Answer:
1: Reflect M across the x-axis
2: Dilate about the center by 3/2
Step-by-step explanation:
Given
See attachment for M and N
Required
Which maps M to N
The coordinates of the radius of the circles are:
![M = (5,5)](https://tex.z-dn.net/?f=M%20%3D%20%285%2C5%29)
![N = (5,-5)](https://tex.z-dn.net/?f=N%20%3D%20%285%2C-5%29)
And the radius of circles are:
![r_M=2](https://tex.z-dn.net/?f=r_M%3D2)
![r_N=3](https://tex.z-dn.net/?f=r_N%3D3)
The first transformation from M to M' is:
- Reflect across the x-axis
The rule is:
![(x,y) \to (x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2C-y%29)
![M(5,5) \to M'(5,-5)](https://tex.z-dn.net/?f=M%285%2C5%29%20%5Cto%20M%27%285%2C-5%29)
<em>At this point, M' and N now have the same center but different radius.</em>
The second transformation from M' to N is:
- Dilate about the center by dividing the radius of N by the radius of M
i.e.
![k =\frac{r_N}{r_M}](https://tex.z-dn.net/?f=k%20%3D%5Cfrac%7Br_N%7D%7Br_M%7D)
![k =\frac{3}{2}](https://tex.z-dn.net/?f=k%20%3D%5Cfrac%7B3%7D%7B2%7D)
<em>At this point, M has been completely mapped to N.</em>
Answer:
1.1.1- Michael has 200 lovebirds in total
1.1.2- There are 40 birds in each cage
1.1.3- 120/80 = 3/2
Step-by-step explanation:
120+80=200
200÷5=40
120÷40=3, 80÷40=2
Answer:C
Step-by-step explanation:
length•width•height
12•4•5.5=264
Answer:
.
Step-by-step explanation:
We have been given a geometric sequence 18,12,8,16/3,.. We are asked to find the common ratio of given geometric sequence.
We can find common ratio of geometric sequence by dividing any number by its previous number in the sequence.
![\text{Common ratio of geometric sequence}=\frac{a_2}{a_1}](https://tex.z-dn.net/?f=%5Ctext%7BCommon%20ratio%20of%20geometric%20sequence%7D%3D%5Cfrac%7Ba_2%7D%7Ba_1%7D)
Let us use two consecutive numbers of our sequence in above formula.
will be 12 and
will be 18 for our given sequence.
![\text{Common ratio of geometric sequence}=\frac{12}{18}](https://tex.z-dn.net/?f=%5Ctext%7BCommon%20ratio%20of%20geometric%20sequence%7D%3D%5Cfrac%7B12%7D%7B18%7D)
Dividing our numerator and denominator by 6 we will get,
![\text{Common ratio of geometric sequence}=\frac{2}{3}](https://tex.z-dn.net/?f=%5Ctext%7BCommon%20ratio%20of%20geometric%20sequence%7D%3D%5Cfrac%7B2%7D%7B3%7D)
Let us use numbers 8 and 16/3 in above formula.
![\text{Common ratio of geometric sequence}=\frac{\frac{16}{3}}{8}](https://tex.z-dn.net/?f=%5Ctext%7BCommon%20ratio%20of%20geometric%20sequence%7D%3D%5Cfrac%7B%5Cfrac%7B16%7D%7B3%7D%7D%7B8%7D)
![\text{Common ratio of geometric sequence}=\frac{16}{3*8}](https://tex.z-dn.net/?f=%5Ctext%7BCommon%20ratio%20of%20geometric%20sequence%7D%3D%5Cfrac%7B16%7D%7B3%2A8%7D)
![\text{Common ratio of geometric sequence}=\frac{2}{3}](https://tex.z-dn.net/?f=%5Ctext%7BCommon%20ratio%20of%20geometric%20sequence%7D%3D%5Cfrac%7B2%7D%7B3%7D)
Therefore, we get
as common ratio of our given geometric sequence.