Answer:
6
Step-by-step explanation:
Total number of subsets is given as 

But the subset of a set consists of the proper subsets, an empty set and the set itself. 
Total number of subsets are 64
Therefore,


Comparing both sides

 
        
             
        
        
        
Question is using standard formula ax+by=c to find the slope by converting into slope intercept form y=mx+b
so we also need to convert ax+by=c into y=mx+b as shown below:



divide both sides by 

Now compare it with y=mx+b, we get 

So using values of a and b, we can find the slope
compare given equation -5x+2y=15 with ax+by=c, we get:
a=-5, b=2
Now plug both into above formula 



Now matching these details with given choices we find that THIRD choice is the final answer.
 
        
             
        
        
        
Answer:
(1,1) x=1 y=1 
Step-by-step explanation:
 
        
             
        
        
        
Complete question :
Cheddar Cheese
$3/lb
Swiss Cheese
$5/lb
Keisha is catering a luncheon. She has $30 to spend on a mixture of Cheddar cheese and Swiss cheese. How many pounds of cheese can Keisha get if she buys only Cheddar cheese? Only Swiss cheese? A mixture of both cheeses?
What linear equation in standard form can she use to model the situation?
Answer:
10 lbs of cheddar cheese 
6 lbs of Swiss cheese 
$3a + $5b = $30
Step-by-step explanation:
Given that :
Cheddar cheese = $3/lb
Swiss cheese = $5/lb
Total amount budgeted for cheese = $30
How many pounds of cheese can Keisha get if she buys only Cheddar cheese? 
Pounds of cheedar cheese obtainable with $30
Total budget / cost per pound of cheddar cheese 
$30 / 3 = 10 pounds of cheedar cheese
Only Swiss cheese? 
Pounds of cheedar cheese obtainable with $30
Total budget / cost per pound of Swiss cheese 
$30 / 5 = 6 pounds of Swiss cheese
A mixture of both cheeses?
What linear equation in standard form can she use to model the situation?
Let amount of cheddar cheese she can get = a 
Let amount of Swiss cheese she can get = b
Hence, 
(Cost per pound of cheddar cheese * number of pounds of cheddar) + (Cost per pound of Swiss cheese * number of pounds of Swiss cheese) = total budgeted amount 
(3 * a) + (5 * b) = $30
$3a + $5b = $30
 
        
             
        
        
        
Answer:
y = 2.5x - 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 2.5 and c = - 8 , then
y = 2.5x - 8 ← equation of line