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

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 :)

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. :)

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

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

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

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]

Plsss help I am falling

Answers

Answer:

that sucks

Step-by-step explanation:

srry man i got nothin

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.

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:

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

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

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

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

5th grade math. correct answer will be marked brainliest

Answers

Answer:

5280

Step-by-step explanation:

Hope this helps!

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:

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 .  

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

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

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.

PLEASE HELP ILL GIVE BRAINLIEST

Answers

Answer:

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

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

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

Find the measure of angle 3

Answers

Answer:

120

Step-by-step explanation:

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

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

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.

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