Write the expression 3m - 4n - 8 as a sum
1 answer:
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Answer:
The coordinates of the lines when both lines meets at point is ( 0, 0 )
Step-by-step explanation:
Given as :
The two lines are
x +
y =
And 4 x + y = 4
The coordinate of the lines are obtained when the two lines intersect
Let the coordinate of intersection points are ( x , y )
Now , The first lines as
x +
y =
Or, Taking LCM we get ,
=
Cross multiplication both sides
Or, 3 × ( 4 x + y ) = 2 × 6
Or, 3 × 4 x + 3 × y = 12
Or, 12 x + 3 y = 12 ...........A
Other line is 4 x + y = 4
i.e 3 × ( 4 x + y ) = 3 × 4
or, 12 x + 3 y = 12 .........B
Solving both the line equations
(12 x + 3 y ) - ( 12 x + 3 y ) = 12 - 12
I.e x = 0 and y = 0
So coordinates are ( x , y ) = ( 0 , 0 )
Hence The coordinates of the lines when both lines meets at point is ( 0, 0 ) Answer
We know that
case a)
the equation of the vertical parabola write in vertex form is
y=a(x-h)²+k,
where (h, k) is the vertex.
Using our vertex, we have:
y=a(x-2)²-1
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
0=a(5-2)²-1
0=a(3)²-1
0=9a-1
Add 1 to both sides:
0+1=9a-1+1
1=9a
Divide both sides by 9:
1/9 = 9a/9
1/9 = a
y=(1/9)(x-2)²-1
the answer is
a=1/9
case b)
the equation of the horizontal parabola write in vertex form is
x=a(y-k)²+h,
where (h, k) is the vertex.
Using our vertex, we have:
x=a(y+1)²+2,
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
5=a(0+1)²+2
5=a+2
a=5-2
a=3
x=3(y+1)²+2
the answer is
a=3
see the attached figure
case a)
the equation of the vertical parabola write in vertex form is
y=a(x-h)²+k,
where (h, k) is the vertex.
Using our vertex, we have:
y=a(x-2)²-1
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
0=a(5-2)²-1
0=a(3)²-1
0=9a-1
Add 1 to both sides:
0+1=9a-1+1
1=9a
Divide both sides by 9:
1/9 = 9a/9
1/9 = a
y=(1/9)(x-2)²-1
the answer is
a=1/9
case b)
the equation of the horizontal parabola write in vertex form is
x=a(y-k)²+h,
where (h, k) is the vertex.
Using our vertex, we have:
x=a(y+1)²+2,
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
5=a(0+1)²+2
5=a+2
a=5-2
a=3
x=3(y+1)²+2
the answer is
a=3
see the attached figure