Rationalize the denominator and simplify

Rationalize The Denominator And Simplify

Answers

Answer 1

Answer:

x² - √3x / x² - 3

Step-by-step explanation:

To Do :-

To rationalize the denominator .

Solution :-

We need to rationalize ,

x/ x + √3

Multiply numerator and denominator by x-√3 :-

x( x - √3 ) / ( x +√3)( x -√3) x² - √3x / (x)² - (√3)² x² - √3x / x² - 3

Related Questions

What is the equation of the line that passes through (4,3) and (2, -1)?

y = 4x -13
y = 6x+4
y = 2x-5
y = 1/2 x -2

Answers

Answer:

y=2x-5

Step-by-step explanation:

By using two-points form:

y-y1/y2-y1=x-x1/x2-x1

p(x1,y1)=(4,3)

p(x2,y2)=(2,-1)

Subtitute points in formula:

y-3/-1-3=x-4/2-4

y-3/-4=x-4/-2

y-3/-2=x-4/-1

1(y-3)=2(x-4)

y-3=2x-8

y=2x-8+3

y=2x-5

Note:if you need to ask any question please let me know.

Pls helppppp,,,,,.....

Answers

Answer:

yall do school right now???and i forgot how to do these sorry

Answer:

18 = 2x-14

or, 2x =18+14

or, 2x =32

or, x=32/2

x=16

2(6x-7)=10

or, 12x-14=10

or, 12x=10+14

or, x=24/12

x=2

I’m new to this app and I need help with those two questions please help!!

Answers

y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

y=-4x²-8x+1

а<0 so we will be looking for maximum

х=-b/2a=8/-8=-1

у=4+8+1=13

Maximum point (-1;13)

You need 675 mL of a 90% alcohol solution. On hand, you have a 25% alcohol mixture. How much of the 25% alcohol mixture and pure alcohol will you need to obtain the desired solution?

Answers

Answer:

90 ml of the 25 percent mixture and 585 of pure alcohol

Step-by-step explanation:

Firstly, you should find the quantity of alcohol in the desired mixture.

675:100*90= 675*0.9= 607.5

Firstly,  define all the 25 percents mixure as x, the pure alcohol weight is y.

1. x+y= 675 (because the first and the second liquid form a desired liquid).

Then find the equation for spirit

The first mixture contains 25 percents. It is x/100*25= 0.25x

When the second one consists of pure alcohol, it contains 100 percents of spirit,  so it is x.

2. 0.25x+y=607.5

Then you have a system of equations ( 1.x+y= 675 and 2. 0.25x+y= 607.5)

try 2-1 to get rid of y

x+y- (0.25x+y)= 675-607.5

0.75x= 67.5

x= 90

y= 675-x= 675-90= 585

It means that you need90 ml of the 25percents mixture and 585 0f pure alcohol

what percent of 70 is 35

Answers

Answer:

50%

Step-by-step explanation:

35 is halve of 70 therefore it is 50%

hope it helps u...........

Please help it’s due today

Answers

Answer:

67 degrees

Step-by-step explanation:

23 + 90 = 113

180 - 113 = 67

Which expression is equivalent to (b^n)m?

Answers

Step-by-step explanation:

By the law of exponent :

(a^n)^m=a^n×m

Option C

b^n×m is the correct answer...

hope it helps

y=4.5x+13.45 y=6x-4.55

Answers

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(

12

,

67.45

)

Equation Form:

x

=

12

,

y

=

67.45

Draw the line segment with endpoints (-5, 9) and (-1, -7) and find the value of y if x=-4;-2.5;-2;-1.5;0 plz answer asap

Answers

Answer:

5, - 1, - 3, - 5, - 11

Step-by-step explanation:

The equation of the line is y=-4x-11. The y values corresponding to x are 5, - 1, - 3, - 5, - 11

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!

Chapter 11 part 2:

What are three different properties of logarithmic functions when encountering the operations of addition, subtraction, and multiplication? Provide an example of each.

Answers

The three main log rules you'll encounter are

log(A*B) = log(A) + log(B)log(A/B) = log(A) - log(B)log(A^B) = B*log(A)

The first rule allows us to go from a log of some product, to a sum of two logs. In short, we go from product to sum. The second rule allows us to go from a quotient to a difference. Lastly, the third rule allows to go from an exponential to a product.

Here are examples of each rule being used (in the exact order they were given earlier).

log(2*3) = log(2) + log(3)log(5/8) = log(5) - log(8)log(7^4) = 4*log(7)

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

Here's a slightly more complicated example where the log rules are used.

log(x^2y/z)

log(x^2y) - log(z)

log(x^2) + log(y) - log(z)

2*log(x) + log(y) - log(z)

Hopefully you can see which rules are being used for any given step. If not, then let me know and I'll go into more detail.

The correlation coefficient, r, between the prices of smartphones, x, and the number of sales of phones, y, equals −0.63.


Select the statement which best describes the relationship between the price and sales.


The value of r indicates that the number of sales decreases as the price decreases.

The value of r indicates that the number of sales decreases as the price stays the same.

The value of r indicates that the number of sales decreases as the price increases.

The value of r indicates that the number of sales is not related to the price.


I think its (C): The value of r indicates that the number of sales decreases as the price increases.

Answers

Answer:

(C) The value of r indicates that the number of sales decreases as the price increases.

ED2021.

The best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.

What is a Negative Correlation Coefficient?

A negative correlation coefficient has a negative sign, and implies a negative relationship between two variables.

This means that, as one variable decreases, the other variable increases.

Thus, a correlation coefficient of -0.63 shows a negative relationship between prices of smartphones and the number of sales.

Therefore, the best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.

Learn more about correlation coefficient on:

https://brainly.com/question/4219149

Question 3 plz show ALL STEPS

Answers

Answer:

7,0, -1 and -2

Step-by-step explanation:

Just substitute the values,

a. f(g(7))=f(-1) [g(7)=-1 given]

            =7 [f(-1)=7 given]

b.f(g(-1))=f(3)=0 [g(-1)=3 Given]

c.g(f(-1))=g(7)=-1 [f(-1)=7 given]

d.g(f(7))=g(5)=-2 [f(7)=g(5) given]

any equations that equal three?

Answers

0+3=3 so I hope that helps
1•3=3 or 4-1=3 try those equations

A capark has 34 rows and each row can acommodate 40 cars. If there are 976 cars parked, how many cars can still be parked?​

Answers

Answer:

384 cars

Step-by-step explanation:

To find the total number of spaces in the carpark, we must multiply the number of rows by how many cars they can accommodate:

34 ⋅ 40 = 1360

As you can see, we have 1360 total spaces. Since there are 976 cars parked, and we want to find out how many spaces are left, we have to subtract the amount of cars parked from the total spaces.

1360 - 976 = 384

Therefore, our answer is 384, specifically, 384 cars.

Answer:

384 cars.

Step-by-step explanation:

40 * 34 - 976

= 1360 - 976

= 384.

Algebra II Part 1
Choose the expression or equation that correctly represents this information
Rose works eight hours a day for five days a week. How many hours will she work in sa
weeks?
hours = 40 = 6
hours = 40.6
hours = 6 = 40

Answers

Answer:

240 i.e 40*6

Step-by-step explanation:

if rose works 8hrs per day then she works 40 hrs per week (5 days) therefore 40 hrs per 6 weeks =40*6=240

Answer:

40

Step-by-step explanation:

Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x – 9y = -72

Answers

24+-3y is the correct answer

the slope-intercept form of the given equation is y = x/3 + 8.

What is the slope?

The increase divided by the run, or the ratio of the rise to the run is known as the line's slope. The coordinate plane describes the slope of the line.

The slope-intercept form of a line is Y = m*X +C.

Given an equation 3x-9y = -72, which we will try to make in the slope-intercept form by using simplification.

3x-9y = -72

9y = 3x + 72

y = 1/3 * x + 8

Therefore y = x/3 + 8 is the slope-intercept form of the given equation.  where its slope is 1/3.

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ2

One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the ren
is 2:1, find the measures of the three angles of the triangle.

Answers

9514 1404 393

Answer:

  90°, 60°, 30°

Step-by-step explanation:

The remaining angles have a ratio of 2:1, so total 3 "ratio units". The first angle is equal to that sum: 3 ratio units, so all of the angles together total 3+2+1 = 6 ratio units. The total of angles is 180°, so each ratio unit is 180°/6 = 30°.

The first angle is 3 ratio units, or 90°.

The second angle is 2 ratio units, or 60°.

The third angle is half that, or 30°.

The three angles are 90°, 60°, 30°.

Solve this inequality:
-9 > 3b + 6

Answers

Answer:

- 5 > b

Step-by-step explanation:

- 9 > 3b + 6

- 9 - 6 > 3b

- 15 > 3b

Divide 3 on both sides,

- 5 > b

Answer:

-5 >b

Step-by-step explanation:

-9 > 3b + 6

Subtract 6 from each side

-9-6 > 3b + 6-6

-15 > 3b

Divide each side by 3

-15/3 > 3b/3

-5 >b

factorise completely 4x^(2 )(x + 1) - 6x (x+1)

Answers

Answer:

[tex] {4x}^{2} (x + 1) - 6x(x + 1) \\ = (x + 1)(4 {x}^{2} - 6 x ) \\ = (x + 1)(2x)(2x - 3)[/tex]

explanation:

first choose the common factor by observation, it is (x + 1):

factorise it out:

= (x + 1)(4x² - 6x)

by observation in (4x² - 6x), common factor is 2x.

Factorise 2x out:

= (x + 1)[2x(2x - 3)]

Answer:

(4x2-6x) (x+1)

now common factor is (x+1) ,so,(4x2-6x) (x+1)

how to work this fraction 4/11+5/22+3/44

Answers

Answer:

29/44

Step-by-step explanation:

[tex]\frac{4}{11} +\frac{5}{22} +\frac{3}{44} =\\[/tex]

-find the common denominator

[tex]\frac{4*4}{4*11} + \frac{2*5}{2*22} +\frac{3}{44} =[/tex]

[tex]\frac{16}{44} +\frac{10}{44} +\frac{3}{44} =[/tex]

-add the fractions and solve

[tex]\frac{16+10+3}{44} =[/tex]

[tex]\frac{29}{44}[/tex]

Hello I'm new can anyone help me with this question?
Thank you so much! <3 xoxo

Answers

Option 4 is going to be the answer

After running 3/4 of a mile tess has only run 1/3 how long is the race in miles but I want to know how you did it

Answers

Take 3/4 and 1/3 multiply the bottom, thats your denominator. Then since you multiplied 4•3, multiply the top by three.

Write the point-slope form of an equation of the line through the points (-4, 7) and (5,-3).
0
A. Y+4= -1; (1 – 7)
B.Y-5 = = 10 (x+3)
OC. y +3 = = 10 (2+5)
D. y - 7= -5° (x+4)

Answers

Answer:

Step-by-step explanation:

There are two possible equations, but neither matches the the choices you listed. The choices seem to have several typographical errors.

Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 =(-10/9)(x + 4).

How to estimate the point-slope form of an equation of the line through the points (-4, 7) and (5,-3)?

Slope

[tex]$= \frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]

= (-3 - 7) / (5 - (-4))

= -10/9

The point-slope equation for the line of slope -(10/9) that passes through the point (5, -3).

y + 3 = (-10/9)(x - 5)

Point slope equation for the line of slope -(10/9) that passes through the point (-4, 7)

Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 = (-10/9)(x + 4).

Therefore, the correct answer is y - 7 = (-10/9)(x + 4).

To learn more about the equation of a line refer to:

https://brainly.com/question/11751737

#SPJ2

I need help plz!!
8.57396817...•5/8 is rational or irrational?

Answers

Answer:

Irrational

Step-by-step explanation:

Any non-zero rational number multiplied by an irrational number will be irrational. We can rewrite this as (8.57... * 5) / 8, but we have no idea how to make 8.57... * 5 rational, or expressed as the quotient of two integers.

Solve the inequality

Answers

Answer:

hope this helps buddy, please mark the brainliest.

Step-by-step explanation:

Please help! Question and answers are in the pic

Answers

So far she worked 4 days at 5 1/2 hours a day for a total of 22 hours.

22 hours x $8.50 = $187

Subtract that from the cost of the computer:

899-187 = $712

She needs $712 more.

Amount she makes per shift: $8.50 x 5 1/2 hours = $46.75

Divide what she needs by amount per shift:

712 / 46.75 = 15.22 shifts

She needs to work 16 more shifts.

urgent image below for the question

Answers

Answer:

240 ft²

Step-by-step explanation:

Surface area of a rectangular prism is,

2(lw+wh+hl)

= 2(7×6+6×6+6×7)

= 240 ft²

I NEED HELP ASAP PLEASE!!!

Answers

Answer:

Hello the answer is A <!!

Answer:

c

Step-by-step explanation:

pi/ 3 * (180/pi)= 180/3

pi/3 = 60 degrees

∫[tex]\frac{x+2019}{x^{2}+9 }[/tex]

Answers

Split up the integral:

[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]

For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get

[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]

and

[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]

Then

[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]

For the following function, one zero is given. Find all other zeros.

f(x)=x3-7x2+17x-15; 2-i

Answers

Answer:

1,-3,-5

Step-by-step explanation:

Given:

f(x)=x^3+7x^2+7x-15

Finding all the possible rational zeros of f(x)

p= ±1,±3,±5,±15 (factors of coefficient of last term)

q=±1(factors of coefficient of leading term)

p/q=±1,±3,±5,±15

Now finding the rational zeros using rational root theorem

f(p/q)

f(1)=1+7+7-15

  =0

f(-1)= -1 +7-7-15

    = -16

f(3)=27+7(9)+21-15

   =96

f(-3)= (-3)^3+7(-3)^2+7(-3)-15

    = 0

f(5)=5^3+7(5)^2+7(5)-15

   =320

f(-5)=(-5)^3+7(-5)^2+7(-5)-15

     =0    

f(15)=(15)^3+7(15)^2+7(15)-15

    =5040

f(-15)=(-15)^3+7(-15)^2+7(-15)-15

     =-1920

Hence the rational roots are 1,-3,-5 !

Other Questions
find the quotient 1/5 / (-5/7) = Determine the sum of the first 33 terms of the following series:52+(46)+(40)+... Which of the following would be considered anthropogenic impacts on the natural environment?a. air pollutionb. introduction of invasive speciesc. burning of fossil fuelsd. all of the above The ratio of Mitchell's age to Connor's age is 8:5. In thirty years, the ratio of their ages will be 6:5. How much older is Mitchell than Connor now? How do you reach enlightenment in Buddhism?A. Through reincarnationB. Through warC. Through tradeD. Through meditation An individual taxpayer reports the following items for the current year: Ordinary income from Partnership A, operating a movie theater in which the taxpayer materially participates $70,000 Net loss from Partnership B, operating an equipment rental business in which the taxpayer does not materially participate (9,000) Rental income from building rented to a third party 7,000 Short-term capital gain from sale of stock 4,000 What is the taxpayers adjusted gross income for the year? The majority of immigrants that entered the United States during the industrial age came from if the ordered pairs (x-2,3y+1) and (y+1,x+3) are equal,find x and yplz help me 3. Find the product, using suitable properties :a) 26 x (-48) + (-48) x (-36)b) 625 x (-35) + (-625) x 65please answer fast 10 marks Because the P-value is ____ than the significance level 0.05, there ____ sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of = 0.05.Do the results suggest that imported lemons cause carfatalities?a. The results suggest that an increase in imported lemons causes car fatality rates to remain the same.b. The results do not suggest any cause-effect relationship between the two variables.c. The results suggest that imported lemons cause car fatalities.d. The results suggest that an increase in imported lemons causes in an increase in car fatality rates. PLEASE HELP ASAP!!! Answer ASAP please! If 1100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Round to two decimal places if necessary. Read the message from your cousin, Benny. Hi, I failed my Mathematics again! My parents scolded me. My sister said I'm lazy. I really hate Mathematics. I'm very depressed. What should I do?Benny in about 80 words, write a message to Benny giving some advice. Why Was The necessity of getting a constitution fromlated by a popularly elected constitution assembly felt after the second popular movement 2062 / 63 ? list the reasons. What does gratiano say when he saw shylock sharpening his knife? Please help me find xNeed help fast!! Independent PracticeWhich model is most appropriate for the set of points?(2, 5), (1, 1), (0, 3), (1, 1), (2, 5)A.exponentialB.linearC.quadratic How many times have I told you ... football in the street? the weight of a body is 420 newton.calculate it's mass