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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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What is the equation of the line passing through the points (–25, 50) and (25, 50) in slope-intercept form?
allochka39001 [22]

The equation of the line passing through the points (-25, 50) and (25, 50) in slope-intercept form is <u>y = 50</u>. Hence, <u>4th option</u> is the right choice.

The slope-intercept form of a line is written as y = mx + b, where m is the slope of the line, and b is the y-intercept.

The slope of a line passing through the points (x₁, y₁) and (x₂, y₂) can be calculated using the formula, slope (m) = (y₂ - y₁)/(x₂ - x₁).

Therefore, slope of the line passing through the points (-25, 50) and (25, 50) can be calculated as m = (50 - 50)/(25 - (-25)) = 0/(-50) = 0.

We can find the equation of the line using the point-slope formula, according to which, a line having a slope m and passing through the point (x₁, y₁) can be written as y - y₁ = m(x - x₁).

Therefore, the equation of the given line can be written as:

y - 50 = 0(x - 25)

or, y - 50 = 0,

or, y = 50.

Therefore, the equation of the line passing through the points (-25, 50) and (25, 50) in slope-intercept form is <u>y = 50</u>. Hence, <u>4th option</u> is the right choice.

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3 0
2 years ago
What number should be added on both sides of the equation to complete the square?x^2-10x=7
ArbitrLikvidat [17]
<span>What number should be added on both sides of the equation to complete the square is (-10/2)^2 or (10/2)^2 or 5^2 or 25.</span>
3 0
3 years ago
an ice cream shop manager lowered the price for a single scoop of ice cream from 2.50 to 2.00 what is the precent of decrease in
igomit [66]
2.50-2.00=0.5
2.50/0.5= 5 = 100%
2.00/0.5=4 = 80%
100-80= 20%
6 0
2 years ago
If TU = 8, UV = 3x, and TV = x + 10, what is TV?
IgorLugansk [536]

The value of TV is 11.

<h3>What is equation?</h3>

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given:

TU= 8, UV = 3x and TV = x+10

TV= TU + UV

x +10= 8+ 3x

-2x = -2

x= 1

Hence, TV = 1+10= 11.

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200 days from March 3 is
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September 19 , 2018 is the answer
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