Rationalize the denominator of the expression 2 - √ 3 / √ 6

Answers

Answer 1

Step-by-step explanation:

[tex] \to \dfrac{2 - \sqrt{3} }{ \sqrt{6} } [/tex]

Conjugate of √a is √a. So, conjugate of √6 is √6. Multiplying √6 with both numerator and denominator.

[tex] \to \dfrac{2 - \sqrt{3} }{ \sqrt{6} } \times \dfrac{ \sqrt{6} }{ \sqrt{6} } [/tex]

[tex] \to \dfrac{ \sqrt{6}( 2 - \sqrt{3} )}{ {(\sqrt{6})}^{2} } [/tex]

[tex] \to \dfrac{ 2 \sqrt{6} - \sqrt{18} }{ 6 } [/tex]

[tex] \to \dfrac{ 2 \sqrt{6} - 3 \sqrt{2} }{ 6 } [/tex]

[tex] \to \dfrac{ \sqrt{6}}{3} - \dfrac{ \sqrt{2} }{ 2 } [/tex]

Hence, rationalised!


Related Questions

What is the area of the shaded region? Use 3.14 for it and round your answer to the nearest tenth opinions:12.6 cm2 6 cm 50.2 cm 78.5 cm 10 cm 201.0 cm​

Answers

Someone please answer I need help on this one to

The librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant took a sample and found the mean to be 880 books. She provides the librarian with an interval estimate of between 790 and 970 books checked out per day. An efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress is

Answers

Answer:

a. 880

Step-by-step explanation:

Options are "a. 880 b. 90 c. 790 d. None of these choices"

Interval estimate of between 790 and 970 books checked out per day.

Lower limit is 790, Upper limit is 970

Point estimate of μ(x) = [Upper limit + Lower limit} / 2

Point estimate of μ(x) = [970 + 790] / 2

Point estimate of μ(x) = 1760/2

Point estimate of μ(x) = 880

So, the efficient, unbiased point estimate of the number of books checked out each day at the New York City Public Library is 880.

Express y-4[y-3(y-2)] -5 in simplest form

Answers

Answer:

y^3 - 9y^2 + 26y - 29

Step-by-step explanation:

y - 4[y - 3(y - 2)] - 5

I'm going to separate it into parts

(y - 3)(y - 2)

y^2 - 5y + 6

(y - 4)(y^2 - 5y + 6)

y^3 - 5y^2 + 6y - 4y^2 + 20y - 24

y^3 - 9y^2 + 26y - 24

y^3 - 9y^2 + 26y - 24 - 5

y^3 - 9y^2 + 26y - 29

Help Please?! ?????????????

Answers

Answer:

Ed's answer of [tex]\frac{3}{8}[/tex] is correct because he divided [tex]\frac{1}{4}[/tex] by [tex]\frac{2}{3}[/tex] to get his answer.

Step-by-step explanation:

To solve for m in [tex]\frac{2}{3}m=\frac{1}{4}[/tex] you want to isolate m by dividing by [tex]\frac{2}{3}[/tex] on both sides, therefore he divided [tex]\frac{1}{4}[/tex] by [tex]\frac{2}{3}[/tex] to get his answer of [tex]\frac{3}{8}[/tex], and his answer is correct.

Boris started to run on a treadmill after setting its timer for 92 minutes. The display says that he has finished 73% of his run. How many minutes have gone by?
Round your answer to the nearest tenth.

Answers

Answer:

67 minutes

Step-by-step explanation:

CAN SOMEONE HELP ME ASAP PLS

Answers

Answer:

10 inches

Step-by-step explanation:

Half of the circle is 5 inches. the other half will be 5, which added together makes 10

10 inches
5+5 cause half the circle 5 so ya :)

If the radius of the circle x² + y2 - 4x - 6y - k = 0 is
4 units, find the value of k.

Answers

Answer: 3

Step-by-step explanation:

Given

The equation of the circle is [tex]x^2+y^2-4x-6y-k=0[/tex]

Using completing the square method

[tex]\Rightarrow x^2+y^2-4x-6y+4-4+9-9-k=0\\\Rightarrow \left( x^2-4x+4\right)+\left( y^2-6y+9\right)-\left( k+4+9\right)=0\\\Rightarrow \left( x-2\right)^2+\left( y-3\right)^2=\left( k+13\right)[/tex]

on comparing with standard form,  [tex]r^2=k+13[/tex]

Insert the value of r

[tex]\Rightarrow 4^2=k+13\\\Rightarrow k=16-13\\\Rightarrow k=3[/tex]

The Smiths painted their house blue. The complete predicate of this sentence is _____.

Smiths
the Smiths

Answers

the smiths but i am not sure

The sales tax in your city is 8.8\%8.8%8, point, 8, percent, and an item costs \$63$63dollar sign, 63 before tax.
How much tax would you pay on that item?

Answers

9514 1404 393

Answer:

  $5.54

Step-by-step explanation:

 8.8% of $63 is ...

  0.088×$63 = $5.544

The tax is rounded to the nearest cent, so you would pay $5.54 in tax.

Answer: 5.54

Step-by-step explanation: khan said it was correct

find K if 4 x square - 2 X square + kx + 5 leaves a remainder -10 when divided by 2x+1​

Answers

Answer:

[tex]k = 31[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 4x^2 - 2x^2 + kx + 5[/tex]

[tex]r = -10[/tex] --- remainder

[tex]d = 2x + 1[/tex] --- divisor

Required

Find k

We have:

[tex]d = 2x + 1[/tex] --- divisor

Equate to 0

[tex]2x + 1 = 0[/tex]

Solve for x

[tex]2x = -1[/tex]

[tex]x =-0.5[/tex]

This means that:

[tex]f(-0.5)=-10[/tex]

So, we have:

[tex]4*(-0.5)^2 - 2*(-0.5)^2 + k*-0.5 + 5 =-10[/tex]

[tex]0.5 -0.5k + 5 =-10[/tex]

Collect like terms

[tex]-0.5k=-10-5-0.5[/tex]

[tex]-0.5k=-15.5[/tex]

Solve for k

[tex]k = -15.5/-0.5[/tex]

[tex]k = 31[/tex]

Which is less: an angle showing a turn 1/3 of a circle or an angle showing a turn through1/4 of a circle ?

Answers

Answer:

1/4 of a circle is less

Step-by-step explanation:

1/4=90°

1/3=120°

Patrica buys a total of 5 party hats and 5 balloons for the children at a party. Each party hat costs $0.50. Patrica spends a total of $7.50 for the party hats and the balloons. Enter an equation that models the situation with b, the cost of 1 balloon.

Answers

Answer:

b=2.5-7.50

Step-by-step explanation: so 5 party hats cost 50 cents, so times that by 5 to get 2.50, and then use the 7.50 and minus it.

Please help me fast i need help
First question: less or greater
Second question: decrease or increase
Third question: would or would not
fourth question: correct or incorrect
You have to choose the answer's
Ok

Answers

Answer:

Look at the image.

Step-by-step explanation:

what time is it from where y’all live ?

Answers

Answer:

1 Pm

Step-by-step explanation:

Answer:

3:18 Pm

Step-by-step explanation:

Nice picture of mute button

Solve the following: You purchase a set of Bluetooth earbuds for $45 and use a $5 off manufacturer's coupon. If sales tax is 8.25%, how much do you pay for the earbuds? Include the dollar sign in your answer and round to two decimal places.

Answers

Answer:

43.3

Step-by-step explanation:

45-5=40,

0.0825*40=3.3

40+3.3=43.3

Identify the graph of exponential graph

Answers

Graph IV

Hope it helps

Is x = 9 in the solution set of the inequality x + 14 < 20
Yes or no

Answers

Answer: No

Step-by-step explanation:

Data: x+14<20

x=9? Is what your trying to find

Step one, Isolate x by subtracting 14 on both sides

X+14-14<20-14=X=6

Reason: Since you are trying to find if x=9, you have to isolate it. The way to do that is to get rid of +14 by subtracting it by 14. However, since what you do to one side you do to the other, you subtract +20 by 14 to get 6.

Since x=6 isn't x=9, the answer is No

Answer: No

I hope this helps!

need it asap!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

perimeter=2(l+w)

26=2(2x-2+10-x)

26=2(x+8)

26/2=x+8

13=x+8

13-8=x

5=x

Answer:

x=5

Step-by-step explanation:

a=2x-2

b=10-x

Formula

2 x(a+b)=26

(2x-2)+(10-x)=26/2

2x-x-2+10=13

x+8=13

x=13-8

x=5

MARK ME BRAINLIEST THANKS MY ANSWER PLEASE

determine the most appropriate hypothesis test to use for the following scenario: the august 2008 edition of academy of management journal featured an investigation of the performance and tiing of corporate acquisitions. the investigations discovered that in random sample of 2778 firms, 748 annouced one or more acquisitions during the year 2000. does the sample provide suffcient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 30%

Answers

Answer:

Since the calculated z =-3.5357 falls in the critical region z ≥ 1.645 we reject H0 and conclude that the sample provides sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is ≥ 30%

Step-by-step explanation:

Testing  hypothesis about a population proportion when sample size is large.

If the sample size is large then the variable

z= p^-p / sqrt [pq/n]

is approximately standard normal.

Formulate the hypotheses as

H0 : p < 30%   against the claim Ha: p ≥ 30%

Choose the significance level ∝= 0.05

the critical region is z ≥ 1.645 because the alternative hypothesis is stated on a greater  than or equal to basis.

Computing

Z= 748-(2778*0.3)/ √2778*30/100*70/100

z= 748-833.4/√583.38

z= -85.4/24.153

z=-3.5357

Since the calculated z =-3.5357 falls in the critical region z ≥ 1.645 we reject H0 and conclude that the sample provides sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is ≥ 30%

The p- value is 0.0002

PLEASE ILL GIVE BRAINLIEST

Ahmed has 31 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 535 cents, how many dimes and how many quarters does he have?

Answers

Answer:

19  dimes and  15  quarters.

Step-by-step explanation:

Lets substitute in the equation

565=10x+25(34-x)

565=10x+850-25x

15x=285

x=19

So...

34-19=15

19 dimes and 15 quarters.
Explanation:
34=x+y
34−x=y
565=10x+25y
Substitute the first equation, so
565=10x+25(34−x)
565=10x+850−25x
15x=285
x=19 dimes
Therefore
34−19= 15 quarters

4. Which function has two
x-intercepts, one at
(5, 0) and one at (-4, 0)

f(x) = (x - 5)(x – 4)

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

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

f(x) = (x + 5)(x +4)

Answers

Answer: B) (x - 5)(x + 4)

Step-by-step explanation:

we’re looking for x intercepts at x = 5 and x = -4

x - 5 = 0; x = 5

x + 4 = 0; x = -4

(x - 5)(x + 4) is your answer

What is the length of YZ?

Answers

Answer:

28.6 units

Step-by-step explanation:

44/36=35/YZ

44 YZ = 35*36

44 YZ = 1260

YZ = 28.6 units

28.6 or 27.6 but I’m pretty sure it’s 28.6

beti ate 1/8 of the cake.nati had 2 smaller pieces.she ate 2/16 of the cake.who ate more cake? what fraction of the cake left?​

Answers

Answer:

Both ate the same amount of cake, there will be 6/8 or 3/4ths of the cake left.

Step-by-step explanation:

2/16 is equivalent to 1/8. Therefore they ate the same amount of cake.

Answer:

they ate the same amount 1/8 and 2/16 are the same thing.3/4

Step-by-step explanation:

they both ate 1/8  so 8/8-2/8=6/8=3/4 of the cake left

Find the surface area of the rectangular prism (type the number
only)
2.6
4.2 ft
6.8 ft
HELP

Answers

74.256 I think . If rounded put 74.3

What are the coordinates of the turning point of the parabola whose equation is y=-x^2+4x+1

PLEASEEE ANSWERRRRRR

Answers

Answer:

The maximum of the parabola lands at (2,5).

The coordinates of the turning point of the parabola whose equation is y=-x²+4x+1 are (2, 5)

What is Coordinate system?

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points.

The equation of Parabola is y=-x²+4x+1

The turning point (vertex) is the point where the derivative is equal to zero.

y=-x²+4x+1

Differentiate the equation

dy/dx=-2x+4

Now equate dy/dx with zero

dy/dx=0

-2x+4=0

-2x=-4

x=2

Now put x value in the equation

y=-(2)²+4(2)+1

y=-4+8+1

y=5

Hence the coordinates of the turning point of the parabola whose equation is y=-x²+4x+1 are (2, 5)

To learn more on Coordinate System click:

https://brainly.com/question/4726772

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How many solutions does the following system have?

y = 4x + 6
y = 4x + 12

A. One Solution
B. Infinitely many solutions
C. No Solution
D. Two Solutions

I WILL MARK BRAINLEST IF YOUR ANSWER IS CORRECT!!!!

Answers

Answer: no solution

Step-by-step explanation:

Solve for x: 2(x + 4) + 6 = 12x - 8

Answers

Answer:

x = 2.2

Step-by-step explanation:

2(x+4)+6 = 12x-8

Use distribution property

2x+8+6 = 12x-8

Combine like terms

2x+14 = 12x-8

Subtract 14 from both sides

2x = 12x-22

Subtract 12x from both sides

-10x = -22

Divide both sides by negative 10

x = 2.2 or x = 11/5 in fractions.

Hope this helps

Mr. Halsey leans a ladder against an 11.5 foot wall the bottom the of the ladder is 3.5 ft from the base of the wall as shown what is the approximate length of the ladder​

Answers

Answer :12 feet
Explanation :(x)^2=(11.5)^2+(3.5)^2
X^2=132.25+12.25
X^2=144.5 then square root it
X=12 feet

Hence, the approximate length of the ladder​ is [tex]12ft[/tex].

What is the approximation value?

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding.

A calculation can be approximated by rounding the values within it before performing the operations.

Here given that,

[tex](x)^2=(11.5)^2+(3.5)^2\\X^2=132.25+12.25\\X^2=144.5 \\X=\sqrt{144.5}\\X=12 feet[/tex]

Hence, the approximate length of the ladder​ is [tex]12ft[/tex].

To know more about the approximation value

https://brainly.com/question/29580932

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what number shoild come next 100,96,88,72​

Answers

Answer - 40

----------

100 - 4

96 - 8

88 - 16

72 - 32

A right cylindrical vase holds 2.50 L of water. If the radius of the vase is 9.00 cm, what is the height of
the vase, rounded to the nearest hundredth of a centimeter? (Note: 1 cm3 = 0.001L)
No website plzzz

Answers

Answer: 9.82cm

Step-by-step explanation:

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