Answer:
Least common multiple (LCM) of 5 and 10 is 10.
 
        
                    
             
        
        
        
Answer:
Kelly owes $16.5
Greg owes $33
Joe owes $64.5
Step-by-step explanation:
Let
Kelly's portion = x
Greg's portion = 2x
Joe's portion = 4x - 1.50
Total bill = $114.00
Total bill = Kelly's portion + Greg's portion + Joe's portion 
114 = x + 2x + (4x - 1.50)
114 = 3x + 4x - 1.50
114 = 7x - 1.50
Add 1.50 to both sides
114 + 1.50 = 7x - 1.50 + 1.50
115.5 = 7x
Divide both sides by 7
x = 115.5 / 7
= 16.5
x = $16.5
Kelly's portion = x
x = $16.5
Greg's portion = 2x
= 2 × 16.5
= $33
Joe's portion = 4x - 1.50
= 4(16.5) - 1.50
= 66 - 1.50
= $64.5
Therefore, 
Kelly owes $16.5
Greg owes $33
Joe owes $64.5
 
        
             
        
        
        
Topic: 
Multiplying Polynomials
Answer:
Polynomial 1:
- Simplified Form: 6x^2 - x - 1
- Name by Number of Terms: trinomial
Polynomial 2:
- Name by Number of Terms: binomial
Polynomial 3:
Step-by-step explanation:
Polynomial 1:



It has 3 terms, so it's a <u>trinomial</u>.
Polynomial 2:
There is one term with x and x is raised to the first degree, so it's <u>linear</u>.
There are 2 terms, so it's a <u>binomial</u>.
Polynomial 3:




Since there are no variables and the answer is just 2, it's a <u>constant</u>.
Note: I took a test on this and it seemed to be all correct
 
        
             
        
        
        
Answer:
b. an = 2 • (-3)^(n - 1)
Step-by-step explanation:
Before we test a solution or two, we can easily discard most of them.
We see the values alternate of signs (-5 for the 2nd term and +162 for the 5th term)... so the progression factor has to be negative (in order to alternate sign).  <u>That already excludes answers A and C.</u>
Normally, a geometric progression has the (n-1) exponent, not (n+1), so our chances seem to be better with B.
We can test both D and B with n = 2, to obtain -6
Let's test answer D before: 

The result is -54, not -6... so it's not the right result.
Let's test answer B then:

Right!  Let's verify with n=5 to get 162:

Confirmed, answer is B. an = 2 • (-3)^(n - 1)
 
        
             
        
        
        
9514 1404 393
Answer:
   42.9 ft
Step-by-step explanation:
The relevant trig relation is ...
   Tan = Opposite/Adjacent
where Opposite in this case is the height of the tree, and Adjacent is the distance to the tree.
   tan(47°) = height/(40 ft)
   height = (40 ft)·tan(47°) . . . . . multiply both sides by (40 ft)
   height ≈ 42.9 ft
The tree is about 42.9 feet tall.