The y-value of the vertex is positive 3, as shown by the +3 on the right hand side of the equation, and the x-value is -1, from the (x+1)^2 (remember, when the number is inside the brackets, flip the sign) The vertex would be (-1, 3)
If you are looking for a rigorous answer (calculus), we must find the mininum point of the equation: f(x) = (x+1)^2 + 3 f
f'(x) = 2(x+1) = 2x + 2
2x + 2 = 0
x = -1
f(1) = (-1 + 1)^2 + 3
f(1) = 0 + 3 = 3
(-1, 3)
The answer is: x = -1, y = +4
Area of larger circle: 3.14 x 5^2 = 78.5
Area of small circle: 3.14 x 2^2 = 12.56
Difference of the 2 areas: 78.5 - 12.56 = 65.94
Probability of being in large circle but not small circle: 65.94 / 78.5 = 0.84 = 84%
The answer is A) 84%
8 kilometers is the answer
Hope this helps!:)
.23 and .24 is your answer.
