Which of the following describes the graph of {x | x < = 1} u {x | x > = 4}? a. closed circles on 1 and 4 with a line segment between b. closed circles on 1 and 4 with arrows pointing outward c. the entire number line d. no solution

b. closed circles on 1 and 4 with arrows pointing outward

Step-by-step explanation:

Which of the following describes the graph of {x | x < = 1} u {x | x > = 4},

We have been given the following set;

x < = 1

This set comprises of real numbers that are less than or equal to 1;

(1, 0, -1, -2, -3, -4, -∞)

On the other hand, the set x > = 4 comprises of real numbers that are greater than or equal to 4;

(4, 5, 6, 7, 8, 9, ∞)

The symbol ∪ means a union of sets. That is the set of numbers that belong in either or both sets;

{x | x < = 1} u {x | x > = 4} is same as writing;

(1, 0, -1, -2, -3, -4, -∞) ∪ (4, 5, 6, 7, 8, 9, ∞)

Therefore, the solution set will be closed circles on 1 and 4 with arrows pointing outward

Closed circles on 1 and 4 with arrows pointing outward ⇒ answer b

Step-by-step explanation:

* Lets study the meaning of the inequality

- If a < x < b, that means the value of x is between a and b

- If a ≤ x ≤ b, that means the value of x is from a to b

- If x < a and x > b, that means the value of x is smaller than a and

 grater than b

- If x ≤ a and x ≥ b, that means the value of x is smaller than or equal a and

 grater than or equal b

* Now lets solve the problem

∵ {x I x ≤ 1}

∴ x is smaller than or equal 1

∵ {x I x ≥ 4}

∴ x is greater than or equal 4

∵ {x I x ≤1} ∪ {x I x ≥ 4}

- The meaning of ∪ is all numbers smaller than or equal 1 and all

  the numbers greater than or equal 4

∴ {x I x ≤ 1} ∪ {x I x ≥ 4} = (-∞ , 1] ∪ [4 , ∞)

- This solution represented graphically by closed circles on 1 and

 4 with arrows pointing outward

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

s

step-by-step explanation: