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grin007 [14]
2 years ago
9

The side length, s, of a cube is 3x + 2y. If V = s3, what is the volume of the cube?

Mathematics
2 answers:
Rom4ik [11]2 years ago
8 0

Answer:

27x^3+8y^3+54x^2y+36xy^2

Explanation:

We have given with a cube whose side is 3x+2y and we need to find  the volume of a cube

Whose volume is defined by v=s^3

So, according to the formula we will get

(3x+2y)^3

Using the fomula

(a+b)^3=a^3+b^3+3a^2b+3ab^2

Here a=3x and b=2y substituting in the formula we will get

(3x+2y)^3=(3x)^3+(2y)^3+3(3x)^2(2y)+3(3x)(2y)^2

After simplification we will get

27x^3+8y^3+54x^2y+36xy^2

Hence, volume of cube is  27x^3+8y^3+54x^2y+36xy^2

Thepotemich [5.8K]2 years ago
6 0
V = (3x + 2y)³ = (3x + 2y)(3x + 2y)(3x + 2y)
V = (9x² + 12xy + 4y²)(3x + 2y)
V = 27x³ + 36x²y + 12y²x +18x²y + 24xy² + 8y³
V = 27x³ + 54x²y + 36y²x + 8y³
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Please help meeee > THANK YOU!!!!!
vovikov84 [41]

Answer:

39.   An adult male Western Banded Gecko is 5 1/2 (or 5.5) inches long.

41.    13,000 feet long, because 1 4/9 of 9,000 is 13,000.

43.  to answer the question we need to know if 35 out of 50 states is equal or greater than 3/4 if that is the case, the Constitution will be ammended, and that is represented like this:

35/50 >= 3/4

that inequality is saying that 35 states out of 50 is equal or greater than 3/4, lets simplify and modify the fractions to compare easily:

35/50 >= 3/4

7/10 >= 3/4

now we need to find the least common multiplier of 10 and 4 to take the fractions to a common denominator and compare easy. Lets multiply numerator and denominator for a correct number to get the fractions to denominator common 20, the lcm:

7/10 >= 3/4

(2/2)(7/10) >= (5/5)(3/4)

2*7/2*10 >= 5*3/5*4

14/20 >= 15/20

we can see that the inequality does not hold, so,

35/50 >= 3/4

does not hold either, therefore the Constitution cannot be ammended

40.  10 students play chess and sudoku,

30*2/5 is 12, out of 12; the number of students that play chess,5/6 play sudoku.

So..12*5/6 is 10 and that is the number of students that play both sudoku and chess.

42. Four fifths of 7/8 will be less than 7/8 (because you've multiplied by a number less than 1).

Similarly, 7/8 of 4/5 will be less than 4/5.

This means that the product will be less than each of the original factors.  

answer: no

44.  The answer is 7/12 because 3/4 - 1/6= 7/12

3/4 converts to 9/12 and 1/6 converts to 2/12. The domanaters stay the same, but 9-2=7. that is how you get 7/12

5 0
3 years ago
Select all answers that have a value of 22?? Help..
Tom [10]

Let's plug in the variables one by one.

6g - 2h

plug in 5 for g and 4 for h

6(5) - 2(4)

multiply

30 - 8

subtract

→ 22

20g

plug in 2 for g

20(2)

multiply

40

2(g + 1)

plug in 10 for g

2(10 + 1)

add

2(11)

multiply

→ 22

4g + 5h

plug in 1 for g and 4 for h

4(1) + 5(4)

multiply

4 + 20

add

24

Therefore, the answers that have a value of 22 are 6g - 2h and 2(g + 1)

6 0
3 years ago
Read 2 more answers
How do you prove each of the following theorems using either a two-column, paragraph, or flow chart proof?
lilavasa [31]

All the theorems are proved as follows.

<h3>What is a Triangle ?</h3>

A triangle is a polygon with three sides , three vertices and three angles.

1. The Triangle sum Theorem

According to the Triangle Sum Theorem, the sum of a triangle's angles equals 180 degrees.

To create a triangle ABC, starting at point A, move 180 degrees away from A to arrive at point B.

We turn 180 degrees from B to C and 180 degrees from C to return to A, giving a total turn of 360 degrees to arrive to A.

180° - ∠A + 180° - ∠B + 180° - ∠C = 360°

- ∠A - ∠B  - ∠C = 360° - (180°+ 180°+ 180°) = -180°

∠A + ∠B  + ∠C = 180°

(Hence Proved)

2. Isosceles Triangle Theorem

Considering an isosceles triangle ΔABC

with AB = AC, we have by sine rule;

\rm \dfrac{sinA}{BC} =  \dfrac{sinB}{AC} =  \dfrac{sinC}{AB}\\

as AB = AC

sin B = sin C

angle B = angle C

3.Converse of the Isosceles theorem

Consider an isosceles triangle ΔABC with ∠B= ∠C, we have by sine rule;

\rm \dfrac{sinA}{BC} =  \dfrac{sinB}{AC} =  \dfrac{sinC}{AB}\\

as  ∠B= ∠C ,

AB = AC

4. Midsegment of a triangle theorem

It states that the midsegment of two sides of a triangle is equal to (1/2)of the third side parallel to it.

Given triangle ABC with midsegment at D and F of AB and AC respectively, DF is parallel to BC

In ΔABC and ΔADF

∠A ≅ ∠A

BA = 2 × DA, BC = 2 × FA

Hence;

ΔABC ~ ΔADF (SAS similarity)

BA/DA = BC/FA = DF/AC = 2

Hence AC = 2×DF

5.Concurrency of Medians Theorem

A median of a triangle is a segment whose end points are on vertex of the triangle and the middle point of the side ,the medians of a triangle are concurrent and  the point of intersection is inside the triangle known as Centroid .

Consider a triangle ABC , X,Y and Z are the midpoints of the sides

Since the medians bisect the segment AB into AZ + ZB

BC into BX + XB

AC into AY + YC

Where:

AZ = ZB

BX = XB

AY = YC

AZ/ZB = BX/XB = AY/YC = 1

AZ/ZB × BX/XB × AY/YC = 1 and

the median segments AX, BY, and CZ are concurrent (meet at point within the triangle).

To know more about Triangle

brainly.com/question/2773823

#SPJ1

8 0
1 year ago
Solve 4(2x − 1) − 3 = 9(x − 4).
OLEGan [10]
The answer is x=29
I hope this helps you
5 0
2 years ago
Read 2 more answers
Three cubic feet of seawater weigh 192 pounds.
sweet-ann [11.9K]

Answer:

<em>3731.2 pounds</em>

Step-by-step explanation:

<em>Aquarium will hold 4.4 * 2.5 * 5.3 = 58.3 cubic feet of sea water.</em>

<em>For 3 cubic feet of sea water, weight is 192 pounds</em>

<em>For 58.3 cubic feet of sea water,</em>

<em>( 192 * 58.3) / 3 = 11193.6 / 3 = 3731.2 pounds</em>

6 0
3 years ago
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