The true statement is that renting from Company B will be cheaper if Samir drives the truck 100 miles. Then the correct option is D.
<h3>What is a linear equation?</h3>
The linear equation is given as,
y = mx + c
Where m = the slope of the line
c is the y-intercept of the line.
Let y be the total amount and x be the number of miles.
Samir can rent a moving truck from Company A for $35 plus $0.50 per mile. Then the equation will be
y = 0.5x + 35 ....1
Company B for $25 plus $0.70 per mile. then the equation will be
y = 0.7x + 25 ....2
For the same rent, the number of miles will be
0.7x + 25 = 0.5x + 35
0.2x = 10
x = 50 miles
Renting from Company B will be cheaper if Samir drives the truck 100 miles. Then the correct option is D.
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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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For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have two points that belong to the AB line:
We can find the slope:
By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to AB will have slope 
, then the equation will be of the form:
We substitute the given point and find b:
Finally, the equation is:
Answer:
