(a-b) X (a+b)
=  aXa - bXa +aXb -bXb (distributing)
Now, cross product of a vector with itself = 0
so, aXa = 0, bXb = 0
Also, aXb = - bXa
so,
(a-b) X (a+b) = 0 + aXb + aXb + 0
= 2aXb
hence, proved :)
        
                    
             
        
        
        
No, because element b has 2 correspondents.
        
                    
             
        
        
        
Start with a proportion, to get the number of degrees in 30 seconds:
         (150 degrees / 5 seconds) = ('D' degrees / 30 seconds) .
Cross multiply the proportion:  (150 x 30) = 5 x D
                                                     4,500  =  5 x D
Divide each side by  5 :                  900 = D
The globe turns 900 degrees in 30 seconds.
How many rotations is that ?
Each rotation is 360 degrees.
So 900 degrees is
                               (900 / 360) = <em>2.5 rotations</em> in 30 seconds.
        
             
        
        
        
Answer:
Answer:
15% off 212.5
30% off 175$
Step-by-step explanation:
15+15=30 so
250/100=2.5
2.5x30=75
250-75
 
        
             
        
        
        
Answer:
67
Step-by-step explanation: Given the quadratic equation $z^2 + bz + c = 0$, Vieta's formulas tell us the sum of the roots is $-b$, and the product of the roots is $c$. Thus,
\[-b = (-7 + 2i) + (-7 - 2i) = -14,\]so $b = 14.$
Also,
\[c = (-7 + 2i)(-7 - 2i) = (-7)^2 - (2i)^2 = 49 + 4 = 53.\]Therefore, we have $b+c = \boxed{67}$.
There are many other solutions to this problem. You might have started with the factored form $(z - (-7 + 2i))(z - (-7 - 2i)),$ or even thought about the quadratic formula.
This is the aops answer :)