The below figure is a parallelogram. find the values for each variable.

The value of x is  22°  and The value of y is  17°  

Step-by-step explanation:

Given figure of parallelogram as show :

Let ∠ A = ( 3 y - 12 )°

    ∠ B = ( 7 y + x )°

And ∠ C = ( 2 x - 5 )°

Now From The property of Parallelogram

Consecutive angles of parallelogram are supplementary

So, from property

∠ A +  ∠ B = 180°    and   ∠ B +  ∠ C = 180°

∴ ( 3 y - 12 )° + ( 7 y + x )° = 180°

Or, ( 3 y + 7 y )° + ( x - 12 )° =  180°

Or, 10 y + x = 180° + 12°

I.e  10 y + x = 192°                              ........1

And ( 7 y + x )° + ( 2 x - 5 )° = 180°

Or, ( 7 y - 5 )° + ( x + 2 x )° =  180°

Or,  7 y + 3 x =  180° + 5°

I.e  7 y + 3 x =  185°                            .........2

Now, from eq 1 and eq 2

  7 y + 3 x =  185°      

 3 × ( 10 y + x ) = 192° × 3

Or, 30 y + 3 x = 576°

So, (  30 y + 3 x ) - ( 7 y + 3 x ) =  576° - 185°

or,  ( 30 y - 7 y ) + ( 3 x - 3 x ) = 391°

so,  23 y = 391°

∴   y =

I.e y = 17°

Put The value of y in eq 1 to get the value of x

I.e  10 y + x = 192°    

or,  10 × 17 + x = 192°  

Or, x = 192° - 170°

I.e x = 22°

Hence The value of x is  22°  and The value of y is  17°   Answer

step-by-step explanation:

from the graph attached below:

domain of graph is the value of x for which the given function profit function p(x) is defined.

(a) the domain represents the number of years for which the outlet will earn a profit.

range of profit function defines the lowest to highest value of profit earned.

(b) the range of this function is (0 , 160 ). for this function, the range represents the outlet's profit earned.

h= 12 inches

step-by-step explanation: