Assume a is not divisible by 10. (otherwise the problem is trivial).
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
<span>Then, a^j - a^i is divisible by 10.</span>
Answer:
c. 40
Step-by-step explanation:
General equation for a circle
(x - a)² + (y - b)² = r²
with (a,b) represents the center, (x,y) represents one of the points lie on the circle, and r represents the radius
Determine r² by substituting the points into the general equation
(x - a)² + (y - b)² = r²
(5 - (-1))² + (-4 - 2)² = r²
(5 + 1)² + (-6)² = r²
6² + 36 = r²
36 + 36 = r²
72 = r²
Determine the equation of the circle
(x - a)² + (y - b)² = r²
(x - (-1))² + (y - 2)² = 72
(x + 1)² + (y - 2)² = 72 (This is the equation of the circle)
The answer is 9/42. might be wrong I'm rusty on this.
Answer:
x = 4
Step-by-step explanation:
Step 1: Write equation
-2x + 1 = -4x + 9
Step 2: Solve for <em>x</em>
- Add 4x to both sides: 2x + 1 = 9
- Subtract 1 on both sides: 2x = 8
- Divide both sides by 2: x = 4
Step 3: Check
<em>Plug in x to verify it's a solution.</em>
-2(4) + 1 = -4(4) + 9
-8 + 1 = -16 + 9
-7 = -7