1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Deffense [45]
3 years ago
12

Explain how to use a polynomial identity to factor x^6-27y^3

Mathematics
2 answers:
Umnica [9.8K]3 years ago
6 0
Dont really no sorry
Taya2010 [7]3 years ago
5 0

This is a sum of cubes:

<em>x</em>⁶ - 27<em>y</em>³ = (<em>x</em>²)³ + (-3<em>y</em>)³

Recall that

<em>a</em>³ + <em>b</em>³ = (<em>a</em> + <em>b</em>) (<em>a</em>² - <em>ab</em> + <em>b</em>²)

So we have

<em>x</em>⁶ - 27<em>y</em>³ = (<em>x</em>² - 3<em>y</em>) ((<em>x</em>²)² - <em>x</em>² (-3<em>y</em>) + (-3<em>y</em>)²)

<em>x</em>⁶ - 27<em>y</em>³ = (<em>x</em>² - 3<em>y</em>) (<em>x</em>⁴ + 3<em>x</em>²<em>y</em> + 9<em>y</em>²)

You might be interested in
What is vertex of x^2+5x-3
Art [367]

\text{The vertex of}\ ax^2+bx+c:\\\\(h,\ k),\ \text{where}\ h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{-(-b^2-4ac)}{4a}

\text{We have:}\\f(x)=x^2+5x-3\\\\a=1,\ b=5,\ c=-3\\\\h=\dfrac{-5}{2\cdot1}=\dfrac{-5}{2}=-2.5\\\\k=f(-2.5)=(-2.5)^2+5(-2.5)-3=6.25-12.5-3=-9.25

\text{Answer: the vertex is in}\ (-2.5;\ -9.25)

6 0
3 years ago
Alex earns 12% commission on any of her monthly sales over $5,000. Her sales for May were $6,750. How much commission did Alex e
valentina_108 [34]
6750/100*12 = 810 is the answer
4 0
3 years ago
Name a number whose square root and cube root are whole numbers
katrin [286]
The whole number is 10 the square root is 9
5 0
3 years ago
Alexei wants to hang a mirror in his boat and put a frame around it. The mirror and frame must have an area of 19.25 square feet
zhuklara [117]

Let

x---------> the thickness of the frame in feet

At-------> Area of the mirror and the frame in square feet

we know that

At=19.25ft^{2} ------> equation 1

At=(3+2x)*(5+2x)\\ At=3*5+3*2x+5*2x+2x*2x\\ At=15+6x+10x+4x^{2} \\ At=4x^{2} +16x+15--------> equation 2

equate equation 1 and equation 2

19.25=4x^{2} +16x+15\\ 4x^{2} +16x+15-19.25=0\\ 4x^{2} +16x-4.25=0

therefore

the answer is the option

C. 4x2 + 16x - 4.25 = 0

5 0
3 years ago
Read 2 more answers
Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5​
Bond [772]

Answer:

The solution to the equation system given is:

  • <u>x = 2</u>
  • <u>y = -1</u>

Step-by-step explanation:

First, we must know the equations given:

  1. 2x + 3y = 1
  2. 3x + y = 5​

Following Crammer's Rule, we have the matrix form:

\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]

Now we solve using the determinants:

x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2

y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

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

And, with the second equation:

  • 3x + y = 5​
  • 3(2) + (-1) = 5
  • 6 - 1 = 5
  • 5 = 5

 

4 0
3 years ago
Other questions:
  • What is the formula for a cone in geometry
    8·2 answers
  • A regulation softball has a circumference of 12 inches. what is the volume of the softball?
    9·1 answer
  • Can you help me with my expanded notation please
    5·1 answer
  • Plz help on 55 if you can!!
    13·2 answers
  • Write a paragraph proof to show that opposite sides of a parallelogram are congruent.
    7·1 answer
  • okay, genuinely does anyone know how this work? if you do could you please explain how you get the answer-
    11·1 answer
  • Lix wants to by a shirt for $25. What is the total cost with a 4.1% sales tax? Round to NEAREST CENT.
    10·1 answer
  • One third the sum of two numbers is 23.If one of the numbers is 29.3,what is the other number​
    15·1 answer
  • F(x) = 14 - 0.5<br> f(30) =
    8·2 answers
  • The points H, I, J and K all lie on the same line segment, in that order, such that the
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!