Answer: -4.25 ≤ x ≤ 6.25
Step-by-step explanation:
The midpoint of a segment is located at the same distance of each of the endpoints of the segment.
The midpoint is at x = 1.
The length of the segment is 10.5, if we divide it by two we have:
10.5/2 = 5.25
Now, if we want the endpoints to be at the same distance of the midpoint, then the endpoints will be:
Xmax = midpoint + 5.25
Xmin = midpoint - 5.25
Then the extremes are:
Xmax = 1 + 5.25 = 6.25
Xmin = 1 - 5.25 = -4.25
Then this segment can be written as:
Xmin ≤ x ≤ Xmax
-4.25 ≤ x ≤ 6.25
The standard form would be x+3y=-27
Answer:
Step-by-step explanation:
Given equation:
On comparing the equation by ax² + bx + x = 0, We get: a = 1, b = 2 and c = 3
To Find the nature of the roots of the equation firstly we need to find the discriminant of the equation. The expression b²- 4ac is called the discriminant.

- Two Distinct real roots, if b² - 4ac > 0
- Two equal real roots, if b² - 4ac = 0
- No real roots, if b² - 4ac < 0

The discriminant is smaller than 0.
- <u>Hence, Equation has no </u><u>real</u><u> roots (no solution)</u>
Part A
5x - 5 >= 10 or-3x + 1 > 13
1) This is a disjunction (OR)
5x - 5 >= 10
5x >= 15
x >= 3
or
-3x + 1 > 13
-3x > 12
x < -4
Answer
x <- 4 or x >= 3
Part C:
1) This is a conjunction (And)
5x+ 3 <= 18 and 4 - x < 6
5x <= 15 and - x < 2
x <= 3 and x > -2
Answer
-2 < x <= 3