Answer:
x = -1
Step-by-step explanation:
3x + 1 = -2
Subtract 1 from both sides.
3x = -2 - 1
Simplify -2 - 1 to 3.
3x = -3
Divide both sides by 3.
x = -1
Answer:
Angular velocity: 
(
)
Linear velocity: 
(
)
Step-by-step explanation:
The gear experiments a pure rotation with axis passing through its center, the angular (
), in radians per second, and linear velocities (
), in inches per second, of a point on the outer edge of the element are, respectively:
(1)
(2)
Where:
- Rotation rate, in revolutions per minute.
- Radius of the gear, in inches.
If we know that 
and 
, then the linear and angular velocities of the gear are, respectively:
()
()
If I am not mistaken, the slope would be -14.
The equation for this problem is “y = x + 3”.
Answer: In this equation, let "x" equal the rate at which the tub will be filled. The tub holds 32 gallons, which will be one-half of the equation. The tub already contains 12 gallons, so this will be half of the other side of the equation. The rate is "x" gallons per minute, and the time it required was 5 minutes, so this would be "5x". Placing all these parts together gives an equation of (32 = 5x + 12) gallons per minute dispensed.
