OK so the factor of 10 is 1 times 10 and 5 times 2
When dilation is about the origin, as it is here in every case, the image point coordinates are the original (pre-image) coordinates multiplied by the scale factor.
1. Multiply every coordinate value by 5:
... W' = (-5, 10), X' = (-15, -5), Y' = (25, -5), Z' = (15, 10)
2. Multiply every coordinate value by 1/3:
... A' = (-2, 5), B' = (0, 5/3), C' = (1, 10/3)
3. A' = (2, 8), B' = (6, 2), C' = (2, 2)
4. The image coordinates are 5 times the original coordinates, so ...
... the scale factor of the dilation is 5.
Answer:
k = 6 : 5 : 4
Step-by-step explanation:
BC : AB : AC = 18 : 15 : 12 = 6 : 5 : 4
EF : DE : DF = 12 : 10 : 8 = 6 : 5 : 4
Answer:
Notebooks cost $2.75 and pens cost $1.10.
He can also buy 3 notebooks.
Step-by-step explanation:
In order to find this, we need to create two equations given each of the situations.
3n + 2p = 10.45
4n + 6p = 17.60
Now to solve for n, multiply the top equation by -3 and add together.
-9n - 6p = -31.35
4n + 6p = 17.60
----------------------
-5n = -13.75
n = 2.75
Now that we have the value of notebooks, we can find the amount for pens using either equation.
3n + 2p = 10.45
3(2.75) + 2p = 10.45
8.25 + 2p = 10.45
2p = 2.20
p = 1.10
Finally, to find the number of notebooks that he can purchase, find the cost of a notebook with 3 pens.
n + 3p
2.75 + 3(1.10)
2.75 + 3.30
6.05
Now divide 22 by that number
22/6.05 = 3.63
Since we can't have fractional notebooks, we round down to 3.
