If the simple interest on $1,000 for 8 years is $ 480 then what is the interest rate?
1 answer:
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Given
We have to set the restraint
because a square root is non-negative, and thus it can't equal a negative number. With this in mind, we can square both sides:
The solutions to this equation are 7 and -2. Recalling that we can only accept solutions greater than or equal to -1, 7 is a feasible solution, while -2 is extraneous.
Similarly, we have
So, we have to impose
Squaring both sides, we have
The solutions to this equation are 5 and 10. Since we only accept solutions greater than or equal to 7, 10 is a feasible solution, while 5 is extraneous.
Step 1. Solve both inequalities for 
:
Step 2. To check a point in the solution of the given system of inequalities, look for the intercepts of the lines
and 
:
(1)
(2)
Replace (1) in (2):
Solve for
:
(3)
Replace (3) in (1):
We can conclude that the point (-2,3) is in the solution of the system if <span>inequalities</span>; also any point inside the dark shaded area of the graph of the system of inequalities is also a solution of the system.
Step 2. To check a point in the solution of the given system of inequalities, look for the intercepts of the lines
Replace (1) in (2):
Solve for
Replace (3) in (1):
We can conclude that the point (-2,3) is in the solution of the system if <span>inequalities</span>; also any point inside the dark shaded area of the graph of the system of inequalities is also a solution of the system.