Answer:
Solutions are 2, -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
or 2, -1 + 1.58 i and -1 - 1.58i
(where the last 2 are equal to nearest hundredth).
Step-by-step explanation:
The real solution is x = 2:-
x^3 - 8 = 0
x^3 = 8
x = cube root of 8 = 2
Note that a cubic equation must have a total of 3 roots ( real and complex in this case). We can find the 2 complex roots by using the following identity:-
a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Here a = x and b = 2 so we have
(x - 2)(x^2 + 2x + 4) = 0
To find the complex roots we solve x^2 + 2x + 4 = 0:-
Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2
= -1 +/- (sqrt( -10)) / 2
= -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
So you need to divide 430 into 25 to get 17.2
So he/she earns $17.20 an hour or in word format :seventeen dollars and twenty cents and hour
B is the answer because domain is x and range is y
Definitions of Right Angles
#831 is one out of the 535 left
1/535
= 0.002
= 0.2%
The probability is 0.2%, which is very low. It's even less than 1%. This means it's still very unlikely to get #831 and more like to get one of the other 534 numbers.
0.2% compared to 99.8%
If you look at these 2 numbers on a number line, you can see 99.8% (the other numbers) is more closer to 100%. This proves Augustin is more likely to chose one of the other numbers and doesn't have to be nervous.
