Answer:
Step-by-step explanation:
just remember that ![\sqrt{x} = x^{1/2} ....... \sqrt[3]{x} = x^{1/3} \\also that (x^{a})^{b} = x^{a*b}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%3D%20x%5E%7B1%2F2%7D%20%20.......%20%20%5Csqrt%5B3%5D%7Bx%7D%20%3D%20x%5E%7B1%2F3%7D%20%5C%5Calso%20%20that%20%28x%5E%7Ba%7D%29%5E%7Bb%7D%20%20%3D%20x%5E%7Ba%2Ab%7D)
1) x^3 = x^ (3/4) ===> FALSE
2) x^3/4 = x^3/4 ===> TRUE
3) x^3/4 = x^3/4 ===> TRUE
4) x^(4/3) = x^(4/3) ===> TRUE
Answer:
K = 10
Step-by-step explanation:
Interior angle adjacent to y = 180-115 = 65
Sum of interior angles in a triangle = 180
This the remaining interior angles for the triangle = 180-65= 115
In other words,
4K+5+6k+10 = 115
Simplify and solve:
10k + 15 = 115
10k = 115-15=100
K= 100/10 = 10
Hope this helps.
Good Luck
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:
Part A: A ratio of 2:1 means that he uses<u><em> </em></u><u><em>2 cups of yellow paint for each cup of blue paint.</em></u>
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Part B: The ratio of yellow to blue is 2:1 = 2/1. So, if for 2 yellow is 1 blue, then for 1 yellow is x:
2/1 = 1/x
x = (1*1) / 2
x = 1/2
<u><em>For each cup of yellow paint, Greg should add 1/2 cup of blue paint.</em></u>
<u><em></em></u>
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Part C: 6 cups cost $54, then 1 cup cost:
54 / 6 = 9
<u><em>The price per cup of yellow paint is $9.</em></u>
<u><em></em></u>
