find the rationalising factor of the irrational number
[tex] - 6 \sqrt{5} [/tex]
​

You can use the same technique I showed in another one of your questions (24467305).

Partial fractions:

[tex]\dfrac2{(2n-1)(2n+1)} = \dfrac a{2n-1} + \dfrac b{2n+1} \\\\ \implies 2 = a(2n+1) + b(2n-1) = (2a+2b)n + a- b \\\\ \implies \begin{cases}2a+2b=0 \\ a-b = 2\end{cases} \implies a = 1, b=-1[/tex]

Then we have a telescoping sum,

[tex]S = \displaystyle \sum_{k=1}^n \frac 2{(2k-1)(2k+1)} \\\\ S = \sum_{k=1}^n \left(\frac1{2k-1} - \frac1{2k+1}\right) \\\\ S = 1-\frac13 + \frac13 - \frac15 + \cdots +\frac1{2n-3}-\frac1{2n-1}+\frac1{2n-1}-\frac1{2n+1} \\\\ S = 1 - \frac1{2n+1} = \boxed{\frac{2n}{2n+1}}[/tex]

(And in case you were actually interested in an infinite sum, we can see that this converges to 1 as n goes to ∞.)

Answer: x = 5 or x = -4

Step-by-step explanation:

Given equation

x² - x = 20

Subtract 20 on both sides

x² - x - 20 = 0

Cross factorize the equation

x          -5

x          4

Factorize the equation

(x - 5) (x + 4) = 0

[tex]\boxed{x=5}[/tex] or [tex]\boxed{x=-4}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: x=6+y/3

Step-by-step explanation:

3x=6+y

x=6+y/3

Answer: this is an impossible question dude or dudett

Step-by-step explanation:

sum of number=30+36+p+40+44=150+p

n=5

average=35

Step-by-step explanation:

average=sum of number÷n

35=150+p÷5

35×5=150+p

175-150=p

25=p

p=25

Answer:

P=25

Step-by-step explanation:

Hi! Let's start with with the average...

First we multiply 35 by the amount of numbers we have

We have 5 including the unidentified

so...

35x5=175

Now since we have 175 we have to add all the other numbers together

30+36+40+44=150

Next we subtract

175-150= 25

P= 25

To check our answer add all of them together

40+30+40+44+25=175

We were right!

Hope this helps! :)

Answer:

m = - 13.5

Step-by-step explanation:

Given

[tex]\frac{2m}{3}[/tex] + [tex]\frac{1}{2}[/tex] - [tex]\frac{m}{5}[/tex] = [tex]\frac{4m}{5}[/tex] + 5

Multiply through by 30 ( the LCM of 3, 2, 5 ) to clear the fractions

20m + 15 - 6m = 24m + 150 , that is

14m + 15 = 24m + 150 ( subtract 24m from both sides )

- 10m + 15 = 150 ( subtract 15 from both sides )

- 10m = 135 ( divide both sides by - 10 )

m = - 13.5

Answer:

The answer must be B because the rest are not possible.

Step-by-step explanation:

Step-by-step explanation:

Each unit would be $4.25

Answer:

8/$34.00 divided by 8 = 1/$4.25. 1 board game costs $4.25. hope this helps

Step-by-step explanation:

- Zombie

4x+3=3x+13(Alternative interior angles)

4x-3x=13-3

x=10

Value of each angle=43 each

Answer:

34024.83

Step-by-step explanation:

Answer:

the answer is 0, 8, 7 , 8

Step-by-step explanation:

0×1+8×1/10+7×1/100+8×1/1000

Step-by-step explanation:

I believe you're supposed to answer the expressions in the parenthesis and then once you get the answer add them to make sure they equal to 2600 cm.

Answer:

C. $2.50

Step-by-step explanation:

x=1 y=5.5

x=2 y=2.5

Answer:

Compare to slope intercept form y=mx+b

Sl

Here the rate of change is $2.50

Hey there!

Guide:

• Negatives are on the LEFT side of the number line

• Positives are on the RIGHT side of the number line.

• Negatives are BELOW 0 (less than 0)

• Positives are ABOVE 0 (more than 0)

• You have to take the value of the LARGER number.

• If your LARGER number is a negative number then your result will be a negative.

• If your LARGER is a positive number then your result will be a positive

• Negative & Negative = Positive

• Negative & Positive = Negative

• Positive & Positive = Positive

• Positive & Negative = Negative

y = -50 + 31

• So, you start from -50 and go UP 31 spaces to the right because “31” is a positive number.. once when you have moved UP your 31 spaces you have reached your answer for this given equation

y = -50 + 31

y = -19

Therefore, your answer is: y = -19

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Part A: Jillian added 7+3 first rather than multiplying 3*16 b/c multiplication comes before addition

Part B:

7 + 3 * (10 - 6) ^2

7+ 3 * (4)^2

7+3 * 16

7 + 48

55

Step-by-step explanation:

Answer:

Part A:

Jillian's error was that they added the 7 and the 3 to get 10 and then multiplied by 16. Jillian should have multiplied the 3 and the 16 first and then added 7. This is because multiplication comes before addition in PEMDAS.

Part B:

7+3×(10-6)^2

7+3×(4)^2

7+3×16

7+48

55

Step-by-step explanation:

PEMDAS

Answer:

a=100 b=50 c=30

Step-by-step explanation:

30+50+a= 180, A= 100.

90+40+b=180, B=50      

A+B+C= 180

100+50+c=180, C=30

Answer:

Option C

Step-by-step explanation:

[tex]( { - 2m}^{3} {p}^{2} ) {}^{4} [/tex]

[tex] {( { - 2m}^{3}) }^{4} \times ( { {p}^{2} )}^{4} [/tex]

[tex] {16m}^{12} \times {p}^{8} [/tex]

Answer:

[tex] {( - 2 {m}^{3} {p}^{2}) }^{4} \\ = { (- 2)}^{4} { {m}^{3} }^{4} { {p}^{2} }^{4} \\ = 16 \times {m}^{12} {p}^{8} \\ c \: is \: ur \: answer \: \\ thank \: you[/tex]

Answer:

the answer = 2,020,500,900

Answer: 0.4

Step-by-step explanation: I love you

Answer:

-6+(-3) OR -6-3= -9

3+(-4)= -1

Step-by-step explanation:

if u nee me to explaiin, jus say thet .

Answer:  2 • (y2 + 11y + 14)

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "y2"   was replaced by   "y^2".  1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

 (((8•(y2))+7y)+4)-(3•((2y2-5y)-8))

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  2y2-5y-8  

The first term is,  2y2  its coefficient is  2 .

The middle term is,  -5y  its coefficient is  -5 .

The last term, "the constant", is  -8  

Step-1 : Multiply the coefficient of the first term by the constant   2 • -8 = -16  

Step-2 : Find two factors of  -16  whose sum equals the coefficient of the middle term, which is   -5 .

     -16    +    1    =    -15  

     -8    +    2    =    -6  

     -4    +    4    =    0  

     -2    +    8    =    6  

     -1    +    16    =    15  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

 (((8•(y2))+7y)+4)-3•(2y2-5y-8)

STEP  

3

:

Equation at the end of step

3

:

 ((23y2 +  7y) +  4) -  3 • (2y2 - 5y - 8)

STEP

4

:

STEP

5

:

Pulling out like terms

5.1     Pull out like factors :

  2y2 + 22y + 28  =   2 • (y2 + 11y + 14)  

Trying to factor by splitting the middle term

5.2     Factoring  y2 + 11y + 14  

The first term is,  y2  its coefficient is  1 .

The middle term is,  +11y  its coefficient is  11 .

The last term, "the constant", is  +14  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 14 = 14  

Step-2 : Find two factors of  14  whose sum equals the coefficient of the middle term, which is   11 .

     -14    +    -1    =    -15  

     -7    +    -2    =    -9  

     -2    +    -7    =    -9  

     -1    +    -14    =    -15  

     1    +    14    =    15  

     2    +    7    =    9  

     7    +    2    =    9  

     14    +    1    =    15  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Answer:

(-3,-10)

Step-by-step explanation:

4 units down means -4 from the y axis

-6 - 4 = -10

Answer:

Its B

Step-by-step explanation:

Answer:

LN = 12

Step-by-step explanation:

L______M_____N

LM = x+3

MN = 2x

LN = 4x

M is the midpoint of LN

LN= ?

LM + MN = LN

x + 3 + 2x = 4x

x + 2x + 3 = 4x

3x + 3 = 4x

-3x         -3x

----------------------

3 = 1x

/1    /1

----------------------

3 = x

LN = 4x

= 4 (3)

= 12

LN = 12

Answer:

LN = 12

Step-by-step explanation:

If LM = X+3, MN = 2x, LN = 4x, and M is between L and N, then LN = 12.

Answer:

+12

Step-by-step explanation: