Chapter 2

You and your family take a summer vacation to Ireland. You discover that the number of Americans visiting Ireland is increasing by \(80,000\) visitors per year. Let \(x\) represent the number of visitors in 1997 . If the number of visitors in 1997 was \(700,000,\) how many visitors were expected in \(2000 ?\) Use unit analysis to check your answer.

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ -x^{3}+2 x\left(x-x^{2}\right) $$

Evaluate the expression. Use estimation to check your answer. $$ -7.85+5.96-(-2.49) $$

Find the difference. $$7 \frac{9}{10}-5 \frac{3}{7}$$

Multiply the matrix by the real number. $$\text { Sample: }-3\left[\begin{array}{rr}1 & -2 \\\\-4 & 0\end{array}\right]=\left[\begin{array}{rr}-3(1) & -3(-2) \\\\-3(-4) & -3(0)\end{array}\right]=\left[\begin{array}{rr}-3 & 6 \\\12 & 0\end{array}\right]$$ $$-8\left[\begin{array}{rr}-4 & -7 \\\3 & 3\end{array}\right]$$

You launch a model rocket that rises 550 feet in 2.75 seconds. It then opens a parachute and falls at a rate of 11 feet per second. What is the rocket's average velocity going up? (TABLE CANNOT COPY)

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ 4 w^{2}-w(2 w-3) $$

Evaluate the expression. Use estimation to check your answer. $$ -13.87-(-13.87)+5.8 $$

Find the difference. $$\frac{5}{12}-\frac{3}{16}$$

You launch a model rocket that rises 550 feet in 2.75 seconds. It then opens a parachute and falls at a rate of 11 feet per second. What is the rocket's velocity coming down? (TABLE CANNOT COPY)

BUYING JEANS You have 58 dollar, and you want to buy a pair of jeans and a \(\$ 20\) T-shirt. There is a \(6 \%\) sales tax. If \(x\) represents the cost of the jeans, then the following inequality is a model that shows how much you can spend on the jeans. $$ x+20+0.06(x+20) \leq 58 $$ Simplify the left side of the inequality.

Evaluate the expression. Use estimation to check your answer. $$ -15.7+0.01+(-34.44) $$

Evaluate the expression. $$a^{4}+8 \text { when } a=10$$

BUYING JEANS You have 58 dollar, and you want to buy a pair of jeans and a \(\$ 20\) T-shirt. There is a \(6 \%\) sales tax. If \(x\) represents the cost of the jeans, then the following inequality is a model that shows how much you can spend on the jeans. $$ x+20+0.06(x+20) \leq 58 $$ If the jeans cost \(\$ 35,\) can you buy both the T-shirt and the jeans?

Evaluate the expression. Use estimation to check your answer. Susmarine DEPTH A submarine is at a depth of 725 feet below sea level. Five minutes later, it is at a depth of 450 feet below sea level. What is the change in depth of the submarine? Did it go up or down?

Evaluate the expression. $$79-v^{3} \text { when } v=4$$

As parts (a) and (b) of Example 3 show, it is sometimes easier to evaluate an expression by simplifying it before substituting, and sometimes easier if you substitute for the variable first. a. Write an expression that is easier to evaluate if you simplify before substituting 12 for \(x\) b. Write an expression that is easier to evaluate if you substitute 12 for \(x\) first.

If \(a\) and \(b\) are positive and \(a

FREIGHT TRAINS A train with 150 freight cars is used to haul two types of grain. Each freight car can haul 97.3 tons of barley or 114 tons of corn. Let \(n\) represent the number of freight cars containing corn. Which function correctly represents the total weight the train can haul? $$ \text { A. } W=97.3(150-n)+114 n \quad \text { B. } W=97.3 n+114(150-n) $$

Evaluate the expression. Use estimation to check your answer. GASOLINE PRICES Last month the price of gasoline was \(\$ 1.19\) per gallon. This month the price of gasoline is \(\$ 1.13\) per gallon. What was the change in the price per gallon of gasoline?

Evaluate the expression. $$t^{2}-7 t+12 \text { when } t=8$$

Which of the following statements is not true? (A) The product of any number and zero is zero. (B) The order in which two numbers are multiplied does not change the product. (c) The product of any number and \(-1\) is a negative number. (D) The product of any number and \(-1\) is the opposite of the number.

Which of the following expressions is equivalent to the expression \(\frac{6 x-4}{-\frac{2}{3}} ?\) (A) \(2(3 x-2) \cdot \frac{3}{2} \quad\) (B) \((6 x-4) \cdot\left(-\frac{2}{3}\right) \quad\) (C) \(-9 x+6 \quad\) (D) \(9 x-6\)

FREIGHT TRAINS A train with 150 freight cars is used to haul two types of grain. Each freight car can haul 97.3 tons of barley or 114 tons of corn. Let \(n\) represent the number of freight cars containing corn. If 90 freight cars contain corn, what is the total weight the train is hauling?

GOLD PRICES IN LONDON At 9 A.M., an ounce of gold sells for \(\$ 287.56\). At noon, gold sells for \(\$ 286.90\) per ounce. At 4 P.M., the final price for the day is \(\$ 287.37\) per ounce. What is the change in the price per ounce of gold from 9 A.M. to noon?

Evaluate the expression. $$2 x^{2}+8 x-5 \text { when } x=3$$

Which of the following has the least value? (A) \(\left[\frac{3}{8}(8-6)+\frac{1}{4}\right] \cdot(-12)\) (B) \(\frac{3}{8} \cdot 8-6+\frac{1}{4} \cdot(-12)\) (c) \(-\frac{3}{8} \cdot 8-6+\frac{1}{4} \cdot 12\) (D) \(-\frac{3}{8} \cdot\left(8-6+\frac{1}{4}\right) \cdot(-12)\)

Which of the following statements is false? (A) The reciprocal of any negative number is a negative number. (B) Dividing by a number is the same as multiplying by the reciprocal of the number. (C) The reciprocal of any positive number is a positive number. (D) The reciprocal of any number is greater than zero and less than 1

FREIGHT TRAINS A train with 150 freight cars is used to haul two types of grain. Each freight car can haul 97.3 tons of barley or 114 tons of corn. Let \(n\) represent the number of freight cars containing corn. If 72 freight cars contain barley, what is the total weight the train is hauling?

GOLD PRICES IN LONDON At 9 A.M., an ounce of gold sells for \(\$ 287.56\). At noon, gold sells for \(\$ 286.90\) per ounce. At 4 P.M., the final price for the day is \(\$ 287.37\) per ounce. What is the change in the price per ounce of gold from noon to 4 P.M.?

Check whether the given number is a solution of the equation. $$x+5=11 ; 7$$

Evaluate the expression. $$\frac{3}{4} \cdot[-7 \cdot(-4-6)+30]-11$$

A set of numbers is closed under an operation if applying the operation to any two numbers in the set results in another number in the set. For instance, positive integers are closed under addition because the sum of any two positive integers is a positive integer. Decide whether the set is closed under the given operation. a. positive integers; subtraction b. integers; addition and subtraction c. integers; multiplication d. integers; division

INVESTING MONEY You receive \(\$ 5000\). You decide to invest the money in a one-year bond paying \(2 \%\) interest and in a one-year certificate of deposit paying \(6 \%\) interest. \- Let \(m\) represent the amount of money invested in the one-year bond. Write a function that represents the total amount of money \(T\) that you have after one year. Simplify the function.

GOLD PRICES IN LONDON At 9 A.M., an ounce of gold sells for \(\$ 287.56\). At noon, gold sells for \(\$ 286.90\) per ounce. At 4 P.M., the final price for the day is \(\$ 287.37\) per ounce. What is the change in the price per ounce of gold from 9 A.M. to 4 P.M.?

Check whether the given number is a solution of the equation. $$12-2 a=18 ; 4$$

Evaluate the expression. $$-3 \cdot\left[\left(2 \frac{9}{14}-3 \frac{3}{7}\right) \cdot \frac{28}{11}\right]+5\left(-9 \frac{1}{5}-9\right)$$

Write the fraction as a decimal. Round to the nearest hundredth if necessary. $$\frac{3}{4}$$

Find the speed and the velocity of the object. A helicopter is descending for a landing at a rate of 6 feet per second.

Write a question that can be represented by the equation. Then use mental math to solve the equation. $$x+4=9$$

Write the fraction as a decimal. Round to the nearest hundredth if necessary. $$\frac{3}{5}$$

Moving The van that you are using to move can hold 16 moving boxes. Each box can hold 60 pounds of books or 15 pounds of clothes. Let \(b\) represent the number of boxes filled with books. Write a function that represents the total weight \(w\) of the boxes in the van.

Check whether the given number is a solution of the equation. $$3+2 d=9+d ; 6$$

Write a question that can be represented by the equation. Then use mental math to solve the equation. $$y-7=3$$

Write the fraction as a decimal. Round to the nearest hundredth if necessary. $$\frac{1}{10}$$

Find the speed and the velocity of the object. A diver plunges to the ocean floor at a rate of 3 meters per second.

Check whether the given number is a solution of the equation. $$3 w-7=w+1 ; 5$$

Write a question that can be represented by the equation. Then use mental math to solve the equation. $$6 x=18$$

Write the fraction as a decimal. Round to the nearest hundredth if necessary. $$\frac{7}{25}$$

Check whether the given number is a solution of the equation. $$6 z+5=8 z-12 ; 8.5$$