The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y)^6 are _____.

2 answers:

5 0

Using the triangle of pascal we have that the expression equivalent to (x + y) ^ 6 is given by:
x ^ 6 + 6x ^ 5y + 15x ^ 4y ^ 2 + 20x ^ 3y ^ 3 + 15x ^ 2y ^ 4 + 6xy ^ 5 + y ^ 6
Therefore, the coefficients of the expansion are given by:
1, 6, 15, 20, 15, 6, 1
Answer:
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y) ^ 6 are 1, 6, 15, 20, 15, 6, 1

Ksivusya [100]3 years ago

5 0

Answer:

1, 6, 15, 20, 15, 6, 1

Step-by-step explanation:

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The ratio of boys to girls at a movie is . If there are 21 girls, how many boys are at the movie?

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2 years ago

Write the point-slope form of the equation for a line that passes through (6,-1) with a slope of 2

Vika [28.1K]

Answer: y + 1 = 2(x-6)

Step-by-step explanation:

Point Slope Form is y-y₁=m(x-x₁), and all you have to so is substitute in the values that you were given. So, the slope is 2, so you substitute that value in for m. Then, you substitute 6 in for x₁ (because 6 is the x value of the coordinate you were given) and you substitute -1 for y₁ (and it becomes positive because two negatives make a positive)

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3 years ago

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What is x^3−3x^2+3x−1 divided by x^2−2x+1 ?

masya89 [10]

Answer:

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3 years ago

Kim took out a $55,000 loan for college. She is borrowing money from two banks. Bank A charges an interest rate of 8%, and Bank

stellarik [79]

Kim's Loan:
Let A = amount borrowed from bank A.
Let B = amount borrowed from bank B.

The total loan is $55,000.
Therefore
A + B = 55000 (1)

Bank A charges 8% interest. The interest after 1 year is 0.08A.
Bank B charges 11% interest. The interest after 1 year is 0.11B.
Total interest after 1 year is $5,000.
Therefore
0.08A + 0.11B = 5000 (2)

From (1), obtain
B = 55000 - A (3)

Substitute (3) into (2).
0.08A + 0.11(55000 - A) = 5000
0.08A + 6050 - 0.11A = 5000
-0.03A = -1050
A = -1050/-0.03 = 35000

Answer: Kim borrowed $35,000 from bank A.

Jack's Loan.
A = loan from bank A.
B = loan from bank B.
The total loan is $10,000.
Therefore
A + B = 10000 (4)

Bank A charges 5% interest and bank B charges 6% interest.
Total interest after 1 year is $530, therefore
0.05A + 0.06B = 530 (5)

From (4), obtain
B = 10000 - A (6)

Substitute (6) into (5).
0.05A + 0.06(10000 - A) = 530
0.05A + 600 - 0.06A = 530
-0.01A = -70
A = -70/-0.01 = 7000

Answer: Jack borrowed $7,000 from bank A.

3 0

3 years ago