Answer:
x = 8, y = 1
Step-by-step explanation:
Given that the triangles are similar then the ratios of corresponding sides are equal, that is
=
( cross- multiply )
4y = 4 ( divide both sides by 4 )
y = 1
Also
=
( cross- multiply )
x = 8
The equation of parabola is 
Comparing with the vertex form of the parabola: 

Hence, the vertex of the parabola is given by (h,k) = (1, -2)
Now, vertex is the midpoint of the focus and the point on the directrix.
Distance, between vertex and focus is p and that of point on the directrix is p.
Now, let us find p

Thus, the focus is given by

And the directrix is given by

Since, a >0 hence, it is an upward parabola.
The graph is shown in the attached file.
Answer:
The value of x is 8
Step-by-step explanation:
Answer:
Domain = {All real values of x EXCEPT x = -5 and x = 7}
Step-by-step explanation:
This is a rational function given as y=\frac{6+9x}{6-|x-1|}y=
6−∣x−1∣
6+9x
The domain is the set of all real value of x for which the function is defined.
For rational functions, we need to find which value of x makes the denominator equal to 0. We need to exclude those values from the domain.
Now
6 - |x-1| = 0
|x-1| = 6
x- 1 = 6
or
-(x-1) = 6
x = 6+1 = 7
and
-x+1=6
x = 1-6 = -5
So, the x values of -5 and 7 makes this function undefined. So the domain is the set of all real numbers except x = -5 and x = 7
Answer:
33
Step-by-step explanation:
Assume that each cell on the grid represents one unit. One can use the formula, (
) to find the area of the triangle. One can see that the base of the triangle is, (11), and the height is (6). Substitute in the given values and solve for the area,


