<span>when you are solving systems of equation with three variables we use the elimination method to make a system of two equations in two variables</span>
I think that translation is the only one that DOES preserve orientation.
Rotation and reflection definitely don't, and I'm not sure about dilation.
Check the picture below.
notice, the focus point is at 4,5 whilst the directrix line is at y = -3, below the focus point, meaning the parabola is vertical and opening upwards.
keeping in mind that the vertex is "p" distance from either of these fellows, then the vertex is half-way between both of them, notice in the picture, the distance from y = 5 to y = -3 is 8 units, half that is 4 units, thus the vertex 4 units from the focus or 4 units from the directrix, that puts it at (4,1), whilst "p" is 4, since the parabola is opening upwards, is a positive 4 then.

6/10 rounded to the nearest tenth inches a hour of rain fell
Answer:
<u>Ques 1)</u>
(-2,12)
<u>Ques 2)</u>
The solution is: (4,1)
<u>Ques 3)</u>
The solution is:
(-4,1)
<u>Ques 4)</u>
The solution is: (-3, 3)
<u>Ques 5)</u>
The solution is: (1,-2)
Step-by-step explanation:
Ques 1)
We have to solve the following system of equation using elimination method.
{5x+y=2
4x+y=4
we will subtract equation (2) from first to obtain:
5x-4x=2-4
x= -2
Now on putting the value of x in first equation we obtain:
5×(-2)+y=2
-10+y=2
y=2+10
y=12
Hence, the solution is:
(-2,12)
Ques 2)
Now again we have to solve using linear combination method.
{2d−e=7
d+e=5
we will add both the equations to get:
2d+d=12
3d=12
d=4
and on putting the value of d in second equation we obtain:
4+e=5
e=5-4
e=1
Hence,
C. The solution is (4, 1).
Ques 3)
5x−y=−21
x+y=−3
we will add both the equation to obtain:
5x+x=-21-3
6x = -24
x= -4
and on putting the value of x in equation (2) we get:
-4+y = -3
y= -3+4
y=1
Hence, the solution is:
(-4,1)
Ques 4)
−3x+9y=36
4x+12y=24
we will divide first equation on both side by 3 and second equation on both side by 4 to obtain the system as:
-x+3y=12
x+3y=6
on adding both the equations we get:
3y+3y=12+6
i.e. 6y=18
i.e. y=3
Hence on putting the value of y in one of the equation we obtain:
x= -3
Hence, the solution is:
(-3,3)
Ques 5)
7/2x−1/2y=9/2
3x−y=5
on multiplying both side of the equation by 2 we obtain:
7x-y=9
Now on subtracting second equation from this transformed equation we obtain:
7x-3x=9-5
4x=4
x=1
Hence on putting the value of x in one of the equations we obtain the value of y as:
y= -2
Hence, the solution is:
(1, -2)