Answer:
Options C. and D. are correct.
Step-by-step explanation:
Let 
Equation of a line is given by 

Put  

Put  

Put 

Put 

Put 

So, points  satisfy the equation
 satisfy the equation 
Therefore,
points  lie on the line through
 lie on the line through  and
 and 
Options C. and D. are correct.
 
        
             
        
        
        
Answer:
15 cm
Step-by-step explanation:
Given that :
Reading at one end, initial reading = 3.5 cm
Reading at the other end, final reading = 18.5 cm
Length of needle :
Final Reading - Initial reading
18.5cm - 3.5cm
= 15cm
 
        
             
        
        
        
A^2 + b^2 = c^2
7^2 + 4^2 = 65
square root of 65 is 8.06
answer: 8.06
        
             
        
        
        
Answer:
The fifth degree Taylor polynomial of g(x) is increasing around x=-1
Step-by-step explanation:
Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:

and when you do its derivative:
1) the constant term renders zero,
2) the following term (term of order 1, the linear term) renders:  since the derivative of (x+1) is one,
 since the derivative of (x+1) is one,
3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero
Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is:  as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1
 as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1 
 
        
             
        
        
        
Answer:
The music director can make 15 groups of performers with 6 sixth grade students and 5 seventh grade students in each group.
Step-by-step explanation:
A school chorus has 90 sixth-grade students and 75 seventh-grade students.
Factor these two numbers:
Find GCF(90,75):
Now,
Therefore, the music director can make 15 groups of performers with 6 sixth grade students and 5 seventh grade students in each group.