The point (a,b) is (5,7) . Therefore, the equation of the line is y=7
The possible ordered pairs whose product will be negative (less than zero) are,
![(x,-y) \: or \: (-x,y)](https://tex.z-dn.net/?f=%28x%2C-y%29%20%20%5C%3A%20or%20%5C%3A%20%20%28-x%2Cy%29%20)
That is all these products will give us,
![- xy](https://tex.z-dn.net/?f=%20-%20xy)
![-xy< 0](https://tex.z-dn.net/?f=%20-xy%3C%200)
The point must be in the second quadrant where x is negative and y is positive.
Or in the fourth quadrant, where y is negative and x is positive.
This is an example of division. 252/6=42. So 42 toys will go into each pinata.
Answer:
therefore the correct options are:
B. the equation is an exponential decay equation.
F. $28000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.
Step-by-step explanation:
i) the cost of an automobile is given by the equation is
C(t) =
, where C(t) represents the cost and t represents the time in years
ii) the above equation is an exponential decay equation. It is a decay equation because growth rate is 0.73 which is less than 1 and greater than zero.
ii) when t = 0 then the cost is C(0) = 28000 represents the initial cost.
iii) from the equation in i) we can understand that the cost depreciates 27% per year over the course of t years.
therefore the correct options are:
B. the equation is an exponential decay equation.
F. $28000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.
Answer:
![(x-7)^2+(y-2)^2=34](https://tex.z-dn.net/?f=%28x-7%29%5E2%2B%28y-2%29%5E2%3D34)
Step-by-step explanation:
We want to find the equation of a circle with a center at (7, 2) and a point on the circle at (2, 5).
First, recall that the equation of a circle is given by:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
Where (<em>h, k</em>) is the center and <em>r</em> is the radius.
Since our center is at (7, 2), <em>h</em> = 7 and <em>k</em> = 2. Substitute:
![(x-7)^2+(y-2)^2=r^2](https://tex.z-dn.net/?f=%28x-7%29%5E2%2B%28y-2%29%5E2%3Dr%5E2)
Next, the since a point on the circle is (2, 5), <em>y</em> = 5 when <em>x</em> = 2. Substitute:
![(2-7)^2+(5-2)^2=r^2](https://tex.z-dn.net/?f=%282-7%29%5E2%2B%285-2%29%5E2%3Dr%5E2)
Solve for <em>r: </em>
<em />
<em />
Simplify. Thus:
![25+9=r^2](https://tex.z-dn.net/?f=25%2B9%3Dr%5E2)
Finally, add:
![r^2=34](https://tex.z-dn.net/?f=r%5E2%3D34)
We don't need to take the square root of both sides, as we will have the square it again anyways.
Therefore, our equation is:
![(x-7)^2+(y-2)^2=34](https://tex.z-dn.net/?f=%28x-7%29%5E2%2B%28y-2%29%5E2%3D34)