You have to find the common difference, the term named in the problem, and the explicit formula.

                                                    Question 1

Given the sequence

31, 61, 91, 121,...

An arithmetic sequence has a constant difference 'd' and is defined by  

computing the differences of all the adjacent terms

61 - 31 = 30, 91 - 61 = 30, 121 - 91 = 30

The difference between all the adjacent terms is the same and equal to

d = 30

As the first term of the sequence is:

a₁ = 31

now substituting a₁ = 31 and d = 30 in the nth term of the sequence

Now, putting n = 36 to determine the 36th term

Thus,  the 36th term is:

                                               Question 2

Given the sequence

-34, -44, -54, -64, ...

An arithmetic sequence has a constant difference 'd' and is defined by  

computing the differences of all the adjacent terms

The difference between all the adjacent terms is the same and equal to

As the first term of the sequence is:

a₁ = -34

now substituting a₁ = -34 and d = -10 in the nth term of the sequence

Now, putting n = 26 to determine the 36th term

Thus, the 26th term is:

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation: