Which statement is true regarding the parallel and
perpendicular lines in the diagram?

MRCORRECT has answered the question

Step-by-step explanation:

Option (3) and (4) are correct .

w║n and n⊥m and w║n so  w⊥m

Step-by-step explanation:

In the given figure, we have a set of lines which are parallel and perpendicular.

Parallel lines are lines in same plane which when extended do not meet and are always same distance apart from each other.

Perpendicular lines are two non-vertical lines in the same plane intersect at right angles.

From the figure given,

w║n and n⊥m as angle between a and n is right angle that is ∠mxn = 90° (given)

Since, w║n so  w⊥m also both w and n shows same property as both are parallel lines.

Thus, option (3) and (4) are correct .

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions