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:
Step-by-step explanation:
This is an exponential equation of the form
Answer:
-7/3
Step-by-step explanation:
slope formula:
y = mx + b
the m is the slope value
<span>x/9 = 8/36 </span>
<span>x = 9 * 8/36 [multiplying each side by 9] </span>
<span>x = 2 </span>
<span> </span>
<span>x/90 = 4.4/12 </span>
<span>x = 90 * 4.4/12 [multiplying each side by 90] </span>
<span>x = 33 </span>
<span>Both proportions should be expressed as lemon juice to water, or water to lemon juice. Either way would give a correct answer: </span>
<span>2/7 = j/28 [lemon juice to water] </span>
<span>8 = j [multiplying each side by 28] </span>
<span>7/2 = 28/j [water to lemon juice] </span>
<span>7j = 56 [multiplying each side by 2j] </span>
<span>j = 8 [dividing each side by 7] </span>
<span>The length proportion is 24 in to 32 ft. </span>
<span>The actual house is 24 ft tall. </span>
<span>Let x represent the doll house height, in inches. Then </span>
<span>x/24 = 24/32 </span>
<span>x = 24 * 24/32 = 18 inches</span>
It would be - 1.75. Hope it helps! :)
