Distance to travel = 20 m.
Let us determine the time, t, that each participant took to complete 20 m.
Barbara:
Average speed = (3 m)/(2 s) = 1.5 m/s
t = 20/1.5 = 13.3 s
Mark:
t = 5 s
Carlos:
y = x + 1
where
y = 20 m
x = time, t
Therefore
t =x = y - 1 = 20 - 1 = 19 s
Summary:
Barbara: 13.3 s
Mark: 5 s
Carlos: 19 s
Answer:
The winner is Mark
He will have 7.75 left from the 20 dollar bill he spent
Answer: Tan(0) = 4/3
Explanation: SOH CAH TOA
Tan = Opposite/ Adjacent
Tan (0) = 4/3
Given:
The quadratic equation is

To find:
The vertex of the given quadratic equation.
Solution:
If a quadratic function is
, then

We have,

It can be written as

...(i)
Here,
.



Putting
in (i), we get
On further simplification, we get
So, the vertex of the given quadratic equation is
.
Therefore, the correct option is A.