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KIM [24]
3 years ago
7

Help PLZZ

Mathematics
1 answer:
Alexus [3.1K]3 years ago
3 0
<h3 /><h3>\huge \rm༆ Answer ༄</h3>

To find slope we use the formula ~

  • \sf \dfrac{y2 - y1}{x2 - x1}

[ Ratio of the difference of y - coordinates of the points and the difference of x - coordinates of the points ]

let's find the slope of line passing through the given points ~

<h3>1. (10 , -9) and (-4 , -14) </h3>

  • \sf \dfrac{ - 9 - ( - 14)}{10 - ( - 4)}

  • \sf \dfrac{ - 9 + 14}{10 + 4}

  • \sf \dfrac{5}{14}
<h3>2. (16 , 6) and (-4 , -14)</h3>

  • \sf \dfrac{6 - ( - 14)}{16 - ( - 4)}

  • \sf \dfrac{6 + 14}{16 + 4}

  • \sf \dfrac{20}{20}

  • \sf1
<h3>3. (9 , -4) and (5 , -20)</h3>

  • \sf \dfrac{ - 4 - ( - 20)}{9 - 5}

  • \sf \dfrac{ - 4 + 20}{4}

  • \sf \dfrac{16}{4}

  • \sf4

<h3>4. (-13 , 20) and (-18 , 20)</h3>

  • \sf \dfrac{20 - 20}{ - 13 - ( - 18)}

  • \sf\dfrac{0}{ - 13 + 18}

  • 0

I hope it helps ~

___________________________________

꧁ \: \: \large \rm{kaul} \: ꧂

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Using the combination formula, it is found that photos of 9 different chairs were shown to the home owner.

The order in which the chairs are chosen is important, hence, the <em>permutation formula </em>is used to solve this question.

<h3>What is the permutation formula?</h3>

P_{n,x} is the number of different permutations of x objects from a set of n elements, given by:

P_{n,x} = \frac{n!}{(n-x)!}

In this problem, two chairs are chosen from a set of n, and there are 72 different outcomes, hence:

P_{n,x} = 72, x = 2

P_{n,x} = \frac{n!}{(n-x)!}

72 = \frac{n!}{(n-2)!}

72 = \frac{n(n - 1)(n - 2)!}{(n-2)!}

n^2 - n = 72

n^2 - n - 72 = 0

Which is a quadratic function with coefficients a = 1, b = -1, c = -72, hence:

\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-72) = 289

Taking the positive root:

x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{289}}{2} = 9

Photos of 9 different chairs were shown to the home owner.

You can learn more about the permutation formula at brainly.com/question/25925367

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