Answer:
$200 + n($200/night) = Total Cost
Step-by-step explanation:
The total cost ($) for staying n nights would be the sum of the $200 cleaning fee plus the number of nights, n, times the nightly rate of $200/night.
$200 + n($200/night) = Total Cost
Answer:
6 in
Step-by-step explanation:
Let x = the side length of the original square.
They removed 3 in from each side of the original square, so the side lengths of the remaining square are x - 3 in.
The area of the smaller square is (x - 3)².
The area of the original square is x²
I assume the area of the smaller square is ¼ that of the original square. Then
1. Solve for x
2. Calculate the side length of the smaller square
(a) x = 2
Side length = x - 3 = 2 - 3 = -1 in.
IMPOSSIBLE. You can't have a negative side length.
(b) x = 6
Side length of smaller square = 6 - 3 = 3 in.
Side length of original square = x = 6 in
Check:
OK.
Answer:
Step-by-step explanation:
s=c+mc
s-c=mc
(s-c)/c=m
E) 2
Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5
Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.