Answer:
Some cities and towns are called municipali- ties. If a city government incorporates by citizen request, it is considered a municipal govern- ment. Cities in Texas operate under one of two types of law—general law or home rule. Small cities with populations of less than 5,000 may incorporate as a general-law city.
Answer:
h(x) = 1/2x + 5
Step-by-step explanation:
Switch the positions of the x and y (f(x)) and solve for y (f(x)).
f(x) = 2x - 10
x = 2y - 10
x + 10 = 2y
(x + 10)/2 = y
1/2x + 5 = y
This can solved graphically, using algebraic manipulation or differential calculus.
Plotting the equation will generate a parabola. The vertex represents the point where the ball will reach the maximum height.
The vertex can be determined by completing the square
h = -16t2 + 45t + 5
h - 5 = -16(t2 - 45/16t)
h - 5 - 2025/64 = -16(t2 - 45/16t + 2025/1024)
(-1/16)(h - 2345/64) = (t - 45/32)^2
The vertex is
(45/32,2345/64) or (1.41,36.64)
The maximum height is 36.64 ft
Using calculus, taking the first derivative of the equation and equating to 0
dh/dt = 0 = -32t + 45
t = 45/32
Substituting this value to the equation
h = -16(45/32)^2 + 45(45/32) + 5
h = 36.64 ft
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135/3=45
20% of 45=9
45+9=54
so each person owes $54 toward bill and tip
Answer: 10y+5x=50
Step-by-step explanation: $10 times y + $5 times x =$50
