Answer:
y=4/5x+1
Step-by-step explanation:
y=mx+b
m = slope = 4/5
b = y-intercept= 1
y=4/5x+1
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)
(m - n)(r - s) Hope this helps and heve a nice day!
Let:
x = first consecutive integer (or first side of △)
x + 1 = second consecutive integer (or second side of △)
x + 2 = third consecutive integer (or third side of △)
The formula for a perimeter of △ is simply the addition of three sides (or length). Since the given perimeter is 114 cm,
x + x+1 + x+2 = 114
3x + 3 = 114
3x = 114 - 3
3x = 111
x = 111 /3 = 37 cm
The three sides are 37 cm, 38 cm, and 39 cm.
This is the same as any math problem you may have solved before.
First, start by isolating the x on one side. I will choose to keep the coefficient positive, so I will add x to both sides.
6>2x+2
Subtract 2
4>2x
Divide by 2
2>x
Or
x<2
