Answer: hello your question is poorly written below is the complete question
Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.
answer:
a ) R is equivalence
b) y = 2x + C
Step-by-step explanation:
<u>a) Prove that R is an equivalence relation </u>
Every line is seen to be parallel to itself ( i.e. reflexive ) also
L1 is parallel to L2 and L2 is as well parallel to L1 ( i.e. symmetric ) also
If we presume L1 is parallel to L2 and L2 is also parallel to L3 hence we can also conclude that L1 is parallel to L3 as well ( i.e. transitive )
with these conditions we can conclude that ; R is equivalence
<u>b) show the set of all lines related to y = 2x + 4 </u>
The set of all line that is related to y = 2x + 4
y = 2x + C
because parallel lines have the same slopes.
Answer and explanation:
A center chord in a circle is the diameter of that circle. Therefore a center chord of a circle is different from other chords that touch two points on the circle but not in the center of the circle. A diameter of a circle is the chord that runs the length of the center of the circle touching two points at the edge of the circle. A diameter is twice the radius of the circle. So if the diameter of the circle is 12cm then the radius of the circle is 6cm
Lines f and g look to be parallel to each other.
z^2 - z - 72
z^2 - 9z + 8z - 72
<u>Step 1</u>: 72 = 9 * 8 and when we subtract -9+8 = -1 and that's how I went from z^2 - z - 72 to z^2 - 9z + 8z - 72.
<u>Step 2</u>: Taking out common value from first and second; and third and fourth.
z^2 - 9z = z(z - 9)
8z - 72 = 8 (z - 9)
z^2 - 9x + 8x - 72
z(z-9) + 8(z-9)
(z-9) (z+8)
