Well 1/3 for savings means that you save 1/3*4500 or 1500 dollars.
You then have $3000 left. Of this if you spend 50% on food, you spend 0.5*3000 or 1500 dollars on food.
3^7 when you are multiplying numbers with the same base add the exponents.
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.
Axis of symmetry for this function will be x=2 because your origin point is always the reference for the line of symmetry. In this case, it as been shifted to the right 2 units giving you x=2. Firstly, the transformation is a horizontal stretch by a factor of 10. Secondly, it is shifted 2 units to the right and finally shifted 7 units down. Remember when a constant is added or subtracted to x in a function, it is shifted the number of u its opposite of the constant. When there is a constant separate from x, such as outside parentheses or absolute value bars, it is shifted up or down the given amount.
