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
I think it would be obtuse, triangle, and a cute
Answer:
31°
Step-by-step explanation:
Rotations about the origin are rigid transformations, meaning that they preserve segment length and angle measure. Therefore, since ∠BCD and ∠B'C'D' are corresponding angles, we know that m∠BCD ≅ m∠B'C'D' = 31°.
Answer:
D
Step-by-step explanation:
multiplying f(x) × g(x) = (2x² + x - 3)(x + 2)
multiply each term in the first factor by each term in the second factor
= x(2x² + x - 3) + 2(2x² + x - 3) ← distributing gives
= 2x³ + x² - 3x + 4x² + 2x - 6 ← collect like terms
= 2x³ + 5x² - x - 6 → D