Identify the center and radius of the circle (x+4)^2+(y-2)^2=16
1 answer:
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Answer:
The Solution of the equation is
x= 5 ±
Step-by-step explanation:
We are supposed to find the solution of the equation by completing square method
our given equation is
2x² + 20x + 10 = 0
Dividing whole equation by 2
we will get
x² + 10 x + 5 = 0
Now we will write the middle term in factor form to see what we will be needing to make it perfect square
it would be written as
x² + 2(5) x + 5 = 0
Now adding 20 on both sides we get
x² + 2(5) x + 5 + 20 = 20
x² + 2(5) x + 25 = 20
(x)² + 2(5) x +(5)² = 20
Now we have the form of a²+2(a)(b) + b²
And also we know that
a²+2(a)(b) + b² = (a+b)²
So our equation becomes
(x+5)² = 20
Taking square root of both sides it becomes
square cuts out with square root so
it becomes
x+5 = ±
We know that
So it becomes
x+5 =±
Subtracting 5 from both sides
it becomes
x= 5 ±
So
The Solution of the equation is
x= 5 ±
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An aquarium tank can hold 6600 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 55 minutes. The second pipe can fill the tank in 66 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?
Given Information:
Time to fill tank by first pipe = 55 minutes
Time to fill tank by first pipe = 66 minutes
Total capacity of tank = 6600 liters
Required Information:
Time required to fill tank when both pipes are working together = ?
Answer:
Time required to fill tank when both pipes are working together = 30 mins
Step-by-step explanation:
The rate of filling the tank of the first pipe is,
first pipe =
The rate of filling the tank of the second pipe is,
second pipe =
Let x is the time to fill the tank when both pipes are used so the equation becomes,
Therefore, it would take 30 minutes to fill the entire tank when both pipes are used to fill the tank.