Answer:
D: {9, 21, 33}
Step-by-step explanation:
Ken worked 2, 8 and 14 hours on 3 separate days.
For working 2 hours, his earnings were f(2) = 2(2) + 5, or 9;
For working 8 hours, his earnings were f(28) = 2(8) + 5, or 21; and
For working 14 hours, his earnings were f(14) = 2(14) + 5, or 33
Thus, the range of this function for the days given is {9, 21, 33} (Answer D)
After 4 atmospheres the diver descends -132 feet because -33*4=-132
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
