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Linear and Quadratic Equations

1.Bill can row 3 mph in still water. It takes him 3 hours 36 minutes to go 3 miles upstream and return. Find the speed of the current. Show your work.

2.Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions. Show your work

x^2 + 16 = 0

3.Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.

A student took out two loans totaling $10,000 to help pay for college expenses. One loan was at 8% simple interest, and the other was at 10%. After one year, the student owed $840 in interest. Find the amount of the loan at 10%. Show your work.

4.The formula s = 16t^2 is used to approximate the distance s, in feet, that an object falls freely (from rest) in t seconds. Use this formula to solve the problem. (Round answer to the nearest tenth.)

A stuntman jumps from a rooftop 330 ft off the ground. How long will it take him, falling freely, to reach the ground? Show your work.

Solution Preview

Dear student, please refer to the attachment for the solutions.

Let the speed of the current be x.
Bill's rowing speed is 3mph in still water.
In the direction of the current, the overall speed is (3+x).
Therefore, the time taken to cover the 3 mile distance in the direction of the current
= 3/((3+x) )
Against the ...

Solution Summary

This solution is comprised of detailed step-by-step calculations and explanation of the given problems. The solution also provides students with a clear perspective of the underlying mathematical concepts.