How can you tell whether an absolute value inequality is equivalent to a compound inequality with AND or to a compound inequality with OR?

It can.

Step-by-step explanation:

First term (t₁) = a = 3, Common difference (d) = 8 - 3 = 5 and last term (tₙ) = 78

78 = 3 + (n - 1)5

⇒ 78 = 3 + 5n - 5

⇒ 78 = -2 +5n

⇒ 78 + 2 = 5n

⇒ 80 = 5n

⇒ n = 16

Therefore, 78 is 16th term of A.P: 3, 8, 13, 18...

4444444444444 i think

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true