Yes, 23 has an inverse mod 1000 because gcd(23, 1000) = 1 (i.e. they are coprime).
Let <em>x</em> be the inverse. Then <em>x</em> is such that
23<em>x</em> ≡ 1 (mod 1000)
Use the Euclidean algorithm to solve for <em>x</em> :
1000 = 43×23 + 11
23 = 2×11 + 1
→ 1 ≡ 23 - 2×11 (mod 1000)
→ 1 ≡ 23 - 2×(1000 - 43×23) (mod 1000)
→ 1 ≡ 23 - 2×1000 + 86×23 (mod 1000)
→ 1 ≡ 87×23 - 2×1000 ≡ 87×23 (mod 1000)
→ 23⁻¹ ≡ 87 (mod 1000)
Answer:
18, is your answer!
Step-by-step explanation:
Take the as together and take the bs together.
5a + 3b - 6a - b.
5a - 6a + 3b - b. Then simplify.
-a + 2b.
That's it.
Answer:
1 (-9, -4)
2 (-6, 2)
Step-by-step explanation:
1- when you reflect along the x axis keep the x the same and change the y.
2- when you reflect along the y axis keep the y the same and change the x.
