The general equation given is x^2 - 4x + y^2 = -3. Transform this to an equation of a circle of the form x^2 + y^2 = r^2.
Use completing the square method:
x^2 - 4x + 4 + y^2 = -3 + 4
(x - 2)^2 + y^2 = 1
the center of the circle is (2,0) and r = 1
To check if it intersects the y axis, find the value of the x-intercept.
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
Answer:
D) x ≤ 3
Step-by-step explanation:
The inequality that matches the graph is x ≤ 3. This is because x is less than or equal to 3 as shown in the graph.
Answer:
x=4
Step-by-step explanation:
since triangles are proportional by 2:1, then:
16/2=3x-4
8=3x-4
3x=12
x=4
Answer:
B.
Step-by-step explanation:
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