rationalise the denominator and simplify

Answers

Answer 1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Answer 2

Step-by-step explanation:

[tex] \bf \underline{Given-} \\ [/tex]

[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ [/tex]

[tex] \bf \underline{What\: to\: do-} \\ [/tex]

To rationalise the denominator

[tex] \bf \underline{Solution-} \\ [/tex]

[tex]\textsf{We have,}[/tex]

[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ [/tex]

[tex]\textsf{The denominator is 5+2√3. Multiplying the numerator and denominator by 7-4√3,}\\[/tex]

[tex]\textsf{we get,}\\[/tex]

[tex] ⟹\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ [/tex]

[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 + 4 \sqrt{3} )(7 - 4 \sqrt{3}) } \\ \\ [/tex]

[tex]\textsf{⬤ Applying Algebraic Identity

(a+b)(a-b) = a² - b² to the denominator}\\[/tex]

[tex]\textsf{We get,}\\[/tex]

[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 {)}^{2} - (4 \sqrt{3} {)}^{2} } \\ \\ [/tex]

[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 8 \sqrt{3 \times 3} }{49 - 48} \\ \\ [/tex]

[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 24 }{1} \\ \\ [/tex]

[tex]⟹(35 - 24) - 6 \sqrt{3} \\ \\ [/tex]

[tex]⟹11 - 6 \sqrt{3} \: \: \: \tt \red{ Ans}. \\ \\ [/tex]

[tex] \bf \underline{Hence \:the \:denominator\: is\: rationalised.}\\[/tex]


Related Questions

9) Use the spinner below to answer the following questions

What is the Expected Value of a single spln?

Answers

Answer:

is that paper or did you write on the screen?

This question concerns bit strings of length six. These bit strings can be divided up into four types depending on their initial and terminal bit. Thus the types are: 0XXXX0, 0XXXX1, 1XXXX0, 1XXXX1. How many bit strings of length six must you select before you are sure to have at least 6 that are of the same type?

Answers

Answer:

We have to choose 21 strings to be sure we have chosen at least 6 strings of the same type.

Step-by-step explanation:

Since the string type is determined by the initial and terminal bits as understood from the question, then the value of the bits between the initial and terminal bits is of no concern to us.

Now, to be sure you have atleast 6 of the same type, we select each string five times. By doing this, we have already selected 20 strings because we have 4 strings there. Now if you choose any of the string one more time, we are certain that we must have chosen atleast 6 strings that are the same. This means we have to choose 21 strings to be sure we have chosen at least 6 strings of the same type.

What's the largest odd number you can make using all four digits 4, 5, 3, 6

Answers

Answer:

6543

Step-by-step explanation:

Not much to explain lol

Required Answer:-

Here,

Odd numbers are 3 and 5.

5>3

The largest odd number =6543

Find the value of x

Answers

x = 10.4 (1dp)

Step-by-step explanation:

Using Pythagoras' theorem, a^2 = b^2 + c^2 where a is the hypotinues; b and c is the two sides

a^2 = b^2 + c^2

12^2 = 6^2 + x^2

144 = 36 + x^2

x^2 = 144 - 36

x^2 = 108

x = _/108

x = 10.4 (1dp)

to my calculations the anwser is x=10.4

Miguel has $25. He spends $6.75 on a movie ticket, $3.70 for snacks, and $2.00 for bus fare each way.

How much money does Miguel have left?

Miguel has $_____
left.

Answers

Answer:

$12.55

Step-by-step explanation:

25-6.75=18.25

18.25-3.70=14.55

14.55-2=12.55

Miguel has $12.55 left

A 3-column table with 4 rows. Column 1 is labeled Inequality with entries 6 greater-than 4, negative 11 less-than negative 3, 7 greater-than negative 6, negative 5 less-than 1. Column 2 is labeled Multiply each side by: with entries 4, 2, 3, 5. Column 3 is labeled New Inequality with entries A, B, C, D. The table gives an inequality and a number to multiply both sides of the inequality by. Identify the new, true inequality. A: B: C: D: Multiplying both sides of an inequality by a positive number the inequality symbol

Answers

Answer:

1.  A

2. B

3. A

4. B

5. A

Step-by-step explanation:

Edge 2022

Answer:

A: 24 > 16B: -22 < -6C: 21 > -18D: -25 < 5E: does not change

Explanation: Correct on Edg 2020.

Is the relation {(2,5), (0, -5), (-2, 6), (2, 3)} a function?

Answers

Answer:

Not a function

Step-by-step explanation:

Multiply. Express your answer in simplest form.
5/9 x 3/10

Answers

Answer:

5/9 x 3/10 = 15/90 as simplified as 1/6 in fraction form.

5/9 multiplied by 3/10 is equal to 1/6 in its simplest form.

We have,

To multiply fractions, we multiply the numerators together and the denominators together.

The resulting fraction is then simplified to its simplest form.

Let's multiply 5/9 by 3/10:

(5/9) x (3/10) = (5 x 3) / (9 x 10) = 15/90

To simplify the fraction 15/90, we can divide both the numerator and denominator by their greatest common divisor, which is 15:

15/90 = (15 ÷ 15) / (90 ÷ 15) = 1/6

Therefore,

5/9 multiplied by 3/10 is equal to 1/6 in its simplest form.

Learn more about fractions here:

https://brainly.com/question/24370499

#SPJ6

Complete the blank with either ∈ or ∉ so that the resulting statement is true. −2​__{−6,−3,−5,−1}

Answers

Answer:

−2​ ∉ {−6,−3,−5,−1}

Step-by-step explanation:

Given

Set = {−6,−3,−5,−1}

Element = -2

Required

The interpretation of the question is to state if -2 is an element of the given set or not

The first thing to do is to check through the set to count the number of occurrence of -2

Looking through Set = {−6,−3,−5,−1}, we have that the occurrence of -2 is 0

This implies that -2 is not an element of the given set and this is represented by the symbol ∉

Hence:

−2​ ∉ {−6,−3,−5,−1}

si me dan 200 pesos a la semana y quiero comprar algo de 15000 pesos cuantas semanas tengo que ahorrar

Answers

Answer:

75 semanas

Step-by-step explanation:

15,000 = 200s

15,000/200 = s

75 = s

What is the approximate area of the triangle below?

Answers

Can you include a picture of the problem theres no information

Answer:

3

Step-by-step explanation:

1+1=2

Cara has saved $4,000 to buy a car. Rick wants to buy a new television set. He has saved 1/10 as much as Cara. How much has Rick saved?

Answers

Answer:

Step-by-step explanation:

4000*1/10= $400

5. *
17 points
Which answer shows 9x 10-written in standard form?
-.000009
.000009
-900,000
.00009

Answers

is there more to the question because u have 9 x 10- and that doesn’t make sense for it to be in standard form the originally problem needs to be in scientific notation what are the numbers after the 10?

The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 330 minutes, the monthly cost will be $141.5. If the customer uses 890 minutes, the monthly cost will be $337.5.

Required:
a. Find an equation in the form y= mx +b, where x is the number of monthly minutes used and y is the total monthly of the Splint plan.
b. Use your equation to find the total monthly cost if 624 minutes are used

Answers

Answer:

a) $141.5 = 330m + b...... Equation 1

$337.5 = 890m + b..... Equation 2

b) $244.4

Step-by-step explanation:

The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 330 minutes, the monthly cost will be $141.5. If the customer uses 890 minutes, the monthly cost will be $337.5.

Required:

a. Find an equation in the form y= mx +b, where x is the number of monthly minutes used and y is the total monthly of the Splint plan.

If a customer uses 330 minutes, the monthly cost will be $141.5.

y = mx + b

$141.5 = 330m + b

If the customer uses 890 minutes, the monthly cost will be $337.5.

$337.5 = 890m + b

Combining the equations

$141.5 = 330m + b...... Equation 1

$337.5 = 890m + b..... Equation 2

b. Use your equation to find the total monthly cost if 624 minutes are used

Combining the equations

$141.5 = 330m + b...... Equation 1

$337.5 = 890m + b..... Equation 2

We Subtract Equation 2 from 1

-196 = -560m

m = -196/-560

m = 0.35

$337.5 = 890m + b..... Equation 2

$337.5 = 890 × 0.35 + b

$337.5 - 311.5 = b

b = 26

When x = 624

y = 624× m + b

m = 0.35 , b = 26

y = 624 × 0.35 + 26

y = 218.4 + 26

y = $ 244.4

16.9 and 1.7 and 0.17 and 2.0 added up

Answers

Answer:

20.77

Step-by-step explanation:

Answer:

20.77

Step-by-step explanation:

Simplify  16.9+ 1.7  to  18.6

18.6 +0.17+2.0

Simplify  18.6+0.17 to  18.77

18.77+2.0

Simplify.

ANddddd the answer is

20.77

at is the equation of the line passing through the points (2/5, 19/20) and (1/3, 11/12) slope-intercept form? y = 1/2 * x - 3/4 y = 1/2 * x + 3/4 y = 3/4 * x - 1/2 y = 3/4 * x + 1/2

Answers

Answer:

Step-by-step explanation:

2/5, 19/20) and (1/3, 11/12) in slope-intercept form? ... B. y = 1/2x + 3/4 ... D. y = 3/4x + 1/2 ... [tex]3}^{2}x = \frac{1}{?27} [/tex]find x​.

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Input the equation of the given line.

The line including (4, 7) and (0, 7).

Answers

Answer:

[tex]y=7[/tex]

Step-by-step explanation:

First, let's use the two given points to find the slope. Remember the slope equation:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

[tex]m=\frac{7-7}{0-4}[/tex]

[tex]m=\frac{0}{-4}[/tex]

[tex]m=0[/tex]

If we're following slope-intercept form, what we have so far is

[tex]y=0x+b[/tex]

Substitute one of the given points for the [tex]x[/tex] and [tex]y[/tex] values in order to find [tex]b[/tex]:

[tex]7=0(4)+b[/tex]

[tex]7=b[/tex]

Now, if we put that back into our slope-intercept equation we get

[tex]y=0x+7[/tex]

or,

[tex]y=7[/tex]

Right off the bat, we can see how we ended up with this equation because both points have the same y-values. This indicates a horizontal line.

I hope this helps!

Are 12:14 and 60:70 equivalent ratios?

yes
no

Answers

Answer:

Yes, they are equalent

Step-by-step explanation:

12:14 = 6:7

60:70 =6:7

both can be simplified to 6:7

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. If you drew one card from a standard deck, would it be "unusual" to draw a 6?

Answers

Answer:

No it's not unusual

Step-by-step explanation:

That's an unusual definition for unusual if you don't mind me saying so.

There are 4 sixes in a standard deck of cards without the jokers. There are 52 cards in that deck

4/52 = 0.077

This is greater than 0.05 so it is not unusual.

Let's add the 2 jokers and see what happens.

4/54 = 0.074

That's still not going to get the situation defined as unusual.

Solve 7b = 91
Please answer

Answers

Answer:

13

Step-by-step explanation:

Divide both sides by 7 so the multiplication cancels out.

Answer:

To get b you’ll have to divide 91 by 7

b=91/7

b=13

Step-by-step explanation:

I hope it helped you, please give me brainliest

At Green Island Farms the annual Turkey Trot is being held. This year’s contestants are Tom Turkey, Gary Gobbler and Donny Drumstick. The turkeys chase little RC cars loaded with feed. The buzzer sounds and the turkeys are off. Gary Gobbler chases his RC car trying to eat that sweet turkey feed for 15 feet before he manages to side swipe the RC car and knock it on its side. All the feed spills out and Gary Gobbler gobbles it down. That silly turkey happily eats his food for 1.75 seconds. A mouse comes out of the hay bale and tries to join Gary Gobbler in his feasting. But Gary Gobbler is scared of mice so when he sees the mouse he freaks out and tears down the racetrack.

Write a similar story for Tom Turkey making sure to include the different segments of the graph.

Answers

Answer:

The company is expected the company will receive

50 points please help please see image below

Answers

Answer:

395.841

Step-by-step explanation:

surface area = 2πrh + 2πr²

where r = 7 m radius

           h = 2 m

plugin values into the formula

surface area = 2πrh + 2πr²

                     = 2π (7) 2  +  2π (7)²

                     = 87.965  +  307.867

                     = 395.841 m²

Answer:

395.841 m²

Step-by-step explanation:

surface area = 2πrh + 2πr² and r = 7 m radius

h = 2 m

Plugin

 2π (7) 2  +  2π (7)²

multiply into itself than add

87.965  +  307.867

add

395.841 m²

Therefore your answer would be 395.841 m²

A 0.8-liter bottle of Mexican wine costs 100 pesos. At that price, how much would a halfgallon jug of the same wine cost in dollars? Mexican peso Dollars per foreign: 0.07855 Foreign per dollar: 12.73

Answers

Answer:

$11.83

Step-by-step explanation:

1 gallon = 3.785 litres

0.5(1/2gallon) = x liters

x = 0.5 × 3.785 liters

x = 1.89271 liters

0.8 liter = 100 pesos

1.89271 liters = x pesos

x = 1.89271 × 100/0.8

x = 236.58875 pesos

Converting to dollars

1 mexican peso = $0.050

236.58875 pesos = x

x = 236.58875 × $0.050

x = $11.8294375

Approximately = $11.83

A half gallon jug of the same wine cost in dollars $11.83

sisktzkyzktRkzkKKRpyxdypzoyzitzotkg​

Answers

(Y2-y1)/(x2-x1) = gradient
Pick two points: (2,6), (4,8)
(8-6)/(4-2) = 2/2 = 1
The gradient is 1

q(x)=2 −2+? please solve this huhu

Answers

Answer:

I mean it would just be q(x) = 0

Step-by-step explanation:

Answer: q=0

Step-by-step explanation: Let's solve for q.

qx=2−2

Step 1: Divide both sides by x.

qx

x

=

0

x

q=0

Answer:

q=0


HELP ME PLEASEE ASAPAPAP PLEASE PLEASE PLEASE PLEASE!!!!!!!!!!!

Answers

Answer: AEC = 80

              X=30

YW ;)

Given 2y =a^x +2a ^-x and a^x>0.
Show that a^x= y + sqrt (y^2-)​

Answers

Answer:

Answer by Yi Jing

Step-by-step explanation:

Consider parallel lines cut by a transversal.

Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On line s where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Answers

Answer:

The alternate exterior angles 2 and 7 are congruent. One way to prove this is through the corresponding angles, vertical angles, and the transitive property.

First, we know <2 and <6 are congruent because of corresponding angles. Then we know they are equal because of the definition of congruent.

Next, we know <6 is congruent to <7 because of vertical angles. Then, we know they are equal because of the definition of congruent.

Finally, we know <2 is equal to <7 because of the transitive property.

Answer:

Here's the sample response!!

Step-by-step explanation:

Because vertical angles are congruent, angles 1 and 4 are congruent. Because corresponding angles are congruent, angles 4 and 8 are congruent. Because angle 4 is congruent to both 1 and 8, angle 1 is congruent to angle 8.

A store has a sale with 10% off every item. When you enter the store, you receive a coupon that states that you receive an additional 40% off. Is this equal to a discount? Explain your answer.


The total percent of reduction is _____% , so this __ * is or is not * __equal to a discount.

Answers

Step-by-step explanation:

Step one:

We are told that the store offers off 10% of sales, this means that the store is offsetting the price down by 10% hence a price reduction.

Moreso, a coupon is a voucher entitling the holder to a discount off a particular product. the coupon is 40%, hence this is equal to a discount, that is price reduction by 40%.

Step two:

Say the price of an item is $100, a coupon if 40% will entitle the holder to only pay $60, that is

=40/100*100

=0.4*100

=$40 off

= 100-40

=$60

The total percent of reduction 10+40= 50%

This is equal to a discount on the sales price

BD bisects ABC.
Find mZABD, mZCBD, and m ZABC.
A
(3x + 6°
D
B (7x – 18)°C

Answers

The answer is 43 because when you multiply 6x6 you get 36 and if you add 6 more you get 42 which is one less that 43

Other Questions
What gave rise to the slave trade?A- The lack of a skilled labor force in the Americas and the decline of the West African population caused residents to seek a living elsewhere.B- The shipment of gold from the Americas to Europe caused plantation owners to seek inexpensive laborers.C- The death of many American Indians to disease and the planting of labor-intensive crops.D- The global expansion of the spice trade and the rise of Christianity in the Americas. Determine the number of solutions to each system of equations.Please put all of the equations in either One Solution, No Solution, or Infinitely Many Solution boxesDUE TONIGHT At the Beltway Outlet store, you buy x computer games for 13$ each and a magazine for 4$. Write an expression in simplest form that represents the total amount of money you spend. Someone please help Which short-term environmental change is most likely to directly affect a population of egrets along the coast of Florida? PLEASE HELP ME PLEASEEEEEEEEE how do skin cells replace itself after an injury?a) skin cells go through the process of budding to make new identical cells.b) skin cells go through the procces of mitosis to make new identical cells.c) skin cells go through the process og photosynthesis to make new identical cells.d) skin cells go through the process of cellular respiration to make new identical cells. la that is cost price of orange.onSelling price of orange is 2and profit is to find it?. Select ALL of the following statements that are incorrect.Solids, liquids, and gases are all able to act as solutes in a solution.Solids, liquids, and gases are all able to act as solvents in a solution.Solids are not able to act as a solvent if a gas is the solute.Gases are not able to act as a solvent if a solid is the solute. 1. What part of the human body has the same role as the power source in a computer?2.What part of the human body has the same role as the keyboard or the mouse on a computer? If\ the\ polynomial\ p\left(x\right)\ =\ 2x^3\ +\ ax^{2\ }-\ 7x\ +b,\ p\left(1\right)\ =\ 3\ and\ p\left(2\right)\ =\ 19,\ find\ a\ \&\ bpls tell fast what is 0.00000000007234 written in scienific from guysss help mee plss Student A spent $9 on a bottle of school glue, a package of colored pencils, and a pencil pouch. Student Bspent $16 on two bottles of school glue, three packages of colored pencils, and a pencil pouch. Student Cspent $17 on a bottle of school glue, two packages of colored pencils, and two pencil pouches.1. Which augmented matrix best represents the system of linear equations that could be used todetermine the price of each item? A farmer has decided to dig an artesian well into the unconfined aquifer below his crops.However, water does not fill his well. Why isn't his well working? List two examples of objects at home that uses chemical energy and describes what the chemical energy is being transformed into Which system helps regulate bodytemperature and water loss?A. OutegumentaryB. IntegumentaryC. Excretory what is the value of Y in this triangle ASAP what is the x and y intercept for 4x+7y=3 I need help ASAP. I will give brainliest Fragmentation occurs when a large area of ecosystem is divided into smaller, isolated areas due to deforestation. After fragmentation, changes to the ecosystem can occur. Which is most likely an effect of fragmentation on an ecosystem?a. Animal species in the fragmented area utilize new food sources in the deforested area.b. Plant species from the deforested area alter conditions at the edge of the fragmented area.c. The nutrient cycle is replenished by new species colonizing the deforested area.d. Most native species disappear from both deforested and fragmented areas. Kim ate 50% of candies in the bag. If Kim ate 35 candies , how many candies were total in the bag?