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aksik [14]
3 years ago
10

Three consectuive integers have a sum of 81

Mathematics
1 answer:
irina [24]3 years ago
8 0
The three consecutive integers are 26, 27, 28

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Which fraction is equivalent to 4/-9 ?<br><br> A) -4/9 <br> B) 4/9 <br> C) -4/-9 <br> D) 9/4
Art [367]
The answer is A  hope this helps

4 0
3 years ago
Read 2 more answers
Pls help with 29..tank you
trapecia [35]

Answer:

See below

Step-by-step explanation:

Let the  2 roots be  A and A^2.

Then A^3 = c/a and A + A^2 = -b/a.

Using the identity a^3 b^3 = (a + b)^3 - 3ab^2 - 3a^2b:-

A^3 + (A^2)^3 =  ( A + A^2)^3 - 3 A.A^4 - 3 A^2. A^2

= (A + A^2)^3 - 3A*3( A + A^2)

Substituting:-

c/a + c^2/a^2 = (-b/a)^3 - 3 (c/a)(-b/a)

Multiply through by a^3:-

a^2c + ac^2 = -b^3 + 3abc

Factoring:-

ac(a + c) = 3abc - b^3

This is not the formula required in the question but let's see if the formula in the question reduces to this. If it does we have completed the proof.

a(c - b)^3 = a(c^3 - 3c^2b + 3cb^2 - b^3) = ac^3 - 3ac^2b + 3acb^2 - ab^3

c(a - b)^3 = c(a^3 - 3a^2b + 3ab^2 - b^3) = ca^3 - 3a^2bc + 3acb^2 - cb^3.

These are equal so we have

ca^3 - 3a^2bc + 3acb^2 - cb^3 = ac^3 - 3abc^2 + 3acb^2 - ab^3

The 3acb^2 cancel out so we have:-

a^3c - ac^3 =  3a^2bc - 3abc^2 + b^3c - ab^3

ac(a^2 - c^2) = 3abc( a - c) + b^3(c - a)

ac(a + c)(a -c) = 3abc(a - c) - b^3 (a - c)

Divide through by (a - c):-

ac(a + c) = 3abc - b^3 , which is the result we got earlier.

This completes the proof.

 

3 0
3 years ago
Read 2 more answers
Someone please help me! Studying for finals and don’t understand how to complete problems like this! Thank you!
Drupady [299]

Answer:

(d). \frac{152}{377}

Step-by-step explanation:

sin² β + cos² β = 1

cos (α + β) = cos α cos β - sin α sin β

cos α = √(1 - \frac{400}{841} ) = 21 / 29

cos β = 12 / 13

sin β = √(1 - \frac{144}{169} ) = 5 / 13

sin α = 20 / 29

cos (α + β) = \frac{21}{29} × \frac{12}{13} - \frac{20}{29} × \frac{5}{13} = \frac{152}{377}

6 0
3 years ago
Which value of x makes 7+5 (x-3)=22 a true statement
slavikrds [6]

Answer:

x=6

Step-by-step explanation:

7+5 (x-3)=22

Subtract 7 from each side

7-7+5 (x-3)=22-7

5(x-3) = 15

Divide each side by 5

5(x-3)/5 = 15/5

x-3 = 3

Add 3 to each side

x-3+3=3+3

x=6

6 0
3 years ago
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Hans typed a 36-word paragraph in 2/3 minute.<br> What is his typing speed, in words per minute?
prisoha [69]

\dfrac{2}{3} minutes= 36 words

1min= 36 \div  \dfrac{2}{3} words

= 36 \times  \dfrac{3}{2}

= 54 words

<h3>His speed is : 54 words/minute </h3>
6 0
3 years ago
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