The graphs below have the same shape. What is the equation of the blue
1 answer:
Answer:
Answer choice C. .
Step-by-step explanation:
The entire question is present in the attached figure.
It is established that
The function f(x) is represented by
,
indicating a parabola that opens upward.
The vertex is situated at the point (0,0).
The function g(x) shares the same parabolic shape.
The vertex of g(x) is located at (-3,1).
Therefore,
The transformation from f(x) to g(x) can be described as:
(0,0) transforms to (-3,1).
(x,y) transforms to (x-3,y+1).
This indicates a shift of 3 units to the left and 1 unit upward.
Thus,
The equation for g(x) in vertex form can be expressed as
.
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Response:
The loop's length is roughly 49.58 km.
Step-by-step details:
Given:
Duration to cycle the loop = 2 hours and 30 minutes
It is known that;
60 minutes = 1 hour
30 minutes = 0.5 hour
therefore, 2 hours and 30 minutes =
∴ Time to cycle the loop = 2.5 hours
Let 's' denote the cycling speed.
Denote the total loop distance as 'd'
From our understanding;
Distance equals speed times time.
Representing this as an equation we have;
Given:
If her speed increased by 1 km/hr, the time taken around the loop would decrease by 7 minutes.
As a result, we can say;
Speed =
The time then will be shortened by 7 minutes.
7 minutes = 0.12 hours
Consequently, time = 2.5 - 0.12 = 2.38
Again, Distance is calculated as speed times time.
This can be expressed with equations;
The distances are equivalent in both scenarios, thus we will determine speed by equating the equations.
So, Speed = 19.83 km/hr
Loop length (d) =
Therefore, the loop length is approximately 49.58 km.