Step 1
<u>Find the measure of angle x</u>
we know that
If ray NP bisects <MNQ
then
m<MNQ=m<PNM+m<PNQ ------> equation A
and
m<PNM=m<PNQ -------> equation B
we have that
m<MNQ=(8x+12)°
m<PNQ=78°
so
substitute in equation A
(8x+12)=78+78-------> 8x+12=156------> 8x=156-12
8x=144------> x=18°
Step 2
<u>Find the measure of angle y</u>
we have
m<PNM=(3y-9)°
m<PNM=78°
so
3y-9=78------> 3y=87------> y=29°
therefore
<u>the answer is</u>
the measure of x is 18° and the measure of y is 29°
30% were sponge cakes because you do 1/5=0.2 or20%+50%=70% and 100%-70%=30% so 30% is your answer.
I'm sorry, but what digit is underlined?
Answer/Step-by-step explanation (ac > b² or b² < ac.
)
A/c to question, we have to show:-
b² >ac in A.P ........ (1)
b² = ac in G.P .....(2)
b² < ac in H.P. ..... (3)
b = a+c/2 (A.P)
b = √ac ( G.P)
b = 2ac/a+c (H.P)
In A.P :
b² > ac = b² - ac
= (a+c/2)² - ac
= (a²+2ac+c²/4) - ac = a² + 2ac + c² - 4ac / 4
= a² - 2ac + c² / 4 = ( a - c ) ² / 4 > 0 Hence, b²>ac
In G.P:-
b = √ac
Hence, b² = ac
In H.P :- b² < ac = ac > b² = ac - b² = ac - ( 2ac / a+c)
= ac(a+c) - 2ac / a+c
= a²c + ac² - 2ac / a+c
= ac(2ac - 2) / a+c > 0
Hence, ac > b² or b² < ac.
Answer:
The no. of possible handshakes takes place are 45.
Step-by-step explanation:
Given : There are 10 people in the party .
To Find: Assuming all 10 people at the party each shake hands with every other person (but not themselves, obviously) exactly once, how many handshakes take place?
Solution:
We are given that there are 10 people in the party
No. of people involved in one handshake = 2
To find the no. of possible handshakes between 10 people we will use combination over here
Formula : 
n = 10
r= 2
Substitute the values in the formula
No. of possible handshakes are 45
Hence The no. of possible handshakes takes place are 45.
