Answer:
The answer to your question is 10.5 in
Step-by-step explanation:
Data
First triangle
height = x
base = 7 in
Second triangle
height = 12 in
base = 8 in
Process
1.- Use proportions to solve this problem, relates the sides of a triangle with the same sides of the other triangle.
2.- Multiply both sides by 7
3.- Simplify
x =
4.- Result
x = 10.5 in
Answer:
35.36 cm
Step-by-step explanation:
The diagonal of a square will be given by
Where a is the length of one side and b is the length of another side. For a square, botj sides are equal hence the diagonal calculations will be as follows
Given that a is 25 then
D=35.3553390593274
Rounding off the nearest two decimal place
D=35.36 cm
Answer:
y = -1/8(x -1)² +4
Step-by-step explanation:
The equation of a parabola can be written from focus and directrix using the form ...
y = 1/(4p)(x -h)² +k
where p is the distance from vertex to focus, and (h, k) is the vertex.
The vertex-focus distance is half the distance from the directrix to the focus. Here, that is ...
p = (2 -6)/2 = -4/2 = -2
The vertex is halfway between the focus and directrix on the same vertical line, so has coordinates ...
(h, k) = ((1, 2) +(1, 6))/2 = (1, 4)
__
Using these values of p and (h, k), we find the equation of the parabola to be ...
y = 1/(4(-2))(x -1)² +4
y = -1/8(x -1)² +4
_____
<em>Additional comment</em>
You can check the graph by considering the definition of a parabola: each point on the curve is equidistant from the focus and the directrix. This is easily verified for points on the horizontal and vertical lines through the focus. For example, point (5, 2) is 4 units from the focus, and 4 units from the directrix.
