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frozen [14]
3 years ago
10

determine the intercepts of the line that correspond to the following table of values. -14,9 -10,18 -6,27

Mathematics
1 answer:
Nataliya [291]3 years ago
8 0

I'll need to assume that your "-14,9" means (-14,9); if so, please use parentheses next time to indicate that you're sharing the coordinates of a point.

As we go from (-14,9) to (-10,18), x increases by 4 and y increases by 9.  Thus, the slope of this line is m = rise / run = 9/4.

We want the intercepts of this line.  Let's use the slope-intercept form y = mx + b.  Substituting the given info:  -10 for x and 18 for y, and m = 9/4, we get:

18 = (9/4)(-10) + b, where b is the y-intercept.

Solving for b, we get 18 + 90/4 = (72+90)/4 = 162/4, or 81/2.

Then b = 81/2, and the equation of the line is y = (9/4)x + 81/2.

Now find the x-intercept.  To do this, let y = 0; then (9/4)x = -81/2,  Mult. both sides by 4 to eliminate the fractions:  9x = -162, or x = -18.  The x-intercept is (-18,0) and the y-intercept is (0,81/2)

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A coin is tossed 4 times. Let E1 be the event "the first toss shows heads" and E2 the event "the second toss shows heads" and so
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P (A∩B) = P(A). P(B)

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                                                                  Head          Tail

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                                                                1/4                  1/4

  P(E2)= 1/2  ---------------  Coin 2             H, H               H,T

                                                                      1/4           1/4

So the events are independent.

The probability of showing heads on both toss is equal to 1/2

The sample space for this experiment consists of 2⁴= 16 sample points, out of which eight will have heads on both toss.

Or in other words ( 1/4* 1/4) = 2/4 = 1/2

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(\stackrel{x_1}{4}~,~\stackrel{y_1}{64})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{96}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{96}-\stackrel{y1}{64}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{4}}}\implies \cfrac{\stackrel{bottles}{32}}{\underset{mins}{2}}\implies \cfrac{\stackrel{bottles}{16}}{\underset{mins}{1}}

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