5/√2+9/√8-2√50+√32 rationalise the denominator and simplify

Answers

Answer 1

The simplification of the expression is  [tex]\frac{15\sqrt{2} }{4}[/tex]

How to rationalize the denominator

First, find the factors of the number that ahs square root

Given,

= [tex]\frac{5}{\sqrt{2} } + \frac{9}{\sqrt{6} } - \frac{2}{\sqrt{50} } + \sqrt{32}[/tex]

Multiply the numerators by the surd of the denominators

= [tex]\frac{5 *\sqrt{2} }{\sqrt{2}*\sqrt{2 } } + \frac{9 *\sqrt{8} }{\sqrt{8}* \sqrt{8} } - \frac{2 *\sqrt{50} }{\sqrt{50 * \sqrt{50} } } + \sqrt{32}[/tex]

Multiply through and find their square root

= [tex]\frac{5\sqrt{2} }{2} + \frac{18\sqrt{2} }{8 } - \frac{10\sqrt{2} }{50} + 16\sqrt{2}[/tex]

To simply, we have

= [tex]\frac{5\sqrt{2} }{2}+ \frac{9\sqrt{2} }{4} + \frac{1\sqrt{2} }{5} + 16\sqrt{2}[/tex]

Find the LCM

= [tex]\frac{10\sqrt{2} + 45\sqrt{2}+ 4\sqrt{2} + 16\sqrt{2} }{20}[/tex]

Add through

= [tex]\frac{75\sqrt{2} }{20}[/tex]

= [tex]\frac{15\sqrt{2} }{4}[/tex]

Thus, the simplification of the expression is  [tex]\frac{15\sqrt{2} }{4}[/tex]

Learn more about surds here:

https://brainly.in/question/4594146

#SPJ1


Related Questions

Mackenzie is designing a rectangular greenhouse. Along one wall is a 7-foot storage area and 5 sections for different kinds of plants. On the opposite wall is a 4-foot storage area and 6 section for plants. All the plant sections are equal length. What is the length of the wall?

Answers

Answer:

3 ft

Step-by-step explanation:

4 + 6x = 7 + 5x

6x - 5x = 7 - 4

x = 3

Câu 1: Giá trị

2
3
2020 -5 lim
- 2020
n
n n
bằng:

A.
2.

B.
.

C.
0.

D.
2
.
3

Answers

Answer:

i dont understan your language plz speak in englosh

Zoe and Hanna share tips in the ratio 3:7
Last week Zoe received £24
How much did Hanna receive last week?

Answers

Answer:

56

Step-by-step explanation:

Zoe : hanna

3         7

Zoe got 24

3*8 = 24

so multiply each side by 8

Zoe : hanna

3*8         7*8

24           56

Hanna got 56

Joe receives a cake for his birthday. He eats $\frac{1}{4}$ of the cake on the first day. On the second day, he eats $\frac{3}{4}$ of the amount of cake that is left after the first day. What fraction of a whole cake is left for Joe to eat on the third day

Answers

Answer:

3 / 16

Step-by-step explanation:

Let The total amount = x

Fraction eaten on first day = 1/4x

Fraction left = x - 1/4x = 3/4x

Fraction of amount left eaten on second day = 3/4 of 3/4x

3/4 * 3/4x = 9/16x

Fraction left :

3/4x - 9/16x = (12x - 9x) /16 = 3/16x

Hence, fraction left = 3/16

GIVE FULL STEP BY STEP OF THIS MATHS WORD PROBLEM
Sohanlal is a gardener. He is paid ₹160 daily, find how much money will he
get in the month of September?

Answers

Answer:

Step-by-step explanation:

days in september=30

salry paid per day=Rs.160

salary paid in 30 days=160×30=Rs.4800

Answer:

4800

Step-by-step explanation:

In the month of September there are only 30 days. So assuming Sohanlal works the entire month of September we will multiply how much he makes daily which is 160 times the amount of days he works which is 30. this will look like this:

160 × 30 = 4800

The ages of several trees in a park are shown below:
2 years, 28 years, 2 years, 20 years, 22 years
What is the mean age of these trees?

56 years
12 years
14.8 years
26 years

Answers

Answer:

C or 14.8

Step-by-step explanation:

You just find the mean.

Arrange the numbers, add them then divide by the amount of numbers.

Hope it helps c:

Find the distance between the
following points using the
Pythagorean theorem: (5, 10)
and (10, 12)

Answers

Answer:

[tex]\displaystyle d = \sqrt{29}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Step-by-step explanation:

*Note:

The distance formula is derived from the Pythagorean Theorem.

Step 1: Define

Identify

Point (5, 10)

Point (10, 12)

Step 2: Find distance d

Substitute in points [Distance Formula]:                                                         [tex]\displaystyle d = \sqrt{(10 - 5)^2 + (12 -10)^2}[/tex][√Radical] (Parenthesis) Subtract:                                                                   [tex]\displaystyle d = \sqrt{5^2 + 2^2}[/tex][√Radical] Evaluate exponents:                                                                       [tex]\displaystyle d = \sqrt{25 + 4}[/tex][√Radical] Add:                                                                                                  [tex]\displaystyle d = \sqrt{29}[/tex]

the length of a rectangle is 8 cm longer than its width. find the dimensions of the rectangle if its area is 108cm
!!no links!!

Answers

Answer:

[tex]4+2\sqrt{31}\text{ by } -4+2\sqrt{31}[/tex]

Or about 15.136 centimeters by 7.136 centimeters.

Step-by-step explanation:

Recall that the area of a rectangle is given by:

[tex]\displaystyle A = w\ell[/tex]

Where w is the width and l is the length.

We are given that the length is 8 centimeters longer than the width. In other words:

[tex]\ell = w+8[/tex]

And we are also given that the total area is 108 square centimeters.

Thus, substitute:

[tex](108)=w(w+8)[/tex]

Solve for w. Distribute:

[tex]w^2+8w=108[/tex]

Subtract 108 from both sides:

[tex]w^2+8w-108=0[/tex]

Since the equation is not factorable, we can use the quadratic formula:

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

In this case, a = 1, b = 8, and c = -108. Substitute and evaluate:

[tex]\displaystyle \begin{aligned} w&= \frac{-(8)\pm\sqrt{(8)^2-4(1)(-108)}}{2(1)} \\ \\ &=\frac{-8\pm\sqrt{496}}{2}\\ \\ &=\frac{-8\pm4\sqrt{31}}{2} \\ \\ &=-4 \pm 2\sqrt{31} \end{aligned}[/tex]

So, our two solutions are:

[tex]w=-4+2\sqrt{31} \approx 7.136 \text{ or } w=-4-2\sqrt{31}\approx -15.136[/tex]

Since width cannot be negative, we can eliminate the second solution.

And since the length is eight centimeters longer than the width, the length is:

[tex]\ell =(-4+2\sqrt{31})+8=4+2\sqrt{31}\approx 15.136[/tex]

So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.

Simplify the variable expression by evaluating its numerical part.
p-7+56 - 12
A. p + 51
B. p+37
O c. p-51
D. p + 49

Answers

The answer to this is B. p+37

Ben is 4 times as old as Ishaan. 6 years ago, Ben was 6 times as old as Ishaan.
How old is Ishaan now?

Answers

Answer:

Ishaan is currently 15 years old.

Step-by-step explanation:

Let B represent Ben's current age and I represent Ishann's current age.

Ben is four times as old as Ishaan. In other words:

[tex]B=4I[/tex]

Six years ago, Ben was six times as old as Ishaan. In other words:

[tex]B-6=6(I-6)[/tex]

Solve for I. Substitute:

[tex](4I)-6=6(I-6)[/tex]

Distribute:

[tex]4I-6=6I-36[/tex]

Subtract 4I from both sides and add 36 to both sides:

[tex]2I=30[/tex]

And divide both sides by two. Hence:

[tex]I=15[/tex]

Ishaan is currently 15 years old.

Answer:

Age of Ishaan = 15 years

Step-by-step explanation:

Let Ishaan's age = x years

Age of Ben = 4 * x = 4x years

6Years ago:

Age of Ishaan = x - 6

Age of Ben = 4x - 6

6 years ago, Ben was 6 times as old as Ishaan

So, Age of Ben = 6 * Ishaan's age

     4x - 6 = 6 *(x-6)

4x - 6 = 6x - 36

Add 36 to both sides

4x - 6 + 36  = 6x  

4x + 30 = 6x

Subtract '4x' from both sides

30 = 6x - 4x  

30 = 2x

2x = 30

Divide both by 2 sides

x = 30/2

x = 15

What type of line is PQ¯¯¯¯¯¯¯¯?




A. median

B. angle bisector

C. side bisector

D. altitude

Answers

Answer:

angle bisector

Step-by-step explanation:

Since the line divided the top angle into two equal pieces we call this an angle bisector.

Dan invests £18790 into his bank account. He receives 5.9% per year simple interest. How
much will Dan have after 2 years? Give your answer to the nearest penny where appropriate.

Answers

Answer: £21007.22

Step-by-step explanation:

First, find the interest amount using the formula SI = (P × R × T) / 100.

SI = interest amount P = principle amount = £18790R = interest rate(in percentage) = 5.9T = time(in years) = 2

SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22

The total amount = principle amount + interest amount

= £18790 + £2217.22 = £21007.22

write the equation of the line that goes through points (0,4) (6,16)

Answers

Answer: Y= 2x

Step-by-step explanation:

Answer:

y=2x-4

Step-by-step explanation:

firstly find the gradient

m=y2-y1/x2-x1

16-4/6-0

12/6

m=2

then use the equation to find the answer

y-y1=m(x-x1)

y-4=2(x-0)

y-4=2x-0

y=2x-4

Complete the missing parts of the
table for the following function. (picture) please answer all asap

Answers

Answer:

x=-1  y = 1/3

x = 1  y = 3

x = 3  y = 27

Step-by-step explanation:

y = 3^x

Let x = -1

y = 3^-1 = 1/3^1 = 1/3

Let x = 1

y = 3^1 = 3

Let x = 3

y = 3^3 = 27

Câu 1: Trong các mệnh đề sau, mệnh đề nào là không đúng ?

A. Nếu a // b và (α) vuông góc a thì (α) vuông góc với b

B. Nếu (α) // (β) và a vuông góc với (α) thì a vuông góc với (β)

C. Nếu a và b là hai đường thẳng phân biệt và a vuông góc (α), b vuông góc với (α) thì a // b

D. Nếu a // (α) và b vuông góc a thì b vuông góc (α)

Answers

Answer:

Hey can you ask this question in English so I can no answer this question in English and then you can convert that my answer in your language as you're I'm Indian so I don't know this language

Step-by-step explanation:

Please don't you think that I'm doing this for points I think I should know this question so can you please answer this you're this and English

(x⁴ + 3x³ – 2x² + 5) + (2x⁴ – 5x³ + 4x – 15).

Answers

Answer:

[tex]\left(x^4+3x^3-2x^2+5\right)+\left(2x^4-5x^3+4x-15\right)[/tex]

[tex]=[/tex] [tex]x^4+3x^3-2x^2+5+2x^4-5x^3+4x-15[/tex]

[tex]=x^4+2x^4+3x^3-5x^3-2x^2+4x+5-15[/tex]

[tex]=x^4+2x^4-2x^3-2x^2+4x+5-15[/tex]

[tex]=3x^4-2x^3-2x^2+4x+5-15[/tex]

[tex]=3x^4-2x^3-2x^2+4x-10[/tex]

[tex]OAmalOHopeO[/tex]

Can you answer this math homework? Please!

Answers

Answer:

y + 2.3 = 0.45x

y = 0.45x - 2.3

-2y = 4.2x - 7.8

-2(0.45x - 2.3) = 4.2x - 7.8

-0.90x + 4.6 = 4.2x - 7.8

-0.90x - 4.2x = -7.8 - 4.6

-5.1x = - 12.4

x = -12.4 / -5.1

x = 2.4

y + 2.3 = 0.45x

y = 0.45(2.4) - 2.3

y = 1.08 - 2.3

y = -1.2

solution is : (2.4, - 1.2)

Step-by-step explanation:

The two lines intersect at answer A. (2.4, -1.2)

Explain the relationship of the meaning of the word isometric to the properties of an isometric or rigid transformation

Answers

Step-by-step explanation:

The iso parts of isometric means same, and It is similar becuase rigid trtransformation and the metric parts means measure. Basically isometric means same measure. Rigid transformation preserve "same measures" like angles and side lengths.

[tex]\text{Solve for 'x':}\\\\3(x+1)=12+4(x-1)[/tex]

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]x = -5[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\3(x+1)=12+4(x-1)\\----------\\\rightarrow 3x + 3 = 12 + 4x - 4\\\\\rightarrow 3x + 3 = 12 -4+4x\\\\\rightarrow 3x + 3 = 8 + 4x\\\\\rightarrow 3x + 3 = 4x + 8\\\\\rightarrow3x + 3 -3 = 4x + 8 - 3\\\\\rightarrow 3x = 4x + 5\\\\\rightarrow 3x - 4x = 4x - 4x + 5\\\\\rightarrow -x = 5\\\\\rightarrow \frac{-x=5}{-1}\\\\\rightarrow \boxed{x = -5}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

x=-5

Step-by-step explanation:

3(x+1)=12+4(x-1)

3(x+1)=8+4x

3x+3=8+4x

3x+3−4x=8

-x+3=8

-x=8-3

-x=5

-x(-1)=5(-1)

-x(-1)=-5

x=-5

How do you solve this problem?

Answers

9514 1404 393

Answer:

  -19.2

Step-by-step explanation:

Fill in the given values and do the arithmetic.

  [tex]\displaystyle x\ \blacksquare\ y=\frac{x}{y}-xy\\\\4\ \blacksquare\ 5=\frac{4}{5}-4\cdot5=0.8-20\\\\\boxed{4\ \blacksquare\ 5=-19.2}[/tex]

6. The right triangles ABC and DEF are
similar. The hypotenuse of AABC
measures 28 cm and the hypotenuse
of A DEF measures 7 cm. If one of the
legs of AABC measures 16 cm, what
does the corresponding leg of ADEF
measure?
F 1 cm
H 12 cm
G 4 cm
J 64 cm

Answers

Answer:

G. 4 cm

Step-by-step explanation:

28 divided by 7 equals 4.

So, 16 divided by 4 equals 4, which is the answer.

4 is the multiple that relates AABC to ADEF.

The table below represents the function f, and the following graph represents the function g.
*
-6
un
4
-3
-2.
-1
0
1
f(x) 8
-2
-8 -10
-8
-2
8.
22
у
4
12
6
- 2
2
4
6
2
-4
6
Complete the following statements.
The functions fand g have

Answers

The functions f and g have different axis of symmetry

The y-intercept of f is higher than the y-intercept of g

Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g

The known value in the question includes the following

The given table of f(x) and x, from which we have;

The point of the minimum value, which is the vertex = (-3, -10)

The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3

The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)

Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6

From the graph of g(x), we have;

The axis of symmetry is the line x = -3

The y-intercept = (0, -2)

Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3

Therefore, we have the correct options as follows;

The functions f and g have different axis of symmetry

The y-intercept of f is higher than the y-intercept of g

Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g

Learn more about parabola here;

https://brainly.com/question/22213822

geometry!!!!!!!!! helppp

Answers

Answer:

Solution given:

Centre (h,k)=(-6,-2)

end points are:

A[tex]\bold{(x_{1},y_{1})=(-1,-9) \:and \:B(x_{2},y_{2})=(-11,5)}[/tex]

Now

distance between A to M is:

AM=[tex]\sqrt{(h-x_{1})²+(k-y_{1})²}[/tex]

AM=[tex]\sqrt{(-6+1)²+(-2+9)²}=8.6[/tex]units

again

distance between B to M is:

BM=[tex]\sqrt{(h-x_{2})²+(k-y_{2})²}[/tex]

BM=[tex]\sqrt{(-6+11)²+(-2-5)²}=8.6[/tex]units

again

Since AM=BM=8.6units

so

M is the centre of the circle.:Yes

Please help me answer this question.

Answers

Answer:

total candy = 54 bags

y=17

x=37

Step-by-step explanation:

5x + 4y = 253

x-y = 20

x = 20+y

5(20+y) + 4y = 253

100 + 9y = 253

9y = 153

y=17

x=37

Please help. Somebody give an answer to this question please. I need a step by step explanation as well.

Answers

Answer:

15d² + 7d - 4

Step-by-step explanation:

Distribute

(5d + 4)(3d -1)

5d (3d - 1) + 4(3d - 1)

Distribute

15d² - 5d + 4(3d- 1)

Distribute

15d² - 5d + 12d- 4

Simplify

15d² + 7d - 4

ANSWER:
15d^2+7d-4

STEP BY STEP:
you can use F.O.I.L. to solve this (first,outer,inner,last)

first you multiply both of the first values in each set of parentheses, 5d and 3d to get 15d^2, then you multiply the terms on the outside, 5d and -1 to get -5d. then multiply the inner values, 4 and 3d to get 12d. because 12d and -5d are like terms, you combine them to get 7d. lastly, you multiply the last values in each parentheses, 4 and -1 to get -4

i need help ASAP please

Answers

Answer:

reflection over Y axis

Step-by-step explanation:

Answer:

I believe it is D) a reflection over the Y-axis

Step-by-step explanation

it is going over the Y-axis as if it is a sort of mirror, if it were going over the x-axis it would be flipped upside down, if it was A the shape would be going over the original shape. I don't know how to explain C. (I hope this helped and I hope it was correct lol)

The reliability coefficient of scores in an end of semester examination. If the variance of the exam score is 100. What is the standard error of measurement ?

Answers

Answer:

I Will explained you youuuuuu<uuuuuuuuuu

the polygons in each pair are similar. find the missing side length.​

Answers

Given:

The polygon in the given figure are similar.

To find:

The missing side length.​

Solution:

We know that the corresponding sides of similar figures are proportional.

The given polygons are similar, so the their corresponding sides are proportional.

[tex]\dfrac{x}{15}=\dfrac{32}{40}=\dfrac{32}{40}[/tex]

So, the missing values in the equation of proportion are 15, 40, 32 respectively.

On solving the above equation, we get

[tex]\dfrac{x}{15}=\dfrac{4}{5}=\dfrac{4}{5}[/tex]

[tex]\dfrac{x}{15}=\dfrac{4}{5}[/tex]

[tex]x=\dfrac{4}{5}\times 15[/tex]

[tex]x=12[/tex]

Therefore, the value of x is 12.

ahla
S : Assignment
乡,一石​

Answers

Answer

what's the question?

Step-by-step explanation:

looks like your question is missing information

Venn diagram of b union b​

Answers

Answer:

let b union b be

B={2,4,6,8} and B= {1,2,3,4,5}

then B union B = {1,2,3,4,5,6,8}

Step-by-step explanation:

Venn diagram of b union b is in the attachment

Hope it is helpful to you

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