To prepare for an upcoming basketball tournament, Coach Somers keeps track of the number of points scored by each player on the
team for various minutes played during the most recent five games. The results for Matt, one of the players, are as follows: In one of game Matt scored 12 points in 20 minutes. In another game he scored 16 points in 28 minutes. Matt then scored 15 points in a game where he played a total of 24 minutes. Finally, Matt scored 18 points during a game where he played for 25 minutes. Using x to represent the number of minutes and y to represent the number of points scored, create a graph to represent this relation
1 answer:
Answer:
The graph is shown in the picture attached.
Step-by-step explanation:
<u>Defining:</u>
- x represents the number of minutes
- y represents the number of points scored
<u>Matt scored:</u>
- 12 points (y) in 20 minutes (x) is shown in the graph as the point (20, 12)
- 16 points (y) in 28 minutes (x) is shown in the graph as the point (28, 16)
- 15 points (y) in 24 minutes (x) is shown in the graph as the point (24, 15)
- 18 points (y) in 25 minutes (x) is shown in the graph as the point (25, 18)
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Answer:
Part 1) "a" value is
Part 2) The vertex is the point
Part 3) The equation of the axis of symmetry is
Part 4) The vertex is a minimum
Part 5) The quadratic equation in standard form is
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
where
(h,k) is the vertex of the parabola
if a > 0 then the parabola open upward (vertex is a minimum)
if a < 0 then the parabola open downward (vertex is a maximum)
The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
so
In this problem we have
-----> this is the equation in vertex form of a vertical parabola
The value of
so
a>0 then the parabola open upward (vertex is a minimum)
The vertex is the point
so
The equation of the axis of symmetry is
The equation of a vertical parabola in standard form is equal to
Convert vertex form in standard form
see the attached figure to better understand the problem
Answer:
The expression provided by the area (square meters) is given by: .
Step-by-step explanation:
The area of the algae colony is a function of the radius r (meters), so .
The radius of the circle formed by the algae colony is a function of time t (in minutes), so . So,
[Substituting the expression for radius]
Then the expression provided by the area (square meters) is given by: .