1/6 to the power of 3

Answer:

16 x ^4  −  96 x^ 3  +  216 x ^2  −  216 x  +  81

Step-by-step explanation:

Use the binomial expansion theorem to find each term. ∑

∑The binomial theorem states ( a + b ) n = n ∑ k = 0 n C k ⋅ ( a n − k b k ) . 4 ∑ k = 0 4 ! ( 4 − k ) ! k ! ⋅ ( 2 x ) 4 − k ⋅ ( − 3 ) k

Expand the summation. 4 ! ( 4 − 0 ) ! 0 ! ⋅ ( 2 x ) 4 − 0 ⋅ ( − 3 ) 0 + 4 ! ( 4 − 1 ) ! 1 ! ⋅ ( 2 x ) 4 − 1 ⋅ ( − 3 ) + 4 ! ( 4 − 2 ) ! 2 ! ⋅ ( 2 x ) 4 − 2 ⋅ ( − 3 ) 2 + 4 ! ( 4 − 3 ) ! 3 ! ⋅ ( 2 x ) 4 − 3 ⋅ ( − 3 ) 3 + 4 ! ( 4 − 4 ) ! 4 ! ⋅ ( 2 x ) 4 − 4 ⋅ ( − 3 ) 4

Simplify the exponents for each term of the expansion. 1 ⋅ ( 2 x ) 4 ⋅ ( − 3 ) 0 + 4 ⋅ ( 2 x ) 3 ⋅ ( − 3 ) + 6 ⋅ ( 2 x ) 2 ⋅ ( − 3 ) 2 + 4 ⋅ ( 2 x ) ⋅ ( − 3 ) 3 + 1 ⋅ ( 2 x ) 0 ⋅ ( − 3 ) 4

Simplify each term.

= 16 x ^4  −  96 x^ 3  +  216 x ^2  −  216 x  +  81

[tex](n \times (12 + 18)) + 43 = 103[/tex]

[tex]30n + 43 = 103[/tex]

Subtract both sides 43

[tex]30n + 43 - 43 = 103 - 43[/tex]

[tex]30n = 60[/tex]

Divide both sides by 30

[tex] \frac{30n}{30} = \frac{60}{30} \\ [/tex]

[tex]n = 2[/tex]

Answer:

$8

Step-by-step explanation:

20% of $40

= [tex]\frac{20}{100}[/tex] × $40

= 0.2 × $40

= $8

$8 is discounted from the regular price

Answer:

$8 off

Step-by-step explanation:

Convert from a percentage to a multiplier by dividing by 100:

[tex]\frac{20}{100}=0.2[/tex]

Then multiply that by the price:

[tex]40*0.2=8[/tex]

meaning the item is $8 off.

You can confirm that like so:

[tex]\frac{8}{40} =0.2\\[/tex]

or 20%

Answer:

f(0) = 2, x = - 2, x = - 1

Step-by-step explanation:

f(0) means what is the value of y when x = 0

x = 0 is a point on the y- axis

Thus when x = 0 , y = 2 , that is

f(0) = 2

(b)

The roots are the values of x on the x- axis where the graph crosses

This occurs at x = - 2 and x = - 1 ← roots

Answer:

Step-by-step explanation:

The quotient is 0.62 and the remainder is 0.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, 2.48 divided by 4.

Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence.

Here,

4|2.48|0.62

  24

  24

_____

   08

   08

_____

    0

So, quotient is 0.62 and remainder is 0.

Therefore, the quotient is 0.62 and the remainder is 0.

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Answer:

y = 5

Step-by-step explanation:

y = (1/4)x + 4

input (x) = 4

plug in 4 for x

y = (1/4)(4) + 4

y = 1 + 4

y = 5

Answer: 5) F:(1,-1)

6) W:(-3,-2)

Step-by-step explanation:

Answer:

y column: 1st = -7 , 2nd = -5 , 3rd = -3 , 4th = -1 , 5th = 1

Answer:

5.3 seconds is needed for one signature.

Hence, for 96 signatures, it would take

[tex]96*5.3=508.8[/tex] seconds.

The number of seconds Lola needs to sign all 96 invitations is,

⇒ 508.8 seconds

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Lola needs to sign 96 invitations.

And, Using a stopwatch that measures time to tenths of a second, it takes Lola 5.3 seconds to sign her full name.

Since, No of invitation's =96

And, Time required to sign 1 invitation = 5.3seconds

So, Let the time required to sign 96 invitation = x

Hence, We get;

x = 5.3 x 96

  = 508.8 seconds

Thus, The number of seconds Lola needs to sign all 96 invitations is,

⇒ 508.8 seconds

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15 students are yet to return for the face to face classes

Given the following parameters

Total number of students in Esteban's classroom = 28 students

If 45% of classmates have returned to face-to-face classes, the total number of classmates that have returned to face-to-face classes is 0.45 * 28 = 12.6

People that are yet to return  = 28 - 12.6

People that are yet to return  = 15.4

This shows that about 15 students are yet to return for the face to face classes

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Answer:

246

Step-by-step explanation:

Given that,

→ what is 492 divided by 2 ?

In mathematical form,

→ 492 ÷ 2

→ 246 {final answer}

Hence, the answer is 246.

Answer:

b = 37

Step-by-step explanation:

3x + 10 = b

(3 x 9) + 10 = 27

27 + 10 = 37

Answer:

b Is 37

Step-by-step explanation:

x Is 9

instead of x you write 9

3x mean 3×X

3×X+10= 3×9+10=27+10=37

The standard form of the equation of line will be;

⇒ 11x + 3y = 9

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The equation of line is,

y = -11/3 x + 3

Since, The standard form of the equation of line will be;

Ax + By = C

Where, A, B and C are integers.

Now, We convert the equation of line in standard form as;

The equation of line is,

y = -11/3 x + 3

Multiply by 3 in both sides,

3 × y = 3 (-11/3 x + 3)

3y = 3 × -11/3 x + 3 × 3

3y = - 11x + 9

3y = - 11x + 9

Add 11x both side;

11x + 3y = - 11x + 9 + 11x

11x + 3y = 9

Thus,

The standard form of the equation of line will be;

⇒ 11x + 3y = 9

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Answer:

-2/5

Step-by-step explanation:

slope equation is as follows -

(y1-y2)/(x1-x2)

now we just put (7,1) and (2,3) into the formula

(1-3)/(7-2)

-2/5

Answer:

12.6 you divide 31.50 by 2.50 pretend the decimal signs aren't there.

Answer:

-2 inches per hour

Step-by-step explanation:

Finding the average rate of change is just like finding the slope. So, take the y values (height) and subtract them and divide that by the difference in the x values (time).

( 3 - 9 ) / ( 8 - 5 )

= -6 / 3

= -2 inches per hour

Answer:

-9.89949493661

Step-by-step explanation:

Answer:

{-11,17}

Step-by-step explanation:

|X – 3|= 14

There are  two solutions to an absolute value, one positive and one negative

x-3 = 14    and x-3 = -14

Add 3 to all sides

x-3+3 =14+3         x-3+3 = -14+3

x = 17                     x = -11

x = {-11,17}

Answer:

(4,2)

Step-by-step explanation:

If you move from left to right your X will change if you move up or down your Y will change.

( can I have brainiest? )

Answer:-2x < 10.

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The unit rate should be 9

Answer:

i think false

Step-by-step explanation:

if im wrong forgive if am right brainliest pls:)

Answer:

Y-intercept: (0, -3)

Step-by-step explanation:

Given the two points, (6, 5) and (3, 1):

We can find the y-intercept by using the slope-intercept form, y = mx + b. However, the first step that we must do is to solve for the slope.

We must first solve for the slope of the line using the following formula:

[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}}[/tex]

Let (x₁, y₁)  = (3, 1)

     (x₂, y₂) = (6, 5)

[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}}[/tex]

[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{5 - 1}{6 - 3}\:=\:\frac{4}{3}}[/tex]

Hence, the slope of the line is:  [tex]\sf{m\:=\frac{4}{3}}[/tex] .

Next, we must determine the y-intercept, which is the point on the graph where it crosses the y-axis, with coordinates of (0, b ).  

In order to find the y-intercept, use one of the given points, (6, 5), and the slope, [tex]\sf{m\:=\frac{4}{3}}[/tex], and substitute these values into the slope-intercept form and solve for the value of b:

y = mx + b

[tex]\displaystyle\mathsf{5\:=\:\frac{4}{3}(6)\:+\:b }[/tex]

5 = 8 + b

Subtract 8 from both sides to isolate b:

5 - 8 = 8 - 8 + b

-3 = b

Therefore, the y-intercept is (0, -3), where b = -3.  

Answer:

<A=67⁰

<B=22⁰

<C=42⁰

Answer:

a = 67° , b = 26° , c = 69°

Step-by-step explanation:

a and 67° are corresponding angles and are congruent , so

a = 67°

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

The triangle on the left has 3 equal sides thus is equilateral with 3 congruent angles of 60°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles , that is

b + 34° = 60° ( subtract 34° from both sides )

b = 26°

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

The vertex of the triangle and 42° are vertically opposite and are congruent

vertex = 42°

The triangle has 2 equal legs and is isosceles with 2 base angles congruent.

c = [tex]\frac{180-42}{2}[/tex] = [tex]\frac{138}{2}[/tex] = 69°

Answer:

x ≈ 3.2

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos29° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{3.7}[/tex] ( multiply both sides by 3.7 )

3.7 × cos29° = x , then

x ≈ 3.2 ( to the nearest tenth )

Answer:

3.2

Step-by-step explanation:

we have two angles, 29 and 90.

we need one more angle to make the total sum of the angles 180.

the angle to do this is 61.

the area of this triangle so far is 2.90244.

using the area, we can find that the x side is 3.23609.

round 3.23609 to the tenth, we get 3.2

Answer:

3,250g

Step-by-step explanation:

22kg = 22,000g - 18,750g = 3250g

Answer:

i wish i could tell you but i suggest that you use a calculator to find your answer.

Step-by-step explanation:

i really hope this helps you!

Answer:

-14.82

Step-by-step explanation:

[tex](x_1,y_1) = (-3,4),~~ (x_2,y_2) = (2,-1)\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 - x_1} =\dfrac{-1-4}{2+3} = \dfrac{-5}5 = -1[/tex]