Chapter 2

A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 378 \(\mathrm{ft}^{2}\). Find the width of the walkway if the garden is \(12 \mathrm{ft}\). wide by 15 \(\mathrm{ft}\). Iong.

For the following exercises, use this scenario: The cost of renting a car is $$\$ 45 /$$ wk plus $$\$ 0.25 / \mathrm{mi}$$ traveled during that week. An equation to represent the cost would be \(y=45+.25 x,\) where \(x\) is the number of miles traveled. What is your cost if you travel 50 mi?

For the following exercises, input the left-hand side of the inequality as a \(Y 1\) graph in your graphing utility. Enter \(y 2=\) the right-hand side. Entering the absolute value of an expression is found in the MATH menu, Num, \(1: a b s(.\) Find the points of intersection, recall \(\left(2^{\text {nd }}\right.\) CALC 5 :intersection, \(1^{\text {st }}\) curve, enter, \(2^{\text {nd }}\) curve, enter, guess, enter). Copy a sketch of the graph and shade the \(x\) -axis for your solution set to the inequality. Write final answers in interval notation. $$ |x+2| \geq 5 $$

An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, \(P,\) who contracted the flu \(t\) days after it broke out is given by the model \(P=-t^{2}+13 t+130,\) where \(1 \leq t \leq 6 .\) Find the day that 160 students had the flu. Recall that the restriction on \(t\) is at most 6 .

For the following exercises, use this scenario: The cost of renting a car is $$\$ 45 /$$ wk plus $$\$ 0.25 / \mathrm{mi}$$ traveled during that week. An equation to represent the cost would be \(y=45+.25 x,\) where \(x\) is the number of miles traveled. If your cost were $$\$ 63.75,$$ how many miles were you charged for traveling?

Solve \(|3 x+1|=|2 x+3|\)

For the following exercises, use this scenario: The cost of renting a car is $$\$ 45 /$$ wk plus $$\$ 0.25 / \mathrm{mi}$$ traveled during that week. An equation to represent the cost would be \(y=45+.25 x,\) where \(x\) is the number of miles traveled. Suppose you have a maximum of $$\$ 100$$to spend for the car rental. What would be the maximum number of miles you could travel?

Solve \(x^{2}-x>12\)

The coordinates on a map for San Francisco are (53,17) and those for Sacramento are \((128,78) .\) Note that coordinates represent miles. Find the distance between the cities to the nearest mile.

\(\frac{x-5}{x+7} \leq 0, x \neq-7\)

\(p=-x^{2}+130 x-3000\) is a profit formula for a small business. Find the set of \(x\) -values that will keep this profit positive.

A small craft in Lake Ontario sends out a distress signal. The coordinates of the boat in trouble were (49,64) One rescue boat is at the coordinates (60,82) and a second Coast Guard craft is at coordinates (58,47) . Assuming both rescue craft travel at the same rate, which one would get to the distressed boat the fastest?

In chemistry the volume for a certain gas is given by \(V=20 T\), where \(V\) is measured in cc and \(T\) is temperature in \({ }^{\circ} \mathrm{C}\). If the temperature varies between \(80^{\circ} \mathrm{C}\) and \(120^{\circ} \mathrm{C}\), find the set of volume values.

A man on the top of a building wants to have a guy wire extend to a point on the ground \(20 \mathrm{ft}\) from the building. To the nearest foot, how long will the wire have to be if the building is \(50 \mathrm{ft}\) tall?

A basic cellular package costs $$\$ 20 / \mathrm{mo} .$$ for \(60 \mathrm{~min}\) of calling, with an additional charge of $$\$ .30 /$$ min beyond that time.. The cost formula would be $$C=\$ 20+.30(x-60) . \text { If you }$$ have to keep your bill lower than $$\$ 50,$$ what is the maximum calling minutes you can use?

If we rent a truck and pay a \(\$ 75 /\) day fee plus \(\$ .20\) for every mile we travel, write a linear equation that would express the total cost per day \(y,\) using \(x\) to represent the number of miles we travel. Graph this function on your graphing calculator and find the total cost for one day if we travel 70 mi.