Answer:
Γ = 15
Step-by-step explanation:
Given
f(x) = x² - 8x + Γ
with a = 1, b = - 8 and c = Γ , then
sum of zeros α + β = - 
= - 
= 8
product of zeros = αβ = 
= Γ
Given α - β = 2 , then
(α - β)² = 2²
α² - 2αβ + β² = 4 → (1)
and
(α + β)² = 8²
α² + 2αβ + β² = 64 → (2)
Add (1) and (2) term by term
2α² + 2β² = 68 ( divide through by 2 )
α² +β² = 34
Substitute α² + β² = 34 into (1)
34 - 2αβ = 4 ( subtract 34 from both sides )
- 2αβ = - 30 ( divide both sides by - 2 )
αβ = 15
Now
αβ = Γ = 15
Thus
f(x) = x² - 8x + 15
Step-by-step explanation:
( vertically opposite angles)
Answer:
Step-by-step explanation:
The <em>change in y</em> is the difference in y-coordinates between the lower right point and the upper left point. Similarly, the <em>change in x</em> is the difference in the x-coordinates of those points.
Answer:
x + y = 36.....Equation 1
x = 7 + 2y...... Equation 2
Step-by-step explanation:
Let the number of:
Orange goldfish = x
Black gold fish = y
Anna has a total of 36 goldfish in her aquarium, some are orange and some are black.
x + y = 36.....Equation 1
The number of orange goldfish is 7 more than twice the number of black goldfish.
x = 7 + 2y...... Equation 2
We can rewrite this as:
x - 2y = 7..... Equation 2
The system of equations below that can be used to describe the number of black and orange goldfish in Anna's aquarium is :
x + y = 36.....Equation 1
x = 7 + 2y...... Equation 2
2. f(x) = x - 2x² - 5 + 10x
=-2x² + 8x - 5
f'(x)= -4x + 8
4. y = 100(45x - 30 - 3x³ + 2x²)
= 100(-3x³ + 2x² + 45x -30)
= -300x³ + 200x² + 4500x - 3000
y' = -900x² + 400x + 4500
