Answer:
The coordinate of the wells are
![(-4 -\sqrt[]{\frac{53}{2}}, 70+15\sqrt[]{\frac{53}{2}})](https://tex.z-dn.net/?f=%20%28-4%20-%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D%2C%2070%2B15%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D%29)
![(-4 +\sqrt[]{\frac{53}{2}}, 70-15\sqrt[]{\frac{53}{2}})](https://tex.z-dn.net/?f=%20%28-4%20%2B%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D%2C%2070-15%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D%29)
Step-by-step explanation:
The y coordinate of the stream is given by
. Also, the y coordinate of the houses are determined by y=-15x+10. We will assume that the houses are goint to be built on the exact position where we build the wells. We want to build the wells at the exat position in which both functions cross each other, so we have the following equation

or equivalently
(by summing 15x and substracting 10 on both sides)
Dividing by 2 on both sides, we get

Recall that given the equation of the form
the solutions are
![x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Taking a =2, b = 16 and c = -21, we get the solutions
![x_1 = -4 -\sqrt[]{\frac{53}{2}}](https://tex.z-dn.net/?f=x_1%20%3D%20-4%20-%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D)
![x_2 = -4 +\sqrt[]{\frac{53}{2}}](https://tex.z-dn.net/?f=x_2%20%3D%20-4%20%2B%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D)
If we replace this values in any of the equations, we get
![y_1 = 70+15\sqrt[]{\frac{53}{2}}](https://tex.z-dn.net/?f=y_1%20%3D%2070%2B15%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D)
![y_2 = 70-15\sqrt[]{\frac{53}{2}}](https://tex.z-dn.net/?f=y_2%20%3D%2070-15%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D)
Answer:
You can manipulate both equations into y = mx + b format and end up with the same result of y = 1.2x + 1.4
Step-by-step explanation:
y + 1 = 1.2(x + 2)
y = 1.2x + 2.4 - 1
y = 1.2x + 1.4
y - 5 = 1.2(x - 3)
y = 1.2x - 3.6 + 5
y = 1.2x + 1.4
So essentially, they're the same equation but in different forms.
Th e answer to this question is is combining like terms on both sides
Volume of the rectangular prism = l * w * h
Diagonal = √l² + w² + h²
= √ 16² + 12² + 8²
= √464
= 21.5