Answer:
7.5 hours
Step-by-step explanation:
We can model an equation for this problem.
We can write:
Where
F is the final temperature (15 degrees we need)
m is the rate of temperature change (2 degrees per hour)
and
t is the time, in hours, it will take (we need to find this)
It is given,
F = 15
m = 2
So, t would be:
F = mt
15 = 2t
t = 15/2 = 7.5
So it will take 7.5 hours
From the equation, it looks like we can set up a triangle like this. One side is x and the other is x + 20 because the northbound car traveled 20 miles farther. The hypotenuse is 100 because they were 100 miles apart.
Next, we can use the Pythagorean Theorem to solve for x:
a² + b² = c²
x² + (x + 20)² = 100²
This simplifies to:
x² + x² + 40x + 400 = 10000
2x² + 40x = 9600
2x² + 40x - 9600 = 0
After that, we can divided each side by 2:
x² + 20x - 4800 = 0
Next, we have to factor:
(x - 60)(x + 80) = 0
x = 60, -80
Since we know that distance can't be negative, 60 is the valid answer in this case.
x = 60
x + 20 = 80
Using this information, we know that the westbound car traveled 60 miles and the northbound car traveled 80 miles.
Answer: Choice C) When you solve for the variable, you will end up with a false statement, like 0 = 2, for an equation with no solution. You will end up with a true statement, like 2 = 2 for an equation with infinitely many solutions.
For example, let's say we had the equation x = x+2. Subtracting x from both sides leads to 0 = 2 which is a false statement. No matter what we replace x with, the equation x = x+2 is always false. That's why we don't have any solutions here.
For an equation like x + 2 = x + 2, subtracting x from both sides leads to 2 = 2 which is always true. A true equation is one where the same number is on both sides. No matter what we replace x with, the equation will be true. Therefore, there are infinitely many solutions.
Answer:
Step-by-step explanation:
A: The starting point is located in Quadrant Q and the finishing point will be located in Quadrant S.
B: The checkpoint is in Quadrant P so it is in the middle of the course. The course will go from Quadrant Q to Quadrant S clockwise.
