Mathematics High School

if 3x - 2y = 9 , 27x³- 8y³= 1377 , prove that xy = 4



plzz answer this question... ​

Answers

Answer 1

Step-by-step explanation:

Here we are given that , the Value of

[tex] 3x - 2y = 9 [/tex] [tex] 27x^3 - 8y^3 = 1377 [/tex]

And we need to find the prove that ,

[tex] xy = 4 [/tex]

We know a identity as ,

[tex] (a-b)^3 = a^3-b^3-3ab(a-b) [/tex]

On cubing both sides of the given equation,

[tex] (3x-2y)^3 = 9^3 [/tex]

Simplify and then substitute ,

[tex] 27x^3-8y^3 -3(3x)(2y)(3x-2y ) = 729[/tex]

[tex] 1377 - 18xy (9) = 729 [/tex]

[tex] 162xy = 1377-729 [/tex]

[tex] xy =\dfrac{648}{162}[/tex]

[tex]xy = 4 [/tex]

Hence Proved !

Related Questions

What is the missing number in this sequence? What is the missing number in this sequence?
(7, 8) (19, 27) (37, 64) (61, 125) (91, 216) (___, 343)

Answers

Answer:

15_789(0)

Step-by-step explanation:

Show that (√7+i√3/√7-i√3 + √7-i√3/√7+i√3) is real​

Answers

Answer:

Step-by-step explanation:

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

Consider,

[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]

On taking LCM, we get

[tex]\rm \:  =  \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]

and

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]

So, using these Identities, we get

[tex]\rm \:  =  \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]

[tex]\rm \:  =  \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]

So, using this, we get

[tex]\rm \:  =  \: \dfrac{2(7 - 3)}{7 + 3} [/tex]

[tex]\rm \:  =  \: \dfrac{2 \times 4}{10} [/tex]

[tex]\rm \:  =  \: \dfrac{4}{5} [/tex]

Hence,

[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]

can someone please help me with this

Answers

Answer:

Perimeter = 18m

Area = 18m²

Step-by-step explanation:

On a rectangle, opposite sides have equal lengths. This means to find the perimeter you would do (3 × 2) + (6 × 2) which is 6 + 12 = 18

The perimeter is 18m

To find the area, you would do length × width. The length is 6 and the width is 3 so 6 × 3 is 18

The area is 18m²

Hope this helps!

The diagram below represent the rate of making copies on a copy machine. Which table represent this rate?

Answers

Answer:

its B

Step-by-step explanation:

what is 26 divide 7,124

Answers

Answer:

1/274

Step-by-step explanation:

Solution 1: Use a fraction simplifier calculator :)

Solution 2: divide by 2 first, then test to find 13, and your there.

Answer: There are two answers ( just for explanation ) 1. 0.0036496350364964    2. 274

Step-by-step explanation:

1. If we do 26 divided by 7124 answer is = 0.0036496350364964  ( check the pic-div1, div2, div3 )

2. If we do 7124 divided by 26 answer is = 274 (check pics-div4, div5)

What are the values of v and w ?

Answers

Apply the same thing here from the other question. V = 36.

36 + 36 + w = 180

72 + w = 180

W = 108



Easy? Please help me

Sarah earns $


8.50

8.50 per hour babysitting. She needs to make at least $

187

187 to buy a new bike.


Write an inequality to represent the number of hours Sarah needs to work to afford the bike.



187

h

≥

8.50

187h≥8.50


187

h

≤

8.50

187h≤8.50


8.50

h

≥

187

8.50h≥187


8.50

h

≤

187

8.50h≤187

Answers

Answer:

The answer is A

Step-by-step explanation:

Hope it helps!

Write 19/25 in decimal form.

Answers

0.76                 19 divided by 27= 0.76

guys pls help me!!!!!!

Answers

Answer:

x= 55

y=125

Step-by-step explanation:

y = 180 - 55

hope it's correct

Tom makes $249.25 in 5 days. How much does he make in 4 days?

Answers

Answer:

$199.4 in four days

$49.85 in one day

Step-by-step explanation:

249.25 / 5  =49.85

49.85 x 4 = 199.4

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The amount that Tom makes in 4 days is $199.4.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that Tom makes $249.25 in 5 days. Therefore, the amount that Tom makes in a day is,

Amount Tom makes in a day = $249.25 / 5 days

                                                = $49.85 per day

The amount of money that Tom can make in 4 days is,

Amount = $49.85 per day × 4 days

              = $199.4

Hence, the amount that Tom makes in 4 days is $199.4.

Learn more about Multiplication here:

https://brainly.com/question/14059007

#SPJ2

at sunrise,the temperature outside was 5 below zero . by noon the temperature dropped 27. what was the temprature at noon

Answers

Answer:

-32

Step-by-step explanation:

hope this helps you with the question

HELP PLEASE!!!!!!!!!

Answers

9514 1404 393

Answer:

  A) W'(-4, 2), ...

Step-by-step explanation:

Put the values of x and y in the translation relation to see what the translated point's coordinates are.

  (x, y) ⇒ (x -7, y +4)

  W(3, -2) ⇒ W'(3 -7, -2 +4) = W'(-4, 2) . . . . . . . . matches only choice A

PLEASE ANSWER IN POINT SLOPE FORM

Answers

Answer:

y-4 =-5(x+1)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y-4 = -5(x- -1)

y-4 =-5(x+1)

Answer:

y-4 = -5 (x- (-1))

Step-by-step explanation:

blank 1 = -4

blank 2 = -5

blank 3 = -1

In ΔBCD, \text{m}\angle B = (5x+14)^{\circ}m∠B=(5x+14)
∘
, \text{m}\angle C = (x+19)^{\circ}m∠C=(x+19)
∘
, and \text{m}\angle D = (2x+19)^{\circ}m∠D=(2x+19)
∘
. What is the value of x?x?

Answers

Answer:

x = 16

Step-by-step explanation:

m<B+m<C+m<D = 180°

5x + 14 + x + 19 + 2x + 19 = 180

8x + 52 = 180

8x = 180 - 52

x = 128/8

x = 16

Ryan has 15 meters of stereo wire He used 7/8 of the wire to hook his new speakers. How much wire did he use?​

Answers

Answer:

13.125 meters

Step-by-step explanation:

7/8 times 15

Find the value of f(5) for the function f(m) = 1 - 4(m/2) *

Answers

Answer:

f(m) = -9

Step-by-step explanation:

We replace m with 5 in the function.

f(m) = 1 - 4(m/2) becomes f(5) = 1 - 4(5/2)

then we solve the numbers in the parenthesis first

= 1 - 4 (5/2)

= 1 - 4 (2.5)

= 1 - 10

= -9

Which number equals (34)−2?

Answers

Answer:

32

Step-by-step explanation:

Please help! GEOMETRY! Branliest!

Answers

Answer:

None

Step-by-step explanation:

It would be easier to ask your teacher instead of getting wrong answers from random people. Ever think of that :0

Answer:

The smallest degree is15°

[tex]\sf x-5=16[/tex]

Answers

Answer:

x=21

Step-by-step explanation:

[tex]x-5=16[/tex]

[tex]x-5+5=16+5[/tex] (Add 5 to bth sides)

[tex]x=21[/tex]

Find the value of x so that | || m. State the converse used

Answers

X = 12 because 14x - 23 = 9x + 60 then you just solve for x

137.8×3.5 with explanation

Answers

Answer:

482.3

Step-by-step explanation:

because 137.8 times 3.5 is

482.3

137.8x3.5 is 482.3 because 137.8 3.5s is 482.3

need a well explained ans ...
● no spams needed
​

Answers

5. We need to subtract 20% from the selling price of 18 000 as that will give his cost price

20/100 X 18 000 = 3600

18 000 - 3600

= 14 400.



7) 20 527,5 Rs

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Question : 1

Cost price of the T.V. is :

[tex]₹ \: 15000[/tex]Question : 2

The scooter cost him :

[tex]₹ \: 21000[/tex]

The solution is in attachment ~

Ben has 69 planks that are of standard size. He would need 5 such planks to make a bookshelf. Find the maximum number of bookshelves Ben can make.​

Answers

Answer:

13

Step-by-step explanation:

69/5=13 remainder 4

u cant make a bookshelf with 4 planks

Answer:

13

Step-by-step explanation:

69 total planks divided by 5 for each bookshelf.

That would be 69÷5=13.8

Seeing as you can't make .8 of a shelf, those planks would just be extra.

Which point is the vertex?
C
B
A
None of the above

Answers

The answer is B because its where the two lines intersect or cross each other

determine the value of x.

No links please!

Answers

Answer:

44.785

Step-by-step explanation:

math can you please help me?​

Answers

Answer:

The answer will be -5

You are welcome:)

Step-by-step explanation:

HELP PLSSS THIS IS HARD SOMEONEEE

Answers

Answer:

correct option is f(x,y) -----> ( -y,x) option 1.

Answer:

correct option is f(x,y) -----> ( -y,x) option 1.

Step-by-step explanation:

HELP HELP HELP HELP HELP HELP
long explanation long please​

Answers

>> Answer

__________

[tex] \: [/tex]

[tex] \frac{x + 2}{x - 1} = ...[/tex]

[tex] \longmapsto \frac{ \cancel{x} + 2}{ \cancel{x} - 1} [/tex]

[tex] \longmapsto \frac{2}{ - 1} [/tex]

[tex] \longmapsto \boxed{ \bold{ \red{ - 2}}}[/tex]

Describe the translation of the point to its image. (-2,-3) to (-2,4)

Answers

Up 8 Units, Hope this helps :)

can someone please help me i need help

Answers

Answer:

None

Step-by-step explanation:

It would be easier to ask your teacher instead of getting wrong answers from random people. Ever think of that :0

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