Line CH contains points (-2, 6) and H(5, -3) What is the slope of G?

Mathematics

1 answer:

Xelga [282]3 years ago

4 0

Answer:

The slope of line G is $\dfrac{- 9}{7}$ .

Step-by-step explanation:

Given as :

The points of the line CH contains

C = $x_1$ , $y_1$ = - 2 , 6

H = $x_2$ , $y_2$ = 5 , -3

Let The slop of line CH = G

Now, slope of line is

G = $\dfrac{y_2 - y_1}{x_2-x_1}$

i.e G = $\dfrac{- 3 - 6}{5 -(-2)}$

Or, G = $\dfrac{- 9}{5 +2}$

Or,G = $\dfrac{- 9}{7}$

So, The slope of the line CH = G = $\dfrac{- 9}{7}$

Hence, The slope of line G is $\dfrac{- 9}{7}$ . Answer

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Consider rolling two fair dice one 3-sided the other 5-sided

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Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose

$1\leq x\leq 3,\quad 1\leq y \leq 5$

We have $P(X=x)=\frac{1}{3}$ and $P(Y=y)=\frac{1}{5}$ , because the dice are fair.

Now we use the assumption of independence to claim that

$P(X=x, Y=y) = P(X=x)\cdot P(Y=y) =\dfrac{1}{3}\cdot\dfrac{1}{5} = \dfrac{1}{15}$

Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:

2 in a unique way (1+1)
3 in two possible ways (1+2, 2+1)
4 in three possible ways
5 in three possible ways
6 in three possible ways
7 in two possible ways
8 in a unique way

This implies that the probabilities of the outcomes of $W=X+Y$ are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5