Answer
Find out the which coordinate pair identifies the center of the circle represented by 4x² + 4y² − 16x − 24y + 36 = 0.
To prove
The general equation of the circle is
(x - h)² + (y - k)² = r²
Where h,k are the centre and r is the radius.
4x² + 4y² − 16x − 24y + 36 = 0
Divided both side by 4.
x² + y² − 4x − 6y + 9= 0
Add and subtract 4 and 9
x² + y² − 4x − 6y + 4 -4 +9 - 9 +9= 0
x² + y² − 4x − 6y + 4 -4 + 9 - 9 +9= 0
x² + 4 - 2× 2 × x + y² + 9 - 2 × 3 × y = 9 + 4 - 9
using the formula ( a + b )² = a² + b² +2ab
(x - 2)² + (y - 3)² = 2²
Compare this with the general equation of circle.
Thus
h = 2 , k = 3
Option A is correct .
A) You divide the previous number in the sequence with 6. (31104/6 = 5184, 5184/6 = 864). Follow this pattern and you can easy find the rest.
b) You divide the previous number by 2. (14/2 = 7, 7/2=7/2)... and so on
Answer:
The wax will fill the mold a bit more than halfway.
Step-by-step explanation:
The volume of a sphere with radius is:
.
The radius of this sphere of wax is ; Its volume would be:
.
Assume that the wax here does not evaporate, combust, or otherwise disappear. .
The volume of a rectangular prism is equal to .
For this mold with a rectangular prism shape:
.
Half of that would be:
.
Compare these two volumes to the volume of wax available:
.
In other words, the wax will fill the mold a bit more than halfway, but not completely.
Answer:
x = 20
Step-by-step explanation:
The goal is to move the x's and the whole numbers to their own sides of the equation. When moving pieces to opposite sides, the signs change (a negative becomes a positive, for example).
3x - 4 = 2(x + 8)
First we're going to use distributive property to remove the brackets in
2(x + 8)
This becomes 2x + 16
3x - 4 = 2x + 16
Moving 2x over...
3x - 2x - 4 = 16
Moving -4 over...
3x - 2x = 16 + 4
Collecting like terms...
x = 20