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Lady_Fox [76]
3 years ago
9

Why do we think 0! = 1?

Mathematics
1 answer:
garri49 [273]3 years ago
4 0

4!=4\times3\times2\times1=24\\3!=3\times2\times1=6\\2!=2\times1\\1!=1\\0!=?

Notice that when we go from 4! to 3! , we divide by 4.

(Because 4!\div 4 = 4\times3\times2\times1\div4=3\times2\times1=3!  <em>the 4's cancel</em>)

And when we go from 3! to 2! , we divide by 3, and etc.

We can use this pattern to see why 0! = 1.

4!=4\times3\times2\times1=24\\3! = 4!\div4=24\div4=6\\2!=3!\div3=6\div3=2\\1!=2!\div2=2\div2=1\\0!=1!\div1=1\div1=1

And so by following the pattern, we determine that 0! = 1

-------------------------------

Note:

There are no factorials of negative numbers, and we can use the pattern to show why:

0!=1\\-1!=0!\div0=1\div0=???!!??!?

You can't divide a number by 0, therefore -1! doesn't exist, so -2! doesn't exist and so on. So you can't do the factorial of any negative number.

(Or at least there no real solutions to negative factorials)

------------------------

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The linear function equation is \boxed{y = \frac{1}{3}x - 4}.

Further explanation:

The formula for slope of line can be expressed as,

\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}

Explanation:

The line intersect \text{y}-axis at \left( {0,- 4} \right).

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The slope can be obtained as follows,

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The slope of the line is \dfrac{1}{3}.

The slope intercept form of the linear equation is given as follows.

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Substitute \dfrac{1}{3} for m and -4 for k in equation y = mx + k.

y = \dfrac{1}{3}x - 4

The linear function equation is \boxed{y = \frac{1}{3}x - 4}.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: graph function, numbers, slope, slope intercept, equation, linear function, linear equation, y-intercept, graph, representation, origin.

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Step-by-step explanation:

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Replace x with y and vice versa:

x = y + 4

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X=-6

Hope I have been of assistance!
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3 years ago
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