For the given sequence we have the formula:
Sₙ = 1 + (n - 1)*2
The 50th square will have 99 shaded squares.
<h3 /><h3>
How many shaded squares are on the n-th square?</h3>
Here we have a sequence:
The first square has 1 shaded squares.
the second square has 3 shaded squares.
The third square has 5 shaded squares.
And so on.
Already you can see a pattern here, each next step we add 2 shaded squares, then we can write the formula:
Sₙ = 1 + (n - 1)*2
Where S is the number of shaded squares and n is the number of the figure.
Then the 50th square will have:
S₅₀ = 1+ (50 - 1)*2 1 + 49*2 = 99
Learn more about sequences:
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<h2>Steps</h2>
- Standard Form Equation: f(x) = ax² + bx + c
So firstly, since (0,5) is one of our values we can plug it into the standard form equation to solve for the c variable (since 0 will cancel out the a and b variable):

Now we know that the value of c is 5. Next, plug in (-1,12) into the standard form equation and simplify (remember to also plug in 5 for the c variable):

Next, plug (2,15) into the standard form equation and simplify:

Now, with our last two simplified equations we will create a system of equations:

Now, I will be using the elimination method with this system. With the system, add up the equations together and you will get:

From here, we can solve for the a variable. With it, just divide both sides by 3:

Now that we know the value of a, plug it into either equation to solve for the b variable:

<h2>Answer</h2>
Putting all of our obtained values together, your final answer is:

As the symmetry of axis is x=6, the mirror point of (2,8) will be (10,8)