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

math can you please help me?​

Answers

Answer:

The answer will be -5

You are welcome:)

Step-by-step explanation:

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

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°

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

need a well explained ans ...
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​

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 ~

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

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]

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

[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]

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

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

determine the value of x.

No links please!

Answers

Answer:

44.785

Step-by-step explanation:

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

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

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:

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)

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

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!

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

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



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!

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

Answers

Up 8 Units, Hope this helps :)

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

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]

Write 19/25 in decimal form.

Answers

0.76                 19 divided by 27= 0.76

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.

guys pls help me!!!!!!

Answers

Answer:

x= 55

y=125

Step-by-step explanation:

y = 180 - 55

hope it's correct

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