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
Blababa [14]
1 year ago
5

Factorise: 27x^3 - 1/216 -9/2x^2 +1/4x

Mathematics
1 answer:
g100num [7]1 year ago
7 0

Answer:

Hello,

Step-by-step explanation:

27x^3-\dfrac{9}{2}x^2+\dfrac{1}{4}x-\dfrac{1}{216}   \\\\=(3x)^3-3*(3x)^2*\dfrac{1}{6} +3*(3x)*(\dfrac{1}{6} )^2-(\dfrac{1}{6} )^3\\\\=\boxed{(3x-\dfrac{1}{6} )^3}

You might be interested in
What is the equation of the line that passes through the points (5, 3) and (-3,-1)?
Liono4ka [1.6K]

Answer:

y=1/2x+1/2

m=1/2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(5,3) and (-3,-1).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (5,3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=5 and y1=3.

Also, let's call the second point you gave, (-3,-1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-3 and y2=-1.

Now, just plug the numbers into the formula for m above, like this:

m=

-1 - 3 over

-3 - 5

or...

m=

-4 over

-8

or...

m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(5,3). When x of the line is 5, y of the line must be 3.

(-3,-1). When x of the line is -3, y of the line must be -1.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (5,3) and (-3,-1).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(5,3). y=mx+b or 3=1/2 × 5+b, or solving for b: b=3-(1/2)(5). b=1/2.

(-3,-1). y=mx+b or -1=1/2 × -3+b, or solving for b: b=-1-(1/2)(-3). b=1/2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(5,3) and (-3,-1)

is

y=1/2x+1/2

7 0
2 years ago
Quadrilateral $abcd$ is a trapezoid with $ab$ parallel to $cd$. we know $ab = 20$ and $cd = 12$. what is the ratio of the area o
alekssr [168]
Draw a diagram to illustrate the problem as shown below.

The area of triangle acb is
A₁ = (1/2)*20*h = 10h

The area of trapezoid abcd is
A₂ = (1/2)*(20+12)*h = 16h

The ratio A₁/A₂ is
A₁/A₂ = (10h)/(16) = 5/8

Answer:
The ratio of triangle acb to the area of trapezoid abcd is 5/8.

4 0
3 years ago
e movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answ
Nimfa-mama [501]

9514 1404 393

Answer:

  4·10 +4·5 = 6·12 -6·2

Step-by-step explanation:

Each outside factor multiplies each inside term.

  4(10 +5) = 6(12 -2)

  4·10 +4·5 = 6·12 -6·2

3 0
2 years ago
22. Francisco is three years more than twice Jenna's age. Harrison is two years less than three times Jenna's age.
Jet001 [13]

Answer:

An expression for Francisco's age in terms of a is (2a+3)

An expression for Harrison's age in terms of a is (3a-2)

An expression for the sum of all  three ages, in terms of a is (6a+1)

Step-by-step explanation:

Let

a -----> Jenna's age

b -----> Francisco's age

c -----> Harrison's age

we know that

Francisco's age is two times Jenna's age plus three years

b=2a+3 -----> equation A

Harrison's age is three times Jenna's age minus two years

c=3a-2 ----> equation B

The sum of all  three ages, in terms of a is

(a+b+c) -----> equation C

substitute equation A and equation B in equation C

a+(2a+3)+(3a-2)

Combine like terms

(a+2a+3a)+(3-2)

6a+1

therefore

An expression for Francisco's age in terms of a is (2a+3)

An expression for Harrison's age in terms of a is (3a-2)

An expression for the sum of all  three ages, in terms of a is (6a+1)

6 0
3 years ago
Two equations are shown: Equation 1: 3 4 (x−12)=12 Equation 2: 3 4 y−12=12 Solve each equation. Then, enter a number in each box
pickupchik [31]

Answer:

The value of X =  24

The value of y = 24

Step-by-step explanation:

love ya kitty~

3 0
3 years ago
Read 2 more answers
Other questions:
  • Lou eats 6/8 of pizza. what fraction of the pizza is left over?
    7·1 answer
  • One meter is approximately equal to 39.39 inches. About how many inches are in 3 meters
    13·2 answers
  • Find the values of x and y that make k || j and
    14·2 answers
  • I need help with “B”
    9·1 answer
  • An equation is shown below: 6(2x-11)+15=21
    7·2 answers
  • Jose and juan went running. jose ran 2 miles less than 1/2 as many miles as juan. jose ran 6 miles. how many miles did juan run?
    13·2 answers
  • The product of 9 and a number increased by the product of 12 and that number decreased by the product of the sum of all and 23 t
    15·1 answer
  • 5m<6m+6 pls help me ​
    12·1 answer
  • 3x + 4y = 8<br> Is it linear? If so how do I graph it
    13·1 answer
  • Which inequality is true? <br>3&lt;2<br>-5&lt;6<br>-6&lt;5<br>-6&gt;-5<br>​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!