Answer:
(A)6
Step-by-step explanation:
Given the quadratic expression: 
We factorize:

Therefore, the missing number that will complete the factorization is 6.
Answer:
A + B + C = π ...... (1)
...........................................................................................................
L.H.S.
= ( cos A + cos B ) + cos C
= { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C
= { 2 · cos [ (π/2) - (C/2) ] · cos [ (A-B) / 2 ] } + cos C
= { 2 · sin( C/2 ) · cos [ (A-B) / 2 ] } + { 1 - 2 · sin² ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A -B) / 2 ] - sin ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - sin [ (π/2) - ( (A+B)/2 ) ] }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - cos [ (A+B)/ 2 ] }
= 1 + 2 sin ( C/2 )· 2 sin ( A/2 )· sin( B/2 ) ... ... ... (2)
= 1 + 4 sin(A/2) sin(B/2) sin(C/2)
= R.H.S. ............................. Q.E.D.
...........................................................................................................
In step (2), we used the Factorization formula
cos x - cos y = 2 sin [ (x+y)/2 ] · sin [ (y-x)/2 ]
Step-by-step explanation:
Answer:
Step-by-step explanation:
<h3>Given</h3>
- Sofa = s
- Love seat = l
- Chair = c
- Sofa and love seat cost = $1300
- Sofa and 2 chairs cost = $1400
- Sofa, love seat and one chair cost = $1600
<h3>To find</h3>
<h3>Solution</h3>
<u>Equations as per given are:</u>
- s + l = 1300
- s + 2c = 1400
- s + l + c = 1600
<u>Subtract equation 1 from equation 3:</u>
- s + l + c - s - l = 1600 - 1300
- c = 300
<u>Considering this in the equation 2:</u>
- s + 2*300 = 1400
- s = 1400 - 600
- s = 800
<u>Substituting s in the equation 1:</u>
- 800 + l = 1300
- l = 1300 - 800
- l = 500
<u>Answer:</u> Love seat costs $500
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.