3x^2 + 3y^2 + 12x − 6y − 21 = 0 => x^2 + y^2 + 4x - 2y - 7 = 0 => x^2 + 4x + 4 + y^2 - 2y + 1 = 12 => (x + 2)^2 + (y - 1)^2 = 12 => centre is (-2, 1)
5x^2 + 5y^2 − 10x + 40y − 75 = 0 => x^2 + y^2 - 2x + 8y - 15 = 0 => x^2 - 2x + 1 + y^2 + 8y + 16 = 32 => (x - 1)^2 + (y + 4)^2 = 32 => centre is (1, -4)
5x^2 + 5y^2 − 30x + 20y − 10 = 0 => x^2 + y^2 - 6x + 4y - 2 = 0 => x^2 - 6x + 9 + y^2 + 4y + 4 = 15 => (x - 3)^2 + (y + 2)^2 = 15 => centre is (3, -2)
4x^2 + 4y^2 + 16x − 8y − 308 = 0 => x^2 + y^2 + 4x - 2y - 77 = 0 => x^2 + 4x + 4 + y^2 - 2y + 1 = 82 => (x + 2)^2 + (y - 1)^2 = 82 => centre is (-2, 1)
x^2 + y^2 − 12x − 8y − 100 = 0 => x^2 - 12x + 36 + y^2 - 8y + 16 = 152 => (x - 6)^2 + (y - 4)^2 = 152 => centre is (6, 4)
2x^2 + 2y^2 − 8x + 12y − 40 = 0 => x^2 + y^2 - 4x + 6y - 20 = 0 => x^2 - 4x + 4 + y^2 + 6y + 9 = 33 => (x - 2)^2 + (y + 3)^2 = 33 => centre is (2, -3)
4x^2 + 4y^2 − 16x + 24y − 28 = 0 => x^2 + y^2 - 4x + 6y - 7 = 0 => x^2 - 4x + 4 + y^2 + 6y + 9 = 20 => (x - 2)^2 + (y + 3)^2 = 20 => centre is (2, -3)
3x^2 + 3y^2 − 18x + 12y − 81 = 0 => x^2 + y^2 - 6x + 4y - 27 = 0 => x^2 - 6x + 9 + y^2 + 4y + 4 = 40 => (x - 3)^2 + (y + 2)^2 = 40 => centre is (3, -2)
x^2 + y^2 − 2x + 8y − 13 = 0 => x^2 - 2x + 1 + y^2 + 8y + 16 = 30 => (x - 1)^2 + (y + 4)^2 = 30 => centre = (1, -4)
x^2 + y^2 + 24x + 30y + 17 = 0
=> x^2 + 24x + 144 + y^2 + 30y + 225 = 352 => (x + 12)^2 + (y + 15)^2 = 352 => center is (-12, -15)
Therefore, 3x^2 + 3y^2 + 12x − 6y − 21 = 0 and 4x^2 + 4y^2 + 16x − 8y − 308 = 0 are concentric.
5x^2 + 5y^2 − 10x + 40y − 75 = 0 and x^2 + y^2 − 2x + 8y − 13 = 0 are concentric.
5x^2 + 5y^2 − 30x + 20y − 10 = 0 and 3x^2 + 3y^2 − 18x + 12y − 81 = 0 are concentric.
2x^2 + 2y^2 − 8x + 12y − 40 = 0 and 4x^2 + 4y^2 − 16x + 24y − 28 = 0 are concentric.
Answer:
Initial population is 3450 in the year 2000 and it decreases 80 every year.
Step-by-step explanation:
We are given with y=-80x+3450 where y is city's population and x is the number of years after 2000.
That is x=0 means the year 2000.
Hence y-intercept will represent the initial population which is nothing but 3450.
Since our equation slope =-80 which is negative means y is decreasing as x increases.
For x raises by 1, y decreases by 80.
That means population decreases by 80 for every year.
Answer:
1 solution
Step-by-step explanation:
y = 1/2x + 4
x + 2y = -8
Solve the second equation for y.
2y = -x - 8
y = -1/2x - 4
The two equations in slope-intercept form are:
y = 1/2x + 4
y = -1/2x - 4
The system consists of two lines with different slopes, so they intercept at a single point which is the solution.
Answer: 1 solution
The dimensions of the builders scale drawing is 40 x 32 inches
<u>Step-by-step explanation:</u>
Let the area of the actual crate be 'a'
Scale factor of Karl = 1:12
Dimensions = 10 x 8 inches
Area = 80 square inches
1:12 = 1/12
1/12 = 80/a
a = 80 x 12
a = 960 square inches
So dimensions are 120 x 96 inches
Builders scale factor = 1:3
Actual Length = 120inches
Actual width = 96 inches
Builders drawing length = 120/3
= 40 inches
Builders drawing width = 96/3
= 32 inches
The dimensions of the builders scale drawing is 40 x 32 inches.
That will be 295.25 how ?? You multiply 8.75 by 40 then subtract 55.75 =295.25