The average rate of change is 1.
Option C:
The coefficient of 
is 40.
Solution:
Given expression:
Using binomial theorem:
Here 
Substitute in the binomial formula, we get
Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.
Let us solve the term one by one.
Substitute these into the above expansion.
The coefficient of is 40.
Option C is the correct answer.
Answer:
27, 29, 31, 33
Step-by-step explanation:
Let x represent the smallest odd integer then...
x+2 represents the second
x+4 represents the third
x+6 represents the fourth
We can use this to set up an equation:
x+x+2+x+4+x+6=120
Combine like terms
4x+12=120
Subtract 12 from both sides
4x=108
Divide both sides by 2
x=27
The integers are 27, 29, 31, 33
5x + -4y = 13
Solving
-5x + -4y = 13
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4y' to each side of the equation.
-5x + -4y + 4y = 13 + 4y
Combine like terms: -4y + 4y = 0
-5x + 0 = 13 + 4y
-5x = 13 + 4y
Divide each side by '-5'.
x = -2.6 + -0.8y
Simplifying
x = -2.6 + -0.8y
Simplifying
3x + -4y + -11 = 0
Reorder the terms:
-11 + 3x + -4y = 0
Solving
-11 + 3x + -4y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '11' to each side of the equation.
-11 + 3x + 11 + -4y = 0 + 11
Reorder the terms:
-11 + 11 + 3x + -4y = 0 + 11
Combine like terms: -11 + 11 = 0
0 + 3x + -4y = 0 + 11
3x + -4y = 0 + 11Combine like terms: 0 + 11 = 11
3x + -4y = 11
Add '4y' to each side of the equation.
3x + -4y + 4y = 11 + 4y
Combine like terms: -4y + 4y = 0
3x + 0 = 11 + 4y
3x = 11 + 4y
Divide each side by '3'.
x = 3.666666667 + 1.333333333y
Simplifying
x = 3.666666667 + 1.333333333y
Answer:
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