What expression represents the value of y?

The expression which represent the value of y is    ( option b )

Step-by-step explanation:

Given as figure :

Right angle Triangle BDC   with right angle at D having

BD = y

DC = w

CB = x

And Triangle CBA with right angle at B having

BA = v

AC = AD + DC = z + w

CB = x

Now from Δ BDC

Pythagoras Theorem

BC² = CD² + DB²

Or, x² = w² + y²  ...1  

From  Δ CBA

AC² = CB² + BA²

Or, ( z + w )² = x² + v²

Or,  z² + w² + 2 z w = x² + v²     ...2

From  Δ BDA

AB² = BD² + DA²

Or, v² = y² + z²    ....3

From eq 1 and eq 2

z² + w² + 2 z w = w² + y² + v²  

Or, z² +  (w² -  w² ) + 2 z w = y² + v²  

Or, z² + 2 z w = y² + v²  

Or, eq  

z² + 2 z w = y² +  y² + z²

Or.  z²  -  z²  + 2 z w = 2 y²

Or,  2 z w = 2 y²

∴  y² = zw

I,e y =  

Hence The expression which represent the value of y is    ( option b )    Answer

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".