Answer:
Polygon Y's area is one ninth (1/9) of Polygon X's area
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
In this problem
Let
z-----> the scale factor
a-----> Polygon Y's area
b----> Polygon X's area
we have
substitute
therefore
Polygon Y's area is one ninth (1/9) of Polygon X's area
The pattern in the given series of amount in the account are in the form of
arithmetic and geometric progression.
Reasons:
The given table of values is presented as follows;
In Option 1, the amount in dollars for each year has a common difference of d = 100
The first term, a = 1,100
Therefore;
The Option 1 can be represented as an arithmetic progression , A.P. in the
form, tₙ = a + (n - 1)·d as follows;
For the Option 1, we have;
For Option 2, it is possible to find;
1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1
Therefore;
The terms in the Option 2 have a common ratio of r = 1.1
The Option 2 is a geometric progression, G.P.
The first term in Option 2 is a = 1,100
Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾
Therefor;
Learn more about arithmetic and geometric progression here: