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2 years ago

Find the value of x.

Mathematics

1 answer:

Karolina [17]2 years ago

8 0

Answer:

x=60º

Step-by-step explanation:

Answer: x=60º

180º-60º=120º

2x=120º

divide by 2 on both sides

x=60º

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Step-by-step explanation:

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The first three steps of completing the square to solve the quadratic equation x² + 4x - 6 = 0, are

slavikrds [6]

Answer:

The next 3 steps are

Step 4: $(x+2)=\pm \sqrt{10}$

Step 5: $x=-2\pm \sqrt{10}$

Step 6: $x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}$

Step-by-step explanation:

Given:

Quadratic Equation is

x² + 4x - 6 = 0

To Find:

x = ?

Solution:

Step 1: x2 + 4x = 6

Step 2: x2 + 4x + 4 = 6 + 4

Step 3: (x + 2)2 = 10

Step 4: $(x+2)=\pm \sqrt{10}$

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3 years ago

Find the generating function for the sequence 1,1,1,2,3,4,5,6,....

marin [14]

Answer:

$P(x)=\dfrac{1}{1-x}+\dfrac{x^3}{(1-x)^2} \quad \text{for} \mid x \mid < 1$ [/tex]

Step-by-step explanation:

The generating function of a sequence is the power series whose coefficients are the elements of the sequence. For the sequence

$1,1,1,2,3,4,5,6,...$

the generating function would be

$P(x)=1+x+x^2+2x^3+3x^4+4x^5+5x^6+...\\$

we can multiply P(x) by x to get

$xP(x)=x+x^2+x^3+2x^4+3x^5+4x^6+...$

Note that

$P(x)-xP(x)=1+(2x^3-x^3)+(3x^4-2x^4)+(4x^5-3x^5)+(5x^6-4x^6)+...\\ \\=1+x^3+x^4+x^5+x^6+...=1+x^3(1+x+x^2+x^3+x^4+...)$

which for $\mid x \mid < 1$ can be rewritten as

$(1-x)P(x)=1+\dfrac{x^3}{(1-x)} \quad \Rightarrow \\\\P(x)=\dfrac{1}{(1-x)}+\dfrac{x^3}{(1-x)^2}$

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2 years ago