given the polynomial : (3x+4)^5. find the coefficient of x³ !​

Answers

Answer 1

Answer:

[tex] \displaystyle 4320 {x }^{3} [/tex]

Step-by-step explanation:

to solve binomials like this there's a way called binomial theorem given by

[tex] \displaystyle {(a + b)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]

but for this question we need the following part

[tex] \displaystyle \boxed{ \binom{n}{k} {a}^{n - k} {b}^{k} }[/tex]

from the question we obtain that a,b and n is 3x,4 and 5 since we want to find the coefficient k should be (5-3) = 2 so we have determined the variables now just substitute

[tex] \displaystyle \binom{5}{2} {(3x)}^{5 - 2} \cdot {4}^{2} [/tex]

simplify which yields:

[tex] \displaystyle \boxed{ \bold{4320 {x }^{3}} }[/tex]

and we are done!


Related Questions

Six liters of paint will cover 50 square meters. How many square meters will nine liters cover?

Answers

Answer:

75 m²

Step-by-step explanation:

Six liters of paint will cover 50 square meters.

  6L ⇒ 50m²

then,

  1L ⇒ 50/6 m²

  9L ⇒ 50 × [tex]\frac{9}{6}[/tex]

       ⇒ 75 m²

Marcella incarica Dora di aiutarla a suddividere 35 perle tra le sue tre figlie. Alla figlia maggiore vuole regalare la metà, alla mediana la terza parte e alla minore la nona parte. Inoltre Marcella vuole dare una perla a Dora come ricompensa. Quante perle riceverà ciascuna figlia?

Answers

Answer:

La hija mayor recibirá 17.5 perlas, la hija del medio recibirá 11.66 perlas, y la hija menor recibirá 3.88 perlas.

Step-by-step explanation:

Dado que Marcella le pide a Dora que la ayude a dividir 35 perlas entre sus tres hijas, y quiere darle la mitad a la hija mayor, la tercera parte a la del medio y la novena a la menor y, además, Marcella quiere darle una perla a Dora como recompensa, para determinar cuántas perlas recibirá cada hija se debe realizar el siguiente cálculo:

35 / 2 = Mayor = 17.5 perlas

35 / 3 = Medio = 11.66 perlas

35 / 9 = Menor = 3.88 perlas

Así, la hija mayor recibirá 17.5 perlas, la hija del medio recibirá 11.66 perlas, y la hija menor recibirá 3.88 perlas.

f(b) = 7b^3 +8b and g(b) = b ^2+ b - 10. What is f(b)-g(b)?

Answers

Answer:

[tex]{ \bf{f(b) - g(b) : }} \\ { \tt{ = ( {7b}^{3} + 8b) - ( {b}^{2} + b - 10)}} \\ = ( {7b}^{3} - {b}^{2} + 7b + 10)[/tex]

Answer:

[tex]f(b) - g(b) = 7b^3 -b^2 + 7b +10[/tex]

Step-by-step explanation:

[tex]f(b) = 7b^3 + 8b \\\\g(b) = b^2 + b - 10\\\\f(b) - g(b) = (7b^3 + 8b ) - ( b^2 + b -10)[/tex]

               [tex]= 7b^3 + 8b - b^2 - b + 10\\\\=7b^3 - b^2 +7b + 10[/tex]

step below. Question 1 Hexagon AGHBGHCGHD GHEGHFGH is a reflected image of hexagon ABCDEF. The midpoints of the sides of hexagon ABCDEF are also shown. Drag the line of reflection, Għ until the image coincides with the preimage. At this location, if the preimage flips about the line of reflection, it will flip onto itself. In how many different positions can you place GHso the image reflects onto the preimage in this manner? Describe the different positions. Be sure to pass the line of reflection through both vertices and midpoints before answering.​

Answers

Answer:

Hexagon AGHBGHCGHDGHEGHFGH coincides with hexagon ABCDEF when GH passes through the midpoints of opposite sides; that is, it is a perpendicular bisector of the two sides. HexagonAGHBGHCGHDGHEGHFGH also coincides with hexagon ABCDEF when the line of reflection joins a pair of vertices opposite one another on the hexagon. There are three perpendicular bisectors and three pairs of opposite vertices. In all, there are six lines of reflection that will map the hexagon back onto itself.

Step-by-step explanation:

please help me i need this asap

Answers

Answer:

-2, -1

Step-by-step explanation:

B is the answer for you. Have a good day!

WILL MARK BRAINLIEST!!
I. Write 2-7i in polar coordinates on the complex plane.
II. Find (1+i)^8 using DeMoivre's theorem.

Answers

I. Polar form = (r,θ) = (7.28,254.05°)
z= -2-i7
r= √-2^2+-7^2= √53= 7.28
θ=tan^-1 (-7/-2) =3.5=74.05
Point lies in the third quadrant
Hence θ=180+74.05=254.05°
Polar form = (r,θ) = (7.28,254.05°)

II. Z=16
De Moivre's theorem states if
z= r(cos(θ) + i sin (θ)) , then z^2=r^2(cos(nθ)+
i sin (nθ))
r= √1^2+1^2= √2
θ= arctan (1/1)= π / 4
z= √2 (cos (π / 4)+i sin (π / 4))
z^8 = (√2 (cos (π / 4)+i sin (π / 4)))^8
= (√2 (cos (8π / 4)+i sin (8π / 4)))^8
=16 (cos(2π) + i sin (2π)
=16




(r,θ) = (7.28,254.05°) are 2-7i in polar coordinates on the complex plane.

What are polar coordinates?

The polar coordinates system is a two-dimensional coordinate system in which each point is determined by distance from the point and an angle from the reference direction.

I. Polar form = (r,θ) = (7.28,254.05°)

z = 2 - i7

r= [tex]\sqrt{ 2^2+-7^2}[/tex]

= √53

 = 7.28

θ = tan^-1 (-7/-2)

  =3.5

  = 74.05

Point lies in the third quadrant

Hence θ = 180+74.05

              = 254.05°

Polar form = (r,θ) = (7.28,254.05°)

II. Z=16

De Moivre's theorem states if

z= r(cos(θ) + i sin (θ)) , then

[tex]z^2=r^2(cos(n\theta)+ i sin (n\theta))[/tex]

[tex]r= \sqrt{1^2+1^2}[/tex]

= √2

θ= arc tan (1/1)

  = π / 4

z= √2 (cos (π / 4)+i sin (π / 4))

z^8 = (√2 (cos (π / 4)+i sin (π / 4)))^8

= (√2 (cos (8π / 4)+i sin (8π / 4)))^8

=16 (cos(2π) + i sin (2π)

=16

Learn more about polar form;

https://brainly.com/question/13640455

#SPJ2

Simplificar 2/3+1/5+2/4

Answers

Answer:

41/30

Step-by-step explanation:

2/3 + 1/5 + 2/4

= 41/30

Record the length of these
segments
PC =
PC' =
units
units

Answers

There's all the lengths so you don't have to search them all up

Find the coordinates of the
midpoint M. *
A(-4,-8) and B(-1,4)
Please provide an explanation

Answers

Answer:

M(-5/2, -2)

Step-by-step explanation:

Add the x-coordinates & divide by 2.

Add the y-coordinates and divide by 2.

x-coordinates: -4, -1

(-4 + (-1))/2 = -5/2

y-coordinates: -8, 4

(-8 + 4)/2 = -4/2 = -2

M(-5/2, -2)

M(-5/2,-2) there u go that should be it

SOMEONE PLEASE HELP ME WITH THIS PROBLEM!!!!

Answers

9514 1404 393

Answer:

  20.0 square units

Step-by-step explanation:

There are many ways the area can be computed here. Perhaps the intended one is to find the length of the third side, then use the usual triangle area formula.

  b = √(c² -a²) = √(9² -7²) = √32 ≈ 5.7

Then the area is ...

  A = 1/2bh = 1/2(5.7)(7) ≈ 20.0

The area is approximately 20.0 square units.

_____

Additional comment

It is highly unusual to make use of rounded intermediate results. That is a guarantee that the final answer will have more error than necessary. Ordinarily, you would never do that.

An alternate solution might be ...

  angle = arccos(7/9) ≈ 38.9°

  area = 1/2(7)(9)sin(38.9°) ≈ 19.8 . . . . square units (assuming the sine value is not rounded to 0.6)

Come get your point with me :)

Answers

Answer:

IK≅WY

Step-by-step explanation:

Can someone help me solving this problem? I'm confuse so I want help..
question :
a) The length and breadth of a rectangular room are 10m and 8m respectively. How many pieces of carpet 5m long and 2m wide are required to cover it's floor?
Please help me solving this problem !

Answers

Answer: 8

Step-by-step explanation:

1. What is the difference between the arithmetic mean and geometric mean between 3 and 27 is

a) 15 b) 6 c) 12 d) o​

Answers

Answer:

So I did my work so many times and I got 9 but I don't know Imaooo sry :)

Step-by-step explanation:

The price of a pair of trainers was £85 The price was reduced to £47 Work out the percentage change in price.

Answers

Answer:

The trainers are 44.71% off the original price i think.

Step-by-step explanation:

What is the surface area of this right circular cone?
radius=12
height=40

Answers

Answer:

2026.75 (units) squared

Step-by-step explanation:

SA of a cone = πr(r+h2+r2)

SA = π(12)(12+√(40^2)+(12^2))

SA = 12π(12+√1744)

Put in calculator and get 2026.75

On a coordinate plane, triangle F D E has points (negative 3, 3), (negative 1, negative 1), (negative 3, negative 1). Triangle C B A has points (3, 3), (3, negative 1), (1, negative 1).
What happens to a point when it is reflected over the y-axis?
The coordinates stay the same.
The x-coordinate changes.
The y-coordinate changes.
Both coordinates change.

Answers

Answer:

When a point is reflected across the y axis the values of x change. They become negative values of x.

Answer:

(B) The x-coordinate changes.

Step-by-step explanation:


Solve for x, then choose
the correct graph.
- 3x > 12

Answers

answer:

-4

Step-by-step explanation:

-3x>12

x<-4

the correct graph is graph b

pa help po pls pls pls​

Answers

Answer:

acute angle and number 3 is obtuse

Step-by-step explanation:

Find the missing angle in the image below. Do not include spaces in your answers ** Can somebody help me fr everybody keep giving me the wrong answer

Answers

Answer:

measure of angle V + measure angle W = VUF

Answer:

∠ VUF = 94°

Step-by-step explanation:

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

∠ VUF is an exterior angle of the triangle, then

∠ VUF = 71° + 23° = 94°

A rocket is launched vertically from the ground with an initial velocity of 64 ft/sec determine the rocket’s maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air. graph if possible also

Answers

Answer:

Step-by-step explanation:

The easiest way to solve this is with calculus, believe it or not. The position function is

[tex]s(t)=-16t^2+64t[/tex]. The first derivative of this is the velocity function:

v(t) = -32t + 64. From physics, we know that at the max height of an object's path, the velocity is equal to 0, so setting this velocity equation equal to 0 and solving for time, will tell us the time it took to get to the max height (which we don't know yet, but we will in a bit):

0 = -32t + 64 and

-64 = -32t so

t = 2 seconds. It takes 2 seconds to reach a max height. Plugging that 2 in for t in the position function will tell you the max height that corresponds to this time:

[tex]s(2)=-16(2)^2+64(2)[/tex] and

s(2) = 64 feet.

So the max height is 64 feet and it is reached at 2 seconds after launching.

Also from physics we know that at halfway through a parabolic path, which is also the max height, we are halfway through time-wise as well. That means that if it takes 2 seconds to reach the max height from the ground, it will take another 2 seconds to fall to the ground.

So the total time the rocket is in the air is 4 seconds: 2 seconds to reach the max height and another 2 to fall back down.

Answer:

Step-by-step explanation:

The sum of a father's and his son's age is 60. Eight years ago, the father's age was 3 times that of his son. How old is each of them?​

Answers

Answer:

Father=41

Son=19

Step-by-step explanation:

Father=f

Son=s

f+s=60

Eight years ago would mean that 16 is subtracted from 60 since there is both of them

3s+s=4s

4s=44

s=11

11+8=19

33+8=41

Which inverse trig function could I use to solve this problem?

Answers

Answer:

Inverse sine

Step-by-step explanation:

Recall the three common trig ratios

Remember SohCahToa

Sine = Opposite over Hypotenuse (SOH)

Cosine = Adjacent over Hypotenuse (CAH)

Tangent = Opposite over Adjacent (TOA)

Now let's look back at the question

It asks us which inverse function would we use to solve for angle Z

Looking at angle Z, we are given it's opposite side length and the hypotenuse ( longest side ).

When dealing with the opposite side length and hypotenuse we use trig function sine.

When trying to find the angle we use inverse so we would use inverse sine to find the measure of angle A

Someone help me with these math problems please
Please

Answers

Answer:

a = 15

34.8 + b = 54.6

Step-by-step explanation:

First one:

5a - 10b = 45  (b = 3)

5a - 10(3) = 45

5a - 30 = 45

5a = 75

a = 15

Second one

b + a + 3a = 54.6

b + 4a = 54.6   ( a = 8.7)

b + 4(8.7) = 54.6

b + 34.8 = 54.6

34.8 + b = 54.6

Answer:

a=15 26.1 + b =54.6

Step-by-step explanation:

for the second question we first multiply 8.7 by 3 which gives us 26.1 and since there is only one answer with 26.1 it's it.

If you vertically compress the absolute value parent function, (x) = |X|, by a
factor of 4, what is the equation of the new function?
O A. g(x) = |4x|
O B. g(x) = 1/4 |x|
O C. g(x) = 4|x|
O D. g(x) = |x-4|

Answers

pls mark me as brainlist

thanks a lot

The dimensions of the rectangular pool shown below are 60 yards by 30
yards. A fence will be built around the outside of the deck. The ratio of the
dimensions of the pool to the dimensions of the fence is .. How many yards
of fence should be purchased to enclose the deck?

Answers

Answer:

ok so we have to find the perimiter so

60+60=120

30+30=60

120+60=180

Hope This Helps!!!

Verda used a sensor to measure the speed of a moving car at different times. At each time, the sensor measured the speed of the car in both miles per hour and kilometers per hour. The table below shows her results

Answers

Answer:

Option A

Step-by-step explanation:

If the speed of a car in miles per hour (m) is proportional to the speed in kilometers per hour (k),

m ∝ k

m = ck

Here, c = Proportionality constant

Therefore, c = [tex]\frac{m}{k}[/tex] should be constant for each value given in the table.

For m = 11 and k = 17.699,

c = [tex]\frac{11}{17.699}[/tex]

c = 0.6215

For m = 26 and k = 41.834,

c = [tex]\frac{26}{41.834}[/tex]

c = 0.6215

For m = 34 and k = 54.706,

c = [tex]\frac{34}{54.706}[/tex]

c = 0.6215

Therefore, c is constant for each value of m and k.

Option A will be the correct option.

Describe how you would simplify rootof300. Be thorough and clear in your explanation.

Answers

300 = 3 x 100
Root 100 is ten
So it would be 10 root 3

I need help with question .

Answers

It would be the third one !!!!!!!!!

Answer:

14.8f + 1.8g + 12.1d

Step-by-step explanation:

combine like terms.

3.6+8.5= 12.1

6.2+8.6= 14.8

-2.7+4.5= 1.8

how do i answer this?​

Answers

Step-by-step explanation:

here is the answer. Hope that helps.

which of the following are solutions to the equation 2cos2x-1=0

Answers

Answer:

x = π/4 and 5π/4

Step-by-step explanation:

Given the expression;

2cos²x - 1 = 0

2cos²x = 0+1

2cos²x = 1

cos²x = 1/2

cos x = ±√1/2

cos x = ±0.7071

x = arccos(±0.7071)

x = ±45 degrees

Convert to radians

Sence 180° = π rad

45°  = x

x = 45π/180

x = π/4

If x = -45°

Since cos is negative in the 3rd quadrant

x = 180 + 45

x = 225°

x = 225π/180

x = 45π/36

x = 5π/4

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