Rationalize the denominator and simplify. √a+1 - 2 / √a+1 + 2

Rationalize The Denominator And Simplify. A+1 - 2 / A+1 + 2

Answers

Answer 1

Answer:

5+a-4√a+1 / a-3

Answer 2

The rationalization of given expression is a+5-4√(a+1)/(a+5).

What is Rationalization?

Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction. That is, remove the radicals in a fraction so that the denominator only contains a rational number.

The given expression is √(a+1)-2/√(a+1)+2.

Multiply both numerator and denominator by (a+1)-2, we get

√(a+1)-2×(a+1)-2/√(a+1)+2×(a+1)-2

= (√(a+1)-2)²/(√(a+1))²+2²

= (√(a+1))²-2×√(a+1)×2+2²/a+1+4

= a+1-4√(a+1)+4/(a+5)

= a+5-4√(a+1)/(a+5)

Therefore, the rationalization of given expression is a+5-4√(a+1)/(a+5).

Learn more about the rationalization here:

https://brainly.com/question/1980047.

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Related Questions

Vinnie is searching online for airline tickets. Two weeks ago, the cost to fly from Denver to Hartford
was $200. Now the cost is $310. What is the percent increase? What would be the percent increase il
the airline charges an additional $50 baggage fee with the new ticket price?
The percent increase of the airline ticket is 11%.
annandad

Answers

Answer:

The ticket increased 57% of its original price

The baggage price was 44.5 increased 0.11% and then became 50

Step-by-step explanation:

So if the amount was 200 and now is 350, we should use division.

200 ÷ 350 = 0.5714285714285714 which you can round to 0.57 or as many digits as the question asked for. In thise case I will use 0.57

0.57 converted to percentage is 57%

About the second question

now you know the amount after increase and the percentage. So all you have to do is reverse.

11% = 0.11

0.11  ✕ 50 = 5.5    

this means the price increased 5.5

50 - 5.5 = 44.5

What is the solution to 2x-8<12?
x<2
x<8
x<10
x<40

Answers

i believe the answer is x&it;10 if it’s incorrect i’m so sorry

cindy bought a new jacket. Jill bought a jacket that costs 3 times as much as Cindy. Altogether their jackets cost 300$. What equation can be used to represent the problem and how much was each of their jackets?

Answers

Answer:

x + 3x = $400

the jacket cost price of Cindy nd Jill is $100 and $300 respectively

Step-by-step explanation:

The computation is shown below:

Here we assume the cindy be x

So the Jill be 3x

Now the equation is

x + 3x = $400

4x = $400

x = $100

So the Cindy jacket cost is $100

And, the Jill jacket cost would be

= 3x

= 3(100)

= $300

Hence, the jacket cost price of Cindy nd Jill is $100 and $300 respectively

Solve
7x + 10 = 3x + 13​

Answers

Answer:

x=3/4

Step-by-step explanation:

Let's solve your equation step-by-step.

7x+10=3x+13

Step 1: Subtract 3x from both sides.

7x+10−3x=3x+13−3x

4x+10=13

Step 2: Subtract 10 from both sides.

4x+10−10=13−10

4x=3

Step 3: Divide both sides by 4.

4x/4=3/4

x=3/4

What is the quadratic formula?

Answers

Answer:

Step-by-step explanation:

Answer:

x = [tex]\frac{-b±\sqrt{b^2-4ac} }{2a}[/tex]

Ignore the capital A for this equation when it is ax^2+bx+c=0

I'm crying I have to get this done in like 30 minutes or else my mom is literally gonna beat my a.ss please

First equation: t=b-4
Second equation: b+t=348

Since t is in terms of b from the first equation, this expression can be substituted into the second equation where t appears. Write an equation that shows this substitution.

Type the equation:

Answers

You got this don’t cry!
The new equation would be
b+b-4=348

Answer:

equation: b+(b-4)=348

Step-by-step explanation:

B+t=348

b+ 1(b-4)=348

b +b -4=348

this is if u want what b is

2b-4=348

2b-4+4=348+4

2b= 352

2b÷2 = 352÷2

b=176

AHHH URGENT ANSWER QUICK I GIVE BRAINLIEST

Answers

Answer:

20/54

Step-by-step explanation:

Can someone plz help! Will mark brainliest if its right

Answers

Answer: that is the answer to both

Step-by-step explanation:

A breakfast on the menu for $7.25 actually costs $7.83, because of the sale tax. Which statements are correct for this situation

Answers

Answer:

you didnt add a picture but i assume you want the percentage of tax which would be 8%

Step-by-step explanation:

A magic square is a square array of numbers arranged so that the numbers in all rows, all columns, and the two diagonals have the same sum. Use the properties of a magic square to fill in the missing numbers in the magic square on the right. CO. 16 24 Use the figure with the letters below to give the missing numbers. CO A= B= C= B 16 D= E= E 24 ​

Answers

Answer:

I think a is 9 cause 9+ 8 is 17 ??

The value of A,B,C,D and E will be 23,25,7 15 ,and 9 respectively.

What is summation?

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, thousand, or a million. There are summations with an infinite set of parameters.

If we make the sum of each side diagonally then the sum should be 48.

So,

D+ 16 + 17 = 48

D = 15

And

15 + B + 8 = 48

B = 25

And,

25 + 16 + C = 48

C = 7

And,

8 + A + 17 = 48

A = 23

And,

15 + E + 24 = 48

E = 9

Hence "The value of A,B,C,D and E will be 23,25,7 15 ,and 9 respectively".

For more information about summation

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A scuba diver is positioned at -30 feet. How many feet will she have to rise to change the position to -12 feet?

Answers

Answer: 18

Step-by-step explanation:

Sheldon gets paid $4 per hour to babysit his cousin. This
weekend, he babysat on both Saturday and Sunday. He
made a total of $56. Sheldon babysat for 8 hours on
Sunday. For how many hours did he babysit on Saturday?
Let x = hours spent babysitting on Saturday. Choose the equation and
solution steps that correctly represent this problem.

Answers

Answer:

6

Step-by-step explanation:

4 times 8 = 32. 56 - 32 = 24. 24 divided by 4 = 6.

Pls help!!! Pls and thank you!! So much

Answers

The measure of angle 1 is 64 degrees

First you need to find the measure of angle 3

To find the measure of angle three subtract 116 from 180 because angle 3 is on a straight line which is equivalent to 180 degrees. Angle 3 is 64 degrees.

Then you add 64 and 52 then subtract that sum by 180 because the measure of a triangle equals 180 degrees.

64+52=116
180-116=64

Therefore angle 1 is 64 degrees

Hope this helps :)

Answer:

I solved it for u!

Hope it helps

Step-by-step explanation:

Another way, it an isosceles triangle so the base will be same, so angle 3 and angle 1 will be same after u find angle 3, then angle 1 will be equal to it

So here angle 3 = 64°

So angle 1= 64°

A $50.00 pair of shoes is disconnected 20%. If sales tax is 8%. What is the amount of tax paid

Answers

Answer:

i think 3.20

Step-by-step explanation:

im not sure

what's the quotient of 35.86÷2.2​

Answers

Answer:

The answer to your question is 16.3.

The area of a square mural pointed on the side of a building is 110 square feet. What is the best estimate of the side length of the mural?

A.10 Feet
B.10.2 Feet
C.10.5 Feet
D.10.8 Feet

Answers

Answer:

C

Step-by-step explanation:

Area of a square equals to the square of its side, therefor the side of a given area for a square is the square root of the area.

[tex]A = a^{2}\\a = \sqrt{A}\\a = \sqrt{110} = 10.48 ft[/tex]

Type in two factors of 26 other than 1 and 26.

Type the factors in the increasing order

Answers

Answer:

1 - 26

2 - 13

3 - n/a

4 - n/a

5 - n/a

6 - n/a

7 n/a

8 n/a

9/10/11/12 - all n/a

13 is the last number

Step-by-step explanation:

Answer:

2 and 13

Step-by-step explanation:

3^(4x-5) = (1/27)^(2x+10) show your work

Answers

Answer:

3^4x-5=1/27^2x+10

We move all terms to the left:

3^4x-5-(1/27^2x+10)=0

Domain of the equation: 27^2x+10)!=0

x∈R

We get rid of parentheses

3^4x-1/27^2x-10-5=0

We multiply all the terms by the denominator

3^4x*27^2x-10*27^2x-5*27^2x-1=0

Wy multiply elements

81x^6-270x^2-135x^2-1=0

We do not support expression: x^6    

   

Step-by-step explanation:

A line perpendicular to y=2/5x+1

Answers

Answer:

        y = -⁵/₂x + b

Step-by-step explanation:

y=m₁x+b₁   ⊥   y=m₂x+b₂   ⇔    m₁×m₂ = -1

{Two lines are perpendicular if the product of theirs slopes is equal -1}

y = ²/₅x + 1    ⇒     m₁ =  ²/₅

²/₅m₂ = -1        ⇒   m₂ = -⁵/₂

So, any line with slope m =  -⁵/₂ will be perpendicular to y = ²/₅x + 1  

Pls help?!?!?! 10 points

Answers

Answer:

I solved it for u!

Hope ot helps!!!

NEED HELP NOW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Factor completely 5x2 − 5x − 100.

Answers

Answer:

5(x - 5)(x + 4)

Step-by-step explanation:

Given

5x² - 5x - 100 ← factor out 5 from each term

= 5(x² - x - 20) ← factor the quadratic

Consider the factors of the constant term (- 20) which sum to give the coefficient of the x- term (- 1)

The factors are - 5 and + 4, since

- 5 × 4 = - 20 and - 5 + 4 = - 1, then

x² - x - 20 = (x - 5)(x + 4) and

5x² - 5x - 100 = 5(x - 5)(x + 4)

Answer:

Step-by-step explanation:

here you go mate

step 1

5x2 − 5x − 100  equation

step 2

5x2 − 5x − 100  factor

5x^2 - 5x - 100 = 5

answer

5(x+4)(x-5)

I am giving all my final points for this one please answer correctly! and thank you

Answers

Answer:

D.

Step-by-step explanation:

You can see that the first value(initial) of y is 20 and the difference of the preceding values is 10 but it is decreasing thus -10


Enter your answers in the boxes.
m =

Answers

Answer:

m = [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

A( [tex]x_{1}[/tex] , [tex]y_{2}[/tex] )

B( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

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

~~~~~~~~~~

(0, 2)

(7, 7)

m = [tex]\frac{7-2}{7-0}[/tex] = [tex]\frac{5}{7}[/tex]

Solve by using substitution
x=3y-1
x+2y=9

Answers

Answer:

x=3y−1x=3y-1

x+2y=9x+2y=9

Replace all occurrences of xx with 3y−13y-1 in each equation.

Tap for fewer steps...

Replace all occurrences of xx in x+2y=9x+2y=9 with 3y−13y-1.

(3y−1)+2y=9(3y-1)+2y=9

x=3y−1x=3y-1

Add 3y3y and 2y2y.

5y−1=95y-1=9

x=3y−1x=3y-1

Solve for yy in the first equation.

Tap for fewer steps...

Move all terms not containing yy to the right side of the equation.

Tap for fewer steps...

Add 11 to both sides of the equation.

5y=9+15y=9+1

x=3y−1x=3y-1

Add 99 and 11.

5y=105y=10

x=3y−1x=3y-1

Divide each term by 55 and simplify.

Tap for fewer steps...

Divide each term in 5y=105y=10 by 55.

5y5=1055y5=105

x=3y−1x=3y-1

Cancel the common factor of 55.

Tap for fewer steps...

Cancel the common factor.

5y5=1055y5=105

x=3y−1x=3y-1

Divide yy by 11.

x=5,y=2

Step-by-step explanation:

please mark me as brainliest thank you

The area of a TV screen is 576 square
inches. If the width of the screen is
32 in., what is the height?

Answers

Answer:

18 inches, assuming that the height is the length of the TV screen.

Step-by-step explanation:

First off, the shape of a TV screen is a rectangle.

To get the area of a rectangle, the equation would be:

H * W = A

where H = height, W = Width, and A = area.

If we pluck in the values given in the question, we get:

H * 32 = 576

To find out H, we have to get rid of the 32.

To do that, we divide both sides by 32.

Therefore, the equation is now:

H = 18.

Thus, the height of the TV screen is 18 inches.

Answer: h = 18 inches

Step-by-step explanation:

Monica swims the 200, 400, and 1,000 meter freestyle swimming events. At the last swimming meet she swam the 200m in 1 minute 4 seconds, 400m in 2 minutes 31 seconds, and the 1,000 meter in 7 minutes 11 seconds. What were her average speeds in all these events (meters/second)?

Answers

Answer:

a) 200 meters = 3.125 meters/seconds

b) 400 meters = 2.649 meters per second

c ) 1000 meters = 2.320 meters per second

Step-by-step explanation:

The formula for Average speed = Distance/ Time

Monica swims the 200, 400, and 1,000 meter freestyle swimming events.

We are to calculate: average speeds in all these events (meters/second).

At the last swimming meet she swam

For the 200m

Time 1 minute 4 seconds

60 seconds = 1 minutes

Hence, Time = 60 + 4 = 64 seconds.

Average speed = 200m/64 seconds

= 3.125 meters/seconds

For 400m

Time = 2 minutes 31 seconds

1 minute = 60 seconds

2 minutes = 60 × 2 = 120 seconds

Total time = 120 + 31 seconds = 151 seconds

Hence, Speed = 400m/151 seconds

= 2.649 meters per second

For 1,000 meter

Total time = 7 minutes 11 seconds.

1 minute = 60 seconds

7 minutes = 60 × 7 = 420 seconds

Total time = 420 + 11 seconds = 431 seconds

Hence, Speed = 1000m/431 seconds

= 2.3201856148 meters per second

Approximately = 2.320 meters per second

Therefore her speed were

a) 200 meters = 3.125 meters/seconds

b) 400 meters = 2.649 meters per second

c ) 1000 meters = 2.320 meters per second

Answer:

3.125m/s

2.469 m/s

2.320 m/s

Step-by-step explanation:

Average speed = total distance / total time

60 seconds = 1 minute

Converting minute into second = (1 x 60) + 4 = 64 seconds

(2 x 60) + 31 = 151 seconds

(7 x 60) + 11 = 431 seconds

Average speed = 200 meters / 64 seconds = 3.125m/s

Average speed = 400 meters / 151 seconds = 2.469 m/s

Average speed = 1000 meters / 431 seconds = 2.320 m/s

Solve for x
2(x + 4) = -6
x=

Answers

Answer:

Step-by-step explanation:

here you go mate :)

step 1

2(x + 4) = -6  solving for x

step 2

2(x + 4) = -6  simplify by distributing

2x+8=-6

step 3

2x+8=-6  subtract 8

2x=-14

step 4

2x=-14  look for the number that can divide them both like 2

2x/2=-14/2

answer

x=-7

What is the value of 1 − 2sin2(105°)?


a Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction

b Negative one-half

c One-half

d StartFraction StartRoot 3 EndRoot Over 2 EndFraction

Answers

Answer:

D. d StartFraction StartRoot 3 EndRoot Over 2 EndFraction

Step-by-step explanation:

What is the value of 1 − 2sin^2(105°)?

Given the expression

1 − 2sin²(105°)

= 1 - 2(sin105)²

= 1 - 2(0.9659)²

= 1 - 2(0.9330)

= 1 - 1.8660

= 0.8660

0.8660 can also be expressed as √3/2

Hence  1 − 2sin²(105°) is  √3/2

Answer: D

Step-by-step explanation:

It IS sqrt3/22

hi, can you please solve that ?

Answers

Answer:

A.

Step-by-step explanation:

You need to solve for p on both inequalities.

4 ≤ p - 8

12 ≤ p

p - 14 ≤ 2

p ≤ 16

This means that p is greater than or equal to 12 but less than or equal to 16.

12 ≤ p ≤ 16

Therefore, the answer is A.

The answer is A :)

-hope it helped

8 1/3 - 4 3/4 I will reward brainlyest

Answers

Answer:

The answer is 3 7/12 Hope this helps :)

Step-by-step explanation:

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