Answer:
Rate of slower bus; 90 km/h
Rate of faster bus; 102 km/b
Step-by-step explanation:
We know that formula do distance is;
Distance = speed/time
We are told that One bus travels 12h slower than the other.
Let speed of slower bus be x.
Thus;
Speed of faster bus = x + 12
Speed of slower bus = x
After 3 hours, distance by faster bus = 3(x + 12)
Speed of slower bus = 3x
Since the towns are 576 km apart, then;
3(x + 12) + 3x = 576
Divide through by 3 to get;
x + 12 + x = 192
2x + 12 = 192
2x = 192 - 12
2x = 180
x = 180/2
x = 90 km/h
Faster bus speed = 90 + 12 = 102 km/h
No, she will not have enough. If you estimate the amount of money it will cost for the turkey sandwich and the large drink, it will cost about $7. She will only have $6.25 after admission costs.
Answer:
Step-by-step explanation:
I used logic and took the easy way around this as opposed to the long, drawn-out algebraic way. I noticed right off that at x = -3 and x = -1 the y values were the same. In the middle of those two x-values is -2, which is the vertex of the parabola with coordinates (-2, 4). That's the h and k in the formula I'm going to use. Then I picked a point from the table to use as my x and y in the formula I'm going to use. I chose (0, 3) because it's easy. The formula for a quadratic is

and I have everything I need to solve for a. Filling in my h, k, x, and y:
and
and
-1 = 4a so

In work/vertex form the equation for the quadratic is

In standard form it's:
