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Alex787 [66]
3 years ago
6

We can calculate the depth ddd of snow, in centimeters, that accumulates in Harper's yard during the first hhh hours of a snowst

orm using the equation d=5hd=5hd, equals, 5, h. How many hours does it take for 111 centimeter of snow to accumulate in Harper's yard?
Mathematics
1 answer:
inna [77]3 years ago
3 0

Answer:

0.2 hours

Step-by-step explanation:

The depth, d of snow (in cm) that accumulates in Harper's yard during the first h hours of a snowstorm can be calculated using the equation:

d=5h

When d=1cm, we want to determine the value of h.

1=5h

h=1/5=0.2

Therefore, it takes 0.2 hours for 1 centimeter of snow to accumulate in Harper's yard.

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Answer:

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Step-by-step explanation:

first subtract 9x from 9x+3y=18

                                   -9x       -9x

so you get 3y=18-9x or 3y=-9x+18 then divide both sides by 3

so you get y=6-3x hope this helps :)

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3 years ago
Give the expression 4n^2t/2n^t-1, write the expression as a binomial.
lubasha [3.4K]

 <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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3 years ago
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