use pascal's triangle to expand the following binomial expression
1.(2k-1/3)⁶​

Answers

Answer 1

9514 1404 393

Answer:

  64k^6 -64k^5 +(80/3)k^4 -(160/27)k^3 +(20/27)k^2 -(4/81)k +1/729

Step-by-step explanation:

The row of Pascal's triangle we need for a 6th power expansion is ...

  1, 6, 15, 20, 15, 6, 1

These are the coefficients of the products (a^(n-k))(b^k) in the expansion of (a+b)^n as k ranges from 0 to n.

Your expansion is ...

  1(2k)^6(-1/3)^0 +6(2k)^5(-1/3)^1 +15(2k)^4(-1/3)^2 +20(2k)^3(-1/3)^3 +...

     15(2k)^2(-1/3)^4 +6(2k)^1(-1/3)^5 +1(2k)^0(-1/3)^6

  = 64k^6 -64k^5 +(80/3)k^4 -(160/27)k^3 +(20/27)k^2 -(4/81)k +1/729


Related Questions

Please help me. Image below.

Answers

Answer:

10 cubes

Step-by-step explanation:

2.5 × 1 × 2 = 5 cm³

5 ÷ 0.5

10 cubes

Answer:

10 cubes

Step-by-step explanation:

1 × 2 × 2.5 = 5cm^3

5 ×× .5 = 10

so 10 cubes would fit

Simplify to a single power of 2

Answers

128? I think because 2x2 than 2x2x2x2x2 is 32 than 32x4

Answer:

2^7

Explanation:

You can add up the square of two and the square of five. This is the easiest way.

Find the area of the shaded figure in the diagram below. Use 3.14 for π and round your answer to the nearest hundredth.

A. 39.57in^2
B. 66.89 in^2
C. 200.67 in^2
D. 118.72 in^2

Answers

Answer:

D

Step-by-step explanation:

diameter of 1 circle = 21.3/3= 7.1

radius of 1 circle= 7.1/3=3.55

area of 1 circle =πr^2=3.14× (3.55)^2=39.57

area of 3 circle= 39.57×3=118.72

therefore,area of shaded portion= area of 3 circle =118.72

Find the percent of change and state whether it was a percent of increase (I) or percent of decrease (D). from $289 to $762

Answers

Answer:

163.67 ( I )

Step-by-step explanation:

Plsss help. giving extra points if correct.

Answers

Answer:

B. ACB AND ACD

Step-by-step explanation:

since you need to prove, you need to show that the figure can work on any 2 triangles… hope it helps.

whats 2+2 UnU thats a hard one ToT

Answers

Answer:

4

MARK ME BRAINLIEST CUZ IM DA SMARTEST :))

the answer to that is 4

PLEASE HELP
On the graph below, Point A is located at the intersection of angle θ and the unit circle.
What are the exact coordinates of point A?

Use the on-screen keyboard to type the answer in the box below.

https://imgur.com/a/UwbnsCV

Answers

Answer:

  1/2,

Step-by-step explanation: Please find the attached image of unit circle.

We have been given that the measure of angle t is 60 degrees. We are asked to find the x-coordinate of the point where the terminal side intersects the unit circle.

We know that x-coordinate on unit circle represents cosine and y-coordinate represents sine of a given angle.

We can see from our attachment that x-coordinate of the point at angle 60 degrees is , therefore, x-coordinate of the angle of 60 degrees, where the terminal side intersects the unit circle is .  

PLEASE HELP ILL GIVE BRAINLIEST

Answers

Answer:

1 and 2 is The first one and 3 and 5 is the second one

Find the measure of angle 3

Answers

Answer:

120

Step-by-step explanation:

There are six households in a rural community. Each household earns $40,000 per year. Suppose that a new resident builds a mansion in the community and that the income in the new household is $4 million per year. After the new resident arrives, the median household income has _____, and the mean household income has _____. increased; increased not changed; increased not changed; not changed increased; not changed

Answers

Answer:

Median income has not changed

Mean income has increased

Step-by-step explanation:

Initial number of houses = 6

Earning per household = $40,000

The initial mean :

$(40,000 * 6) / 6 = $40000

Initial median :

40000, 40000, 40000, 40000, 40000, 40000

= 1/2(n+1)th term,

Median = 40000

A 7th household earns 4,000,000

Mean = ((40000*6) + 4,000,000) / 7 = $605,714

Median = 1/2(n+1)th term

40000, 40000, 40000, 40000, 40000, 40000, 4000000

Median = 4th term = 40000

Use the shapes to answer the questions that follow:

Answers

Answer:

50%

Step-by-step explanation:

Theres 10 shapes and 5 of them are yellow. So that is 5/10 which equals 50%

hope this helps <3

Answer:

50%

Step-by-step explanation:

5/10 are yellow so 5% I think

Hello Good morning can someone give me the answer of this operation?

39 + 1 - 24 / 6=

Also can you tell me the order? :> Thanks!!

Answers

Answer:

The answer is 36

Step-by-step explanation:

Because 39+1=40

So then 40-24=16

and then divided by 6 is 36 because when you divide you multiply

What number must you add to the polynomial below to complete the square?

x2 + 15x

Answers

Answer:

The number [tex]\frac{225}{4}[/tex] is added to the polynomial below to complete the square.

Step-by-step explanation:

Perfect square binomial:

A perfect square binomial is given by:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

In this question:

We have that:

[tex]a^2 + 2ab + b^2 = x^2 + 15x + ?[/tex]

Since [tex]a = x[/tex], we have that:

[tex]2ab = 15x[/tex]

[tex]2b = 15[/tex]

[tex]b = \frac{15}{2}[/tex]

Completing the square:

The term that completes the square is [tex]b^2[/tex]. So

[tex]b^2 = (\frac{15}{2})^2 = \frac{225}{4}[/tex]

The number [tex]\frac{225}{4}[/tex] is added to the polynomial below to complete the square.

Does anyone know the answer

Answers

Answer:

d = 126, z = 28

Step-by-step explanation:

The angle with the variable is diagonal from the 105 degree angle. In this case, that means that they are equivalent. So, 105+21 = 126. d = 126 :)

A music store sells both electric and
acoustic guitars. One month, the store
sold 12 electric guitars. If that was 60%
of their sales for the month, how many
guitars did they sell that month in all?

Answers

Answer:

sorry :/ im not sureee but they would have sold 20  

Step-by-step explanation:

They sold 20 guitars that month.

Step-by-step explanation:

[tex] \frac{12 \times 100}{60} = total[/tex]

[tex] \frac{1200}{60} = 20[/tex]

Which statement is true?

Group of answer choices

An equilateral triangle is never an acute triangle.

An isosceles triangle is sometimes a scalene triangle.

An acute triangle is always an equilateral triangle.

A equilateral triangle is always an isosceles triangle.

Answers

Answer:

An equilateral is always an isosceles triangle.

Step-by-step explanation:

Kdksksksnsksksnssnzhzhs

Find the amount of wood trim needed to frame a circular window with a diameter of 1.75 ft. Use 3.14 for n.​

Answers

Answer:

2.40 ft I believe

Step-by-step explanation:

divide diameter by two

put 3.14 time diameter divided by two and square it

3 toys cost x kobo. How many toys can be bought with #3.00?​

Answers

Answer:

ok so you say I don't know for 10000000000 year's the end. :)

5.
Multiply.
(3x + 2)(x - 3)

Answers

Answer: 3x^2 - 7x - 6

Step-by-step explanation:

Answer:

3x^2-7x-6

Step-by-step explanation:

(3x+2)(x-3)

3x^2-9x+2x-6

3x^2-7x-6

Hope this helps.

25) Margie needs to borrow $9,000 from a local bank. The
loan has a 8.5% interest rate for 4 years. What will
Margie's monthly payment be?
A) $ 221,850.00
B) $3060.00
C) $250.0
D) $ 221.85

Answers

Answer:

B) $3060.00

Step-by-step explanation:

8.5% of 9,000 equals 765, then 765 multiplied by 4 equals 3060.

I think that it will take Margie 4 years to pay back the bank. And the interest rate that the bank charges is 8.5% per month.

I'm not sure if this is correct

If the scale of the map is 1 inch = 125 miles, two points that are 3.75 inches apart will actually be approximately how many miles away from each other? 292 375 469 1,125

Answers

Answer:

469 miles

Step-by-step explanation:

1 in = 125 miles

3.75 in =?

3.75 x 125 = 468.75 miles

468.75 rounds up to 469 miles

5th grade math. correct answer will be marked brainliest

Answers

Answer:

5280

Step-by-step explanation:

Hope this helps!

Plsss help I am falling

Answers

Answer:

that sucks

Step-by-step explanation:

srry man i got nothin

find the rule for the following geometric sequence: 4, -12, 36, -108, ....what is n7

Answers

Answer:

the rule is *-3,n7=-2916

Step-by-step explanation:

n4=108

n5=108*-3=-324

n6=-324*-3=972

n7=972*-3=-2916

PLSSS HELP PANICKING
The sum of Alex and John's money is $48. Alex has $3 more than twice the amount John has. How much money do they each have? ​

Answers

Answer:

John has $15 and Alex has $33

Step-by-step explanation:

a systems of equations can be made from the information on the problem

x+y=48

x=2y+3

since x= 2y+3 substitute 2y+3 in the firat equation to get:

(2y+3)+y=48  -> 3y+3=48 -> 3y=45  -> y=15

plug in 15 for y in the second equation to solve for x

x+15 =48 --> x=33

Candice and Joe went to Sawcon, the concert tickets for the concert Sawcon was 50 dollars each person. Plus tax they add 2.5 dollars. Since they have a discount they minus 10.5. How much are the tickets now?

Answers

Answer:

they would be $42.00

Step-by-step explanation:

50 + 2.50= 52.50

52.50-10.50=42.00

If f(1)=1, f(2)=4 and f(n)=3f(n-1)-f(n-2) then find the value of f(4).

Answers

Answer:

29

Step-by-step explanation:

f(3)=3f(2)-f(1)=3x4-1=11

f(4)=3f(3)-f(2)=3x11-4=29

In the map below, Side P Q is parallel to Side S T.

Triangle P Q R. Side P Q is 48 kilometers and side P R is 36 kilometers. Triangle S R T. Side R T is 81 kilometers.

What is the distance between S and T? If necessary, round to the nearest tenth.
21.3 km
60.8 km
108 km
117 km

answer C.

Answers

the 3rd choice 108 kilometers

Answer:

C.

Step-by-step explanation:

Need help on the picture i attached

Answers

Answer:

1.) Standard form -            

2.) Center (1,-3)

3.) Radius r=4

4.) Diameter d=8

5.) Circumference 25.12

6.) Area 50.24

7.) Graph              

Step-by-step explanation:

In London today, twice the low temperature was less than three times
the low temperature minus ten. In interval form, what are the possible
temperatures?

Answers

I need more information
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