Respuesta :
The possible value of x = 4, dimensions 8 by 9 by 1 (option D), if the volume of a box is [tex]2 x^{3} + 4 x^{2} -30x[/tex].
Step-by-step explanation:
The given is,
[tex]2 x^{3} + 4 x^{2} -30x[/tex]................................(1)
Step:1
Check for option A,
x = 1, dimensions 8 by 9 by 1
From the equation (1),
Volume = [tex]2 (1^{3}) + 4 (1^{2} )-30(1)[/tex]
[tex]=2+4-30[/tex] = -24...................(2)
From the dimensions,
Volume = ( 8 × 9 × 1 )
= 72............................................(3)
From equation (2) and (3)
-24 ≠ 72
So, X=1; dimensions 8 by 9 by 1 is not possible.
Check for option B,
x = 1, dimensions 2 by 5 by 3
From the equation (1),
Volume = [tex]2 (1^{3}) + 4 (1^{2} )-30(1)[/tex]
[tex]=2+4-30[/tex] = -24...................(4)
From the dimensions,
Volume = ( 2 × 5 × 3 )
= 30.........................................(5)
From equation (4) and (5)
-24 ≠ 30
So, X=1; dimensions 2 by 5 by 3 is not possible.
Check for option C,
x = 4, dimensions 2 by 5 by 3
From the equation (1),
Volume = [tex]2 (4^{3}) + 4 (4^{2} )-30(4)[/tex]
[tex]=2(64)+4(16)-30(4)[/tex]
[tex]= 128+64-120[/tex]
= 72.............................................(6)
From the dimensions,
Volume = ( 2 × 5 × 3 )
= 30............................................(7)
From equation (6) and (7)
72 ≠ 30
So, X=4; dimensions 2 by 5 by 3 is not possible.
Check for option C,
x = 4, dimensions 8 by 9 by 1
From the equation (1),
Volume = [tex]2 (4^{3}) + 4 (4^{2} )-30(4)[/tex]
[tex]=2(64)+4(16)-30(4)[/tex]
[tex]= 128+64-120[/tex]
= 72............................................(8)
From the dimensions,
Volume = ( 8 × 9 × 1 )
= 72............................................(9)
From equation (8) and (9)
72 = 72
So, X=4; dimensions 8 by 9 by 3 is possible.
Result:
The possible value of x = 4, dimensions 8 by 9 by 1 (option D), if the volume of a box is [tex]2 x^{3} + 4 x^{2} -30x[/tex].
