Answer:
To prove:
X+Y.Z=(X+Y).(X+Z)
Taking R.H.S
= (X+Y).(X+Z)
By distributive law
= X.X+X.Z+X.Y+Y.Z --- (1)
From Boolean algebra
X.X = X
X.Y+X.Z = X.(Y+Z)
Using these in (1)
=X+X(Y+Z)+Y.Z
=X(1+(Y+Z)+Y.Z --- (2)
As we know (1+X) = 1
Then (2) becomes
=X.1+Y.Z
=X+Y.Z
Which is equal to R.H.S
Hence proved,
X+Y.Z=(X+Y).(X+Z)
It’s 2/15
It’s just 2x1 and 3x5
4t+2c=200
2t+7c=400
I will solve for c in terms of t first
4t+2c=200
2c=200-4t
c=100-2t
Then I will substitute this in for c in the second equation to make it single variable
2t+7c=400
2t+7(100-2t)=400
2t+700-14t=400
300t=12
t=25
Tables cost $25 each
Plug t back into one of the ORIGINAL equations to find the cost of chairs
4(25)+2c=200
100+2c=200
2c=100
c=50
Chairs cost $50 each
Hope this helps! :)