Chapter 2

For Problems \(93-106\), evaluate each algebraic expression for the given values of the variables. $$ -x^{2}-y^{2} \text { for } x=-3 \text { and } y=-4 $$

Blake Scott leaves \(\frac{1}{4}\) of his estate to the Boy Scouts, \(\frac{2}{5}\) to the local cancer fund, and the rest to his church. What fractional part of the estate does the church receive?

For Problems \(93-106\), evaluate each algebraic expression for the given values of the variables. $$ -x^{2}+y^{2} \text { for } x=-2 \text { and } y=6 $$

A triangular plot of ground measures \(14 \frac{1}{2}\) yards by \(12 \frac{1}{3}\) yards by \(9 \frac{5}{6}\) yards. How many yards of fencing are needed to enclose the plot?

For Problems \(93-106\), evaluate each algebraic expression for the given values of the variables. $$ -a^{2}-3 b^{3} \quad \text { for } a=-6 \text { and } b=-1 $$

For her exercise program, Laian jogs for \(2 \frac{1}{2}\) miles, then walks for \(\frac{3}{4}\) of a mile, and finally jogs for another \(1 \frac{1}{4}\) miles. Find the total distance that Lian covers.

For Problems \(93-106\), evaluate each algebraic expression for the given values of the variables. $$ -a^{3}+3 b^{2} \text { for } a=-3 \text { and } b=-5 $$

For Problems \(93-106\), evaluate each algebraic expression for the given values of the variables. $$ y^{2}-3 x y \text { for } x=0.4 \text { and } y=-0.3 $$

Give a step-by-step description of the best way to add the rational numbers \(\frac{3}{8}\) and \(\frac{5}{18}\).

For Problems \(93-106\), evaluate each algebraic expression for the given values of the variables. $$ x^{2}+5 x y \quad \text { for } x=-0.2 \text { and } y=-0.6 $$

Give a step-by-step description of how to add the fractions \(\frac{5}{4 x}\) and \(\frac{7}{6 x}\)

The will of a deceased collector of antique automobiles specified that his cars be left to his three children. Half were to go to his elder son, \(\frac{1}{3}\) to his daughter, and \(\frac{1}{9}\) to his younger son. At the time of his death, 17 ears were in the collection. The administrator of his estate borrowed a car to make \(18 .\) Then he distributed the cars as follows: Elder son: \(\quad \frac{1}{2}(18)=9\) Daughter: \(\quad \frac{1}{3}(18)=6\) Younger son: \(\quad \frac{1}{9}(18)=2\) This takes care of the 17 cars, so the administrator then returned the borroned car. Where is the error in this solution?

Your friend keeps getting an answer of 16 when simplifying \(-2^{4}\). What mistake is he making and how would you help him?

Explain how you would simplify \(\frac{12 x^{2} y}{18 x y}\).