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2 years ago

Without actually writing the formula, explain how to expand (x + 3)7 using the binomial theorem.

Mathematics

2 answers:

dusya [7]2 years ago

8 0

To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal’s triangle.

For the first term, write x to the 7th power and 3 to the 0 power. Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7.

Simplify by evaluating the coefficients and powers of 3.

GenaCL600 [577]2 years ago

8 0

Answer:

1)To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal’s triangle.

2)For the first term, write x to the 7th power and 3 to the 0 power. Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7.

3)Simplify by evaluating the coefficients and powers of 3.

Step-by-step explanation:

Choose any answer above; either way there all correct

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If p is a polynomial show that lim x→ap(x)=p(a

Lostsunrise [7]

Let p(x) be a polynomial, and suppose that a is any real number. Prove that

lim x→a p(x) = p(a) .

Solution. Notice that

2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .

So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x – 2.

Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| < 1, so −2 < x < 0. In particular |x| < 2. So

|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|

= 2|x|^3 + 5|x|^2 + |x| + 2

< 2(2)^3 + 5(2)^2 + (2) + 2

= 40

Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2 + x − 2| < ε/40 · 40 = ε.

3 0

2 years ago

Jacinta buys 4 pounds of turkey and 2 pounds of ham. She pays a total of $30, and the turkey costs $1.50 less per pound than the

marissa [1.9K]

Given

jacinta buys 4 pounds of turkey and 2 pounds of ham & pays a total of $30, turkey costs $1.50 less per pound than the ham.

find out the combined cost of 1 pound of turkey and 1 pound of ham

To proof

As given in the question

jacinta buys 4 pounds of turkey and 2 pounds of ham

total pay by jacinta = $30

let us assume that the price of the ham = x

as given in the question

turkey costs $1.50 less per pound than the ham

turkey costs becomes = x - 1.50

then the equation becomes

30 = 4 (x - 1.50) + 2x

30 = 4x + 2x - 6

36 = 6x

x = 6

thus

ham cost per pound = $6

turkey cost per pound = 6 - 1.50

= $ 4.5

Now find out

cost of 1 pound of turkey + 1 pound of ham = $ 6 + $ 4.5

= $ 10.5

Hence proved

5 0

2 years ago

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Hannah and Corrine are playing a game by rolling two cubes, each numbered 1 through 6. If the sum of the numbers on the cubes is

Katarina [22]

Answer:

D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

Step-by-step explanation:

To get a sum of 7 by rolling two cubes, we need to get one of the combinations from the list below:

1 on the first cube, 6 on the second cube

6 on the first cube, 1 on the second cube

2 on the first cube, 5 on the second cube

5 on the first cube, 2 on the second cube

3 on the first cube, 4 on the second cube

4 on the first cube, 3 on the second cube

Therefore, the correct answer option is D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

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2 years ago

a basketball player made 27 free throws in her last 45 tries. what is the experimental probability that she will make her next f

Strike441 [17]

Hey mark me brainlest but ur answer is 27/45

Bess ur day.

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2 years ago

Fiona started her study of bacteria growth with 1,000 bacteria in a petri dish. After 1 hour, the count was increased to 1,800.

SOVA2 [1]

F (x)=1000×1.8^x is the equation.

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2 years ago

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