and . So we have a remainder of
and . Subtracting this from the previous remainder gives a new remainder
and . Subtracting this from the previous remainder gives a new one of
and we're done since 2 does not divide . So we have
Note: When I use the double equal sign, I mean the triple bar used with modular arithmetic
10^3 = 1000 == -1 (mod 1001)
10^3 == -1 (mod 1001)
(10^3)^672 == (-1)^672 (mod 1001)
(10^(3*672) == 1 (mod 1001)
10^2016 == 1 (mod 1001)
10*10^2016 == 10*1 (mod 1001)
10^2017 == 10 (mod 1001)
Final Answer: 10
Answer:
3 movie tickets would cost 44.8 5 popcorns would cost 85
Step-by-step explanation:
29.4 divided by 2 equals 14.7
29.4 plus 14.7 equals 44.8
68 divided by 4 17
68 plus 17 equals 85
Answer:
Step-by-step explanation:
The coefficients of the quadratic x^2 + 7x + 3 are a = 1, b = 7 and c = 3.
The discriminant is b^2 - 4ac, or 49 - 4(1)(3), or 49-12, or 37.
Because the discriminant is positive, we know that this quadratic equation has two real, different solutions.
-7 ± √37
x = --------------- => x = (-7 + √37)/2 and x = (-7 - √37)/2
2
In words: This quadratic equation has two real, unequal solutions involving the radicand 37.