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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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1. SPOTLIGHTS Ship A has coordinates (–1, –2) and Ship B has coordinates (–4, 1). Both ships have their spotlights fixated on th
Alexeev081 [22]

Answer:

( 5 , 10 )

Step-by-step explanation:

Solution:-

- There are two ships, A and B, currently located by their respective coordinates in the cartesian coordinate system:

          <u>Position of ship A: ( - 1 , -2 )</u>

          <u>Position of ship B: ( -4 , 1 )</u>

- Both ships try to locate a lifeboat. The spotlights used by each ship are modelled as straight line functions of cartesian coordinate originating from their respective ships.

- Spot lights for each ship were able to locate the same lifeboat. The respective spotlights are modelled by the following functions:

         <u>Spotlight Ship A: y = 2x</u>

         <u>Spotlight Ship B: y = x + 5 </u>

- To locate the position of the lifeboat with respect to the origin ( 0 , 0 ) we will use the spotlight model functions and equate them. This is because the spotlights must converge or meet at the position of lifeboat provided the lifeboat is found by both ships.

- Therefore,

       

         Spotlight A = Spotlight B

         y = 2x = x + 5

         2x = x + 5

         x = 5 , y = 10

<u>Answer:</u> <em>The two spotlight meet at the coordinates ( 5 , 10 ). This is also the position of the lifeboat located by both the ships</em><em>. </em>

       

7 0
3 years ago
Translate the verbal phrase into a algebraic expression pls
erica [24]
2 × (x + 3) < 5
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4 0
3 years ago
What is the HCF of 66, 121 ,132
gayaneshka [121]
11

66=11×6
121=11×11
132=11×12
5 0
3 years ago
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Pleas help ill appreciate it asap pleas
Mashcka [7]

Answer:

I think it would be 3y+3y-12 because 6y=3y+3y

Step-by-step explanation:


4 0
3 years ago
Read 2 more answers
Thanks for your response!<br> Question will be show✔
algol13
<h3>Answer:</h3>

\large\boxed{-1\frac{16}{25},\,\frac{6}{40},\,0.35,\,1\frac{3}{4}}

<h3>Step-by-step explanation:</h3>

In this question, it's asking you to put the numbers that were given from <em>least </em>to <em>greatest.</em>

Our given numbers are:

  • \frac{6}{40}
  • 0.35
  • 1\frac{3}{4}
  • -1\frac{16}{25}

Now, lets sort them out.

We know that negative numbers would be the least. Sicne there's only one negative number, we would put that first because it's the least out of the numbers.

\frac{6}{40} would go next. To make it easier, we can turn it into a decimal. \frac{6}{40} = 0.15 when you divide.

0.35 will go next. This would be bigger than 0.15, but lower than the next number.

1\frac{3}{4} would go last, due to the fact that it's the greatest. 1\frac{3}{4} is the same as 1.75

When you put them in order, you should get -1\frac{16}{25},\,\frac{6}{40},\,0.35,\,1\frac{3}{4}

<h3>I hope this helped you out.</h3><h3>Good luck on your academics.</h3><h3>Have a fantastic day!</h3>
4 0
3 years ago
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