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Compute the area of the circular sidewalk shown here. Use your calculator's value of $\pi$ and round the answer (only) to hundredths. (FIGURE CAN'T COPY)
Three equations follow. One is an identity, another is a contradiction, and a third has a solution. State which is which.$2(x-5)+13-1=9-7+2 x$$2(x-4)+13-1=9+7-2 x$$2(x-5)+13-1=9+7+2 x$
Solve using the quadratic formula. Answer in exact and approximate form: $3 x^{2}-10 x=9$
Determine the domain:a. $y=\sqrt{2 x-5}$b. $y=\frac{5}{2 x^{2}+3 x-2}$
Match the correct graph to the conditions stated for $m$ and $b .$ There are more choices than graphs. (GRAPH CAN'T COPY)a. $m<0, b<0$b. $m>0, b<0$c. $m<0, b>0$d. $m>0, b>0$e. $m=0, b>0$f. $m<0, b=0$g. $m>0, b=0$h. $m=0, b<0$
The general form of a linear equation is $a x+b y=c,$ where $a$ and $b$ are not simultaneously zero. (a) Find the $x$ - and $y$ -intercepts using the general form (substitute $0 \text { for } x, \text { then } 0 \text { for } y)$ Based on what you see, when does the intercept method work most efficiently? (b) Find the slope and $y$ -intercept using the general form (solve for $y$ ). Based on what you see, when does the intercept method work most efficiently?.
Eating out: In $1990,$ Americans bought an average of 143 meals per year at restaurants. This phenomenon continued to grow in popularity and in the year 2000 the average reached 170 meals per year. (a) Find a linear equation with $t=0$ corresponding to 1990 that models this growth, (b) discuss the slope ratio in context, and (c) use the equation to estimate the average number of times an American will eat at a restaurant in 2006 if the trend continues.
Prison population: In $1990,$ the number of persons sentenced and serving time in state and federal institutions was approximately $740,000 .$ By the year $2000,$ this figure had grown to nearly 1,320,000 (a) Find a linear equation with $t=0$ corresponding to 1990 that models this data, (b) discuss the slope ratio in context, and (c) use the equation to estimate the prison population in 2007 if this trend continues.
Prescription drugs: Retail sales of prescription drugs have been increasing steadily in recent years. In $1995,$ retail sales hit $\$ 72$ billion. By the year 2000 , sales had grown to about $\$ 146$ billion.(a) Use the relation (year, retail sales of prescription drugs) with $t=0$ corresponding to 1995 to find a linear equation modeling the growth of retail sales.(b) Discuss what the slope indicates in this context.(c) According to this model, in what year will sales reach $\$ 250$ billion? (d) According to the model, what was the value of retail prescription drug sales in $2005 ?$ (e) How many years after 1995 will retail sales exceed $\$ 279$ billion? (f) If yearly sales totaled $\$ 294$ billion, what year is it?
Internet connections: The number of households that are hooked up to the Internet (homes that are online) has been increasing steadily in recent years. In $1995,$ approximately 9 million homes were online. By 2001 this figure had climbed to about51 million. (a) Use the relation (year, homes online) with $t=0$ corresponding to 1995 to find an equation model for the number of homes online.(b) Discuss what the slope indicates in this context.(c) According to this model, in what year did the first homes begin to come online? (d) If the rate of change stays constant, how many households will be on the Internet in $2006 ?$ (e) How many years after 1995 will there be over 100 million households connected? (f) If there are 115 million households connected, what year is it?
Depreciation: Once a piece of equipment is put into service, its value begins to depreciate. A business purchases some computer equipment for $\$ 18,500 .$ At the end of a 2 -yr period, the value of the equipment has decreased to $\$ 11,500 .$ (a) Use the relation (time since purchase, value) to find a linear equation modeling the value of the equipment.(b) Discuss what the slope and $y$ -intercept indicate in this context. (c) What is the equipment's value after 4 yr? (d) How many years after purchase will the value decrease to $\$ 6000 ?$ (e) Generally, companies will sell used equipment while it still has value and use the funds to purchase new equipment. According to the function, how many years will it take this equipment to depreciate in value to $\$ 1000 ?$
Investing in coins: The purchase of a "collector's item" is often made in hopes the item will increase in value. In $1998,$ Mark purchased a $1909-\mathrm{S}$ VDB Lincoln Cent (in fair condition) for $\$ 150 .$ By the year $2004,$ its value had grown to $\$ 190 .$ (a) Use the relation (time since purchase, value) with $t=0$ corresponding to 1998 to find a linear equation modeling the value of the coin. (b) Discuss what the slope and $y$ -intercept indicate in this context.(c) How much will the penny be worth in $2009 ?$(d) How many years after purchase will the penny's value exceed $\$ 250 ?$ (e) If the penny is now worth $\$ 170,$ how many years has Mark owned the penny?
