The fireworks display occur at 550.331 ft
The generic equation for a hyperbola provided by: is the best method for solving the problem in this instance.
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We presume that the y-axis is where the hyperbola's longer axis lies.
In this instance, the sound traveled a total of 1100 meters, and the value of a can be calculated as follows:
2a = 1100
a = 550ft
Given that the two people are 3 miles apart, we can calculate the value of c in feet as follows:
1 mile = 5280 feet
∴ 3 miles = 15840 ft = c
And this is how we may determine what b is worth:



Our equation is thus given by:

And for this case we want to find the value of x when y = 3ft=15840ft and solving for x we get,





x = 550.331 ft.
The fireworks display occur at 550.331 ft.
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Answer:
The triangle ABC and A'B'C' are similar to each other by AA criterion.
Step-by-step explanation:
The dilation is the enlargement and compression of the a figure. The angles remains same but the sides changes according to the scale factor.
Therefore, the preimage and image are always similar.
According to the angle sum property the sum of all interiors angles of a triangle is always 180 degree.





Since the value of x is 50, therefore the measure of angles A,B and C are 48, 52 and 80.
Apply angle sum property is A'B'C'.





Since the value of x is 50, therefore the measure of angles A',B' and C' are 48, 52 and 80.


By AA criterion we can say that ΔABC∼ΔA'B'C.