Answer: I believe it would be $600
Step-by-step explanation:
I need to know the question that tells us what the other parts are.
All sides are the same, hence, all three angles are the same, and each one of them is 60 degrees. Due to that:
7x + 4 = 60
7x = 56
x = 56/7 = 8
8y + 12 = 60
8y = 48
y = 48/8 = 6
I believe A and B are the ones. As for explaining? hmm. I would honestly say that any number to the right of a number is a tenth of the place above it. But then again, it's optional to explain ;P
Answer:
It will take 5.61 seconds for the coin to reach the stream.
Step-by-step explanation:
The height of the coin, after t seconds, is given by the following equation:
![h(t) = -16t^{2} + 72t + 100](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-16t%5E%7B2%7D%20%2B%2072t%20%2B%20100)
How long will it take the coin to reach the stream?
The stream is the ground level.
So the coin reaches the stream when h(t) = 0.
![h(t) = -16t^{2} + 72t + 100](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-16t%5E%7B2%7D%20%2B%2072t%20%2B%20100)
![-16t^{2} + 72t + 100 = 0](https://tex.z-dn.net/?f=-16t%5E%7B2%7D%20%2B%2072t%20%2B%20100%20%3D%200)
Multiplying by (-1)
![16t^{2} - 72t - 100 = 0](https://tex.z-dn.net/?f=16t%5E%7B2%7D%20-%2072t%20-%20100%20%3D%200)
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots
such that
, given by the following formulas:
![x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cfrac%7B-b%20%2B%20%5Csqrt%7B%5Cbigtriangleup%7D%7D%7B2%2Aa%7D)
![x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20%5Cfrac%7B-b%20-%20%5Csqrt%7B%5Cbigtriangleup%7D%7D%7B2%2Aa%7D)
![\bigtriangleup = b^{2} - 4ac](https://tex.z-dn.net/?f=%5Cbigtriangleup%20%3D%20b%5E%7B2%7D%20-%204ac)
In this question:
![16t^{2} - 72t - 100 = 0](https://tex.z-dn.net/?f=16t%5E%7B2%7D%20-%2072t%20-%20100%20%3D%200)
So
![a = 16, b = -72, c = -100](https://tex.z-dn.net/?f=a%20%3D%2016%2C%20b%20%3D%20-72%2C%20c%20%3D%20-100)
![\bigtriangleup = (-72)^{2} - 4*16*(-100) = 11584](https://tex.z-dn.net/?f=%5Cbigtriangleup%20%3D%20%28-72%29%5E%7B2%7D%20-%204%2A16%2A%28-100%29%20%3D%2011584)
![t_{1} = \frac{-(-72) + \sqrt{11584}}{2*16} = 5.61](https://tex.z-dn.net/?f=t_%7B1%7D%20%3D%20%5Cfrac%7B-%28-72%29%20%2B%20%5Csqrt%7B11584%7D%7D%7B2%2A16%7D%20%3D%205.61)
![t_{2} = \frac{-(-72) - \sqrt{11584}}{2*16} = -1.11](https://tex.z-dn.net/?f=t_%7B2%7D%20%3D%20%5Cfrac%7B-%28-72%29%20-%20%5Csqrt%7B11584%7D%7D%7B2%2A16%7D%20%3D%20-1.11)
Time is a positive measure, so we take the positive value.
It will take 5.61 seconds for the coin to reach the stream.