Factor x^2-10x+25,please show work

1 answer:

5 0

This is relatively easy because that 25 is a perfect square, whose (square) roots are 5 and -5. x^2-10x+25 = (x - 5)(x - 5). Note how (-5)(-5) = +25, and how -5x - 5x = -10x.

The roots are { (x-5), (x-5) }.

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How many 10-digit ternary strings are there that contain exactly two 0s, three 1s, and five 2s?

Svet_ta [14]

There are $\dbinom{10}2$ ways of picking 2 of the 10 available positions for a 0. 8 positions remain.

There are $\dbinom83$ ways of picking 3 of the 8 available positions for a 1. 5 positions remain, but we're filling all of them with 2s, and there's $\dbinom55=1$ way of doing that.

So we have

$\dbinom{10}2\dbinom83\dbinom55=\dfrac{10!}{2!(10-2)!}\dfrac{8!}{3!(8-3)!}\dfrac{5!}{5!(5-5)!}=2520$

The last expression has a more compact form in terms of the so-called multinomial coefficient,

$\dbinom{10}{2,3,5}=\dfrac{10!}{2!3!5!}=2520$

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Step-by-step explanation:

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What is the equation of the line that passes through the points (4/5,1/5) and (1/2,3/2)?

Setler [38]

Answer:

$y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})$ point-slope form

$13x+3y=11$ (standard form)

Let me know if you prefer another form.

Step-by-step explanation:

The slope of a line can be found using $\frac{y_2-y_1}{x_2-x_1}$ provided you are given two points on the line.

We are.

Now you can use that formula. But I really love to just line up the points vertically then subtract them vertically then put 2nd difference over 1st difference.

(4/5 , 1/5)

-( 1/2 , 3/2)

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

3/10 -13/10

2nd/1st = $\frac{\frac{-13}{10}}{\frac{3}{10}}=\frac{-13}{3}$ is our slope.