What are the first 4 terms use the explicit rule:
f(n)= 3n-1
(show your work)

Step-by-step explanation:

We are given the rule [ f(n) = 3n - 1 ] and n represents the term.

First term:

f(n) = 3n - 1

f(1) = 3(1) - 1

f(1) = 3 - 1

f(-1) = 2

Second term:

f(n) = 3n - 1

f(2) = 3(2) - 1

f(2) = 6 - 1

f(2) = 5

Third term:

f(n) = 3n - 1

f(3) = 3(3) - 1

f(3) = 9 - 1

f(3) = 8

Fourth term:

f(n) = 3n - 1

f(4) = 3(4) - 1

f(4) = 12 - 1

f(4) = 11

As you can see, the common difference is 3.

Best of Luck!

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

answer would be 8.64 or s = 11π/4 inches

step-by-step explanation:

s = r θ  

where s = arc length  

r = radius = 3 inches  

θ = central angle in radians = ( π /180)*165  

s = 3(π/180)*165  

= 8.64 inches