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:
y = 1
Step-by-step explanation:
The slope is 0.
y = (0)x + b
y = b
The line passes through (0, 1).
(x, y)
Put y as 1.
1 = b
The y-intercept is 1.
y = 1
Answer:
34 rolls
Step-by-step explanation:
For Frank to cover his whole ceiling, he needs paper that will cover
20 ft x 20 ft
20 x 20 = 400 ft
So, Frank needs to cover 400 ft of the ceiling. He has to split up this large need for paper into smaller rolls, because the rolls he can buy are small.
If each roll has 12 ft, we need to find how many 12-feet are in 400 feet.
To do this, we should divide
400 / 12
= 33.333
Because Frank cannot cover the whole ceiling using only 33 rolls, he has to buy an additional roll to make sure he can cover the extra area [that would be left over if he were to only buy 33 rolls, which would only cover 396 feet]
So, Frank will need to buy 34 rolls to have enough paper to entirely cover his ceiling.
