Rationalise the denominator of: -7/(√11 - √5)​

Answers

Answer 1

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

Given,

[tex] \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} }} \\ [/tex]

The denominator is √11 - √5.

We know that

Rationalising factor of √a-√b is √a+√b.

Therefore, the rationalising factor of √11-√5 is √11+√5.

On rationalising the denominator them

[tex] \longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} \times \dfrac{(\sqrt{11} + \sqrt{5})}{(\sqrt{11} + \sqrt{5})} }} \\ [/tex]

Multiplying (√11 + √5) with both the numerator of the fraction.

[tex] \longrightarrow \sf{\quad { \dfrac{-7(\sqrt{11} + \sqrt{5}) }{(\sqrt{11} - \sqrt{5})(\sqrt{11} + \sqrt{5})} }} \\ [/tex]

Performing multiplication in the numerator and by using identity (a + b)(a - b) = a² - b², solving further in the denominator.

[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{(\sqrt{11})^2 - (\sqrt{5})^2} }} \\ [/tex]

Writing the squares of the numbers in the denominator.

[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{11 -5} }} \\ [/tex]

Performing subtraction in the denominator.

[tex] \longrightarrow \quad \underline{ \boxed{ \dfrac{ \textbf{ \textsf{-7 }}\sqrt{ \textbf{ \textsf{11 }}} - \textbf{ \textsf{7}}\sqrt{ \textbf{ \textsf{5 }}}}{ \textbf{ \textsf{ 6}}}} } \\ [/tex]

Hence, the denominator is rationalised.


Related Questions

What is the iterative rule for the following sequence?
4, 4/5, 4/25, 4/125, ...

A.) an=4•(1/5)^n-1
B.) an=4•(1/5)^n
C.) an=1/5•4^n-1
D.) an=1/5•4^n

Answers

Answer:

A.) 4 * (1/5)^(n-1)

Step-by-step explanation:

a1 = 4 * (1/5)^(1-1) = 4* (1/5)^0 = 4*1 = 4

a2 = 4 * (1/5)^(2-1) = 4 * (1/5)^1 = 4 * 1/5 = 4/5

a3 = 4 * (1/5)^(3-1) = 4 * (1/5)^2 = 4 * 1/25 = 4/25

a4 = 4 * (1/5)^(4-1) = 4 * (1/5)^3 = 4 * 1/125 = 4/125

a5 = 4 * (1/5)^(5-1) = 4 * (1/5)^4 = 4 * 1/625 = 4/625

. . .

The required iterative rule for the following sequence is [tex]a_n=4*(1/5)^{n-1}[/tex]. Option A is correct.

Given sequence,
4, 4/5, 4/25, 4/125, ...

What is geometric progression?

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
The given sequence is 4, 4/5, 4/25, 4/125, ...

Common ratio among the proceeding terms,
r = 4/5/4
r = 1/5
The required general term can be described as [tex]a_n=4*(1/5)^{n-1}[/tex].

Thus, the required iterative rule for the following sequence is [tex]a_n=4*(1/5)^{n-1}[/tex]. Option A is correct.

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which is colder -3°c or -2°c

Answers

-3°C is the coldest temperature

Answer:

-2 is colder

Step-by-step explanation:

Becuase when you get to the negative the Closest number to 0 is greater which means -2 is closer to 0 which makes it colder.

(Hope this helps can I pls have brainlist (crown)☺️)

write 47% as a fraction is simplest form.

Answers

Answer:

47/100

Step-by-step explanation:

47 = 0.47 = 47/100

The US dollar can be exchanged for other types of currency in the world the exchange rate is always changing suppose one eruro is equivalent to two dollars
HELP DUE TODAY! PLS HELPP



1. 2. 5. 10. Euro

2. ? ? ? US dollars

Answers

Answer:

$2, $4, $10, $20

Step-by-step explanation:

1*2=2

2*2=4

5*2=10

10*2=20

guys pls help me!!!!!!

Answers

Answer:

X would also be 59° due to the Corresponding property.

Brainlest Evaluate (-2-2-1/2)³​

Answers

Decimal form -91.125

Exact form -729/8

Answer:

[tex]\sf\longmapsto \: \frac{ - 792}{8} [/tex]

Step-by-step explanation:

[tex]\sf\longmapsto \: (−4− \frac{1}{2} ) {}^{3} [/tex]

[tex]\sf\longmapsto \: (− \frac{9}{2} ) {}^{3} [/tex]

[tex]\sf\longmapsto \: \frac{ - 729}{8} [/tex]

[tex]\sf\longmapsto \: Decimal: -91.125[/tex]

17 + 16s = -16 + 19s
Solve for s

Answers

Answer:

s is equal to 11

Hope this helps

Answer:

s=11

Step-by-step explanation:

17 + 16s= - 16 + 19s

resta 19s en los dos lados

17+ 16s – 19= -16

combina 16s y 19s para obtener -3s

17 – 3s = -16

reta 17 de -16 para obtener -33

-3 =

divide -33 entre -3 para obtener 11

s=11

9. The repair order is a legal document because

People say it’s B or C, which one is correct.

Correct gets brainliest!!!

Answers

Answer:

C is the correct answer cos it is paid by the customer

I am confused if someone could explain this it would be greatly appreciated

Answers

the question is asking for a point at which the two values would intersect, so i think that it is looking for a solution. in this case, i would solve the equations: y=0.15x+19 and y=0.19x.
the point of intersection for these equations is (475, 90.25). you are looking for the x value, so the answer would be 425 minutes of calling for the two plans’ costs to be equal.

What is the x and y intercept of 2.5x+8y=240 please show your work.

Answers

Answer:

The x and y intercept are (96,30)

Step-by-step explanation:

8y=240-2.5x

y=240/8-2.5x/8

y=30-0.3125x

The y intercept=30

The x intercept=96 thus 30=0.3125x,x=30/0.3125

THANK YOU TO WHOEVER DOES THIS <3

Answers

Answer:

2436 cubic centimeters

Step-by-step explanation:

11 * 14 = 154

14 * 7 / 2 = 49

154 + 49 = 203

203 * 12 = 2436

the average age of teacher at school is 36 years.mr Smith age is 11/9 of the average. how old is Mr Smith?​

Answers

Answer: 44

Step-by-step explanation:

I'm positive this is right! Have a good day! Hope this helps! Please give brainliest, i would help a lot if you did, but its fine if you don't Just have a good rest of the day!

What is the equation of a line that passes through the point (8, -2) and is parallel to the line whose equation is 3x + 4y = 15?

Answers

Answer:

y = -3/4x + 4 or 3x + 4y = 16

Step-by-step explanation:

Step 1

Find the slope of the given line

we have

3x + 4y = 15

Isolate the variable y

Subtract 3x from both sides

3x + 4y -3x = 15-3x

Divide by 4 both sides

y = -3/4x + 15/4

the slope of the given line is

m = -3/4

Step 2

Find the equation of the line that passes through  the point  and is parallel to the given line

we know that

if two lines are parallel, then their slopes are equal

The equation of the line into point-slope form is equal to

y - y₁ = m(x-x₁)

we have

m= -3/4

(x1,y1) = (8,-2)

substitute in the equation

y + 2= -3/4(x-8)

y = -3/4x + 6 - 2

y = -3/4x + 4 or 3x + 4y = 16

therefore

the answer is

y = -3/4x + 4

or

3x + 4y = 16

Will give 5 points for answer

Answers

Answer:

1and 3 are not a function 2 and 4 are a function 6 not enough

Step-by-step explanation:

Lucía makes braided key chains out of cotton cord. For every 8 feet of cotton cord she has, she can make 3 braided key chains. PART A Use a model to represent the relationship between the feet of cotton cord and the number of key chains. PART B Use the model to explain how to find the number of feet of cotton cord Lucia needs to make 5 key chains.​

Answers

Lucía needs 13.33 feet of cotton.

Since Lucía makes braided key chains out of cotton cord, and for every 8 feet of cotton cord she has, she can make 3 braided key chains, to represent the relationship between the feet of cotton cord and the number of key chains and find the number of feet of cotton cord Lucia needs to make 5 key chains, the following calculations must be performed, through a cross multiplication:

8CC = 3KC 3 = 8 5 = X 5 x 8/3 = X 40/3 = X 13.33 = X

Therefore, Lucía needs 13.33 feet of cotton.

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Help please guys is this right?

Answers

Answer: Correct, are you dragging the line across?

After a 25% discount the price of a T shirt was $12 what was the price before the discount?

Answers

Answer:The price before the discount is $ 16The population last year is 5280Solution:B) After a 25% discount, the price of a T-shirt was $12.

Step-by-step explanation:G

Answer:

$16

Step-by-step explanation:

25% is equal to 1/4.

1/4 of 16 is 4.

so if you subtract 4 from 16, it equals 12.

have a lovely day <3

The sum of the real numbers x and y is 11. Their difference is 5. What is the value of xy?

Answers

Answer:8

Step-by-step explanation:

Answer:

xy=24

Step-by-step explanation:

x+y=11

x-y=5

x=y+5

y+5+y=11

2y=6

y=3

x=8

xy=24

CAN SOMEONE HELP ME ASAP: Write 0.0000000642 in scientific notation.

Answers

Answer:

6.42 × 10-8.

Step-by-step explanation:

vububTodyksyk

Answer:

6.42 x [tex]10^{-8}[/tex]

Step-by-step explanation:

0.0000000642 in scientific notation = 6.42 x [tex]10^{-8}[/tex]

If A : B = 5 : 8 and B : C = 4: 3, A : B : C =??​

Answers

Answer:

A:B:C = 5:8:6

Step-by-step explanation:

You don't have to change A, you only have to change B and C in the second ratio given. First, B is 8 and secondly, B is 4. You can multiply 4 in the second ratio and make it 8, but, remember, always do the same change to the other side too. So, if you change the 4 to 8 by multiplying by 2, multiply 3, which is C, by 2 too. Then, you get B:C as 8:6. Lastly, you get the final answer as 5:8:6.

A water tank has two valves, one for inlet pipe and the other is outlet pipe. If the tank is empty the inlet valve is

opened, the tank will be full of water after 5 hours. If the tank is full and the outlet valved is opened, the tank

will be emptied in 8 hours. Suppose the tank is empty and both valves are opened, in how many hours will the

tank be full?

Answers

Let V be the volume of the tank. The inlet pipe fills the tank at a rate of

V / (5 hours) = 0.2V / hour

and the outlet pipe drains it at a rate of

V / (8 hours) = 0.125V / hour

With both valves open, the net rate of water entering the tank is

(0.2V - 0.125V ) / hour = 0.075V / hour

If t is the time it takes for the tank to be full, then

(0.075V ) / hour • t = V

Solve for t :

t = V / ((0.075V ) / hour)

t = 1/0.075 hour

t ≈ 13.333 hours

4 cm
15 cm

-
Find volume

Answers

Answer:

The answer is 753.98224.

V=πr^2h, so v=pie4^2*15

Therefore, V=πr2h=π·42·15=753.98224

Step-by-step explanation:

The volume = [tex](\frac{22}{7} )(4^{2} )(15)[/tex]

= 754.285714

please give me a brainliest answer

mr. tyler has a total of $5,000 in savings account and in a mutual fund. If he has x dollars in the savings account, how much dollars does he have in the mutusl fund?

Answers

5000-x is the number of dollars in the mutual fund

Mr. Tyler has $(5000 - x) in the mutual fund, where is amount in the saving account.

If Mr. Tyler has $5,000 in total, and x dollars in the savings account.

The amount he has in the mutual fund can be calculated by subtracting the amount in the savings account from the total amount.

Amount in the mutual fund = Total amount - Amount in the savings account

Here, Total amount = $5000 and Amount in the savings account = x

Substituting the values back to the formula as

Amount in the mutual fund = $5,000 - x

So, Mr. Tyler has $(5000 - x) in the mutual fund.

Learn more about Mutual Fund here:

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Dalawang batong itim

Answers

Sa tabi mo.

[tex] \: \: [/tex]

Step-by-step explanation:

I havenot understand queation

Can someone help me with number 5 :((

Answers

the answer is 83
a10=11+(10-1)8

8h-2>3h+2
solve for h

Answers

Answer:

h >4/5

Step-by-step explanation:

8h-2>3h+2

Subtract 3h from each side

8h-3h-2>3h-3h+2

5h-2> 2

Add 2 to each side

5h-2+2> 2+2

5h >4

Divide by 5

5h/5 >4/5

h >4/5

Answer:

H can be any number larger than 4/5, i'm pretty sure

Step-by-step explanation:

8h-2>3h+2

8h-3h>2+2

5h>4

h>4/5

can somebody please just help me do not answer if you do not know

Answers

Answer:

it could be 34 , 34 and 82

or 34 , 73 and 37

Step-by-step explanation:

angles in a triangle add up to 180. in and isosceles triangle two angles are always the same so there will be 2 possible outcomes.

pls mark brainalist

The expression - 250 + 16z represents a submarine that began at a depth of 250 feet below sea level
and ascended at a rate of 16 feet per minute. What was the depth of the submarine after 9 minutes?

Answers

= -250 + 16z
= -250 + 16(9)
= -250 + 144
= -106 feet

Help please thank you!

Answers

The photo below has the answer

plz help me help me help me

Answers

The answer is this :) hope I helped

Answer:

Step-by-step explanation: 16 is for the apple juice for when the orange juice is 8 since orange juice is half of the apple juice. For the last one the apple juice is 32 and the orange juice is 16

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