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Brrunno [24]
3 years ago
9

Which of the following is one of the special product formulas?

Mathematics
2 answers:
polet [3.4K]3 years ago
7 0

Answer:

c .Perfect square trinomials

d.Difference of perfect squares

Step-by-step explanation:

We have to find the special product formulas.

a.Perfect square monomials

It is of the form x^2

It is not a special product formulas.

b.Difference of terms

It is of the form

x-y

It is not a special product formulas.

c.Perfect square trinomials

It is of the form

(x+y)^2=x^2+y^2+2xy

It is a special product formulas.

d.Difference of perfect squares

It is of the form

x^2-y^2

(x+y)(x-y)

Therefore, it is a special product formulas.

Klio2033 [76]3 years ago
4 0

Answer:

Perfect square trinomials and difference of two squares are just to binomials being multiplied, and they are special because there is a specific formula for them. Perfect square trinomial:(a+b)^2, a^2+2ab+b^2. Difference of squares: (a+b)(a-b), a^2-b^2

Step-by-step explanation:

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Answer:

32.

Step-by-step explanation:

I accidentally put my age too high. Im only in middle school but 32 could be one answer. If two sides are the same then it could be an isoceles triangle or whatever.

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Find the number of ways to purchase 3 different kinds of drinks from a selection of 10 drinks.
Genrish500 [490]
The correct answer is 120.
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How do the values in Pascal’s triangle connect to the coefficients?
damaskus [11]

Explanation:

Each row in Pascal's triangle is a listing of the values of nCk = n!/(k!(n-k)!) for some fixed n and k in the range 0 to n. nCk is <em>the number of combinations of n things taken k at a time</em>.

If you consider what happens when you multiply out the product (a +b)^n, you can see where the coefficients nCk come from. For example, consider the cube ...

  (a +b)^3 = (a +b)(a +b)(a +b)

The highest-degree "a" term will be a^3, the result of multiplying together the first terms of each of the binomials.

The term a^b will have a coefficient that reflects the sum of all the ways you can get a^b by multiplying different combinations of the terms. Here they are ...

  • (a +_)(a +_)(_ +b) = a·a·b = a^2b
  • (a +_)(_ +b)(a +_) = a·b·a = a^2b
  • (_ +b)(a +_)(a +_) = b·a·a = a^2b

Adding these three products together gives 3a^2b, the second term of the expansion.

For this cubic, the third term of the expansion is the sum of the ways you can get ab^2. It is essentially what is shown above, but with "a" and "b" swapped. Hence, there are 3 combinations, and the total is 3ab^2.

Of course, there is only one way to get b^3.

So the expansion of the cube (a+b)^3 is ...

  (a +b)^3 = a^3 + 3a^2b +3ab^2 +b^3 . . . . . with coefficients 1, 3, 3, 1 matching the 4th row of Pascal's triangle.

__

In short, the values in Pascal's triangle are the values of the number of combinations of n things taken k at a time. The coefficients of a binomial expansion are also the number of combinations of n things taken k at a time. Each term of the expansion of (a+b)^n is of the form (nCk)·a^(n-k)·b^k for k =0 to n.

6 0
3 years ago
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STatiana [176]

Answer:

To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and f^{-1}(x)= \frac{ln\ x+4}{2}

Step-by-step explanation:

Data provided in the question

f(x) = e^2x - 4

Now

to find the inverse let

So,

y = e^2x - 4

Now

Replace x and y

Therefore

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Now compute the value of y

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Now take ln on both sides:

The equation is

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ln(x+4) = 2y

y = ln(x+4) ÷ 2

f^{-1}(x)= \frac{ln\ x+4}{2}

Therefore,  To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and f^{-1}(x)= \frac{ln\ x+4}{2}

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