Set up the following scenarios as equations or inequalities and then solve for the desired quantity.

1) Sales, given in thousands, for a particular company in 1990 were at 140.5 and in 2000 at 180.5. Estimate the sales for the years 1997 and 2003. Let x = 0 correspond to 1990. Using the distance formula, find the approximate distance between the values in 1997 and 2003. Explain the difference between using the distance formula and simply subtracting the 2 estimated values.

2) An individual is trying to ensure that he or she earns an A (90%) in a particular college course. Assume all grades thus far are weighted equally. The grades for the course are 88, 92, 83, 76. All that is left is a final exam that counts as two grades. What grade is needed to ensure the student makes an A in the course?

3) A printing company charges $15.00 per order plus $0.10 per page for printing flyers. A second company charges $12.00 per order plus $0.15 per page. Find the equilibrium point, and explain what this point means in the context of the data.

Solution Summary

This solution shows step-by-step calculations to determine the intersection of two lines for each scenario. All workings and formulas are shown with explanations.

A. The solutions of line m are (3,3),(5,5),(15,15),(34,34),(678,678), and (1234,1234).
b. The solutions of line n are (3,-3),5,-5),(15,-15),(34,-34),(678,-678), and (1234,-1234).
c. Form the equations of both the lines
d. What are the co ordinates of the point of intersection of lines m and n?
e. Write the co-ordinat

For the first 5 questions, consider the set of intersection points of two equations, and let a1 be the number of distinct affine real intersections with multiplicity one, let a2 be the number of distinct affine real intersections with multiplicity two, let b be the numberof distint complex non-real affine intersections and let

I want a solution that explains why three lines that intersect at only one point is not independent. And is there a way of proving that only one of them is dependent? How do we differentiate between dependent and independent linear systems?
Please see the attached diagram for the full problem outline.

Question 1 - Draw the graphs of 2x-y-1 = 0 and 2x + y = 9; Write down the co-ordinates of the point of intersection of the twolines.
Question 2 - Solve graphically x + y + 2 = 0 and 3x - 4y = 5. Write down the co-ordinates of the point of intersection of the twolines.
Question 3 - Solve graphically x = 4 and 3x - 2y = 10. W

Please help me with these problems and please show all work and steps to your solutions. This will help me better understand the problems once I have the answer and the steps for it. Thanks!
Please show work
1. How do we write the equation of a horizontal line? What would be an example?
2. How do we write the equation of

1. How do we write the equation of a horizontal line? What would be an example?
2. How do we write the equation of a vertical line? What would be an example?
3. The points (3,9), (5,13), (15,33), (34,71), (678, 1359), and 1234,2471) all lie on M. The points (3,-9), (5,-11), (15,-21), (43,-40), (678, -684), and (1234, -124

#1 The largest possible domain of the function f(x) = sqrt{[x-1]/[x+2]} is the set
(A) all x except x=-2
(B) x < -2 or x greater or = 1
(C) none of the above.
#2 The solution of the inequality (x-3)(x^2-3x+2) > 0 is
(A) 1 < x < 2 and x > 3
(B) x > 3
(C) none of the above.
#3 In the triangle whose sides are 3 , 4 , and

1. Why do intersecting lines represent a unique solution? Give examples to support your answer.
2. What is the significance of the name 'linear equation' to its graphical representation?
3. The solutions of line m are (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471).
The solutions of line n are (3, -9)

4) Line L is defined by the following equation:
Line M is defined by:
Find a and b, if known that lines are parallel to each other.
5) Line L is defined by intersection of two planes
2x+3y?z = 1 and -2x+y+2z = 0
Plane P is defined by -2x + y ?z = 4
Find any directional vector for the line, point of intersection of line a