Use the model to solve for x.

A) x = 2

B) x = 4

C) x = 8

D) x = 12

=========================================================

Work Shown:

A = 1+sqrt(2)

B = 1-sqrt(2)

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

Using A and B, let's add and subtract those values

A+B = (1+sqrt(2))+(1-sqrt(2))

A+B = 1+sqrt(2)+1-sqrt(2)

A+B = 1+1+sqrt(2)-sqrt(2)

A+B = 2

and

A-B = (1+sqrt(2))-(1-sqrt(2))

A-B = 1+sqrt(2)-1+sqrt(2)

A-B = 1-1+sqrt(2)+sqrt(2)

A-B = 2sqrt(2)

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

Next, square both sides of the A equation

A^2 = (1+sqrt(2))^2

A^2 = (1+sqrt(2))(1+sqrt(2))

A^2 = 1(1+sqrt(2))+sqrt(2)(1+sqrt(2))

A^2 = 1+sqrt(2)+sqrt(2)+sqrt(2)*sqrt(2)

A^2 = 1+2sqrt(2)+2

A^2 = 3+2sqrt(2)

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

Do the same for B

B^2 = (1-sqrt(2))^2

B^2 = (1-sqrt(2))(1-sqrt(2))

B^2 = 1(1-sqrt(2))-sqrt(2)(1-sqrt(2))

B^2 = 1-sqrt(2)-sqrt(2)-sqrt(2)*(-sqrt(2))

B^2 = 1-2sqrt(2)+2

B^2 = 3-2sqrt(2)

There's a bit of nice symmetry going on with A^2 and B^2, due to A and B having similar symmetric structures themselves.

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

Lets add A^2 to B^2

A^2+B^2 = (3+2sqrt(2)) + (3-2sqrt(2))

A^2+B^2 = 3+2sqrt(2) + 3-2sqrt(2)

A^2+B^2 = 3+3+2sqrt(2)-2sqrt(2)

A^2+B^2 = 6

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Now onto the final event

We'll use the difference of squares rule twice

Afterward, apply substitution using the previous sections above.

A^4 - B^4 = (A^2)^2 - (B^2)^2

A^4 - B^4 = (A^2-B^2)(A^2+B^2)

A^4 - B^4 = (A-B)(A+B)(A^2+B^2)

A^4 - B^4 = (2sqrt(2))(2)(6)

A^4 - B^4 = 2*6*2*sqrt(2)

A^4 - B^4 = 24*sqrt(2)

(1+sqrt(2))^4 - (1-sqrt(2))^4 = 24*sqrt(2)

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

To check this with your calculator, you can type in the following

(1+sqrt(2))^4 - (1-sqrt(2))^4 - 24*sqrt(2)

The result you should get should be 0, or very close to it

I'm using the property that if x = y, then x-y = 0.

Answer:

1. Add 4 to both sides. 3x-4+4=8+4

2. Divide 3 from both sides. 3x/3=12/3

3. Solution. x=4.

Step-by-step explanation:

Answer:

x = undefined

Step-by-step explanation:

Expand brackets

4x - 1 = 4x + 4

Rearrange and make like terms next to each other

4x - 4x = 4 + 1

0x = 5

x = 5/0

when 0 is the denominator the answer is undefined

Answer: from what i calculated there is no solution

Step-by-step explanation:

Answer:

[tex]\boxed { x > -1}[/tex]

Step-by-step explanation:

Solve the following inequality:

[tex]8x - 9 > - 17[/tex]

-Add [tex]9[/tex] to both sides:

[tex]8x - 9 + 9 > -17 + 9[/tex]

[tex]8x > -8[/tex]

-Divide both sides by [tex]8[/tex]:

[tex]\frac{8x}{8} > \frac{-8}{8}[/tex]

[tex]\boxed { x > -1}[/tex]

-The number line (graphed):

Answer:

I cant see

Step-by-step explanation:

Answer:

dont have an answer yet...question too small to see...

Step-by-step explanation:

Answer:

Step-by-step explanation:

23.74, .43, .2734, .0347, .0043

Answer:

we need to know what the question is.

Step-by-step explanation:

Answer:

10,500.93 feet

Step-by-step explanation:

From the question, we are told that Tom walks 3.2km every morning.

1 mile = 1.609km

1 mile = 5280 feet

Step 1

1.609km = 1 mile

3.2km = x mile

Cross Multiply

x mile × 1.609km = 3.2km × 1 mile

x mile = 3.2km × 1 mile/1.609.

= 1.9888129273 miles

1 mile = 5280 feet

1.9888129273miles = y

Cross Multiply

y = 1.9888129273 × 5280 feet/1 mile

= 10500.932256 feet

Approximately = 10,500.93 feet

Therefore, Tom walks for 10,500.93 feet

10560

Answer:

10,500.93 feet

Step-by-step explanation:

Answer:

personally I believe its 6..

Step-by-step explanation:

10% of 200 is 20. if 10% is 20 then each part would equal 2. 2×3 is equal to 6

Answer:

$203

Step-by-step explanation:

To find the cost he pays back you need to mulitply 200 x 3% x 6 months.

Because you can't multiply with different units, you convert them to the same unit. (Numeric form)

To convert, we divide 3% by 100 and get 0.03

6 MONTHs is equal to 1/2 of a year which is also 0.5.

Now that all of our numbers are using the same units, we can multiply.

200(0.03)(0.5)

200 x 0.03 is 6

6 x 0.5 is 3.

We need to add the total amount her brother pays her back and the interest.

He pays her $200 for the Tablet and gives her $3 for the interest.

200+3=203.

Answer:

Step-by-step explanation:

A quadratic equation has equal/repeated solutions when a discriminant (Δ) is equal 0.

The formula of a discriminant (Δ) of equation

[tex]ax^2+bx+c=0\\\\\Delta=b^2-4ac[/tex]

We have the equation

[tex]4x^2+8x+p=0\to a=4;\ b=8;\ c=p[/tex]

substitute

[tex]\Delta=8^2-4\cdot4\cdot p=64-16p\\\\\Delta=0\iff64-16p=0[/tex]

subtract 64 from both sides

[tex]-16p=-64[/tex]

divide both sides by (-16)

[tex]\dfrac{-16p}{-16}=\dfrac{-64}{-16}\\\\p=4[/tex]

SP of a machine = Rs. 990

Profit% = 10 %

SP of other machine = Rs. 1960

loss% = 2 %

his gain or loss percentage​

We know that,

CP * (100 + profit%)/100 = SP

So,

First machine :

CP * (100 + 10)/100 = 990

⟹ CP = 990 * 100/110

⟹ CP = Rs. 900

Second machine :

We know that,

CP * (100 - loss%)/100 = SP

⟹ CP * (100 - 2)/100 = 1960

⟹ CP = 1960 * 100/98

⟹ CP = Rs. 2000

Now,

We have to find the total loss or profit percentage.

We observe that,

SP > CP.

so, a gain is occured.

gain % = gain/CP * 100

gain = SP - CP

So,

gain% = (2950 - 2900)/2900 * 100

⟹ gain% = 50/29

⟹ gain% = 1.72 %

∴ A gain of 1.72% is occured in the whole transaction.

I hope it will help you.

Regards.

Answer:

HELLO SISO❤

IT'S ME YIREN

Step-by-step explanation:

→ CP of machine = (SP * 100) / (100 + Profit%) = (990 * 100) / (100 + 10) = (990 * 100) / 110 = Rs. 900 . Case 2) :- shopkeeper sells another machine for Rs. 1960 at a loss of 2%

Answer:

42/5

Step-by-step explanation:

If you multiply the denominator (5) by the whole number you would get 40, so then, you add this to the numerator (2), you would get 42 after. So the answer would be 42/5 (you keep the denominator). You can trust my answer because I'm n middle school and this was in like elementary school :P

Answer:

A (-7,0)

Step-by-step explanation:

I just drew it cause it's way easier than typing out :)

Answer:

14824

Step-by-step explanation:

the product is 14824

Answer:

If you are multiplying (-45)(158)(73)(-1) your answer is 519,030.

Step-by-step explanation:

Answer:

f(5)=225 and f(10)=250

Step-by-step explanation:

The bigger bag have 13/60 kilogram more coffee.

A fraction is defined as numerical representation for part of a whole which represents a rational number.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 12 + 2 = 14

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 12 -2 = 10

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

Given that the bags come in two 4/5 kilogram and 7/12 kilogram

⇒ 4/5

⇒ 7/12

We will first establish that there has a comparable denominator.

Multiply by (12/12) in the fraction 4/5

⇒ 4/5 (12/12)

⇒ 48/60

Multiply by (5/5) in the fraction 7/12

⇒ 7/12 (5/5)

⇒ 35/60

Determine the difference between fractions as :

⇒ 48/60 - 35/60

⇒ 13/60 kilogram

Hence, the bigger bag have 13/60 kilogram more coffee.

Learn more about fraction here:

brainly.com/question/10354322

#SPJ5

Answer:

9 R 1

Step-by-step explanation:

73/8 = 9 R 1

we know 8x 9 = 72 so we know we have a remainder of 1

Answer:

3-6 I think

Step-by-step explanation:

Answer:

Neither Dom or Riley is correct

Step-by-step explanation:

The change in temperature between 12PM and 6AM can be obtained by subtracting the 12PM temperature from the 6AM temperature because temperature increases as the hours of the day go by.

To carry out this subtraction on the number line, the following steps should be taken;

(i) Mark the numbers corresponding to 6AM and 12PM temperatures on same number line.

(ii) From the number corresponding to the 12 PM temperature, find out how many steps that are needed to reach the position of the number corresponding to the 6AM temperature.

This number of steps represents the temperature change between the 12PM temperature and the 6 AM temperature.

m = 36

Work

45 + 2.50m = 3.75m

       -3.75m    -3.75m

45 - 1.25m = 0

- 45             - 45

-1.25m = -45

-1.25     -1.25

    m = 36

Answer:

D i'm pretty sure

Step-by-step explanation:

Answer: $2.19

Step-by-step explanation: you have to find the surface area. Add 10*7*2 and 7*1.25*2 and 1.25*10*2 and then multiply by 0.012! Then you can get your answer. (17.5 + 140 + 25)*0.012. I think this is right. Sorry if itś not.

Answer:

I can only help with 5 and 6 which both are A.

Explanation:

that's because Cosine is adjacent to the angle (the angle being 30 degrees and the side next to it is 43mm) divided by the hypotenuse (longest side of a right triangle. The 50 mm). A way you can remember the sin, cosine and tangent is SOH CAH TOA. Sine=opposite over hypotenuse, Cosine = adjacent over hypotenuse, Tangent = opposite over adjacent. For the next one, it is the same principal. X is adjacent to 22 degrees and the other number is the hypotenuse so it has to be Cosine.

Answer:

[tex]\frac{4a-2}{2a+1}[/tex]

Step-by-step explanation:

Factorise the numerator and denominator

8a² - 2 ← factor out 2 from each term

= 2(4a² - 1) ← 4a² - 1 is a difference of squares

= 2(2a - 1)(2a + 1)

4a² + 4a + 1 ← is a perfect square

= (2a + 1)²

Thus

[tex]\frac{8a^2-2}{4a^2+4a+1}[/tex]

= [tex]\frac{2(2a-1)(2a+1)}{(2a+1)(2a+1)}[/tex] ← cancel (2a + 1) on numerator/ denominator

= [tex]\frac{2(2a-1)}{2a+1}[/tex]

= [tex]\frac{4a-2}{2a+1}[/tex]

Step-by-step explanation:

Original formula: T^2 = 2p + as

T^2 - 2p = as

s = (T^2 - 2p) / a