The sum of two numbers is 24<br> and their quotient is 3.<br> What are the two numbers?

Expand (2 + a)9 using Pascal’s triangle.

Natalija [7]

Answer:

Step-by-step explanation:

The Pascal triangle is used to determine the coefficients of the terms when we expand the expression.

1 $(A + B) ^ 0$ = 1

1 1 $(A +B ) ^ 1 = 1A + 1B$

1 2 1 $(A+ B) ^ 2 = 1A^2 + 2 AB + 1B^2$

By extending the triangle, you will get the 9th row, which is your expression, of the coefficients. that is

1 9 36 84 126 126 84 36 9 1

Now, fill in AB in the gaps.

1AB + 9 AB + 36AB + 84AB + 126AB + 126AB +84AB + 36AB + 9AB + 1AB

Next, you need to go from the left to fill out the exponent of A and it will go down from 9 (the exponent of the whole thing) . That is

$1A^9B+9A^8B+36A^7B+84A^6B+126A^5B+126A^4B+84A^3B+36A^2B+9A^1B+1A^0B$

Next will be the exponent of B. this time, you go from the right and do the same with A. You can go from the left also, but go up from 0 to 9 for the exponent of B

$1A^9B^0+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+1A^0B^9$

The last step is just to simplify the A^0=1 and B^0 =1 at the first and the last terms.

$A^9+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+B^9$

Hope you can learn the method

5 0

3 years ago

Why is 1/2 greater than 1/4

Mkey [24]

Answer:

its because 1/2 = 0.50 and 1/4 = 0.25

and 0.50 is greater than 0.25

~batmans wife

7 0

3 years ago

Use parallelogram ABCD. What are the values of x and y?<br><br> x = <br> y =

Tasya [4]

Answer:

x = 17 and y = 10

Step-by-step explanation:

ABCD is a parallelogram

So AB = CD and AD = BC

so

3x - 9 = 42

3x = 51

x = 17

and

4y - 3 = 37

4y = 40

y = 10

Answer

x = 17 and y = 10

6 0

3 years ago

Read 2 more answers

Find the two smallest possible solutions to part 1a

bixtya [17]

<h3>Answer: A. 5/12, 25/12</h3>

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Work Shown:

12*sin(2pi/5*x)+10 = 16

12*sin(2pi/5*x) = 16-10

12*sin(2pi/5*x) = 6

sin(2pi/5*x) = 6/12

sin(2pi/5*x) = 0.5

2pi/5*x = arcsin(0.5)

2pi/5*x = pi/6+2pi*n or 2pi/5*x = 5pi/6+2pi*n

2/5*x = 1/6+2*n or 2/5*x = 5/6+2*n

x = (5/2)*(1/6+2*n) or x = (5/2)*(5/6+2*n)

x = 5/12+5n or x = 25/12+5n

these equations form the set of all solutions. The n is any integer.

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The two smallest positive solutions occur when n = 0, so,

x = 5/12+5n or x = 25/12+5n

x = 5/12+5*0 or x = 25/12+5*0

x = 5/12 or x = 25/12

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Plugging either x value into the expression 12*sin(2pi/5*x)+10 should yield 16, which would confirm the two answers.

7 0

3 years ago

Read 2 more answers

The city is planning to add a fish pound to a neighborhood park. the figure below is a scale drawing of the fish pound. its scal

CaHeK987 [17]

Answer: Sorry if it's wrong I hope I helped you

5 0

2 years ago

The sum of two numbers is 24 and their quotient is 3. What are the two numbers?