What is the factored form of 8x^3 - 27y^3?

A. (2x + 3y)(4x^2 - 6xy + 9y^2)

B. (2x – 3y)(4x^2 + 9xy + 6y^2)

C. (2x – 3y)(4x^2 + 6xy + 9y^2)

D. (2x + 3y)(4x^2 - 9xy + 6y^2)

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Work Shown:

A = 1+sqrt(2)

B = 1-sqrt(2)

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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)

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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)

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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.

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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)

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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:

x+2y=-8

Step-by-step explanation:

Slope of given line = 2

Slope of the perpendicular line = -1/2

Equation of perpendicular line is (y-y1)=m(x-x1)

y-(-3)=-1/2(x-(-4))

y+3=-1/2(x+4)

2y+6=-x-2

x+2y=-8

Answer:

i believe the answer is 4

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

can you please mark this brainliest if it helped? <3

Answer:

x =14

Step-by-step explanation:

-1/2 x+1 = -x+8

Add x to each side

-1/2 x +x+1 = -x+x+8

1/2x +1 = 8

Subtract 1 from each side

1/2x +1-1- =8-1

1/2x = 7

Multiply each side by 2

1/2x *2 =7*2

x =14

Answer:

y=-3x-5

Step-by-step explanation:

y = mx+b

m= -11 - 1

       2 - -2

y=-3x+b

(-2,1) and (2,-11)

is

y=-3x-5

Hope this Helps:)

Step-by-step explanation:

f(3) = -3(3)-2

=-9-2

=-11

Answer:

Step-by-step explanation:

If you check the measurement

of the other line, it will NOT match the one

on the side. It is a few centimeters bigger than the bottom.

hope this helps! <3

Answer:

[tex]\Large \boxed{\sf 40}[/tex]

Step-by-step explanation:

The triangle is a right-angled triangle

Use Pythagorean Theorem formula to solve for hypotenuse

[tex]\displaystyle c=\sqrt{a^2+b^2}[/tex]

Substitute in the values

[tex]\displaystyle c=\sqrt{24^2+32^2}=40[/tex]

Step-by-step explanation:

y<3x-6,x=0 for y>-3x-5,y=0

y<-6 x<-5/3

y=0,x>2 x=0, y>-5

therefore, values of x will be 2<x>-5/3

and values of y will be -5<y>-6

so the point will be (-9,-1)

hope it helps.

Answer:

$3,000

Step-by-step explanation:

you add $3 to $12 and that's $15.so,know you multi..15 by 200.

Answer:

6

Step-by-step explanation:

So, the absolute value of −6 will be the distance from −6 to 0 on the number line, and it is 6.

Answer:

C (6)

Step-by-step explanation:

The absolute value of -6 is 6 since it's 6 spots away from the 0 on the number line

Answer:

50%

Step-by-step explanation:

10 divided by 2 is 5. 5 is 50% of 10, and if you add 5 to 10, you get 15.

Answer:

yes

Step-by-step explanation:

well converse is

If q, then p

and inverse is

If no p, then not q

butttttt lets put this in human terms

If I am allergic to donuts, then I don't like to eat donuts.

and the inverse is

If I don't like to eat donuts, then I am allergic to donuts.

It is true no matter what! However, there could also be other reasons you don't liek donuts but nonthless this is one true reason that exists bc converse.

Answer:

6 to 4 or 3 to 2

Step-by-step explanation:

To sove we need to find hypatonuse which you can do by counting across the bottom whichis 4 units and across the top which is 6 units so 6/4 which is 3 to 2 or 6 to 4

Answer:

J. $950

Step-by-step explanation:

p(n)= 10n-50

p(n)=10(100)-50

P(n)=1000-50

950

Answer:

y = 119

x = 29

Step-by-step explanation:

Answer:

IT dependsssss

Step-by-step explanation:

what kind?

Answer:

x = 3

Step-by-step explanation:

First, isolate the variable by subtracting 5 on both sides:

3x=9

Then, divide both sides by 3:

x = 3

Answer:

(d/f)-1=x

Step-by-step explanation:

d=f+fx

d-f=fx

(d-f)/f=x

(d/f)-1=x

Answer:

-7 < k < 7

Step-by-step explanation:

The absolute value of the variable k will be less than 7.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result. The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

A number k is less than 3 units from 10. Then the equation is given as

k + 3 < 10

Simplify the equation, then the value of the variable k will be

k + 3 < 10

k < 10 - 3

k < 7

The absolute value of the variable k will be less than 7.

Your question was incomplete, your question was probably be...

A number k is less than 3 units from 10.

What's the absolute value inequality?

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

Ans

Add 15 to 6  so w= 21

Step-by-step explanation:

Answer:

If one angel is 74 so the solution is

[tex]74 + 2x = 180 \\ 2x = 180 - 74 \\ x = 106 \div2 \\ \: x = 53 \\ u = 74 \\ v = 53 \\ w = 53[/tex]

Step-by-step explanation:

Please mark as brainliest

Answer:

63 people

Step-by-step explanation:

Given parameters:

Number of students survey = 32

Number of those that liked ice-cream = 8

Total population size  = 252

Unknown:

How many people in the population should prefer ice cream  = ?

Solution:

  From the survey;

    8 out of 32 students prefer ice cream;

     8 : 32

     1: 4

This shows that 1 out of 4 students will prefer ice cream

NOw to the total population;

  If out of 4 students, 1 prefers ice-cream;

     Out of 252 students   y will prefer ice-cream

     Number of students that prefers ice-cream = [tex]\frac{252}{4}[/tex] = 63people

Answer:

Johnny earns 50 cents each hour, x.

Step-by-step explanation:

Answer:

Ariana wanted to buy cashews at the grocery store. Cashews are $0.5 per ounce. If Ariana has $10 how many ounces of cashews can she buy

Answer:

ill suck ya wang

Step-by-step explanation:5$ and ill suck yo wang to do your homework

Answer:

It is C.

Step-by-step explanation:

If you multiply 2 times 2 you get 4. Then multiply 4 by 5 and you get 20.

Therefore, it is C.

Answer:

30 student

Step-by-step explanation:

150/5=30

Answer:

he unit rate would be 30 students per class.

Step-by-step explanation: One way to find the  unit rate in this scenario, we could divide the total students by the number of classes. (150/5) The simplified fraction would be 30/1, or 30 students per class. Hope this help You!!!!!!!!!!!!!

Answer:

b. Graph each equation. c. How long will it be before Alberto has read more ... Since the answer works in both equations, (3.1, 115) ... First, solve the first equation for y to get 2x − 6 = y.

Answer:

A = 0.5714

basically the answer is option (d)

Answer:

acc. to me it should be

[tex] \sqrt{50} [/tex]

Answer:

13.9

Step-by-step explanation:

Speed=distance/time

S=75,000/5,400

S=13.8 repeating OR (rounded) 13.9 m/s