Find the equation for given of the following lines.
a. The line containing P(0, $-_2$) and parallel to the x-axis
b. The line containing P($-_4$, 5) and parallel to the y-axis

A farmer has 800 yd of fencing to enclose a rectangular pasture. One side of the pasture borders a river and does not need to be fenced. If side a must be twice as long as side b parallel to the river, what are the dimensions of the rectangular pasture?

For given of the following (arithmetic or geometric) sequences, discover the pattern and find a function whose domain is the set of natural numbers and whose outputs are the terms of the sequence:
a. 2, 4, 6, 8, 10, .....
b. 1, 3, 9, 27, 81, ......
c. $\sqrt3$, $\sqrt3$, $\sqrt3$, $\sqrt3$, ......
d. $3^{-1}$ , $3^{-\frac 1 2}$, 1, $3^{\frac1 2}$, 3 , .......

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, W is the set of whole numbers, and S is the set of irrational numbers, find given of the following:
a. $Q \cup S$
b. $Q \cap S$
c. $Q \cap R$
d. $S \cap W$
e. $W \cup R$
f. $Q \cup R$

Miriam is four years older than Ricardo. Ten years ago Miriam was 3 times as old as Ricardo was then.
a. How old are they now?
b. Determine whether your answer is correct by checking that it satisfies the conditions of the problem.

Ten years from now Alex’s age will be 3 times her present age. Find Alex’s age now.

An estate of $2,000,000 is left to four siblings. The eldest is to receive 3 times as much as the youngest. The other two siblings are each to receive$16,000 more than the youngest. How much will each receive?

Matt has twice as many stickers as David. If David has d stickers, and Matt gives David 10 stickers, how many stickers does each have in terms of d?

Use the fact that each prime in the prime factorization of $a^3$ (a is a whole number) appears a number of times that is a multiple of 3 to prove that $\sqrt[3] 2$ is irrational.

The following sets of ordered pairs are functions. Give a rule that could describe given function.
a. {($-_1$, 2), (0, 0), (1, $-_2$), $(2^{\frac{1}{2}}, {{-_2}^{\frac{1}{2}}})$}
b. {($-_6$, 0), (0, 6), (5, 11), ($\sqrt3$, $\sqrt3$ + 6)}
c. {($-_1$, 1), (1, 1), (2, 4), ($\sqrt3$, 3)}

If a school has w women and m men and you know that there are 100 more men than women, write an algebraic equation relating w and m.

Write an irrational number whose digits are 4s and 5s.

The following sets of ordered pairs are functions. Give a rule that could describe given function.
a. {($-_1$, 3), (0, 0), (1, $-_3$), ($3^{-\frac{1}{2}}$, $-{_3}^{\frac{1}{2}}$) }
b. {($-_5$, 0), (0, 5), (5, 10), ($\sqrt5, \sqrt 5 + 5$)}
c. { (0, 0), ($\sqrt3$, 3), ($-_{\sqrt 5}$, 5), ( $\frac {1} {\sqrt6}$ , $\frac 1 6$ ) }

Students were asked to write an algebraic expression for the sum of five consecutive natural numbers. One student wrote x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 5x + 10. Another wrote (x - 2) + (x - 1) + x + (x + 1) + (x + 2) = 5x.
a. Explain who is correct and why.
b. Does either approach prove that the sum of five consecutive integers equals 5 times the middle integer?
c. Does the statement in part (b) generalize to the sum of five consecutive terms in every arithmetic sequence? Justify your answer.