If
[tex] \frac{3 + \sqrt{2} }{3 - \sqrt{2} } [/tex]
=a+b×
[tex] \sqrt{2} [/tex]
, find the values of a and b.

With Full Workings.
Please hurry!​

Answers

Answer 1

Answer:

The answer is

[tex] a = \frac{11}{7} \\ b = \frac{6}{7} [/tex]

Step-by-step explanation:

[tex] \frac{3 + \sqrt{2} }{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} } \\ = \frac{9 + 3 \sqrt{2} + 3 \sqrt{2} + 2}{9 - 3 \sqrt{2} + 3 \sqrt{2} - 2 } \\ = \frac{11 + 6 \sqrt{2} }{7} \\ = \frac{11}{7} + \frac{6}{7} \sqrt{2} \ [/tex]

In comparison

Then

[tex]a = \frac{11}{7} \\ b = \frac{6}{7} [/tex]


Related Questions

Which classification is most precise for each figure?

A. Quadrilateral
B. Kite
C. Parallelogram

PLEASE ANSWER THIS QUESTION AND I WILL GIVE YOU 20 POINTS AND MAKE YOU BRAINIEST!!!!

Answers

Answer:

c. parallelogram

Step-by-step explanation:

The given figure is a parallelogram.

What is Quadrilateral?

A quadrilateral is a four-sided polygon, having four edges and four corners.

In the given quadrilateral, opposite sides are parallel.

Opposite sides are congruent.

Opposite angles are congruent.

Same-Side interior angles are supplementary.

Each diagonal of a parallelogram separates it into two congruent triangles.

The diagonals of a parallelogram bisect each other.

Hence, the given figure is a parallelogram.

To learn more on Quadrilateral click:

https://brainly.com/question/29934440

#SPJ2

Are these triangles similar? Why?

A. Yes, SSS~ Postulate

B. Yes, SAS~ Postulate


C. Yes, AA~ Postulate


D. No, they are not similar.

Answers

it looks like yes, SSS

Answer:

Step-by-step explanation:

<Q is common to both triangles.

130 / 40 = 3.25

Call DQ = x

40/130 = x / (x + 72)       Cross multiply

40*(x + 72) = 130*x

40x + 2880 = 130x      Subtract 40 x from both sides

2880 = 90 x                 Divide by 90

x = 32

(72 + 32)/32 = 104/32 = 3,25

The ratios are the same.

Therefore the triangles are similar by SAS

Please help me answer this last question.
The function shown describes f(x), the cost (in hundreds of thousands of dollars) of making x bicycles (in thousands).

f(x)= 1.25 + 0.35x
B. What is the cost to make 4,000 bicycles? Show your work.

Answers

Answer:

1401.25

Step-by-step explanation:

F(4000)= 1.25+0.35(4000) = 1401.25

A cylinder has volume 45 pi and radius 3. What is its height?

Answers

Answer:

Height = [tex]\frac{5}{\pi }[/tex]

Step-by-step explanation:

V = Volume

r = Radius

h = Height

[tex]h=\frac{V}{\pi *r^{2} }[/tex]

[tex]h=\frac{45}{\pi *3^{2} }[/tex]

[tex]h=\frac{5}{\pi}[/tex]

I hope this helps

Mrs. Duncan pours
8.4 liters of punch
into 3 serving
bowls. If she
poured an equal
amount of punch
into each bowl,
how many liters of
punch are in each
bowl?

Answers

Answer:

divide 8.4 with 3

the answer is 2.8

8.4 into 3 bowls
8.4 divided into 3=2.8l

Solve for x in the diagram below.
(2x + 45)°

Answers

Answer:

x=45 (degrees)

Step-by-step explanation:

(2x+45)+x= 180 (linear pair)

3x+45=180

3x=180-45

3x=135

x=45 (degrees)

Answer:

x=45  

Step-by-step explanation:

(2x+45)+x= 180                                     (linear pair)

3x+45=180

3x=180-45

3x=135

x=45

On a test Darra scored 36 points. If there were 40 points posible what grade did she get?

Answers

Answer:

90%/A

Step-by-step explanation:

if this helped please mark brainiest.

Answer:

She got a 90%

Step-by-step explanation:

You have to divide the number you got with the number that you can get out of. (36/40=0.9) and then convert the decimal to a percentage

agree or desagree ? ..........​

Answers

Answer:

Disagree.

If you rotate the octagon 90° it will look the same.

good luck, i hope this helps :)

Answer:

Disagree

Step-by-step explanation:

If you have any shape and you rotate it 90 degrees, it moves down and to the right, not onto itself.

Challenge: Perla worked 4 hours at her job on Saturday and then spent $12.75, in the supermarket, on her way home. She worked 5 hours on Sunday and earned 1.5 times her normal hourly rate because it was a holiday. She spent $8.50, at the florist, on her way home on Sunday. If Perla had $70.75 after her spending, determine her normal hourly rate.
Write and solve an equation.
Note:
decide what your variable represents (example: x is number of hours)
only use 1 variable.
Work backward to check your final answer

Answers

W=normal hourly wage

4W-12.75+5*1.5W-8.50=70.75

4W-12.75+7.5W-8.50=70.75

11.5W-21.25=70.75

11.5W=92

W=8

Normal hourly rate is $8/hour

Check

32-12.75+60-8.50=70.75


Simplify the expression ​

Answers

Answer:(6-[tex]\sqrt{7}[/tex][tex].^{2}[/tex]

Step-by-step explanation:Ignore the point, put it withou the point

sjsjsnbebdbwhhahshhwhwhw

If Amy has two apples and drops one, how many does she have now?

Answers

She still has two since she only dropped it and hasn’t eaten it yet

What is the answer to -2 3/4 ÷ 5/-9 ??

Answers

Answer:23 /180

Step-by-step explanation:

−23/ 4 /5 /−9=  23 /180

Answer: 99/20

Step-by-step explanation:

-2 3/4 / 5/-9

-11/4/5/9

11/4*5/9

99/20

Simplify. 1.5m ^7(-4m ^5)^2


A.-6m^14

B.24m^14

C.12m^17

D.24m^17

Answers

Answer:

D. 24m^17

Step-by-step explanation:

Answer:

D. 24m^17

Step-by-step explanation:

Tell whether each proportion is true or false and prove your answer.

Answers

Answer:

the proportion is false

Step-by-step explanation:

5.5/7.5 = 11/15

3.5/7= 1/2

Solve 5(11x - 2) = 155

Answers

Answer:

5(11x-2) = 155

55x - 10 = 155

55x = 165

x = 165/55

x = 3

Step-by-step explanation:

hope it helps

What’s the correct answer

Answers

Answer:

I guess y is also 0 not sure

It’s called the origin

Find all the real solutions of x^3 – 2x^2 – 5x + 6 = 0.

Answers

Answer:

x=1 or x=-2 or x=3

Step-by-step explanation:

your answer is most likely one of the three

sorry if its incorrect :9

Please answer this !!!!!!!!
Then maybe you will be the Brainlist!!!!

Answers

Answer:

A. 60

B. 50

C. 5

Hope this helped :3

ANSWERS

A THE INITIAL SPEED OF CAR IS O KM/H

B THE HEIGEST SPEED OF VAN IS 50 KM/H

C FOR 10 sec THE VAN IS TRAVELING FASTER THAN CAR

PLEASE MARK ME AS BRAINLIEST

Find the degree of the monomial.
6r2n4t

Answers

Answer:

idek

Step-by-step explanation:

Write about a
way
how
you have used mathematics inside or outside of school. *


Plsss help it is important

Answers

Answer:

I have used mathematics at the store when i am buying something.

Step-by-step explanation:

HELP ME 7th grade math
What is the total amount of cardboard needed to manufacture this polyhedron? (Find the surface area)
​Plz answer

Answers

the answer is 62.715 :)

Can someone please help me ​

Answers

Answer: 7 root 3 or simplified = 12.12435565 = 12.12 (2 d.p)

Step-by-step explanation:

tan(30) = 7 / x

x= 7/ tan(30)

x= 7 root 3

What inverse operation should be used to isolate the variable in the equation k − 9 = 10?

Answers

Answer:

+9

Step-by-step explanation:

k-9=10

the opposite of -9 is +9

k=19

hope this helps x

brainliest plzz

Help with belll ringer !!!

Answers

Answer:13 inches

Step-by-step explanation:

0 Example: Loan payments of $400 due 95 days ago and $700 due today
are to be repaid by a payment of $600 thirty days from today and the
balance in 125 days. If money is worth 6% and the agreed focal date is
125 days from today, what is the size of the final payment?​

Answers

Answer:

[tex]X=\$519.48[/tex]

Step-by-step explanation:

From the question we are told that

Loan 1 [tex]X_1=\$400[/tex]

Loan 1 due [tex]t_1=95days[/tex]

Loan 2 [tex]X_2=\$700[/tex]

Loan 2 due[tex]t_2=0days[/tex]

Payment [tex]Y=\$600[/tex]

Worth of money [tex]w=6\%[/tex]

Payment due [tex]t=30days[/tex]

Focal date [tex]t_f=125days[/tex]

Generally [tex]\$400[/tex] was due 95days ago

Therefore

[tex]125+90=220days[/tex](total days to consider)

Therefore

[tex]300+400 =700[/tex] is due today

125days left

Given

600 due in 30days

[tex]125-30=95days[/tex]

Generally the Final payment is mathematically given by

[tex]400(1+ 0.06*\frac{220}{365} ) + 700(1+0.06*\frac{125}{365} )=600(1+0.06*\frac{95}{365} )+X[/tex]

[tex]X=1128.9692 - 609.3698[/tex]

Therefore the

[tex]X=\$519.48[/tex]

Lin is solving the inequality 15−x<14. She knows the solution to the equation 15−x=14 is x=1 How can Lin determine whether x>1 or x<1 Is the solution to the inequality?

Answers

Answer:

x > 1

Step-by-step explanation:

Given the inequality ; 15 - x < 14

Since the solution to the equation 15−x=14 is x=1 ;

Then we obtain the value of x for which the inequality expression is true :

If x > 1 ; take x = 2

15 - 2 < 14

13 < 14 (true)

If x < 1 ; take x = 0

15 - 0 < 14

15< 14 (not true)

Hence, solution is x > 1

20 subtracted from the product of x and 10

Answers

Answer:

10x-20

Step-by-step explanation:

x times 10 is 10x

10x - 20 = 10x - 20

in conclusion you cannot subtract a number from a variable

20 subtracted from the product of x and 10?

answer : 10x-20

5 The area of a rectangular lawn is 255 m². If its length is 15 m, find its perimeter.​

Answers

Area of a rectangular lawn = l×b

255=15×x

Hence the breadth is 17 m

Hence perimeter =2(l+b)=2(15+17)=64

I do not know how to find the x in this situation can anyone help?

Answers

Answer and Step-by-step explanation:

Essentially, the figure FEHG got scaled by a factor of 1.5, and turned into BADC

So 2.4 times 1.5 is 3.6

3.6 = x

Hope this helps! #teamtrees #WAP (Water And Plant)

Answer:

The x would be 3.6

Step-by-step explanation:

If you see the relation or ration between the ABCD triangle and the EFGH then we can see that the side 2 is multiplied by 1.5 to get to 3. so you do the same thing to 2.4 and multiple that by 1.5 and 3.6.

Help I’m confused big points to who can solve this

Answers

Answer:

n = 2

Step-by-step explanation:

Given nx + y = 4, if we rearrange in slope-intercept form: y = -nx + 4

This means that the y-intercept is 4. Point "A" is the y-intercept, which would make OA = 4, and OB = 1/2(4) = 2.

We can now solve for n. The slope here is "-n", also represented by rise/run or OA/-OB = 4/-2 = -2.

-n = -2,

n = 2

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