8th Grade Functions: Bike Race
2 answers:
Answer:
Juan wins the race
Step-by-step explanation:
<u>The graph is shown in attached image.</u>
<u />
The black line is Juan's graph.
The green line is Antonio's graph.
The graph shows the distance (y-axis) with time (x-axis).
The end of the curve(s) means the end of the race. Both curve's ending point in y-axis is 4 miles so the end of the race is 4 miles.
But in x-axis, we see the time:
Juan finishes at 13 minutes
Antonio finishes at 15 minutes
<u>Definitely Juan wins the race</u>
You might be interested in
Answer:
When we have a quadratic equation:
a*x^2 + b*x + c = 0
There is something called the determinant, and this is:
D = b^2 - 4*a*c
If D < 0, then the we will have complex solutions.
In our case, we have
5*x^2 - 10*x + c = 0
Then the determinant is:
D = (-10)^2 - 4*5*c = 100 - 4*5*c
And we want this to be smaller than zero, then let's find the value of c such that the determinant is exactly zero:
D = 0 = 100 - 4*5*c
4*5*c = 100
20*c = 100
c = 100/20 = 5
As c is multiplicating the negative term in the equation, if c increases, then we will have that D < 0.
This means that c must be larger than 5 if we want to have complex solutions,
c > 5.
I can not represent this in your number line, but this would be represented with a white dot in the five, that extends infinitely to the right, something like the image below:
