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:
the answer is 80
Step-by-step explanation:
QR=ST: 7x+3=5x+25
2x=22
x=11
7(11)+3=80 5(11)+25=80
Answer:
The equation of the function in slope-intercept form is y = 3 x + 5 .
Step-by-step explanation:
Given as :
A line passes through the point ( - 1 , 2 )
i.e ( x , y ) = ( - 1 , 2 )
The slope of the line is 3
The equation of line in slope intercept form
y - 
= m ( x - 
)
Where m is the slope of the line
So, y - 2 = 3 ( x - ( - 1 ) )
Or, y - 2 = 3 ( x + 1 )
Or, y - 2 = 3 x + 3
Or, y = 3 x + 3 + 2
∴ y = 3 x + 5
Hence The equation of the function in slope-intercept form is y = 3 x + 5 . Answer
Answer:
a) 3,6,9,12,15,..
b) Common Ratio is 3
c) Recursive Formula : aₙ= aₙ₋₁ + d where a₁=3 and d= 3
Step-by-step explanation:
a) Create your own arithmetic sequence. Write out the first 3 terms.
Consider the sequence: 3,6,9,12,15,..
a₁ = 3
a₂ = 6
a₃ = 9
b) What is the common difference of your sequence?
6-3 = 3
9-6 = 3
12 -9 =3
So, common difference is 3
c) Write the recursive formula representing your sequence.
a₁ = 3
a₂ = aₙ₋₁ + d
= a₁ + d
= 3+ 3 = 6
a₃ = aₙ₋₁ + d
= a₂ + d
= 6+3 = 9
so, recursive formula is aₙ = aₙ₋₁ + d where a₁ = 3 and d= 3
