To rationalize the denominator of 2/square 13+ squared 11 , you should multiply the expression by which fraction?

Answers

Answer 1

Answer:

You should multiply the expression by [tex]\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex]

Explanation:

To rationalize any expression, you must multiply it by its conjugate. A conjugate is defined as a similar expression to the original one but with an opposite sign

This means that:

The conjugate of a + b would be a -  b

Now, the given expression is [tex]\frac{2}{\sqrt{13}+\sqrt{11}}[/tex]

Consider the denominator:

From the above, we can conclude that the conjugate of [tex]\sqrt{13}+\sqrt{11}[/tex] is [tex]\sqrt{13}-\sqrt{11}[/tex]

And, remember that we need to keep the value of the expression unchanged. This means that we must multiply both the numerator and the denominator by the same value

Therefore:

You should multiply the expression by [tex]\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex] in order to rationalize the denominator

Hope this helps :)

Answer 2

Answer:

[tex] \frac { \sqrt { 13 } - \sqrt { 11 } } { \sqrt { 13 } - \sqrt { 11 } } [/tex]

Step-by-step explanation:

We are given the following expression and we are to determine the expression that we need to multiply it with in order to rationalize the denominator:

[tex] \frac { 2 } { \sqrt { 13 } + \sqrt { 11 } } [/tex]

To rationalize its denominator, we must multiply it with its conjugate.

For the denominator of the given expression, its conjugate would be [tex] \sqrt { 13 } - \sqrt { 11 } [/tex].

So to rationalize the expression, we would multiply it with:

[tex] \frac { \sqrt { 13 } - \sqrt { 11 } } { \sqrt { 13 } - \sqrt { 11 } } [/tex]


Related Questions

Plz help me it’s due tomorrow

Answers

Answer:

7

Step-by-step explanation:

Again just cross multiplication.

84 = 12m

Divide each side by 12.

m = 7.

At Manny's taco shop, you can get an order of chips and two tacos for $9.25. The cost for two orders of chips and five tacos is $21.75. What is the cost of an order of chips?

Define your variables:

Write your system of Equations:

Solve The System:

Answer The Question Being Asked:

Topic: Applying Systems of Equations

Answers

Define your variables:

At Manny's taco shop, you can get an order of chips and two tacos for $9.25. The cost for two orders of chips and five tacos is $21.75.

x = Chipsy = Tacos

Write your system of Equations:

You can get an order of chips and two tacos for $9.25.

1 Chips + 2 Tacos = 9.25

x + 2y = 9.25

The cost for two orders of chips and five tacos is $21.75.

2 Chips + 5 Tacos = 21.75

2x + 5y = 21.75Solve The System:

First equate the coefficient - in this case x:

(x + 2y = 9.25) * 2 = 2x + 4y = 18.50

2x + 4y = 18.50

2x + 5y = 21.75

Minus the equations from each other to remove the coefficient you equated:

(2x + 5y) - (2x + 4y) = 21.75 - 18.50

(2x - 2x) + (5y - 4y) = 21.75 - 18.50

y = 3.25Answer The Question Being Asked:What is the cost of an order of chips?

1 Taco = $3.25

y = 3.25

Substitute this into the equation.

x + 2y = 9.25

x + (2 * 3.25) = 9.25

x + 6.50 = 9.25

Rearrange to find x:

x = 9.25 - 6.50

x = 2.75

Chips = $2.75

$2.75

Triangle A'B'C' is a dilation of

triangle ABC. what is the scale
factor?

enter your answer in the box



Answers

The scale factor is 1/2

What is the perimeter of the figure shown?
A)22ft
B)84ft
C)30ft
D)36ft

Answers

Answer:

D

Step-by-step explanation:

The perimeter of the figure is the total distance around the figure.

Add each side to find the total distance.

10 + 8 + 8 + 2+2 + 6 = 36

which sentence can reperesent the inequality 3.5x>7?

A) The sum of 3.5 and a number is greater than 7

B) The sum of 3.5 and a number is greater than or equal to 7

C) The product of 3.5 and a number is greater than 7

D) The product of 3.5 and a number is greater than or equal to 7​

Answers

Answer:

Option C

Step-by-step explanation:

Given in an inequality in variable x as

[tex]3.5x>7[/tex]

In Algebra 3.5x represents the product of 3.5 with x

So the given inequality is equivalent to

the product of 3.5 and a number x is greater than 7.

Hence option C is right

C) The product of 3.5 and a number is greater than 7

Answer:

The product of 3.5 and a number is greater than or equal to 7.

Step-by-step explanation:

which expression is equivalent to the expression (7×2)^7​

Answers

Answer:

9^7

Step-by-step explanation:

7*2=9

For St. Patrick's day, Mrs. G's sixth grade class was given a choice of four different drinks. One quarter of the class chose green milkshakes, one third of the class chose green ginger ale, one eighth of the class chose the green milk and one sixth of the class chose green juice. How many students did not have a drink?

Answers

Answer:

1/8 of the number of students

Step-by-step explanation:

1/4 + 1/3 + 1/8 + 1/6 =

= 6/24 + 8/24 + 3/24 + 4/24

= 21/24

= 7/8

7/8 of the class chose drinks.

1 - 7/8 = 8/8 - 7/8 = 1/8

That means that 1/8 did not have a drink.

Since we don't know the number of students in her class, we cannot tell the number of students who did not have a drink, but we do know it is 1/8 of the number of students.

What is the volume of the following rectangular prism?

Answers

Answer:

The volume of the rectangular prism is [tex]8\frac{1}{2}\ units^{3}[/tex]

Step-by-step explanation:

we know that

The Volume of a rectangular prism is equal to

[tex]V=BL[/tex]

where

B is the area of the base

L is the length of the prism

In this problem we have

[tex]B=2\frac{1}{8}\ units^{2}=\frac{8*2+1}{8}=\frac{17}{8}\ units^{2}[/tex]

[tex]L=4\ units[/tex]

substitute

[tex]V=(\frac{17}{8})(4)=\frac{17}{2}=8\frac{1}{2}\ units^{3}[/tex]

3. What’s the answer to this question please

Answers

C

the answer should be C because the 45.75 represents the price of the fruit trees and if x was 88 that means there are 88 fruit trees

pls mark brainliest!!

Answer:

The correct option is C.

Step-by-step explanation:

Is six grade at carter middle school conducted a survey of 300 students to determine your favorite ice cream flavor of the students surveyed 20% selected chocolate chip cookie dough

Answers

20% of 300 would come out to be 60 six graders who think cookie dough is best

60 like cookie dough? I don't understand what you are getting at.

what is the exact volume of the cylinder?

Answers

Answer:

54π in³

Step-by-step explanation:

The volume (V) of a cylinder is calculated using the formula

V = πr²h ( r is the radius and h the height )

here r = 3 and h = 6, thus

V = π × 3² × 6 = π × 9 × 6 = 54π in³ ← exact value

EASYY 90 POINTSS, I WILL GIVE BRAINLEASSTTTT..1


3. The triangle will be dilated by a scale factor of 2.5.
(a) What is the length of each of the sides after the dilation?
(b) Draw the new image and label it .

Answers

Answer:

Part a) The length of each of the sides after the dilation is

[tex]A'B'=30\ units[/tex]

[tex]B'C'=25\ units[/tex]

[tex]A'C'=35\ units[/tex]

Part b) The graph in the attached figure

Step-by-step explanation:

Part a) What is the length of each of the sides after the dilation?

In this problem we have that the scale factor is 2.5

The scale factor is greater than 1

so

The dilation is an enlargement

To find the length of each of the sides after the dilation, multiply the original length by the scale factor

so

[tex]A'B'=AB*2.5=12*2.5=30\ units[/tex]

[tex]B'C'=BC*2.5=10*2.5=25\ units[/tex]

[tex]A'C'=AC*2.5=14*2.5=35\ units[/tex]

Part b) Draw the new image and label it

using a graphing tool

see the attached figure

Answer:

Do you still need help with this? If so just say if you do in the comments and I can probably help.

Step-by-step explanation:

What is the volume of the square pyramid with base edges 12 cm and height 12 cm?

Answers

Answer:

V=144

Step-by-step explanation:

To find the volume of a pyramid, use the formula V=B•h, B being the base and h the height. So 12•12=144.

The answer is 576 cm

.......................................

find the product of -4x 3 y 2(7xy 4)

Answers

Answer:

What are the signs between the numbers?

Step-by-step explanation:

Answer:

The product of -4x^3y^2(7xy^4) is (2^6•7y^6x)

least to greatest 1 8/35, 1.3, 5/4​

Answers

Answer:1/3  <  1 8/35  <  5/4

Step-by-step explanation:

Showing Work

Rewriting as fractions if necessary:

43/35, 1/3, 5/4

The least common denominator (LCD) is: 420.

Rewriting as equivalent fractions with the LCD:

516/420, 140/420, 525/420

Ordering these fractions by the numerator in order from least to greatest:

140/420 < 516/420 < 525/420

Therefore, your input in order from least to greatest is:

1/3 < 1 8/35 < 5/4

what is the mean absolute deviation for the data 30,30,35,35,40?
Please help me...I need the answer as fast as possible. Thanks! :D

Answers

Answer:

34

Step-by-step explanation:

30+30+35+35+40=170

Since there are 5 numbers You have two divide 170/2=34

Glad i could help!

Malcolm coasted 32 miles from Moonridge to Mentone and then pedaled back hard. If she round trip took 4 hours, what was Malcolm's average speed in miles per hour?

Answers

Answer:

Roughly around 7mph

Step-by-step explanation:

what is the frequency of a wave if the wavelength is 100 m and the speed is 200 m/s?​

A. 2 Hz
B. 100vHz
C. 0.5 Hz
D. 200,000 Hz

Answers

Answer:

The frequency is 2Hz

Step-by-step explanation:

Using the formula

Wavelength = speed / Frequency

Arranging the equation

Frequency = Speed / Wavelength

Frequency = 200 / 100

Frequency = 2 Hz

(2a/a+3b) + 10 = b

Rearrange and make “a” as subject

Answers

Answer:

a = -2b - 10

Step-by-step explanation:

a + 3b + 10 = b

a + 10 = -2b

a = -2b - 10

I have a question. I'm doing a project and want to see how many people would like dogs or cats please comment your answer and if you give me a reason i will give you 5 stars its for 15 points!

Answers

i like both, but i have cats

Answer:

I like dogs because its much fun to play with them, instead of a cat and you can go on a walk with them.

Step-by-step explanation:

What type of triangle would have these angle measures?

Answers

Answer:

Right triangle

Step-by-step explanation:

because it has one 90 degree angle

Step-by-step explanation:

It's a RIGHT TRIANGLE because one of the angles has measure 90°.

Equilateral triangle has every angle with the same measure of 60°.

Isisceles triangle has two equal angle with the same measure.

FOR 37 POINTS AND BRAINIEST IF U GET THIS RIGHT
What are the square roots of 36/100 ?
A - 6/10 and 6/10
B- ⅗ and ⅗
C- 9/25 and 9/25
D-18/50 and 18/50

Answers

Answer:

A

Step-by-step explanation:

6 x 6 = 36

10 x 10 = 100

Answer:

A

Step-by-step explanation:

6x6=36

10x10=100

I need
PART A:
PART B:
PART C:
PART D:

Answers

Answer:

See below.

Step-by-step explanation:

Solve the equation using each of the properties listed.

3n - 5 = -8(6 + 5n)

3n - 5 = -48 - 40n              Distributive Property

3n + 40n - 5 = -48

43n - 5 = -48                      Addition Property of Equality

43n = -48 + 5

43n = -43                           Addition Property of Equality

n = -43/43

n = -1                                  Division property of Equality

Answer:

Guess that was the answwr

Step-by-step explanation:

A computer rounded the number 129. 257 to the nearest hundredth what is this number rounded to the nearest hundredth

Answers

129.26 because 7 is over 5

How to solve this!! Please!

Answers

Answer:

k^2 -3k +9/2

(k-3/2)^2

Step-by-step explanation:

k^2 -3k

Take b/2 and then square it to find the term to complete the square

(-3/2) ^2 = 9/4

k^2 -3k +9/2

The expression factors to (k-b/2)^2

(k-3/2)^2

9 is 15% of what number? Enter your answer in the box​

Answers

Answer:

60

Step-by-step explanation:

Is means equals and of means multiply

9 = 15% * N

Change to decimal form

9 = .15 N

Divide each side by .15

9/.15 = .15N/.15

60 = N

Answer: hi the answer is 60 hope i helped

Step-by-step explanation:

Plz help !! Needed to graduate

Answers

Answer:

the second one

Step-by-step explanation:

Just put the equation in the quadratic formula but first get it in the ax^2+bx+c=0 form for that take 1 to the other side and subtract it

[tex]8x^2-2x-1\\a=8,b=-2,c=-1[/tex]

the quadratic formula is shown in the picture along with the rest of the working

the answer is the second option :)

hope this helps, best of luck graduating :)

Answer:   [tex]\bold{\dfrac{2\pm \sqrt{36}}{16}}[/tex]

Step-by-step explanation:

[tex]8x^2-2x-1=0\quad \rightarrow \quad a=8,\ b=-2,\ c=-1\\\\\\Quadratic\ formula: x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(8)(-1)}}{2(8)}\\\\\\.\ =\dfrac{2\pm \sqrt{4+32}}{16}\\\\\\.\ =\dfrac{2\pm \sqrt{36}}{16}[/tex]

Television sizes are determined by the length of their diagonal measure. Michael just bought a new television. The height of the television is 40 inches and the length is 71.5 inches. Using the Pythagorean Theorem, what is the size of Michael’s new television? Round your answer to the nearest whole inch (whole number).

Part A: What parts of the right triangle have you been given? Are you looking for a leg or the hypotenuse? The legs have already been given. I’m looking for the hypotenuse.

Part B: Set-up your equation by substituting the correct numbers in to the formula.
71.5^2+40^2=c^2

Part C: Solve for the missing length. Remember to show ALL work for each step.


Part D: What is the size of the television rounded to the nearest whole inch (whole number)?
PART A AND B ARE DONE ALREADY
I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER.

Answers

Answer:

Part A) The legs have already been given. I’m looking for the hypotenuse

Part B) [tex]c^{2}=40^{2} +71.5^{2}[/tex]

Part C) The missing length is [tex]81.93\ in[/tex]

Part D) [tex]82\ in[/tex]

Step-by-step explanation:

Part A) What parts of the right triangle have you been given? Are you looking for a leg or the hypotenuse?

we know that

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2} +b^{2}[/tex]

where

c ----> is the hypotenuse of the right triangle

a and b -------> are the legs of the right triangle

In this problem we have

[tex]a=40\ in[/tex]

[tex]b=71.5\ in[/tex]

so

The legs have already been given. I’m looking for the hypotenuse

Part B) Set-up your equation by substituting the correct numbers in to the formula

we have

[tex]a=40\ in[/tex]

[tex]b=71.5\ in[/tex]

substitute in the Pythagoras Theorem and solve for c (hypotenuse)

[tex]c^{2}=40^{2} +71.5^{2}[/tex]

Part C) Solve for the missing length

we have

[tex]c^{2}=40^{2} +71.5^{2}[/tex]

solve for c

[tex]c^{2}=1,600 +5,112.25[/tex]

[tex]c^{2}=6,712.25[/tex]

[tex]c=\sqrt{6,712.25}\ in[/tex]

[tex]c=81.93\ in[/tex]

Part D) What is the size of the television rounded to the nearest whole inch (whole number)?

[tex]81.93=82\ in[/tex]

Final answer:

The Pythagorean Theorem is used to find the size of the TV, which is the hypotenuse in this scenario and equals to approximately 82 inches when rounded to the nearest whole inch.

Explanation:

Since we've set up our equation as 71.5^2+40^2=c^2, we can now simply solve for c, which is our hypotenuse, and in this case, represents the size of the television.

To do so, calculate the square of both given sides and add them: (71.5)^2 + (40)^2 = 5112.25 + 1600 = 6712.25.

The next step is to take the square root of that sum to get the length of the hypotenuse/c: sqrt(6712.25) = ~81.94 inches

Part D: Now, to answer the final part of your question, if we round this result to the nearest whole inch, we get 82 inches as the size of the new television.

Learn more about Pythagorean Theorem here:

https://brainly.com/question/28361847

#SPJ3

Order the decimal numbers below from the smallest on the left to largest on the right
0.8, 0.088, 0.84, 0.0837

Answers

Answer:

0.0837 ,  0.088 ,  0.8 ,  0.84

Step-by-step explanation:

Solve the system of equations and choose the correct answer from the list of options
2x + y = -4

Answers

X=-2-1/2y should be the answer

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