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.

Write three quadraticequations, with a, b, and c (coefficients of x2, x, and the constant) as:
Integers
Rational numbers
Irrational numbers
Do you find any striking difference between the graphical representation of quadraticequationsandlinearequations? Explain the differences and comment on the responses posted

Write a quadratic equation (see attachment)
How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only give the solution? Is it possible to have different quadraticequations with the same solution? Explain. Provide your classmate's with one or two solutio

1. Form each of the following:
? A linear equation in one variable
? A linear equation in two variables
? A quadratic equation
? A polynomial of three terms
? An exponential function
? A logarithmic function

i) Solve he following equation by the quadratic formula :
3X^2 + 4X -23 = 0
ii) Find the values of x and y that satisfy the equations here given
( use the simultaneous equation method ) :
3x + 2y = 22
2x + 3y = 23
iii) Solve graphically the following equations: show the graph as a part of the solu

Solve: (y - 3/4)^2 = 17/16
Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula. 1/x + 1/x+6 = 1/5
A merchant has two kinds of paint. If 9 gal of the inexpensive paint is mixed with 7 gal of the expensive paint, the mixture will be worth $19.70 per gallon. If 3 gal of the ine

Please see the attached file for the fully formatted problems.
1. Decide all values of b in the following equations that will give one or more real number solutions.
Solve the following three quadraticequations, using what you consider to be the optimum method for each problem (factoring, square root method, etc.). Why

1. Determine which of the following are linearequationsand which are not linearequations. State the reason for your answer.
(a) x + y = 1000
(b) 3xy + 2y + 15z - 20 = 0
(c) 2xy + 4yz = 8
(d) 2x + 3y 4z = 6.

Determine the number and types of solutions for the following
quadraticequations
x2 - 5x = -6
Determine the value of c for which the following quadraticequations
will have one root.
(see attachment for the rest)

A step-by-step procedure is given for applying the quadratic formula to solve for x. The quadratic formula considered is as follows: x^2-x-6=0. In this example, the quadratic formula is presented accompanied by an explanation of the meaning for each term. The process is shown for assigning values to each element in the quadrat