BRAINLY AND 20 PTS TO WHOEVER GETS IT RIGHT

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

A line that includes the points

timofeeve [1]

Answer:

p = -12

Step-by-step explanation:

I used graph paper to graph point (-7,-6) then i used the slope to continue to graph the rest of the points until i got to (-1,-12).

7 0

4 years ago

Express the first quantity as a percentage of second quantity $45, $120.

Pachacha [2.7K]

Answer: 37.5%

Step-by-step explanation:

Percentage = Given Quantity/Total Quantity*100

So here, it will be like: 45/120*100

=0.375*100

=37.5%

5 0

2 years ago

Fiona and Camilla took a load of peaches to the farmer’s market. During the first hour, they sold ½ of the peaches plus ½ of a p

Lana71 [14]

They took 101 peaches to market.

Check:

In the 1st hour, they sold (101/2 + 1/2) = 102/2 = 51. They had 50 left.

In the 2nd hour, they sold (50/3 + 1/3)=51/3=17. They had (50-17)=33 left.

In the 3rd hour, they sold (33/4 + 3/4) = 36/4 = 9. They had (33-9) = 24 left.

In the final hour, they sold (24/5 + 1/5) = 25/5 = 5. They had (24-5) = 19 left. yay!

Fiona and Camilla took their 19 remaining peaches and went home. Sharing with
their parents and their brother Rowlf, each person had 3.8 peaches for dinner.
There was a lot of activity in the bathroom overnight.

================================================

The key to solving this one is to work it backwards.

-- They had 19 peaches left at the end of the day.

-- During the final hour, the 1/5 of a peach that they sold left them with 19,
so they had 19-1/5 before they sold the 1/5 of a peach.
The 19-1/5 was 4/5 of what they had at the beginning of the final hour.
So, at the beginning of the final hour, they had (5/4)x(19.2) = 24 .

-- During the 3rd hour, the 3/4 of a peach that they sold left them with 24,
so they had 24-3/4 before they sold the 3/4 of a peach.
The 24-3/4 was 3/4 of what they had at the beginning of that hour.
So, at the beginning of the 3rd hour, they had (4/3)x(24.75) = 33 .

Do the same for the 2nd hour.

Then do the same for the 1st hour.

And you'll work your way back up to 101 peaches.

4 0

3 years ago

Point K is on line JL. given JL =4x, JK= 2x+3, and KL=x, determine the numerical length of kl

balandron [24]

Hi! I'm happy to help!

Our total line is JL (4x), and it is split into two parts: JK, and KL. We have our values, and we know that JK+KL=JL, so we can substitute our values and solve for x:

4x=(2x+3)+(x)

4x=3x+3

To solve for x, we have to isolate it on one side of the equation.

First, let's subtract 3x from both sides so that we can isolate x:

4x=3x+3

-3x -3x

x=3

So, our x=3, which means that KL=3.

I hope this was helpful, keep learning! :D

5 0

3 years ago