Answer:
(0, -3)
Step-by-step explanation:
The solution to the system of equations is the point at which they intersect. The problem statement tells you that point is (x, y) = (0, -3).
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Often, for a system defined using functional notation, we don't care about the value of the function. We only care about the value of x where the functions have the same value. That is ...
the solution to f(x) = g(x) is x = 0.
Sales tax and tip will increase the price of an item.
The cost of each meal is: $10.89
Let the cost of both meals be x.
A 20% tip means that, the current price is:
A 6% sales tax on the meal means that, the current price is:
So, we have:
The amount paid is $27.72
So, the equation becomes
Make x the subject
So, the cost of each meal is:
Hence, the cost of each meal is: $10.89
Read more about sales tax at:
Let's analyze the changes made to the parent function one by one:
STEP 1: Horizontal translation.
If we transform
We're performing a change in the form of
This kind of changes result in a horizontal translation, k units to the left if k is positive, k units to the right if k is negative. In this case, k=2, so the original graph is shifted 2 units to the left.
STEP 3: Vertical stretch.
If we transform
We're performing a change in the form of
This kind of changes result in a vertical stretch with scale factor k. If k is negative, the function is also reflected across the x axis. In this case, k=3, so the original graph is stretched vertically, with scale factor 3.
STEP 3: Vertical translation.
If we transform
We're performing a change in the form of
This kind of changes result in a vertical translation, k units down if k is positive, k units up if k is negative. In this case, k= -4, so the graph is shifted 4 units down.
All, in all, the original graph is shifted 2 units to the right, then it's stretched vertically with scale 3, and then it's shifted 4 units down. The order is important!