Answer:
The length of segment QM' = 6
Step-by-step explanation:
Given:
Q is the center of dilation
Pre-image (original image) = segment LM
New image = segment L'M'
The length of LQ = 4 
The length of QM = 3
The length of LL' = 4
The original image was dilated with scale factor = 2
QM' = ?
To determine segment QM', first we would draw the diagram obtained from the given information.
Find attached the diagram
When a figure is dilated, we would have similar shape in thus cars similar triangles.
Segment L'M' = scale factor × length of LM
Let LM = x
L'M' = 2x
Using similar triangles theorem, ratio of their corresponding sides are equal.
QM/LM = QM'/L'M'
3/x = QM'/2x
6x = QM' × x
Q'M' = 6
The length of segment QM' = 6
 
        
                    
             
        
        
        
Step-by-step explanation:
$7 = 1 package socks
%56 = ??
$56/$7 × 1 package socks
= 8 × 1 
= 8 package socks
Hope it helps!
 
        
             
        
        
        

The rows add up to 

, respectively. (Notice they're all powers of 2)
The sum of the numbers in row 

 is 

.
The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When 

,

so the base case holds. Assume the claim holds for 

, so that

Use this to show that it holds for 

.



Notice that






So you can write the expansion for 

 as

and since 

, you have

and so the claim holds for 

, thus proving the claim overall that

Setting 

 gives

which agrees with the result obtained for part (c).
 
        
             
        
        
        
Answer:
Subsets of the given set = 32
Proper subset of the given set = 31
Step-by-step explanation:
Given set is {18, 8, 14, 9, 6} having 5 elements.
We know number of subsets of a set having n elements are represented by 

where n is the number of elements in the set.
Therefore, subsets of the given set = 
= 32
Since original set itself is a subset of its own, is not a proper subset.
Therefore, proper subset of a set = 
= 
= 32 - 1
= 31
 
        
             
        
        
        
Answer:
0.1
Step-by-step explanation:
(9,4) (5,1)     , plug in the numbers,
, plug in the numbers,  =
=  , to write it as a decimal, you divide the numerator by the denominator, 0.1
, to write it as a decimal, you divide the numerator by the denominator, 0.1