how do you do this? appreciated for your help

Given info:- X = √(4-√7) and Y = √(4+√7)

Find the value of [(X-Y)/√3]²+(X²Y+XY²)²+(X+Y)²?

Explanation:-

Given that:

X = √(4-√7)

It can be written as

On multiplying and dividing by 2 in the squre root

⇛ X = √[2{(4-√7)}/2]

⇛ X =√[(8-2√7)/2]

⇛ X =√[{(7+1)-2√7{/2]

⇛ X =√[{(√7)²+(√1)²-2(√7)(√1)}/2]

It is in the form of a²-2ab+b²

Where , a = √7 and b = √1

⇛X = √[{(√7-√1)}²/2] [∵(a-b)² = a²-2ab+b²]

⇛ X = (√7-√1)/√2

⇛ X = (√7-1)/√2 — — — — Eqⁿ(1)

and

Y = √(4+√7)

It can be written as

On multiplying and dividing by 2 in the squre root

⇛ Y = √[{2(4+√7)}/2]

⇛ Y =√[(8+2√7)/2]

⇛ Y =√[{(7+1)+2√7}/2]

⇛ Y =√[{(√7)²+(√1)²+2(√7)(√1)}/2]

It is in the form of a²+2ab+b²

Where , a = √7 and b = √1

⇛Y = √[{(√7+√1)}²/2] [∵(a+b)² = a²+2ab+b²]

⇛ Y = (√7+√1)/√2

⇛ Y = (√7+1 )/√2 — — — — Eqⁿ(2)

On adding Eqⁿ (1) & Eqⁿ(2)

→ X+Y = (√7-1)/√2+(√7+1)/√2

→ X+Y = (√7-1+√7+1)/√2

→ X+Y = (2√7 )/√2

→ X+Y = (√2×√2×√7)/√2

→ X+Y = √2×√7

→ X+Y = √14 — — — — Eqⁿ(3)

On Subtracting Eqⁿ(2) from Eqⁿ(1)

→ X-Y =[(√7-1)/√2]-[(√7+1)/√2]

→ X-Y =[ (√7-1 )-(√7+1)]/√2

→ X-Y = (√7-1-√7-1)/√2

→ X-Y = (-1-1)/√2

→ X-Y = -2/√2

→ X-Y = -(√2×√2)/√2

→ X-Y = -√2 — — — — Eqⁿ(4)

On multiplying Eqⁿ(1)& Eqⁿ(2)

→ XY = [(√7-1)/√2][(√7+1)/√2]

→ XY = (√7-1)×(√7+1)/(√2×√2)

→ XY = [(√7)²-(1)²]/(2) [∵(a+b)(a-b) = a²-b²]

→ XY = (7-1)/2

→ XY = 6/2

→ XY = 3 — — — — — Eqⁿ(5)

Now,

The value of [(X-Y)/√3]²+(X²Y+XY²)²+(X+Y)²

It can be written as

⇛[(X-Y)²/3] + [ XY(X+Y) ]²+(X+Y)²

From Eqⁿ(3), Eqⁿ(4)& Eqⁿ(5)

⇛ [(-√2)²/3] + [ 3(√14)]²+(√14)²

⇛ (2/3) + (9×14)+(14)

⇛ (2/3)+(126)+(14)

⇛ (2/3)+140

⇛ [2+(3×140)]/3

⇛(2+420)/3

⇛ 422/3

Therefore, the value of [(X-Y)/√3]²+(X²Y+XY²)²+(X+Y)² is 422/3.

If you have any doubt, then you can ask me in the comments.

Answer: y=9

Step-by-step explanation:

both points have 9 as the y coordinate

Answer:

27

Step-by-step explanation:

Answer:

x = 2

y = -2

Step-by-step explanation:

N.B. Assuming the first equation is actually 3x + 4y = -2

The elimination method is an incredibly useful tool used to save large amounts of time when working with small systems of equations.

First, set one variable in the top equation to have an equal coefficient as that same variable in the bottom equation.

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

Then, you are left with this.  Simply subtract the equations.

9x + 12y = -6

9x - 10y = 38

0  + 22y = -44

Then, simply solve

y = -2

9x + 20 = 38

9x = 18

x = 2

Hope it helps :) and let me know if you want me to elaborate.

Answer:

¡¡ Only

Step-by-step explanation:

-8-2x < - 4

-2x < - 4+8

-2x < 4

x > - 2

Answer:

19 houses

Step-by-step explanation:

90*(2/5)=36

90-36=54

54*(2/3)=37

54-37=19

Answer:

116°

Step-by-step explanation:

Interior angles in a triangle are added up to 180°.

Therefore,

(14x + 4)° + (5x - 1)° + (2x + 9 )° = 180°

Now you can solve this equation and find the value of x.

[tex](14x + 4) + (5x - 1) + (2x + 9 ) = 180[/tex]

[tex]14x+4+5x-1+2x+9=180[/tex]

[tex]14x+5x+2x+4-1+9=180[/tex]

[tex]21x+12=180[/tex]

[tex]21x=180-12[/tex]

[tex]21x=168[/tex]

[tex]\frac{21x}{21}= \frac{168}{21}[/tex]

[tex]x=8[/tex]

Now let's find the value of angle A

14x + 4

14 × 8 + 4

116°

Answer:

A≈78.54in²

Step-by-step explanation:

Can I have brainliest pls?

Answer:

5/16

Step-by-step explanation:

Im guessing your asking for the recipricol of 3 1/5

Turn to improper fraction, 16/5

recipricol means to flip so it's 5/16

Answer:

A: 720 miles

Step-by-step explanation:

Since in 2 hours he drives 120 miles we can calculate the rate for 1 hour by diving the miles by 2

1 hour he will have driven 60 miles

Since we are looking for how much would be driven in 12 hours we multiply 60 by 12. Giving us 720 miles in 12 hours

Answer:

1. 40/8 = 5

2. 3x5 : 5x5

3. 15:25

There are 15 boys to 25 girls in the class

Step-by-step explanation:

total cost of the hotels is 2,296

Answer:

hahshdbdndjksosondndndud

Answer:

No, only for right angle Δ

Step-by-step explanation:

It is only used for right angle triangles

Answer:

B) CD

Step-by-step explanation:

Perpendicular means a line that bisects the other at 90°.

In this case, you are trying to find a perpendicular line to line BC, which can be two choices, AB & DC.

In this case, B) CD is your answer, as it is the only one that shows up (AB does not).

~

Answer:

segment CD

Step-by-step explanation:

Perpendicular segments form a 90 degree angle (aka right angle). Segment BC appears to be perpendicular to both AB and CD. I use the phrasing "appears to be" since it's not entirely clear if they actually are perpendicular. The use of a square angle marker would indicate the segments form a 90 degree angle. Such a symbol is missing.

Hope it help and if it its correct please give brainliest  

Stay Safe and healthy

Thank You

Answer:

2.50

Step-by-step explanation:

If 4= $5.00

then divided 5.00 by 4=1.25

so 1 = 1.25

1.25x2=2.50

Therefore 2 tastykake snack cakes = $2.50

Answer:

The answer is 2.5

Step-by-step explanation:

5 divided by 4 = 1.25

1.25 times 2 = 2.5

brainliest :)

Answer:

[tex]T(2,4) and U(11,13)[/tex]

Step-by-step explanation:

Answer:

-3 ≤ x < 2

Step-by-step explanation:

Answer:

x=3 and y= 4 / 3 (Fraction)

Step-by-step explanation:

Substitute x for 6y-5.

2(6y−5)−3y=2

Add 6y and 3y, and multiply 5 by 2/Simplify the equation.

9y−10=2

Add  10 to both sides, and then divide each side by 9.

9y−10+10=2+10

9y / 9 = 12 / 9

y = 4/3.

Repeat the process but replace y with 4/3!

Answer:

x=3

y= 4/3

Step-by-step explanation:

2(6y-5)-3y=2

y= 4/3

x=6x 4/3-5

x=3

Answer:

f(t) = 80 + 120 e^(-0.08 t)

Step-by step explanation:

The exponent is negative, so this is an example of exponential decay.  As t increases, the exponent becomes more and more negative.  So e^(-0.08 t) gets closer and closer to 0.  Meaning f(t) gets closer and closer to 80.

Answer: you can use a calculator, -0.75

Step-by-step explanation:

-2+-8+9

The + and - make a - so you can simplify to

-2-8+9

-1x3

-3/4

Answer:

20 feet

Step-by-step explanation:

The area formula is lw=A, where l is the length, w is the width, and A is the area. So, plug in the known variables. This creates the equation l15=300. Then, solve for l by dividing both sides by 15. Therefore, l=20. You can check your answer by plugging in all of the variables to create the equation 20*15=300. This is a true statement, thus 20 feet must be the correct length.

Answer:

1

2

3

4

5 6 7 8 9

6

7

8

9

Step-by-step explanation:

thats how you do it : ))))

Answer:

$180

Step-by-step explanation:

simple interest means that interest is paid every year on the original $200

To find 3% of 200, you multiply 200(.03) = $80.

$200(3)=$60

Since the interest is the same, 3(60) = $180

Hope this helps

Answer:

You can use the model to show the fractions alongside each other.

Step-by-step explanation:

Answer:

It is 0.8 + n = 4.5 that is the right answer

Answer: 0.8 plus n equals 4.5

Step-by-step explanation:

Answer:

133.5

An easy way of doing this is to ignore the decimal so consider it as 89 instead because 0 is insignificant. So do 89x15 = 1335 we know that 8.90 has 1 decimal place because 0 is not significant so you just add 1 decimal place which becomes 133.5