At a convention of science teachers, various attendees are asked to name their favorite subject in high school.

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

Kipish [7]

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

4 0

3 years ago

PV=k with constant k P and V vary directly or inversely?

sladkih [1.3K]

In order to keep the constant, the same and not vary there must be an indirect or inverse relationship to always maintain the value of k.

Thus both P and V are inversely related to each other.

6 0

2 years ago

The Bowen family's pancake recipe uses 2 teaspoons of baking powder for every

Veseljchak [2.6K]

Answer:

6 teaspoon of salt

Step-by-step explanation:

All you need to do is find how many teaspoon of salt they have in total which in this case they have 1 and there are 3 1/3s in 1 teaspoon then you just have to do 3 times 2 and you get 6teaspoon of salt.

Hope this helps!

5 0

3 years ago

How to solve this problem?

valentinak56 [21]

Very nice handwriting but the math and English are confusing.

Let's assume we're told

$\displaystyle 45 = \sum_{i=1}^9 (x_i - 10)^2$

The subscript is important.

I think we're told the similar sum with 11 gives the smallest possible value for the sum. This is a rather cagey way of telling us 11 is the mean of the nine points. The mean is the number which minimizes the sum of squared deviations.

$\displaystyle 45 = \sum_{i=1}^9 (x_i - 10)^2 = \sum x_i^2 - 20 \sum x_i + 9(100)$

$\displaystyle \sum x_i^2= 20 \sum x_i - 900$

If 11 is the mean, the sum of the points is 9(11)=99.

$\displaystyle \sum x_i^2= 20 (99) - 900 = 1080$

Answer: 1080

6 0

3 years ago

NEWSPAPERS Tamika delivered 50- newspapers last summer. Write 50% as a product of the same factor. Then find the value.

Annette [7]

This question was not written correctly

Complete Question

NEWSPAPERS Tamika delivered 50² newspapers last summer. Write 50² as a product of the same factor. Then find the value.

Answer:

The value is 2500

Step-by-step explanation:

We are told in the above question that:

Tamika delivered 50² newspapers last summer.

Writing 50² as a product is given as:

50 × 50

Hence, the value of 50 × 50

= 2500.

Therefore, the value is 2500

5 0

2 years ago