Answer:
x^4-3x^3+2x^2+2x-2
Step-by-step explanation:
Multiply the second the second parentheses by each term from the first parentheses
Distribute x^3 through the parentheses
Then collect all like terms to get an answer of x^4-3x^3+2x^2+2x-2
Answer:
y=-3/5x+4
Step-by-step explanation:
Pick any two points the line goes through.
I picked
(0,4) and (5,1)
There are a few ways to do this but ultimately, it’s the same concept. I will use slope-intercept form which for me was always easier.
y=mx+b where m is the slope and b is the y-intercept. The y-intercept is the point where the line crosses the y-axis which in this case is point (0,4) so the b=4.
To find the slope, use rise/run between the two points you chose. Point (5,1) is 3 units UNDER point (0,4) so now we have -3/run because -3 is the “rise”. After you count down 3 units always go right. After going right 5 units, you touch point (5,1). So the “run” is 5. Which means that the slope is -3/5.
m=-3/5 and b=4
So the equation is:
y=-3/5x+4
Hope this helps!!
Answer should be b, not 100% sure
1
:x
2
+y
2
−6x−9y+13=0
(x−3)
2
+(y−
2
9
)
2
−9−
4
81
+13=0
(x−3)
2
+(y−
2
9
)
2
=
4
65
Here,
r
1
=
2
65
C
1
=(3,
2
9
)
Equation of another circle-
S
2
:x
2
+y
2
−2x−16y=0
(x−1)
2
+(y−8)
2
−1−64=0
(x−1)
2
+(y−8)
2
=65
Here,
r
2
=
65
C
2
=(1,8)
Distance between the centre of two circles-
C
1
C
2
=
(3−1)
2
+(8−
2
9
)
2
C
1
C
2
=
4+
4
49
=
2
65
∣r
2
−r
1
∣=
∣
∣
∣
∣
∣
∣
65
−
2
65
∣
∣
∣
∣
∣
∣
=
2
65
∵C
1
C
2
=∣r
1
−r
2
∣
Thus the two circles touches each other internally.
Since the circle touches each other internally. The point of contact P divides C
1
C
2
externally in the ratio r
1
:r
2
, i.e.,
2
65
:
65
=1:2
Therefore, coordinates of P are-
⎝
⎜
⎜
⎜
⎜
⎜
⎛
1−2
1(1)−2(3)
,
1−2
1(8)−2(
2
9
)
⎠
⎟
⎟
⎟
⎟
⎟
⎞
=(5,1)
Therefore,
Equation of common tangent is-
S
1
−S
2
=0
(5x+y−6(
2
x+5
)−9(
2
y+1
)+13)−(5x+y−2(
2
x+5
)−16(
2
y+1
))=0
2
−6x−9y−13
+x+8y+13=0
4x−7y−13=0
Hence the point of contact is (5,1) and the equation of common tangent is 4x−7y−13=0.
Answer:
9
Step-by-step explanation:
8/12=2/3
6/9=2/3
