Answer:
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Step-by-step explanation:
Cost of 3 gallons of milk =3.79
Amount Kari paid =20
difference =20-3.79 = 16.21
so she will receive 16.21 back
Answer:
y =( -1/2 )x + 2
Step-by-step explanation:
first step is to determine the slope of the line ( which is the rise over the run) or symbolically slope is defined as m= ∆x / ∆y, so plugging those values we get...
m= ∆x / ∆y = (-1 - 0) / (4 - 2) = -1 / 2
so next is to find the zero( y-intercept) of the function by ....
y = mx + b
y = ( -1/2)x + b (since m is equal to -1/2)
2 = ( -1/2)0 + b
2= b
Answer:
See below.
Step-by-step explanation:
We know that the equation 
is a true equation for a particular value of x.
Now, let's see what happens if we divide everything by 4. In other words:
Divide:
So, we get .
When we divided everything by 4, we used the division property of equality. Under this property, the equation remains the same even if we divided since we did the <em>same thing to both sides of the equation. </em>
Therefore, 
is also true for the same value of x because it is just a simplified version of .
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.
