Through: (-3,-5), perp. to y=-1/3x+2

1 answer:

7 0

Y = -1/3x + 2.....the slope here is -1/3. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, flip the slope and change the sign. So the slope is -1/3.....flip it and it becomes - 3/1....change the sign and it becomes 3/1 or just 3. So ur perpendicular line will have a slope of 3.

y = mx + b
slope(m) = 3
(-3,-5)....x = -3 and y = -5
now sub into the formula and find b, the y int
-5 = 3(-3) + b
-5 = -9 + b
-5 + 9 = b
4 = b
so ur perpendicular equation is : y = 3x + 4 <===

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If two standard six-sided dice are tossed, what is the probability that a 5 is rolled on at least one of the two dice? express y

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We define the probability of a particular event occurring as:
$\frac{number\ of \ desired\ outcomes}{number\ of\ possible\ outcomes}$

What are the total number of possible outcomes for the rolling of two dice? The rolls - though performed at the same time - are independent, which means one roll has no effect on the other. There are six possible outcomes for the first die, and for each of those, there are six possible outcomes for the second, for a total of 6 x 6 = 36 possible rolls.

Now that we've found the number of possible outcomes, we need to find the number of desired outcomes. What are our desired outcomes in this problem? They are asking for all outcomes where there is at least one 5 rolled. It turns out, there are only 3:

(1) D1 - 5, D2 - Anything else, (2), D1 - Anything else, D2 - 5, and (3) D1 - 5, D2 - 5

So, we have $\frac{3}{36} = \frac{1}{12}$ probability of rolling at least one 5.