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Oksana_A [137]
3 years ago
5

Give the expression 4n^2t/2n^t-1, write the expression as a binomial.

Mathematics
1 answer:
lubasha [3.4K]3 years ago
7 0

 <span>binomial </span>is an algebraic expression containing 2 terms. For example, (x + y) is a binomial.

We sometimes need to expand binomials as follows:

(a + b)0 = 1

(a + b)1 = a + b

(a + b)2 = a2 + 2ab + b2

(a + b)3 = a3 + 3a2b + 3ab2 + b3

<span>(a + b)4</span> <span>= a4 + 4a3b</span><span> + 6a2b2 + 4ab3 + b4</span>

<span>(a + b)5</span> <span>= a5 + 5a4b</span> <span>+ 10a3b2</span><span> + 10a2b3 + 5ab4 + b5</span>

Clearly, doing this by direct multiplication gets quite tedious and can be rather difficult for larger powers or more complicated expressions.

Pascal's Triangle

We note that the coefficients (the numbers in front of each term) follow a pattern. [This was noticed long before Pascal, by the Chinese.]

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

You can use this pattern to form the coefficients, rather than multiply everything out as we did above.

The Binomial Theorem

We use the binomial theorem to help us expand binomials to any given power without direct multiplication. As we have seen, multiplication can be time-consuming or even not possible in some cases.

<span>Properties of the Binomial Expansion <span>(a + b)n</span></span><span><span>There are <span>\displaystyle{n}+{1}<span>n+1</span></span> terms.</span><span>The first term is <span>an</span> and the final term is <span>bn</span>.</span></span><span>Progressing from the first term to the last, the exponent of a decreases by <span>\displaystyle{1}1</span> from term to term while the exponent of b increases by <span>\displaystyle{1}1</span>. In addition, the sum of the exponents of a and b in each term is n.</span><span>If the coefficient of each term is multiplied by the exponent of a in that term, and the product is divided by the number of that term, we obtain the coefficient of the next term.</span>
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elixir [45]

Answer:

30

Step-by-step explanation:

1.Substitute the x for 12.

2.Multiply the 2 by 12.

3.Then add 6 to your answer.

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3 years ago
$5,000 is invested in two different accounts yielding 3% and 3.5% interest. The interest earned on the two accounts is $155. Let
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3 years ago
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Help please explain how you got the answer
pychu [463]

Answer: V≈900 ft³

Step-by-step explanation:

Formula

V=πr²h

Given

r=5 ft

h=12 ft

Solve

V=πr²h

V=π(5)²(12)

V=π(25)(12)

V=300π

V≈300(3)

V≈900 ft³

Hope this helps!! :)

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5 0
3 years ago
Jai Narayan sells two radio sets for 2288 each.
san4es73 [151]

Answer:

1%

Step-by-step explanation:

S.P of each radio=$ 2288

Total S.P=2\times 2288=$4576

Gain=10%

Lose=10%

C.P=\frac{S.P\times 100}{100+gain(in\;percent)}

C.P=\frac{S.P\times 100}{100-loss(in\;percent)}

By using the formula

C.P of one radio=\frac{2288\times 100}{110}=$2080

C.P of another radio=\frac{2288\times 100}{100-10}=$2542.2

Total C.P of two radios=2080+2542.2=$4622.2

Total C.P >Total S.P

Loss=S.P-C.P

Loss=4622.2-4576=$46.2

Loss%=\frac{Loss}{C.P}\times 100

Loss %=\frac{46.2}{4622.2}\times 100=1%

Hence, his loss 1%

5 0
3 years ago
Is this expression equivalent?<br> 3v+v and 12v over 3
xeze [42]
Yes this is equal because 3v+v is 4v and if you divide 12v by 3 you also get 4v
7 0
3 years ago
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