Answer: <em>x</em> = 20
Step-by-step explanation:
If line <em>m</em> is parallel to line <em>n</em>, the two angles given will be congruent because they will be alternate exterior angles (which are congruent).
This means we will set them equal to each other and solve for <em>x</em>.
Given:
(4<em>x</em> - 23) = (2<em>x</em> + 17)
Add 23 to both sides of the equation:
4<em>x</em> = 2<em>x</em> + 40
Subtract 2<em>x</em> from both sides of the equation:
2<em>x</em> = 40
Divide both sides of the equation by 2:
<em>x</em> = 20
The slope of parallel lines is equal and the slope of perpendicular lines is a negative multiplicative inverse of each other.
<h3>What is the standard equation of a line?</h3>
The standard equation of a line is given by
y = mx+c
Here m is the slope and c is the y-intercept
The slope can be determined by
m = (y₂ -y₁)/(x₂ -x₁)
A square is a polygon with four sides, the opposite sides are parallel and all the sides are equal, all the angles have an equal measure of 90 degrees.
Two lines are parallel to each other when they are at a fixed distance always and never intersect with each other.
The slope of the lines parallel to each other is equal.
Two lines are said to be perpendicular when they intersect at 90 degrees.
The slope of two perpendicular lines has a product of -1.
To known more about the standard equation of a line
brainly.com/question/12452575
#SPJ1
The result is
9
a
2
−
16
The reason is the following:
The problem is an example of a notable product: "the sum multiplied by the diference is equal to the difference of squares", that is to say:
(
a
+
b
)
⋅
(
a
−
b
)
=
a
2
−
b
2
.
By applying this to our question, we obtain that:
(
3
a
−
4
)
⋅
(
3
a
+
4
)
=
(
3
a
)
2
−
(
4
)
2
=
9
a
2
−
16
.
7 + 5 + 2 = 14 because seven plus five is twelve, twelve plus two is fourteen.