Answer:
Step-by-step explanation:
Since the center of dilation is not at the origin, we can use the following formula in order to find the coordinates of the vertices of the triangle D'E'F':
Where "O" is the center of dilation at (a,b) and "k" is the scale factor.
In this case you can identify that:
Therefore, susbtituting values into the formula shown above, you get that the coordinates ot the resulting triangle D'E'F, are the following:
Vertex D' →
Vertex E' →
Vertex F' →
Answer: a) Number of nickels, dimes, and quarters are 80, 120, 300 respectively.
b) The coins are worth of 91 dollars i.e. $91 in the piggy bank.
Explanation:
Since we have given that
For every 2 nickels there are 3 dimes ,
So, their ratio will be 2:3
and for every 2 dimes there are 5 quarters.\,
So, their ratio will be 2:5
Now, we'll first find the ratio of nickles to dimes to quarters i.e.
Nickle Dimes Quarters
2 3
2 5
So, it becomes ,
Nickle : Dimes : Quarters
2×2 : 3×2 : 3×5
4 : 6 : 15
Now, let the number of nickle be 4x
Let the number of dimes be 6x
Let the number of quarters be 15x
According to question,
So, number of nickels is given by
Number of dimes is given by
Number of quarters is given by
As we know that
So, According to our question, we get
Hence,
a) Number of nickels, dimes, and quarters are 80, 120, 300 respectively.
b) the coins are worth of 91 dollars i.e. $91 in the piggy bank.