Marriage penalty eliminated.
The value of the expression 4220 + 0.25(x - 30,650)is the 2006 federal income tax for a single taxpayer with taxable income of x dollars, where x is over $30,650 but not over $74,200.
a) Simplify the expression.
b) Find the amount of tax for a single taxpayer with taxable income of $40,000.
c) Who pays more, a married couple with a joint taxable income of $80,000 or two single taxpayers with taxable incomes of $40,000 each?

I've come up with 2 solutions and not sure which one is correct please help..

a) Simplify the expression.
4220 + .25x - .25*30650
4220+.25x - 7226.5
.25x + -3442.5

1. Do the problem "Tables and Seats" in this topic. As you work on the problem, see if you can arrive at your solution from several different approaches. Upload your completed solution and methods.
2.Reflect on the aspects of algebraic thinking you discovered in the problem that were applicable to your problem-solving strateg

Let F be an extension field of K. Clearly F is a vector space over K. Let u be an element of F. Show that the subspace spanned by {1, u, u^2, ...} is a field IF and ONLY IF (iff) u is algebraic over K.
Let S be the subspace of F.
Hint for the "-->" of proof. If S is a field and u is not equal to 0, then 1/u is in S. What d

See the attached file.
1) Compute the Cayley tables for the additive group Z and for the multiplicative group
Z of non-zero elements in Z.
2) Let G be a group written additively. Recall that the order of an element a is the
minimal natural number n such that na = 0. If such n does not exits then one says that
the order

Suppose that L has transcendence degree n over K and that L is algebraic over K(α1, . . . , αn). Show that α1, . . . , αn is a transcendence basis for L over K.
Might help:
Theorem - Definition: Let L be an extension of K, A a subset of L. The following are equivalent:
(1) A is a maximal algebraically

One of the most often misunderstood concepts in math is divisibility. Divisibility is a different operation than division and the two are often confused.
The solution describes the seven key properties of divisibility and proves them mathematically to show the reader that they are true and why they are important.
The seven

Please see the attachment to see these questions properly.
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Question 1
If [K:F] is finite and u is algebraic over K ,prove that [F(u):F] divides [K(u):F]
Hint:[F(u):F] and [K(u):F(u)] are finite by Theorems 10.4,10.7 and 10.9
Apply Theorem 10.4 to
Theorem 10.4
Le

A car has a tank that holds 12 3/8 gallons of gasoline. Mr. Brown fills his tank and drives along the highway until he runs out of gas. If his car averages 19 2/5 mpg, how far has he traveled?

1. Three prizes are to be distributed in a Creative Design Talent Search Contest. The value of the second prize is five-sixths the value of the first prize, and the value of the third prize is fourth-fifths that of the second prize.
a. Express the total value of the three prizes as an algebraic expression.
b. Comment on the ki