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2 years ago

Consecutive integers are integers that

Mathematics

1 answer:

gogolik [260]2 years ago

6 0

Answer: The three numbers are 10, 11, and 12.

10+11+12 = 33

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

Work Shown:

x = smallest number
x+1 = middle number
x+2 = largest number

Each is a positive whole number

Add them up and set the result equal to 33. Solve for x.

(x) + (x+1) + (x+2) = 33

3x+3 = 33

3x+3-3 = 33-3 .... subtract 3 from both sides

3x = 30

3x/3 = 30/3 ..... divide both sides by 3

x = 10

x+1 = 10+1 = 11

x+2 = 10+2 = 12

Note how 10+11+12 = 33 to help confirm our answer.

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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

2 years ago

Why do you think we have to separate items in a list using commas

stich3 [128]

Answer:

I think we have to use commas in lists because if we didn't it would be all together and it would be more hard to read.

Step-by-step explanation:

I hope this helps

8 0

2 years ago

How do I make a the subject?<br><br> S= a/4 + 8u

Crazy boy [7]

S= a/4 + 8u

S - 8u = a/4 (First you subtract 8u from both sides)

4(S - 8u) = a ( Then you multiply both sides by 4)

Final answer:
4(S - 8u) = a

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2 years ago

Solve the compound inequality 4x – 7 > 5 or 5x + 4 ≤ –6

bija089 [108]

Answer:

inequality form: x $\leq$ -2 or x > 3

interval notation form: (-∞,-2] ∪ (3,∞)

Step-by-step explanation:

I attached a picture that shows all the work. You begin by isolating then solving for x on both sides. Then form a solution using the information found out about x. For example, you can combine the found inequalities for x to solve that x must be GREATER than 3 while being LESS than -2. Using that you can form an line and make a line. Remember, when writing in interval notation form you always begin from the left to the right (in reference) to the number line.

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1 year ago

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kotegsom [21]

Step-by-step explanation:

24²+7²=25²

576+49=625

625=625

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3 years ago