6. Rectangular stage. One side of the rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the side?

7. Avoiding a collision. A car is travelling on a road that is perpendicular to a railroad truck. When the car is 30 meters from the crossing, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing.

8. winter wheat. While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kms, then what is the area of each field?

9. Venture capital. Henry invested $12,000 in a new restaurant. When the restaurant was sold two years later, he received $27,000. Find his average annual return by solving the equation 12,000(1 + r)^2 = 27,000.

Let u,v <- C^n and set A := I + uv^H <- C^nxn.
(a) Suppose A is invertible. Prove that Inverse(A) = I_n + auv^H , for some a <- C. Give an expression for a.
(b) For what u and v is A singular?
(c) Suppose A is singular. What is the null space of A, N(A) in this case?

1. An initial investment of $1000 is appreciated for 8 years in an account that earns 9% interest, compounded annually. Find the amount of money in the account at the end of the period.
2. Let f(x) = 3x. Find f(2).
3. Solve the equation 1296 x = 6
4. If $ 2500 is invested in an account that pays interest compo

Should algebra be taught to everyone? Who should study algebra? The statements below serve as possible answers to these questions and are only 'food for thought.' I welcome your constructive ideas and comments on one or several of them.
Whether you agree or do not agree, the study of algebra is good for the brain. The b

Elementary Algebra: Basic Operations with Polynomials)
2. Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?
A. -6x2 + 25x + 6
B. 6x2 + 5x + 6
C. 6x2 - 5x + 6
D. 6x2 - 5x - 6
E. 6x2 - 13x - 6
(Elementary Algebra: Substituting Values into Algeb

Please help me learn how to write these two proofs correctly for my Modern Algebra class.
Please submit all work as either a PDF or MS Word file.
** Please see the attached file for the complete problem description **

1. Write the interval notation for the graph up through 10.
-¥Ü-20____-10___0___10___)20_______30______?
2. Write in interval notation the real numbers between 0 and 1.
3. Write in interval notation the set of real numbers between -2 and 2, inclusive.

What type of Algebra problems covered in an Algebra 1 course do you find to be the most challenging? Why? What did you learn from the experience of an Algebra 1 course and how did you overcome this challenge? If you could provide some tips or advice to new Algebra 1 students, what would you share with them?

A student got 50% of the questions on an algebra test correct. If he answered 10 out of the first 12 questions asked correctly but missed 3/4 of the remaining questions, how many questions were on the test?

Consider two linear function: f(x) and f -1(x), their lines intersect at a point with a x-coordinate of 10 and the slope of f(x) is 1/2
*Find the SI equation
*Find x= f -1 (y) then express the inverse function in terms of x: y = f-1(x)
*graph the two lines on the same set of axes, clearly showing all four x and y interce