First we need to convert the given equation to standard form, only then we can find the center and radius of the circle.
![x^{2} + y^{2} +18x+14y+105=0 \\ \\ x^{2} +18x+ y^{2}+14y=-105 \\ \\ x^{2} +2(x)(9)+ y^{2}+2(y)(7)=-105 \\ \\ x^{2} +2(x)(9)+ 9^{2} + [y^{2}+2(y)(7)+7^{2}] =-105+9^{2}+7^{2} \\ \\ (x+9)^{2}+ (y+7)^{2}=25 ](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%2B%20y%5E%7B2%7D%20%2B18x%2B14y%2B105%3D0%20%5C%5C%20%20%5C%5C%20%0A%20x%5E%7B2%7D%20%2B18x%2B%20y%5E%7B2%7D%2B14y%3D-105%20%5C%5C%20%20%5C%5C%20%0A%20x%5E%7B2%7D%20%2B2%28x%29%289%29%2B%20y%5E%7B2%7D%2B2%28y%29%287%29%3D-105%20%5C%5C%20%20%5C%5C%20%0Ax%5E%7B2%7D%20%2B2%28x%29%289%29%2B%209%5E%7B2%7D%20%2B%20%5By%5E%7B2%7D%2B2%28y%29%287%29%2B7%5E%7B2%7D%5D%20%20%3D-105%2B9%5E%7B2%7D%2B7%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%0A%20%28x%2B9%29%5E%7B2%7D%2B%20%28y%2B7%29%5E%7B2%7D%3D25%20%20%0A%20%20)
The standard equation of circle is:

with center (a,b) and radius = r
Comparing our equation to above equation, we can write
Center of circle is (-9, -7) and radius of the given circle is 5
Answer:
7 1/2
Step-by-step explanation:
2 1/2 times 3 is 7 1/2
Answer:
400 square meters
Step-by-step explanation:
We can first solve this problem with each unit representing 1 centimeter, and then scale up at the very end. The shape that we have a parallelogram. The base is 8 cm, and the height is 2 cm. The formula for the area of a parallelogram is just
, so the area of the parallelogram is 16 square centimeters. However, now we scale up. Since each centimeter correlates to 5 meters, each little box will correlate to 25 square meters. Therefore,
square meters is our answer
Ray wants to buy an item worth 500$ in the most cost-effective way. Let's study each of the 3 cases and see with option is the best.
In the first option, he'll buy the item at list price with a coupon for $10 off. So he'll buy it at 500-10 =$490.
In the second option, he'll buy a membership for $35 and then get the item at a 15% discount. With a 15% discount, the price of the item will be 500 - (500*0.15) = 500 - 75 = $425. And with the membership price, he'll pay a total of 425 + 35 = $460.
The third option is to buy the item online at a 10% discount and pay $4 for the shipping. At 10% discount, the price of the item will be 500 - (500*0.1) = 500 - 50 = $450. And with cost of the shipping, he'll pay a total of 450+4 = $454.
So if he chooses the first option, he'll pay $490. With the second, he'll pay $460. And finally with the third, he'll pay $454.
So the third option is the most cost-effective, buying the item at $454.
Hope this helps! :)