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

Please answer correctly !!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!

Answers

Answer:

180-[tex]x^{2}[/tex]

Step-by-step explanation:

How can we write 1.25+1.25 +1.25 as a multiplication, using words, and as a single number? Make sure you answer all three parts of this question.

Answers

Answer:

1) 1.25*3

2) 1.25 multiplied by 3

3) 3.75

Step-by-step explanation:

Solve plzzz ASAP due today

Answers

Answer:

#3- x=2.73

#4- x=8

Step-by-step explanation:

Answer: X = 3 / X = 8

Step-by-step explanation:

3. (Angles add up to 180)

30x + 4 + 86 = 180

30x + 90 = 180

subtract 90 from both sides

30x = 90

Now divide by 30

x = 3

Check your work ( input 3 to the equation)

30(3) + 4 + 84

90+ 90 = 180  it works :)  

4. (Angles are adjacent to each other so there equal)

10x - 3 = 77

add 3 to both sides

10x = 80

divide it by 10

x = 8

Check your work ( input 8 to the equation )

10(8) -3 = 77

80 - 3 = 77

77 = 77

please help me in this question​

Answers

Step-by-step explanation:

c)16 km

bcoz

3⅑ X 5⅐

=16km

Answer: (c) 16 kilometers

=========================================================

Work Shown:

Convert each mixed number to an improper fraction.

3 & 1/9 = 3 + 1/9

3 & 1/9 = 3*(9/9) + 1/9

3 & 1/9 = 27/9 + 1/9

3 & 1/9 = (27+1)/9

3 & 1/9 = 28/9

The car's average speed is 28/9 km per hour.

5 & 1/7 = 5 + 1/7

5 & 1/7 = 5*(7/7) + 1/7

5 & 1/7 = 35/7 + 1/7

5 & 1/7 = (35+1)/7

5 & 1/7 = 36/7

The time the car travels is 36/7 hours.

----------------------

We did the conversions so we can multiply the values easier.

Distance = Rate*Time

Distance = (28/9)*(36/7)

Distance = (28*36)/(9*7)

Distance = (4*7*9*4)/(9*7)

Distance = (4*4)/(1)

Distance = 16 kilometers

10. if ABC is equilaterteral, solve for x​

Answers

Answer:

13

Step-by-step explanation:

If ABC is equilaterteral then all the angles must be equal and 60°

8x - 44 = 60 add 44 to both sides

8x = 104 divide both sides by 8

x = 13

HELP ME PLEASEEEEEEE


The graph of line g is shown below.



Which equation describes a line parallel to line g that has a y-intercept at (0, −1)?

Answers

Answer:

is the graph of y=-2x-1

The equation of line which is parallel to given line is , [tex]y=-\frac{1}{2}x-1[/tex]

Option H is correct.

Equation of line :

Given line is passes through points [tex](-4,6)[/tex] and [tex](4,2)[/tex]

Slope of given line is,

                  [tex]Slope=\frac{2-6}{4+4}=-\frac{1}{2}[/tex]

Since, all parallel lines have the same slope.

So that, slope of line parallel to given line is also equal to [tex]-\frac{1}{2}[/tex]

Equation of required is,

               [tex]y=-\frac{1}{2}x+c[/tex]

Since, line passes through point [tex](0,-1)[/tex]

So that,  [tex]c=-1[/tex]

Equation of required line become, [tex]y=-\frac{1}{2}x-1[/tex]

Learn more about the equation of line here:

https://brainly.com/question/18831322

*
Evaluate the function.
w(x)=-3x - 4; Find w(7)

Answers

Answer:

w(7)= -25

Step-by-step explanation:

-3(7)-4

-21-4

w(7)= -25

Jenna took a math test and answered 15 out of 20 answers correctly. What percent of the questions did she answer correctly?

Answers

Answer:

75%

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

15   x  5           75

----      =          -------

20  x  5           100

Cent means 100, so percent literally means per 100 like in century or centennial. So, I put it into a fraction over 100. Now it is 75 per 100. If you remember, per 100 is percent, it means the answer id 75 percent. You can also write it as 75%.

WORTH 40 POINTS

ANSWER ASAP

Explain if possible

Answers

Answer:

I think A

Step-by-step explanation:

What is the range of the following relation?

Answers

Answer:

[0,-infinity[

Step-by-step explanation:

you look on the starting point and the ending point of the y-axis (♾ is always opened [ )

0,- infinity
Hope this helps :)

solve for x.........

Answers

Answer:

61

Step-by-step explanation:

A triangle's total degrees is 180. You add the two angles they give you and then subtract the sum from 180. In number 9, the answer is 61. 47+72=119, 180-119= 61.

Can someone please help me with this pleaseeeee ?!?!?!?!?! Don’t say nothing if you don’t know the answer

Answers

6)
-4
-1
2
5
8

7) each time the x column goes up 1, the fx column goes up 3

These are the only ones i know. Sorry i cant be more helpful :(

What is the length of mm?
**8
A. 12
B. 16
C. 8
D. 4

Answers

Answer:

D.4

length of nm is 4.....

Answer:

heyo! the answer is A. 12

Step-by-step explanation:

i got it right on my test, have a great day :)

Maya is going to an amusement park. The price of admission into the park is $10, and once she is inside the park, she will have to pay $2 for every ride she rides on. How much money would Maya have to pay in total if she goes on 15 rides? How much would she have to pay if she goes on rr rides?

Answers

Answer:

the answer is 40 dollars

Step-by-step explanation:

all you have to do is multiply 15x2 and then add 10

Answer:

$40 dallors.

Step-by-step explanation:

First you would do, 2 times 15 and get 30.

Then do 30 plus 10 to get $40 dallors.

Which statement best explains the relationship between lines FG and HJ?

Answers

Answer:

D.

Step-by-step explanation:

From the figure, we have

The coordinates of the point F are: (-4,1).

The coordinates of the point G are: (0,-2)

The coordinates of the point J are: (0,4) and

The coordinates of the point H are: (-4,-2).

Now, the slope of the line FG is :

S=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}S=

x

2

−x

1

y

2

−y

1

S=\frac{-2-1}{0+4}S=

0+4

−2−1

S=\frac{-3}{4}S=

4

−3

And, the slope of the line HJ is:

S=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}S=

x

2

−x

1

y

2

−y

1

S=\frac{-2-4}{-4-0}S=

−4−0

−2−4

S=\frac{3}{2}S=

2

3

Now, the slope of FG=\frac{1}{slope of HJ}theslopeofFG=

slopeofHJ

1

\frac{-3}{4}=\frac{2}{3}

4

−3

=

3

2

which is not possible, thus They are not perpendicular because their slopes are not negative reciprocals.

A(3,-4) and B(-1,3).
how to find the distance and show work for it

Answers

Answer:

8.06

Step-by-step explanation:

d = √( [tex]x_{1}[/tex] - [tex]x_{2[/tex] ) + ( [tex]y_{1}[/tex] - [tex]y_{2}[/tex] )

d = √ ( 3 - (-1) )² + ( -4 - 3 )²

d = √(4)² + (-7)²

d = √16 + 49

d = √65

d = 8.06


NEED ANSWER ASAP

WILL MARK BRAINLIEST

What is the slope of the line given, f(0) = -5 and f(4) = 11?

Answers

Answer:

The slope is 4.

Step-by-step explanation:

We are given that f(0)=-5 and f(4)=11.

This means that we have the two points (0, -5) and (4, 11).

So, we can use the slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let (0, -5) be (x₁, y₁) and let (4, 11) be (x₂, y₂). Substitute appropriately:

[tex]m=\frac{11-(-5)}{4-0}[/tex]

Evaluate:

[tex]m=\frac{16}{4}=4[/tex]

Hence, the slope of the line given f(0)=-5 and f(4)=11 is 4.

solve for the variable
7x = 49
-4x= -40
x/2 = 6
x/9 = -2

Answers

Answer:

71012-18

Step-by-step explanation:

For 7x = 49 you need to divide 7 to both sides

For -4x=-40 you need to divide -4 to both sides

For x/2 = 6 you need to multiply 2/1 to both sides

For x/9 =- 2 you need to multiply 9/1 to both sides


Draw JKL on the coordinate plane given the above information.
translate FGH 3 units down and 2 units left followed by a rotation counterclockwise 90°.Then followed by a dilation by a scale factor of 2.

Answers

Step-by-step explanation:

Hope this helps, happy learning!!!

The diagram of translatation FGH 3 units down and 2 units left followed by a rotation counterclockwise 90° is attached below.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form.

Depending on the scale factor, the object's size can be raised or lowered.

The translate FGH 3 units down and 2 units left followed by a rotation counterclockwise 90°.Then followed by a dilation by a scale factor of 2.

F ( -1, 0)

G (1, 0)

H ( -1, 1)

Thus, counterclockwise 90°

F' ( 0, 1)

G' (0, -1)

H' ( -1, -1)

Scale factor = 2

Then

F'' ( 0, 2)

G'' (0, -2)

H'' ( -2, -2)

The diagram of translatation FGH 3 units down and 2 units left followed by a rotation counterclockwise 90° is attached below.

To learn more about dilation, refer to;

brainly.com/question/13176891.

#SPJ2

Graph the system of inequalities . Which two quadrants does the solution lie in?

someone help a brotha out

Answers

Answer:

Quads 1 and 2

Step-by-step explanation:

Option A or quadrants 1 and 2 is the correct answer:)

Complete Eduardo's definition of parallel lines: "If two coplanar lines are both perpendicular to a third line in the same plane, all of the angles formed between the two lines and the third line are "Explain your answer.​

Answers

Appendicular because science isn’t everything.

This is ,y las question can some one help

Answers

Answer:

yo no se mijo habla espanol

Emily purchased 5 packages of bottled water for $14.95. Each package of bottled water cost the same amount.
What is the cost per package of bottled water?

Answers

the cost per package is 2.99 i believe this is correct could be wrong .
$2.99


step by step: you have to divide

so you would divide 14.95 and 5 which would get u 2.99

hope this helps

pls help ASAP will give brainlist

Answers

Answer:

Triangular Prism

Step-by-step explanation:

Congruent means the same or identical. The cross-section of the sphere is not the same as its base which is just a point. The cross-section of the cone is not circle like its base. The cross-section of the square pyramid is not a square. The cross-section of the last shape, the prism is a triangle like its base.

can someone help me lol​

Answers

Answer: 51
80+49=129
180-129= 51

The length, breadth and height of a rectangle block are 10 cm , 15 cm and 25 cm. The LENGTH : BREADTH : HEIGHT ratio of the block is
a,2 : 3: 5
b,5 :2 : 3
c,3 : 2 : 5
d,1 : 3 : 5

Answers

[tex] \LARGE{ \underline{ \tt{Required \: answer:}}}[/tex]

We have to find the simplest ratio between length, breadth and the height.

Here,

Length = 10 cmBreadth = 15 cmHeight = 25 cm

Note:

Always check the units first.Then find the HCF of the numbers to simplify them into the simplest ratio.

So,

HCF of 10, 15 and 25 is 5. Cancelling with respect to 5.

Then, the ratio will be 2:3:5 (Option A)

⛱️ [tex] \large{ \blue{ \bf{FadedElla}}}[/tex]

Step-by-step explanation:

if you divide everything by five you will get ur answer

Subtract 6x10^-8 from the product of 8.5x10^-2 and 5x10^-5 and convert into scientific notation

Answers

Answer:

If you meant both of them together, it would be 499932.085

If you meant each of them, the 8.5 would be−67.915  and 5 would be 499932

Step-by-step explanation:

Consider these numbers, ordered from least to greatest. Negative 1.8, negative 1 and one-fourth, negative 0.2, blank, one-half, 90 percent A number line going from negative 2 to positive 1. Which values could correctly fill in the blank? Select all that apply.

Answers

Answer:

10%

-0.1

1/4

Step-by-step explanation:

Complete question

Consider these numbers, ordered from least to greatest. Negative 1.8, negative 1 and one-fourth, negative 0.2, blank, one-half, 90 percent A number line going from negative 2 to positive 1. Which values could correctly fill in the blank? Select all that apply. 10% 1 -0.1 -1 One-fourth

step-by-step explanation

On the number line, numbers increase from left to right.

The blank is between -0.2 and 1/2.

Only numbers greater than -0.2 and less than 1/2 can fill the blank.

Range = -0.2<x<1/2

From the values given,

1) 10% = 10/100 = 1/10 = 0.1

-0.2<0.1<1/2

2) -0.2<1

But, 1>1/2

3) -0.2<-0.1<1/2

4) -0.2>-1

5) -0.2<1/4<1/2

Therefore, only 10%, -0.1, and 1/4 can fill in the blank correctly because they satisfy the range -0.2<x<1/2

Answer:

A

C

E

THE ANSWER BOIIIIIIIIIIIIIIIIIIIIIII!

Step-by-step explanation:

Mofor spent half of his weekly allowance on
clothes. To earn more money his parents let
him clean the oven for $8. What is his
weekly allowance if he ended with $15?
Please explain how you got the answer.

Answers

His weekly allowance would be $14 ; first you have to do 15-8= $7, because he got 8 dollars from cleaning the oven. Then you multiply the $7 by 2 because he had this much left after buying clothes, making his allowance twice as much, so 7 x 2= $14

PLZZ HELP ITS FROR A TEST THAT I EED TO PASS !!!!!
Frankenstein is definitely a classic and he can still manage to get a few scares, but the also classic Werewolf has seen better days. The Werewolf is often the target of scares and has an equation perpendicular to Frankenstein's. Frankenstein's equation is`y=x+5` and the Werewolf's equation passes through the point `\left(-1,-2\right).` What is the Werewolf's equation?

Answers

Answer:

3)-rightx (877

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