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KonstantinChe [14]
4 years ago
15

Expand using pascal triangle (3x+2)^4

Mathematics
1 answer:
Liula [17]4 years ago
6 0

Answer:

The answer is

<h3>81x⁴ + 216x³ + 216x² + 94x + 16</h3>

Step-by-step explanation:

(3x + 2)⁴

<u>Using the Pascal's triangle</u>

For an exponent of 4 we have

( a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b³

Using a = 3x and b = 2 we have

( 3x +2)⁴ = ( 3x)⁴ + 4 [ (3x)³(2) ] + 6[ (3x)²(2)²] + 4 [ 3x(2)³ ] + 2⁴

Expand and simplify

That's

➢ ( 3x +2)⁴ = 81x⁴ + 4[ (27x³)(2) ] + 6 [ (9x²)(4) ] + 4 [ 3x(8) ] + 16

➢ 81x⁴ 4( 54x³) + 6(36x²) + 4( 24x) + 16

We have the final answer as

<h3>81x⁴ + 216x³ + 216x² + 94x + 16</h3>

Hope this helps you

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Free points tonight &lt;3
kirill [66]

Answer:

awww tysm! ill try to help you! :)                                                                          Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
-14n=-280<br>solve for n​
Andreyy89

Answer:

the answer is:.......

..n=20

6 0
3 years ago
Read 2 more answers
Which expressions are equal to 6^3•2^6/ 2^3
True [87]

Answer:

2^6 x 3^3 and 12^3

Step-by-step explanation:

First, solve

6^3 x 2^6/2^3

216 x 64/8

13824/8 = 1728

lets solve for the answers

6^3 = 216

Therefore, 6^3 is not an answer

2^6 x 3^3= 64 x 27 = 1728

because both expressions are equal to 1728, this is an answer. this answer can also eliminate 2^3 x 3^3 because it has a lower exponent than the answer that is equal to 1728. therefore, the value of it must be smaller than 1728

12^3 = 1728

This answer is correct, because both values are equal to each other, meaning that 12^6 is larger than 1728  

Therefore, your answers will be 2^6 x 3^3 and 12^3          

3 0
3 years ago
Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven. Pick a U.S. city
insens350 [35]

Answer:

<u>1. New York City:</u> The initial charge is $ 2.50 plus $ 0.50 per 1/5 mile when traveling above 12 mph or per 60 seconds in slow traffic or when the vehicle is stopped. There are other surcharges for overnight, rush hour or congestion.

<u>2. Boston:</u> First 1/7 Mile: $2.60  and each 1/7 Mile thereafter: $0.40.

<u>3. Houston:</u> First 1/11 mile  $2.80 , each additional 1/11 mile  $0.20 . Rate per mile after first mile  $2.20 and wait time per minute  $0.40.

Step-by-step explanation:

Normally, there's a standard fare for each city, so for answering the question we picked three well-known cities for comparing the fares.

<u>1. New York City:</u> The initial charge is $ 2.50 plus $ 0.50 per 1/5 mile when traveling above 12 mph or per 60 seconds in slow traffic or when the vehicle is stopped. There are other surcharges for overnight, rush hour or congestion.

<u>2. Boston:</u> First 1/7 Mile: $2.60  and each 1/7 Mile thereafter: $0.40.

<u>3. Houston:</u> First 1/11 mile  $2.80 , each additional 1/11 mile  $0.20 . Rate per mile after first mile  $2.20 and wait time per minute  $0.40.

4 0
4 years ago
A ball is thrown into the air with an upward velocity of 28 ft/s. its height,h, in feet after t seconds is given by the function
ddd [48]

<span>h= (-16t^2 + 28t + 7)  </span>

find the derivative to get time<span>
<span>
h' = (-32t + 28)

When the ball reaches its maximum height, its vertical velocity (h’) will be 0 </span></span>

<span>
<span> 0 = -32t + 28 </span></span>

-32t=-28

<span><span>-28/-32 =  </span>0.875 seconds </span><span>
<span>
The ball reaches its maximum height in 0.875 seconds after being thrown; plug and chug and:

h= (-16(0.875)^2 + 28(0.875) + 7) = 19.25 feet</span></span>

 

Max height = 19.25 feet, time = 0.88 seconds


8 0
3 years ago
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