1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bess [88]
4 years ago
14

Find the value of:

3}+8 y^{3} " alt=" 27x^{3}+8 y^{3} " align="absmiddle" class="latex-formula"> if 3x+2y = 20 and xy = \frac{14}{9}
Mathematics
1 answer:
kirill [66]4 years ago
5 0
27x^3+8y^3=(3x)^3+(2y)^3=(3x+2y)[(3x)^2-3x\cdot2y+(2y)^2]\\\\=(3x+2y)[(3x)^2+2\cdot3x\cdot2y+(2y)^2-3\cdot3x\cdot2y]\\\\=(3x+2y)[(3x+2y)^2-18xy]=(*)\\---------------------------\\3x+2y=20\\\\xy=\frac{14}{9}\\------------------------------\\(*)=20\cdot(20^2-19\cdot\frac{14}{9})=20\cdot(400-18\cdot\frac{14}{9})=20\cdot(400-2\cdot14)\\\\=20\cdot(400-28)=20\cdot372=7440



a^3+b^3=(a+b)(a^2-ab+b^2)\\\\(a+b)^2=a^2+2ab+b^2
You might be interested in
Find the number of unique permutations of the letters in the word: ONGOING
Kazeer [188]

Answer:

<h2>The Number of unique permutation is  6,615</h2>

Step-by-step explanation:

  This particular permutation  deals with words that have repeated letters.

Given word = "ONGOING"

the formula for the permutation is

= \frac{n!}{mA! mB!.....mZ!}

where   n   is the amount of letters in the word, and  m A , m B , ... , m Z  are the occurrences of repeated letters in the word. Each   m  equals the amount of times the letter appears in the word.

So in the word  "ONGOING"

n= 7

mO= 2

mN= 2

mG=2

permutations = \frac{7!}{2!2!2!} \\\\permutations= \frac{7*6*5*4*3*2*1}{(2*1)*(2*1)*(2*1)}

permutations=  \frac{52920}{8} \\permutation = 6,615

8 0
3 years ago
Prove that 5^7+5^6 is divisible by 6.
pishuonlain [190]

Answer:

The Proof for 5^{7}+5^{6}\ is\ divisible\ by\ 6 is below.

Step-by-step explanation:

To Prove:

5^{7}+5^{6}\ is\ divisible\ by\ 6

Proof:

We know law of indices

a^{m}.a^{n}=a^{m+n}

Therefore,

Step 1: Applying law of indices

\dfrac{5^{7}+5^{6}}{6}=\dfrac{5^{6}.5^{1}+5^{6}}{6}

Step 2: Taking common 5^{6} we get

\dfrac{5^{7}+5^{6}}{6}=5^{6}\times (\dfrac{5^{1}+1}{6})

Step 3: 5^{1} = 5 so add 5 + 1 we get

\dfrac{5^{7}+5^{6}}{6}=5^{6}\times \dfrac{6}{6}

Step 4: Cancel 6 from both denominator and numerator we get

\dfrac{5^{7}+5^{6}}{6}=5^{6}\times 1=5^{6} ...That is Divisible by 6 Proved

7 0
3 years ago
Explain your steps to solve 3x +4/+2 = 29.
bulgar [2K]

Answer:

X=18

Step-by-step explanation:

3x+4/2 = 29

Multiply both sides by 2 :

2(3x+4)/2 = 29*2

Simplify :

3x+4= 58

Subtract 4 from both sides :

3x + 4 - 4 = 58 - 4

Simplify  :

3x = 54

Divide both sides by 3:

3x / 3 = 54 /3

Simplify  :

X = 18

Hope it Helps :) !!!!

5 0
4 years ago
Solve the equation and state a reason for each step.<br>find x. show steps.<br><br>8x - 4 = 5x + 8
romanna [79]
Subtract 5x from both sides to make: 3x-4=8. Add four to both sides and divide by three, x=4.
4 0
3 years ago
What's the slope of this graph
Contact [7]

Answer:

Slope= -1

Step-by-step explanation:

Rise over run

2 to the right 2 down = 2/-2

Simplify to -1

3 0
3 years ago
Read 2 more answers
Other questions:
  • Jacob knows that 120 means “1 divided by 20.” He uses this to find the decimal equivalent for 120. Enter a digit into each box t
    14·1 answer
  • Drag each label to the correct location on the graph. Not all tiles will be used.
    8·2 answers
  • Select the expression that has a sum of 75/100
    11·1 answer
  • Help please... <br> find the midpoint of the line segment with the given endpoints
    12·1 answer
  • I need help asap I’m overtime
    12·1 answer
  • Find the x and y intercepts of 4x - 5y = 40<br><br> Is this correct and can someone explain why??
    9·1 answer
  • Which of the following are adjacent angles?
    15·1 answer
  • Guys I need y’all help ! ASAP . Pleaseeeee !!!!!
    9·1 answer
  • If a=3 and b=-1 what is the value of ab-b^2<br><br>a -20<br>b 8<br>c -2<br>d 16​
    7·2 answers
  • I need help w this asap
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!