Mathematics, 09.04.2020 22:06 Thefiles

If the volume of a box is 2x3 + 4x2 − 30xwhich of the dimensions are possible with the given x-value?

A. x = 1; dimensions: 8 by 9 by 1
B. x = 1; dimensions: 2 by 5 by 3
C. x = 4; dimensions: 2 by 5 by 3
D. x = 4; dimensions: 8 by 9 by 1

Answers: 1

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Answers

Answer from: Prettygirlbuggy

The possible value of x = 4, dimensions 8 by 9 by 1 (option D), if the volume of a box is $2 x^{3} + 4 x^{2} -30x$ .

Step-by-step explanation:

The given is,

$2 x^{3} + 4 x^{2} -30x$ ................................(1)

Step:1

Check for option A,

x = 1, dimensions 8 by 9 by 1

From the equation (1),

Volume = $2 (1^{3}) + 4 (1^{2} )-30(1)$

=2+4-30 = -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 = $2 (1^{3}) + 4 (1^{2} )-30(1)$

=2+4-30 = -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 = $2 (4^{3}) + 4 (4^{2} )-30(4)$

=2(64)+4(16)-30(4)

= 128+64-120

= 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 = $2 (4^{3}) + 4 (4^{2} )-30(4)$

=2(64)+4(16)-30(4)

= 128+64-120

= 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 $2 x^{3} + 4 x^{2} -30x$ .

Answer from: Quest

step-by-step explanation:

every triangle measures a total of 120 degrees. you have to find angle c. we know that isosceles triangles angles are equal. 60 degrees plus 60 degrees gives you 120.

Answer from: Quest

step-by-step explanation:

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