If ∠C and ∠D are vertical angles and m ∠ C = x + 5 and m ∠ D = –2x + 80, what is m ∠ C?
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Answer:
0.6 probability that
Step-by-step explanation:
The probability distribution is given in the table.
Probability that x is between -2 and 2.
Between -2 and 2, inclusive, we have -2, 0 and 2. So
From the table:
. So
0.6 probability that
We will be using the Point Slope formula which is
The information we are given is that m = -4 and the point is (2,-5), so we can input it into the equation.
This simplifies into
Then we can subtract 5 from each side to get the answer:
Remember that c is the initial height. Since we the rocket is in a 99-foot cliff, c=99. Also, we know that the velocity of the rocket is 122 ft/s; therefore v=122
Lets replace the values into the the vertical motion formula to get:
Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:
Now we can apply the quadratic formula
where a=-16, b=122, and c=198
or 
or 
or 
Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.
Lets replace the values into the the vertical motion formula to get:
Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:
Now we can apply the quadratic formula
Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.