Answer:

Step-by-step explanation:
Convert each to a improper fraction



are there any answers you can choose from
Answer:
centre = (- 3, - 2) , radius = 1
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + 6x + y² + 4y + 12 = 0 ( subtract 12 from both sides )
x² + 6x + y² + 4y = - 12
Use the method of completing the square on the x and y terms
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(3)x + 9 + y² + 2(2)y + 4 = - 12 + 9 + 4
(x + 3)² + (y + 2)² = 1 ← in standard form
with centre = (- (- 3), - (- 2)) and r² = 1, that is
centre = (- 3, - 2) and radius = 1
Answer:

Step-by-step explanation:

Answer:
The recoil velocity of the gun is
and is pointing in opposite direction to the velocity of the bullet.
Step-by-step explanation:
Use conservation of linear momentum, which states that the momentum of the bullet (product of the bullet's mass times its speed) should equal in absolute value the momentum of the recoiling gun (its mass times its recoil velocity).
We also write the mass of the bullet in the same units as the mass of the gun (for example kilograms). Mass of the bullet = 0.010 kg
In mathematical terms, we have:
