modulo 35 since (24,35)=1, i.e. 24 and 35 are coprime.
=>
x^12 ≡ ± 1 modulo 35. ...........(1)
and
x^85 ≡ x^(85-3*24) ≡ x^(85-72) ≡ x^(13) ≡ 6 mod 35 ............(2)
Substituting (1) in (2)
x^(12)*x ≡ 6 mod 35
=>
(+1)*x = 6 mod 35 or (-1)*x ≡ 6 mod 35
x ≡ 6 mod 35 x ≡ -6 mod 35 (rejected)
=> x=6
So
6^85 ≡ 6 mod 35
If any clarifications are needed or if you find any errors, please post.
Answer:
That should be the answer
Step-by-step explanation:
the formule is y = mx +b
m is the slope and b is the y-intercept
9514 1404 393
Answer:
1080 minutes
Step-by-step explanation:
The greatest common factor (GCF) of the two times is 15 minutes, so their least common multiple is (120×135)/15 = 1080 minutes.
In that time, Kayla will have watched 9 shows, and Josh will have watched 8.
It will be 1080 minutes before they start again at the same time.
