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castortr0y [4]
3 years ago
7

The terms of the binomial expansion are written below using the patterns. (m + 2)4 = (1)(m4)(20) + (4)(m3)(21) + (6)(m2)(22) + (

4)(m1)(23) + (1)(m0)(24) Simplify each term to complete the expansion.
Mathematics
1 answer:
lorasvet [3.4K]3 years ago
4 0

Answer:

(m + 2)^4 = m^4+ 8 m^3 + 24 m^2 + 32 m + 16

Step-by-step explanation:

(m + 2)^4 = (1)(m^4)(2^0) + (4)(m^3)(2^1) + (6)(m^2)(2^2) + (4)(m^1)(2^3) + (1)(m^0)(2^4)

2^0 is 1 also m^0 is 1

2^2= 4, 2^3= 8 , 2^4= 16

(m + 2)^4 = (1)(m^4)(1)+ (4)(m^3)(2) + (6)(m^2)(4) + (4)(m^1)(8) + (1)(1)(16)

(m + 2)^4 = m^4+ 8 m^3 + 24 m^2 + 32 m + 16


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Three years hence a father will four times as old as his son will be. Before two years he was seven times as old as his son was.
myrzilka [38]

Answer: The father is 37 years and the son is 7 years

Step-by-step explanation:

Let x represent the present age of the father.

Let y represent the present age of the son.

Three years hence a father will four times as old as his son will be. This means that

x + 3 = 4(y + 3)

x + 3 = 4y + 12

x - 4y = 12 - 3

x - 4y = 9- - - - - - - - - - - - - - - -1

Before two years he was seven times as old as his son was. This means that

(x - 2) = 7(y - 2)

x - 2 = 7y - 14

x - 7y = - 14 + 2

x - 7y = - 12- - - - - - - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

3y = 21

y = 21.3 = 7

Substituting y = 7 into equation 1, it becomes

x - 4 × 7 = 9

x - 28 = 9

x = 9 + 28

x = 37

7 0
3 years ago
Read 2 more answers
There was a sample of 650 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 7.8% eac
Nimfa-mama [501]

Answer:

y = 650·0.922^t

Step-by-step explanation:

At the end of each year, 92.2% of the amount at the beginning of the year remains. That is, the beginning amount is multiplied by 0.922. The exponent t in 0.922^t tells how many times (years) that multiplication has taken place. At the end of t years, the amount remaining in milligrams (y) is ...

y = 650·0.922^t

5 0
3 years ago
Plz help.<br><br> Find the perimeter of the window to the nearest tenth.
Stels [109]
Let's solve this problem step-by-step.

STEP-BY-STEP EXPLANATION:

First, we will establish that the shape of the window is a semi-circle. This means we must use the formula for the perimeter of a semi-circle to obtain the perimeter of the window.

The formula for the perimeter of a semi-circle is as follows:

Let perimeter of window or semi-circle = P

P = [ 2( Pi )r / 2 ] + 2r

Where r = radius of circle or semi-circle

From this, we will simply use the value of the radius given from the diagram in the problem and substitute it into the formula to obtain the perimeter of the window.

P = [ 2( Pi )r / 2 ] + 2r

r = 20

THEREFORE:

P = [ 2( Pi )( 20 ) / 2 ] + 2( 20 )

P = 20( Pi ) + 40

P = 102.83...cm^2

P = 102.8cm^2 ( to the nearest tenth )

FINAL ANSWER:

Therefore, the perimeter of the window is 102.8cm^2 ( to the nearest tenth ).

Hope this helps! :)
Have a lovely day! <3
4 0
3 years ago
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o-na [289]
42 grams
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Round 0.868 to the nearest tenth.
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Answer: 0.9

Step-by-step explanation:

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