We have two unknowns: x and y. Now, we have to formulate 2 equations. The first would come from the use of the given ratio:
We use the distance formula to find the distance between coordinates:
3/4 = √[(x-4)²+(y-1)²] / √[(4-12)²+(1-5)²]
√[(x-4)²+(y-1)²] = 3√5
(x-4)²+(y-1)² = 45
x² - 8x + 16 + y² - 2y + 1 = 45
x² - 8x + y² - 2y = 28 --> eqn 1
The second equation must come from the equation of a line:
y = mx +b
m = (5-1)/(12-4) = 1/2
Substitute y=5 and x=12 for point (12,5)
5 = (1/2)(12) + b
b = -1
So, the second equation is
y = 1/2x -1 or x = 2 + 2y --> eqn 2
Solving the equations simultaneously:
(2 + 2y)² - 8(2 + 2y) + y² - 2y = 28
Solving for y,
y = -2
x = 2+2(-2) = -2
Therefore, the coordinates of point A is (-2,-2).
Answer:
- Decay rate, r = 0.014
- Initial Amount =120,000

- P(10)=104,220
Step-by-step explanation:
The exponential function for growth/decay is given as:

In this problem:
The city's initial population is 120,000 and it decreases by 1.4% per year.
- Since the population decreases, it is a Decay Problem.
- Decay rate, r=1.4% =0.014
- Initial Amount =120,000
Therefore, the function is:

When t=10 years

Answer:
y=-4x+9
Step-by-step explanation:
y-y1=m(x-x1)
y-(-3)=-4(x-3)
y+3=-4(x-3)
y=-4x+12-3
y=-4x+9
<span>Ans : a)
What is the standard deviation of this sampling distribution?
Ď /âšn
= 60/âš840
=2.0702
b)
1 standard deviation of the mean
= (1) 2.07
= 2.07
c)
272+/- 1(2.07)
(269.93, 274.07)</span>
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