Answer:
f(n) = f(n - 1) + 3
Step-by-step explanation:
Substitute 
to get the recursive formula.
OPTION 1: f(n) = f(n - 1) + 3
Substituting n = 1.
f(1) = f(1 - 1) + 3 = 0 + 3 = 3.
Substituting n = 2.
f(2) = f(2 - 1) + 3 = f(1) + 3 = 3 + 3 = 6.
Substituting n = 3.
f(3) = f(3 - 1) + 3 = f(2) + 3 = 6 + 3 = 9.
The numbers match the given sequence. So, we say the above recursive formula represents the sequence.
OPTION 2: f(n) = f(n - 1) + 2
Substituting n = 1
f(1) = f(0) + 2 
3.
So, this is eliminated.
Similarly, OPTION 3 and OPTION 4 can be eliminated as well.
The river will not reach a level of 7 ft. after 5 hours.
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the height of the water level after x hours.
Since the river is 1 ft below its average water level and begins to rise by a constant rate of 1.5 ft per hour. Hence:
b = -1, m = 1.5. The equation becomes:
y = 1.5x - 1
To reach a level of 7 ft. That is y = 7:
7 = 1.5x - 1
1.5x = 8
x = 5.3 hours
The river will not reach a level of 7 ft. after 5 hours.
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Answer:
Step-by-step explanation:
do the thing times 2
Let X = the number of hours the server works.
The equation for the amount Nick spends is 15x + 47
The next job pays 14x + 54
Set the equations to equal and solve for x:
15x + 47 = 14x +54
Subtract 14x from both sides:
X + 47 = 54
Subtract 47 from both sides:
X = 7
Now replace x with 7 in the second equation:
14x + 54 = 14(7) + 54 = 98 +54 = 152
The job would pay $152 and be 7 hours long.
