Answer:
α² +β² = 3 4/9
Step-by-step explanation:
Assuming α and β are solutions to the equation, it can be factored as ...
(x -α)(x -β) = 0
Expanding this, we get ...
x² -(α +β)x +αβ = 0
Dividing the original equation by 3, we find ...
x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ ⇒ (α+β) = -1/3, αβ = -5/3
We know that the square (α+β)² can be expanded to ...
(α +β)² = α² +β² +2αβ
α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ
Substituting the values for (α+β) and αβ, we find the desired expression is ...
α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9
α² +β² = 3 4/9
Step-by-step explanation:
The answer to this question is D.
Answer: The correct answer is Choice A (6, -1).
Since we have the slope and the equation, we can find the y-intercept and write the equation of the line.
y = -0.75x + b
5 = -0.75(-2) + b
5 = 1.5 + b
b = 3.5
Therefore, the equation is y = -0.75x + 3.5.
Now, just plug in the points until one of that satisfies the equation. The point (6, -1) will satisfy the equation.
Answer:
49.93
Step-by-step explanation:
it is 0.07 away from 50
Answer:
468.74.
Step-by-step explanation:
We have been given that z varies directly as x and inversely as y. We can represent this information in an equation as:
First of all, we will find constant of variation using our given equation.
Upon substituting our given values in our equation, we will get:
Therefore, z is approximately 468.74.