The cruise control function on georgina's car should keep the speed of the car within 3 miles per hour of the set speed. the set speed is 55 miles per hour. write a compound inequality to show the leaves that are within each range. then graph the solutions.

Given,

Set speed of car = 55,

∵ The speed of the car within 3 miles per hour of the set speed.

So, the maximum speed of car = 55 + 3,

And, the minimum speed of car = 55 - 3

Let x shows the current speed of car,

x ≤ 55 + 3 or x ≥ 55 - 3

x - 55 ≤ 3 or x - 55 ≥ - 3

x - 55 ≤ 3 or -(x-55) ≤ 3

⇒ | x-55 | ≤ 3

Which is the required compound inequality,

Now, 55 - 3 ≤ x ≤ 55 + 3

52 ≤ x ≤ 58

⇒ [52, 58]

Which is the solution of the above compound inequality.

Also, the graph is shown below.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i