A) show that $n(2n + 1)(7n + 1)$ is divisible by 6 for all integers $n$.b.find all integers $n$ such that $n(2n + 1)(7n + 1)$ is divisible by 12.

Answers

Answer 1

Answer: Hi,

A)
$(n(2n+1)(7n+1))/(6) \n= (14n^3+9n^2+n)/(6) \n= (12n^3+6n^2)/(6) + (2n^3+3n^2+n)/(6) \n=2n^3+n^2+ (n(2n^2+3n+1))/(6) \n= 2n^3+n^2+ (n(n+1)(2n+1))/(6) \n= 2n^3+n^2+ 1^2+2^2+3^2+...+n^2\ is\ an\ integer.$

B)
Only if n=4*k or n=4*k+1 , k beeing an integer.

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John's race car memorabilia rose in value 6% last year. It is now worth $141.12. What was it worth a year ago? A. $84.67 B. $85.20 C. $133.13 D. $134.65

Answers

1.06 x A = 141.12

A = 133.13

the answer is C

What is 1 - 27/44 = in its simplest form?

Answers

$1 - (27 )/(44)=(44)/(44)-(27 )/(44)=(17 )/(44)$

$1-(27)/(4)=(44)/(44)-(27)/(44)=(44-27)/(44)=(17)/(44)$

Identify the domain and the range of the function

Answers

Answer: The first

D: [-3,∞)

R: [-1,∞)

The second

D: [-3,2)

R:[-5,4]

Step-by-step explanation:

3n-5=-8(6+5n) SOLVE

Answers

It's gonna be a long problem: Remember PEMDAS
3n-5=8(6+5n)
3n-5= 48 + 40n Distribute 8 into parenthesis
3n-3n-5=48+40n-3n Put variable on one side.
-5-48=48-48+37n Isolate the variable
-43/37=37n/37 Isolate variable more
-1.162=n Simplify
The answer is repeating; that is a shortened version.

t's gonna be a long problem: Remember PEMDAS

3n-5=8(6+5n)

3n-5= 48 + 40n Distribute 8 into parenthesis

3n-3n-5=48+40n-3n Put variable on one side.

-5-48=48-48+37n Isolate the variable

-43/37=37n/37 Isolate variable more

-1.162=n Simplify

The answer is repeating; that is a shortened version.

Evaluate the expression below for x = 4, y = –5, and z = 2. 3x^2 -4y+xza. 12
b. 36
c. 52
d. 76