We are given original equation: 
We need to find the enter and radius of a circle using the completing the square method.
The steps are as following :
Step 1 [original equation]: x^2 − 10x + y^2 + 12y = 20 .
Step 2 [group like terms]: (x^2 − 10x) + (y^2 + 12y) = 20
Step 3 [complete the quadratics]: (x^2 − 10x + 25) + (y^2 + 12y + 36) = 20 + (25 + 36).
Step 4 [simplify the equation]: (x^2 − 10x + 25) + (y^2 + 12y + 36) = 64.
Step 5 [factor each quadratic]: (x − 5)^2 + (y + 6)^2 = 8^2
Step 6 [identify the center and radius]: Center = (5, −6) Radius = 8.
<h3>Step 6 is incorrect.</h3><h3>The center should be (5,-6).</h3><h3> Replace − 5 with + 5 and replace + 6 with − 6.</h3>
Answer:
7.211
Step-by-step explanation:
-For two points in the complex plane, the distance between the points is the modulus of the of the difference of the two complex numbers.
-Point 2-4i has the coordinates (2,-4)
-Point 6+i has the coordinates (6,1)
#We must find the distance between the two coordinates (2,-4) and (6,1):
Hence, the distance between the two points is 7.211
Answer:
The sides are
6
inches,
8
inches and
10
inches
Explanation:
I'd suggest that the question should read 'The perimeter of a triangle is 24 inches. The longest side is 4 inches longer than the shortest side, and the shortest side is three-fourths the length of the middle side. How do you find the length of each side of the triangle?'
In this case the question can be answered. If
x
is the length of the middle side, then the shortest side is 3/4x and the longest side is 3/4x+4
x+3/4x+3/4x+4=24
10/4x=20
x=8
Then the shortest side is 6and the longest side is 10
Step-by-step explanation:
Answer:
(p×2)+3
Step-by-step explanation:
I'm not too sure, I've only just started practicing this stuff?
Answer:
During the year 2021.
Step-by-step explanation:
As we have a function that defines the annual per capita out-of-pocket expenses for health care, we can work with it.
Knowing that, <u>we clear x</u> (<em>this is the number of years past the year 2000, so it will contain our desired information</em>).
Now, as we want to know when are the per capita out-of-pocket expenses for health care predicted to be $1400, and <em>this total is our variable y</em>, then
Finally, we know that <u>x is the number of years past the year 2000</u>, so the answer is that during the year 2021, <em>the per capita out-of-pocket expenses for health care are predicted to be $1400</em>.
