Answer:
Adult tickets sold: 156
Step-by-step explanation:
Adult ticket: x
Student ticket: y
x + y = 260 ===> -6(x + y = 260) ===> -6x -6y = -1560
6x + 4.5y = 1404 ===> 6x + 4.5y = 1404
________________
add the two equations to eliminate a variable: -1.5y = -156
divide by -1.5: y = 104
substitution to find x:
x + y = 260
x + 104 = 260
x = 156
Answer:
The angular velocity is 6.72 π radians per second
Step-by-step explanation:
The formula of the angular velocity is ω =
, where v is the linear velocity and r is the radius of the circle
The unit of the angular velocity is radians per second
∵ The diameter of the tire is 25 inches
∵ The linear velocity is 15 miles per hour
- We must change the mile to inch and the hour to seconds
∵ 1 mile = 63360 inches
∵ 1 hour = 3600 second
∴ 15 miles/hour = 15 × 
∴ 15 miles/hour = 264 inches per second
Now let us find the angular velocity
∵ ω =
∵ v = 264 in./sec.
∵ d = 25 in.
- The radius is one-half the diameter
∴ r =
× 25 = 12.5 in.
- Substitute the values of v and r in the formula above to find ω
∴ ω = 
∴ ω = 21.12 rad./sec.
- Divide it by π to give the answer in terms of π
∴ ω = 6.72 π radians per second
The angular velocity is 6.72 π radians per second
Answer:
Step-by-step explanation:
Vertically opposite angles are equal.
8y + 36 = 14y -24 Subtract 36 to both sides
8y = 14y - 24 - 36 Combine
8y = 14y - 60 Subtract 14y from both sides
8y - 14y = - 60
-6y = -60 Divide by - 6
-6y/-6 = -60/-6
y = 10
===========================
x +48 = 64 Subtract 48 from both sides
x +48 - 48 = 64-16
x = 16
Translation means you are shifting the line either up or down.