The question is this: Rationalize the denominator and simplify.

Plssss hurry & answer this!!!!

The Question Is This: Rationalize The Denominator And Simplify. Plssss Hurry & Answer This!!!!

Answers

Answer 1

9514 1404 393

Answer:

  [tex]\dfrac{20+5\sqrt{3}}{13}[/tex]

Step-by-step explanation:

Multiply numerator and denominator by the "conjugate" of the denominator.

  [tex]\dfrac{5}{4-\sqrt{3}}=\dfrac{5(4+\sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}=\dfrac{20+5\sqrt{3}}{4^2-(\sqrt{3})^2}=\boxed{\dfrac{20+5\sqrt{3}}{13}}[/tex]

__

This is done in different scenarios in order to take advantage of the factoring of the difference of squares. Square root terms and imaginary terms in the denominator can be eliminated in this way.

  a² - b² = (a -b)(a +b)


Related Questions

What is the gcf of 51 and 3

Answers

Answer:

3

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor (GCF).

The factors of 51: 1, 3, 17 and 51.The factors of 3: 1,3

So the greatest number of both is 3

Hope this helps

interquartile range of the wingspans of 74, 71, 75, 80, 67, 84, 77

Answers

Answer: 9

Step-by-step explanation:

Population size=7

Lower quartile=71

Upper quartile=80

67 Is or es el 67

Jajaja

Parallel lines e and f are cut by transversal b. Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 10) degrees. At the intersection of lines b and f, the bottom left angle is (3 x minus 15) degrees. What is the value of x? 1 5 25 37

Answers

Answer:

The Answer would be C

Step-by-step explanation:

Answer: It is C. 25

Step-by-step explanation:

on edge 2020

after scoring a touchdown the billies linked up for the kickoff . the kicker kicked the football 60 yards deep into the end zone. the hang time on the ball was 8.5 seconds . what was the average speed of the ball​

Answers

Answer:

7 seconds i think let me know if its wrong

Step-by-step explanation:

3. Three of the following statements are true.
Which one is NOT true?
1-12] > 1
10> -4
120 >1-101
61-3

Answers

Answer:

The correct answer is A or option 1

Landon is building new bookshelves for his bookstore's new mystery section. Each shelf can hold 34 books. There are 1,265 mystery books. How many shelves will he need to build?

Answers

Answer:

37.2 = 38

Step-by-step explanation:

After divideing 1265 by 34, you will get 37.2. As you cannot have books not in bookshelves, you will have to round up and have 38 bookshelves.

NEED ASAP . Plz help

Answers

It’s 4 and what they said

Evaluate -9x-2 when x =-4

Answers

Answer:

34

Step-by-step explanation:

So -9x is 36,36-2=34

Answer:

34

Step-by-step explanation:

-9(-4)-2

36-2

34

The area of the triangle is 22.4cm^2.
Calculate the length, b, of the longest side of the triangle.

Please help, I will mark first correct answer brainliest.

Answers

Answer:

The longest side length b is approximately 13.172 cm

Step-by-step explanation:

The given parameters are;

The area of the triangle = 22.4 cm²

The given angles of the triangle = ∠97°

The given side of the triangle = 3.7 cm

The formula for the area of a triangle, A = 1/2 × a × b × sin(C)

Where;

a, and b are the side legs forming the angle C

Therefore,  we have;

A = 22.4 = 1/2 × 3.7 × a × sin(97°)

a =  22.4/(1/2 × 3.7 × sin(97°)) ≈ 12.199

a ≈ 12.199 cm

Therefore, by cosine rule, we have;

b² = a² + c² - 2 × a × c × Cos(B)

Substituting the values, gives;

b² = 12.199² + 3.7² - 2 × 12.199 × 3.7 × Cos(97°)

b² ≈ 173.507

∴ b ≈ √173.507 ≈ 13.172

b ≈ 13.172 cm

chemical formula for lithium bromide

Answers

Answer:

The molecular or chemical formula of Lithium Bromide is LiBr. Lithium Monobromide is synthesized by treating lithium carbonate (Li2CO3) with hydrobromic acid (HBr). The salt forms cubic crystals which are similar to sodium chloride.

Step-by-step explanation:

hope this helped:)

Answer:

lithium bromide is a chemical compound of lithium and bromine

Step-by-step explanation:

Br-Li+

what does 28-8 represent?

Answers

Step-by-step explanation:

subtraction if that wut u askim

Relationship B has a greater rate than Relationship A. This graph represents Relationship A. Which equations could represent Relationship B? Select each correct answer.

Answers

Answer:

The answer is A. Sorry, i dont have enough time to support my answer. I am rushing sdjeuesjcvjs

What is the value of x in the figure below? In this diagram, ABD ~ CAD. А с B 13 D3 A. 16 B. 208 C. 39 D. 48 E. 13/16 F. 139​

Answers

F. Square root of 39

Step-by-step explanation:

Value of [tex]\boldsymbol{x}[/tex] is [tex]\boldsymbol{\sqrt{39}}[/tex] units.

Option F. is correct.

Define similar triangles.

Two triangles are said to be similar if their sides are proportional and their corresponding angles are equal.

[tex]\bigtriangleup ABD \sim \bigtriangleup CAD[/tex]

[tex]\boldsymbol{\frac{AD}{CD}=\frac{BD}{AD} }[/tex]

  [tex]\frac{x}{13}=\frac{3}{x}[/tex]

  [tex]x^2=39[/tex]

   [tex]x=\sqrt{39}[/tex] units.

Value of [tex]\boldsymbol{x}[/tex] is [tex]\boldsymbol{\sqrt{39}}[/tex] units.

Option F. is correct.

Find out more information about triangle here:

https://brainly.com/question/2773823?referrer=searchResults

Find the slope of the following graph and Identify the type of
Slope:

Answers

Answer:

undefined

Step-by-step explanation:

Horizontal lines have no slope. The line on the graph is vertical, so we can't really tell what slope it is. But there isn't any run and only rise, therefore the slope is "undefined."

Does this graph represent a function? Why or why not?
10
10
A. No, because it is not a straight line.
B. Yes, because it passes the horizontal line test.
c. Yes because it passes the vertical line test
D. No, because it fails the vertical line test.

Answers

Answer:

No because it does no pass the vertical line test

Step-by-step explanation:

(Urgent please help!!!) Maria earned $5,250; $4,800; $3,990 and $5,120 from her home business during the last four months. What was her average monthly income during this period?

Answers

5250 + 4800 + 3990 + 5120
19160 / 4 = $4,790 average monthly income

Which of the following values are solutions to the inequality 9 > - 3 - 4x

Answers

Answer:

the answer is 12

Step-by-step explanation:

Answer:

x>−3

Step-by-step explanation:

Help!!! Worth 12 points !!!! I’ll mark brainliest!!!❤️

Answers

Answer:

good handwritting the first is 87

Step-by-step explanation:

How do you solve n=17

Answers

Answer:

uhm chile anyways

Step-by-step explanation:

i just want points lol

Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer than its width. The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height. Complete the equation that models the volume of the tray in terms of its width, x, in centimeters.

Answers

Answer:

Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer than its width.

The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height.

Complete the equation that models the volume of the tray in terms of its width, x, in centimeters.

3x2 + 15x = 252

Is it possible for the width of the tray to be 7.5 centimeters?

no it is too large

Step-by-step explanation:

An equation is formed when two equal expressions. The equation that models the volume of the tray in terms of its width, x, in centimeters is 3x² + 15x - 252 = 0.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the width of the rectangular prism die be represented by x.

Given that the length of the tray should be five centimeters longer than its width. Therefore, the length and the width of the prism can be written as,

Width = x

Length = x + 5

Further, it is given that the volume of die is 252 cubic centimeters in order for the dice to roll properly. Also, the height of the prism is 3 centimeters. Therefore, the Volume can be written as,

Volume = Length × Width × Height

252 = (x + 5) × x × 3

252 = 3x(x+5)

252 = 3x² + 15x

3x² + 15x - 252 = 0

Hence, the equation that models the volume of the tray in terms of its width, x, in centimeters is 3x² + 15x - 252 = 0.

Learn more about Equation:

https://brainly.com/question/2263981

#SPJ5

Seth has game and education apps on his tablet. He noticed that he has 5 game apps for every 2 education apps. Which of the following is another way to write this ratio?

2:3
2:5
3:2
5:2
Question 4(Multiple Choice Worth 3 poi

Answers

Answer:

it would be 5:2

Step-by-step explanation:

none of these are equivalent to the ratio and 2:5 would be 2 to 5

Answer:

5:2

Step-by-step explanation:

The Lopez Family meets with a financial planner who advises them to save 15% of their income per month for college savings for their children. They earn $8,540 per month. How much will the Lopez family save each month for future college expenses?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

Answers

Answer:

$1281.00

Step-by-step explanation:

8540*15%=1281

For each triangle, check all that apply.
PHOTO ABOVE
⚠️TEST

Answers

Answer:

Step-by-step explanation:

Triangle A - Equilateral triangle because all the angles are equal which means all the sides will be equal.

Triangle B - Isosceles Triangle because 2 sides are equal (we know this because 2 of the angles are equal)

Triangle C - Equilateral triangle because all the sides are equal.

Triangle D - Scalene triangle because all the sides have different lengths.

2,11,20 find the t15

Answers

Answer:

128

Step-by-step explanation:

There is a common difference between consecutive terms, that is

11 - 2 = 20 - 11 = 9

This indicates the sequence is arithmetic with n th term

[tex]t_{n}[/tex] = t₁ + (n - 1)d

where t₁ is the first term and d the common difference

Here t₁ = 2 and d = 9 , thus

t₁₅ = 2 + (14 × 9) = 2 + 126 = 128

Can someone help me with part b on this question please?

Answers

9514 1404 393

Answer:

  12.0 cm

Step-by-step explanation:

The Pythagorean theorem applies:

  (12 cm)² +b² = (17 cm)²

  b² = (289 -144) cm² = 145 cm²

  b = √145 cm ≈ 12.04 cm

  b ≈ 12.0 cm . . . . rounded to 1 decimal place

3 pounds of peanuts for 7.50 how much per pound?

Answers

Answer:

$2.50

Step-by-step explanation

7.50 divided by 3 is 2.50

Answer:

$2.50 per pound

Step-by-step explanation:

7.50/3

$2.50

In triangle ABC, the measure of angle A is 48° and the measure of angle C is 24°. What type of triangle is triangle ABC?

Answers

Answer:108 degrees

Step-by-step explanation:

Answer:

Scalene triangle

Step-by-step explanation:

24+48= 72

180-72=108

All three angles are different meaning that the triangle must be a scalene triangle.

sandy is having a thanksgiving feast for her family of 24. she is deciding between these two options. Help please which one is better and why . Due in three hours!!!

Answers

Answer:

option b

Step-by-step explanation:

n(A)=10
n(B) = 12
n(AUB) = ?​

Answers

Answer:

n(AUB) = 33

Step-by-step explanation:

U is the 21'st letter of the alphabet so

9 + 1 + 2 + 21 =33

n(AUB) = 33

What is the slope of the line that passes through the points (5,-11) and (-9,17)?

Answers

Answer:

-2

Step-by-step explanation:

m=y2-y1

    x2-x1

Answer:

-2=slope

Step-by-step explanation:

17--11=28

-9-5= -14

28/-14= -2

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