Speed of the plane: 250 mph
Speed of the wind: 50 mph
Explanation:
Let p = the speed of the plane
and w = the speed of the wind
It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. So we set up a system of equations.
600
m
i
3
h
r
=
p
−
w
600
m
i
2
h
r
=
p
+
w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation. I'll solve for x in the first equation:
200mph = p - w
Add w to both sides:
p = 200mph + w
Now we can substitute the x that we found in the first equation into the second equation so we can solve for w:
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
Divide by 2:
50mph = w
So the speed of the wind is 50mph.
Now plug the value we just found back in to either equation to find the speed of the plane, I'll plug it into the first equation:
200mph = p - 50mph
Add 50mph on both sides:
250mph = p
So the speed of the plane in still air is 250mph.
Answer:
6
Step-by-step explanation:
First, simplify the exponents:
2*(3^6*3*-5)
2*((3*3*3*3*3*3)*(1/3*3*3*3*3))
2*(729*0.00411522633)
Then solve from there:
2*2.99999999457
5.99999998914
Since there is only whole numbers and a fraction present, im assuming you have to round:
5.99999998914
6
6 is your answer
Hope this helps!
Answer: Do 1.25(19,000.00) and you get 23,750
Step-by-step explanation:
Answer:
The answer is that both plans are equal.
Step-by-step explanation:
you start by putting the plans into an equation then you set them equal to each other. you need to assign a variable for the number of months. we'll call it M. It would look like this:
plan A - 25 + 8M
plan B - 5 + 12M
25 + 8M = 5 + 12M
Then you solve which looks like this:
25 + 8M = 5 + 12M
-8M -8M
25 = 5 + 4M
-5 -5
20 = 4M
/4 /4
5 = M
Now we aren't done after finding out what M equals. We still need to know what each plan will cost. So, we substitute what M equals into the equation. if they both end up equaling the same thing then its equal. if you get two different numbers they aren't. it would look like this:
25 + 8(5) = 5 + 12(5)
25 + 40 = 5 + 60
65 = 65
They are equal. Both plans will cost 65 dollars.
