Answer:
see explanation
Step-by-step explanation:
(5)
Since ∠EBA = 90° then ∠ABD = 90° ( straight angle ) and
∠ABC + ∠CBD = ∠ABD, that is
2x + 3x - 10 = 90, simplifying
5x - 10 = 90 ( add 10 to both sides )
5x = 100 ( divide both sides by 5 )
x = 20, thus
∠ABC = 2x = 2 × 20 = 40°
∠CBD = 3x - 10 = (3 × 20) - 10 = 60 - 10 = 50°
(6)
4x - 18 = 3x + 7 ( vertical angles are congruent )
Subtract 3x from both sides
x - 18 = 7 ( add 18 to both sides )
x = 25
7y = 5y + 28 ( vertical angles are congruent )
Subtract 5y from both sides
2y = 28 ( divide both sides by 2 )
y = 14
Answer:30 tests
Step-by-step explanation:
16=2/3 -4
20=2/3
10=1/3
30tests
You find a triangle with two of the points. Use rise over run (up or down and left or right) See how many squares rise takes and how many squares run takes. Then with rise/run simplfy the fraction and you should get the slope.
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:
Exponential Growth
Step-by-step explanation:
