Answer:
1
Step-by-step explanation:
All the numbers provided can have a factor of 1.
eg.)
1*24=24
1*14=14
1*21=21
This is because there is only one factor they all commonly share, 1.
So 2x+12=5x-9
you want all of the unknowns on one side and all of the known values on the other or
subtract 2x from both sides
12=3x-9
add 9 to both sides
21=3x
divide both sides by 3
7=x
4(9+7) = 36+28 = 64
open the parentheses, then simplify.
Answer:
x = 10°
Step-by-step explanation:
a). Since, opposite angles of a cyclic quadrilateral are supplementary angles"
Therefore, in cyclic quadrilateral ABDE,
m∠ABD + m∠AED = 180°
110° + m∠AED = 180°
m∠AED = 180° - 110°
= 70°
b). AD = ED [Given]
m∠EAD = m∠AED [Since, opposite angles of equal sides are equal in measure]
m∠EAD = m∠AED = 70°
By triangle sum theorem in ΔABD,
m∠BAD + m∠ABD + m∠ADB = 180°
m∠BAD + 110° + 40° = 180°
m∠BAD = 180 - 150
= 30°
m∠AEB = m∠AED + m∠DAB [By angles addition postulate]
m∠AEB = 70° + 30°
= 100°
By triangle sum theorem in the large triangle,
x° + m∠AEB + m∠EAB = 180°
x° + 100° + 70° = 180°
x = 180 - 170
x = 10°
When 
, we have
and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)
Suppose this is true for 
, that
Now for 
, we have
so we know the left side is at least divisible by 
by our assumption.
It remains to show that
which is easily done with Fermat's little theorem. It says
where 
is prime and 
is any integer. Then for any positive integer 
,
Furthermore,
which goes all the way down to
So, we find that
QED
