Answer:
- 494
Step-by-step explanation:
Breaking down the summation into it;s component parts
= 4k -  k(k + 1) ← substitute k = 19
 k(k + 1) ← substitute k = 19
= (4 × 19 ) - 1.5 × (19 × 20)
= 76 - (1.5 × 380)
= 76 - 570
= 494
 
        
                    
             
        
        
        
Answer:
 -7/4 
Step-by-step explanation:
You are looking for the composite g(f(2)). The simplest way to solve this is to evaluate f(2) and enter the solution in to your g function. 
g(f(2))=g(-(2)^2-2(2)+4)=g(-4-4+4)=g(-4)
g(-4)=4/(-4(-4)-2)=4/(16-2)=4/14=2/7
Therfor, g(f(2))=2/7  **I'm assuming the -4x-2 is all in the denominator of the g(x) function. If -2 is not in the denominator you would have 
g(f(2))=4/(-4(-4)) -2=4/16 -2=1/4 -2=1/4-8/4= -7/4 
 
        
             
        
        
        
Answer:
Talking 65 minutes, $ 6.50 must be paid.
Step-by-step explanation:
Since your cell phone plan is by the minute, and each minute of use cost $ 0.10, to create a relation that represents the amount spent, A, per minute, m, of call time, and then use the relation to find the amount spent if you talk 65 minutes, the following calculations must be performed:
0.10 x M = A
0.10 x 65 = A
6.50 = A
Thus, talking 65 minutes, $ 6.50 must be paid.
 
        
             
        
        
        
Answer:
I) f + g = 10/3 
II) 4f + 2g = 20/3
III) f = 2 and g = 4/3
Step-by-step explanation:
From the chart, 
P = 25 
q = 40
The total number of one centimeter lines in the first n diagrams is given by the expression 
2/3n^3 + fn^2 + gn. 
When n = 1, the total number of line = 4. So,
2/3(1)^3 + f(1)^2 + g(1) = 4
2/3 + f + g = 4
Make f+g the subject of formula 
f + g = 4 - 2/3
f + g = (12 - 2)/3
f + g = 10/3 ......(1)
When n = 2
Total number of line = 12
2/3(2)^3 + f(2)^2 + g(2) = 12
2/3×8 + 4f + 2g = 12
16/3 + 4f + 2g = 12
4f + 2g = 12 - 16/3
4f + 2g = (36 - 16)/3
4f + 2g = 20/3 ......(2)
(iii) To find the values of f and g, solve equation 1 and 2 simultaneously 
f + g = 10/3 × 2
4f + 2g = 32/3 
2f + 2g = 20/3
4f + 2g = 32/3
- 2f = - 12/3
f = 12/6
f = 2
Substitutes f in equation 1
f + g = 10/3 
2 + g = 10/3
g = 10/3 - 2
g = (10 - 6)/3
g = 4/3
 
        
             
        
        
        
6.42 pm is the answer. You can think backward 8 hours before 2:12 am, which is 6:12pm. Now, go 'forward' a half an hour<span>, to 6:42pm. Answer: 6:42pm.</span>