Answer:
Eq: (x+a/2)²+(y+1)²=(a²-8)/4
Center: O(-a/2, -1)
Radius: r=0.5×sqrt(a²-8)
Mandatory: a>2×sqrt(2)
Step-by-step explanation:
The circle with center in O(xo,yo) and radius r has the equation:
(x-xo)²+(y-yo)²=r²
We have:
x²+y²+ax+2y+3=0
But: x²+ax=x²+2(a/2)x+a²/4-a²/4= (x+a/2)²-a²/4
And
y²+2y+3=y²+2y+1+2=(y+1)²+2
Replacing, we get:
(x+a/2)²-a²/4+(y+1)²+2=0
(x+a/2)²+(y+1)²=a²/4-2=(a²-8)/4
By visual inspection we note that:
- center of circle: O(-a/2, -1)
- radius: r=sqrt((a²-8)/4)=0.5×sqrt(a²-8). This means a²>8 or a>2×sqrt(2)
Answer:
x=y^2-2
Step-by-step explanation:
This graph, is a parabola that opens to the right.
To answer this question, we just use the vertex form of a sideways parabola- x=a(y-k)^2+h.
In this case, the vertex is (-2, 0), and our value of a is 1, since it opens to the right.
This gives us: x=1(y-0)^2+(-2)
Which simplifies to: x=y^2-2.
Also, the answer to the previous two questions are wrong.
The D value (Domain) is actually [2, ∞)
The R value (Range) is actually "All real numbers" (-∞, ∞)
Let me know if this helps!
Answer:
Katherine: 920
Crystal: 552
Step-by-step explanation:
The total amount earned by each is 1472
The ratio of the earnings is Katherine / Crustal = 5/3
The total number of shares = 5 + 3 = 8
So the proportion for Katherine
5/8 = x / 1472 Cross multiply
8x = 5 * 1472
8x = 7360
x = 7360/8
x = 920
And the proportion for Crystal is
3/8 = x / 1472 Cross multiply
8x = 3 * 1472
8x = 4416
x = 4416 / 8
x = 552
