Helll
rectangle lmno is reflected over the x-axis to create rectangle l'm'n'o'. if a line segment is drawn from point m to point m', which statement would best describe the relationship between segment m m prime and the x-axis?
they are diameters of concentric circles.
they share the same midpoints.
they are perpendicular to each other.
they share the same endpoints.

  they are perpendicular to each other

step-by-step explanation:

the only answer choice that isn't complete nonsense is the one shown above.

the x-axis is not the diameter of any circle.

the x-axis has no midpoint.

the x-axis has no endpoints.

a line segment joining any point and its reflected image will be perpendicular to (and bisected by) the line of reflection, no matter what that line is. you can take advantage of this fact to construct the reflected image.

they are perpendicular to each other.

step-by-step explanation:

when you make the rectangle lmno on the graph, you reflect it over the x-axis so it goes up or down on the y-axis, and then the letters flip spots as well.   the other line that makes it perpendicular is the x-axis line. the x-axis line and the line connecting m and m' create a 90   degree intersection creating perpendicular lines.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.