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)
2, 3, 5. I just solved them and they look equivalent.
Answer:
y=-3x-3
Step-by-step explanation:
Rotate 90 degrees
find slope
find y intercept
write equation
Answer:
You <u>solve</u> the equation.
Step-by-step explanation:
The process of finding variable values that make the equation true is called <em>solving</em> the equation.
