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mathematics
contemporary mathematics

Contemporary Mathematics 1st Edition OpenStax - Solutions

Find Tuyet's payment for a month when 12 units of water are used.Graph and interpret applications of slope-intercept.The equation \(P=31+1.75 w\) models the relation between the amount of Tuyet's monthly water bill payment, \(P\), in dollars, and the number of units of water, \(w\), used.
Interpret the slope and \(P\)-intercept of the equation.Graph and interpret applications of slope-intercept.The equation \(P=31+1.75 w\) models the relation between the amount of Tuyet's monthly water bill payment, \(P\), in dollars, and the number of units of water, \(w\), used.
Graph the equation.Graph and interpret applications of slope-intercept.The equation \(P=31+1.75 w\) models the relation between the amount of Tuyet's monthly water bill payment, \(P\), in dollars, and the number of units of water, \(w\), used.
Find the amount Bruce is reimbursed on a day when he drives 0 miles.Graph and interpret applications of slope-intercept.Bruce drives his car for his job. The equation \(R=0.575 m+42\) models the relation between the amount in dollars, \(R\), that he is reimbursed and the number of miles, \(m\), he
Find the amount Bruce is reimbursed on a day when he drives 220 miles.Graph and interpret applications of slope-intercept.Bruce drives his car for his job. The equation \(R=0.575 m+42\) models the relation between the amount in dollars, \(R\), that he is reimbursed and the number of miles, \(m\),
Interpret the slope and \(R\)-intercept of the equation.Graph and interpret applications of slope-intercept.Bruce drives his car for his job. The equation \(R=0.575 m+42\) models the relation between the amount in dollars, \(R\), that he is reimbursed and the number of miles, \(m\), he drives in
Graph the equation.Graph and interpret applications of slope-intercept.Bruce drives his car for his job. The equation \(R=0.575 m+42\) models the relation between the amount in dollars, \(R\), that he is reimbursed and the number of miles, \(m\), he drives in one day.
Find Cherie's salary for a week when her sales were \(\$ 0\).Graph and interpret applications of slope-intercept.Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation \(S=400+0.15 c\) models the relation between her weekly salary, \(S\), in dollars
Find Cherie's salary for a week when her sales were \(\$ 3,600\).Graph and interpret applications of slope-intercept.Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation \(S=400+0.15 c\) models the relation between her weekly salary, \(S\), in
Interpret the slope and \(S\)-intercept of the equation.Graph and interpret applications of slope-intercept.Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation \(S=400+0.15 c\) models the relation between her weekly salary, \(S\), in dollars and
Graph the equation.Graph and interpret applications of slope-intercept.Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation \(S=400+0.15 c\) models the relation between her weekly salary, \(S\), in dollars and the amount of her sales, \(c\), in
Find the cost if the number of guests is 40 .Graph and interpret applications of slope-intercept.Costa is planning a lunch banquet. The equation \(C=450+28 g\) models the relation between the cost in dollars, \(C\), of the banquet and the number of guests, \(g\).
Find the cost if the number of guests is 80 .Graph and interpret applications of slope-intercept.Costa is planning a lunch banquet. The equation \(C=450+28 g\) models the relation between the cost in dollars, \(C\), of the banquet and the number of guests, \(g\).
Interpret the slope and \(C\)-intercept of the equation.Graph and interpret applications of slope-intercept.Costa is planning a lunch banquet. The equation \(C=450+28 g\) models the relation between the cost in dollars, \(C\), of the banquet and the number of guests, \(g\).
Graph the equation.Graph and interpret applications of slope-intercept.Costa is planning a lunch banquet. The equation \(C=450+28 g\) models the relation between the cost in dollars, \(C\), of the banquet and the number of guests, \(g\).
\(\begin{cases}2 x-6 y=0 & \text { A: }(3,1) \\ 3 x-4 y=5 & \text { B: }(-3,4)\end{cases}\)Determine if the points are solutions to the given system of equations.
\(\left\{\begin{array}{l}-3 x+y=8 \\ -x+2 y=-9\end{array}\right.\)A: \((-5,-7)\)B: \((-5,7)\)Determine if the points are solutions to the given system of equations.
\(\left\{\begin{aligned} x+y & =2 \\ y & =\frac{3}{4} x\end{aligned}\right.\)A: \(\left(\frac{8}{7}, \frac{6}{7}\right)\)B: \(\left(1, \frac{3}{4}\right)\)Determine if the points are solutions to the given system of equations.
Determine if the points are solutions to the given system of equations. 2x+3y = 6 y A: (-6,2) x+2 B: (-3,4)
\(\left\{\begin{aligned}-x+y & =2 \\ 2 x+y & =-4\end{aligned}\right.\)Solve the following systems of equations by graphing.
\(\left\{\begin{array}{l}y=x-2 \\ y=-3 x+\end{array}\right.\)Solve the following systems of equations by graphing.
\(\left\{\begin{array}{l}y=\frac{2}{3} x-2 \\ y=-\frac{1}{3} x-5\end{array}\right.\)Solve the following systems of equations by graphing.
\(\left\{\begin{aligned}-x+3 y & =3 \\ x+3 y & =3\end{aligned}\right.\)Solve the following systems of equations by graphing.
\(\left\{\begin{aligned} 2 x-y & =4 \\ 2 x+3 y & =12\end{aligned}\right.\)Solve the following systems of equations by graphing.
\(\left\{\begin{aligned}-x+2 y & =-6 \\ y & =-\frac{1}{2} x-1\end{aligned}\right.\)Solve the following systems of equations by graphing.
\(\left\{\begin{aligned} 3 x+5 y & =10 \\ y & =-\frac{3}{5} x+1\end{aligned}\right.\)Solve the following systems of equations by graphing.
\(\left\{\begin{aligned} 4 x & =3 y+7 \\ 8 x-6 y & =14\end{aligned}\right.\)Solve the following systems of equations by graphing.
\(\left\{\begin{aligned} 2 x+y & =-4 \\ 3 x-2 y & =-6\end{aligned}\right.\)Solve the systems of equations by substitution.
\(\left\{\begin{array}{l}2 x+y=-2 \\ 3 x-y=7\end{array}\right.\)Solve the systems of equations by substitution.
\(\left\{\begin{array}{cc}x-2 y & =-5 \\ 2 x-3 y & =-4\end{array}\right.\)Solve the systems of equations by substitution.
\(\left\{\begin{array}{ccc}x-3 y & = & -9 \\ 2 x+5 y & = & 4\end{array}\right.\)Solve the systems of equations by substitution.
\(\left\{\begin{array}{rlc}-2 x+2 y & = & 6 \\ y & = & -3 x+1\end{array}\right.\)Solve the systems of equations by substitution.
\(\left\{\begin{aligned} 3 x+4 y & =1 \\ y & =-\frac{2}{5} x+2\end{aligned}\right.\)Solve the systems of equations by substitution.
\(\left\{\begin{aligned} x & =2 y \\ 4 x-8 y & =0\end{aligned}\right.\)Solve the systems of equations by substitution.
\(\left\{\begin{aligned} y & =\frac{7}{8} x+4 \\ -7 x+8 y & =6\end{aligned}\right.\)Solve the systems of equations by substitution.
\(\left\{\begin{aligned} 5 x+2 y & =2 \\ -3 x-y & =0\end{aligned}\right.\)Solve the systems of equations by elimination.
\(\left\{\begin{aligned} 6 x-5 y & =-1 \\ 2 x+y & =13\end{aligned}\right.\)Solve the systems of equations by elimination.
\(\left\{\begin{aligned} 2 x-5 y & =7 \\ 3 x-y & =17\end{aligned}\right.\)Solve the systems of equations by elimination.
\(\left\{\begin{aligned} 5 x-3 y & =-1 \\ 2 x-y & =2\end{aligned}\right.\)Solve the systems of equations by elimination.
\(\left\{\begin{array}{l}3 x-5 y=-9 \\ 5 x+2 y=16\end{array}\right.\)Solve the systems of equations by elimination.
\(\left\{\begin{aligned} \frac{1}{3} x-y & =-3 \\ x+\frac{5}{2} y & =2\end{aligned}\right.\)Solve the systems of equations by elimination.
\(\left\{\begin{aligned} 6 x+3 y & =9 \\ 2 x+y & =3\end{aligned}\right.\)Solve the systems of equations by elimination.
\(\left\{\begin{aligned} \frac{2}{3} x+y & =5 \\ 2 x+3 y & =11\end{aligned}\right.\)Solve the systems of equations by elimination.
\(\left\{\begin{aligned} 3 x+y & =-3 \\ 2 x+3 y & =5\end{aligned}\right.\)Solve the system of equations by graphing, substitution, or elimination.
\(\left\{\begin{array}{l}y=x+2 \\ y=-2 x+2\end{array}\right.\)Solve the system of equations by graphing, substitution, or elimination.
\(\left\{\begin{array}{l}y=\frac{3}{2} x+1 \\ y=-\frac{1}{2} x+5\end{array}\right.\)Solve the system of equations by graphing, substitution, or elimination.
\(\left\{\begin{aligned} x+y & =-4 \\ -x+2 y & =-2\end{aligned}\right.\)Solve the system of equations by graphing, substitution, or elimination.
\(\left\{\begin{aligned}-2 x+3 y & =3 \\ x+3 y & =12\end{aligned}\right.\)Solve the system of equations by graphing, substitution, or elimination.
\(\left\{\begin{aligned} x+3 y & =-6 \\ y & =-\frac{4}{3} x+4\end{aligned}\right.\)Solve the system of equations by graphing, substitution, or elimination.
\(\left\{\begin{array}{l}4 x-3 y=8 \\ 8 x-6 y=14\end{array}\right.\)Solve the system of equations by graphing, substitution, or elimination.
\(\left\{\begin{aligned} x & =-3 y+4 \\ 2 x+6 y & =8\end{aligned}\right.\)Solve the system of equations by graphing, substitution, or elimination.
Jackie has been offered positions by two cable companies. The first company pays a salary of \(\$ 14,000\) plus a commission of \(\$ 100\) for each cable package sold. The second pays a salary of \(\$ 20,000\) plus a commission of \(\$ 25\) for each cable package sold. How many cable packages would
Drew burned 1,800 calories Friday playing 1 hour of basketball and canoeing for 2 hours. Saturday she spent 2 hours playing basketball and 3 hours canoeing and burned 3,200 calories. How many calories did she burn per hour when playing basketball? How many calories did she burn per hour when
Mitchell currently sells stoves for company \(A\) at a salary of \(\$ 12,000\) plus a \(\$ 150\) commission for each stove he sells. Company B offers him a position with a salary of \(\$ 24,000\) plus a \(\$ 50\) commission for each stove he sells. How many stoves would Mitchell need to sell for
The total number of calories in 2 hot dogs and 3 cups of cottage cheese is 960 calories. The total number of calories in 5 hot dogs and 2 cups of cottage cheese is 1,190 calories. How many calories are in a hot dog? How many calories are in a cup of cottage cheese?Translate to a system of equations
Andrea and Bart go to the local farmers market to purchase some fruit. Andrea buys 4 apples and 5 oranges, which cost \(\$ 3.10\); Bart buys 4 apples and 6 oranges, which cost \(\$ 3.40\). What is the cost of an orange? What is the cost of an apple?Translate to a system of equations and solve.
Jack and jill go to a local farmers market to purchase some fruit. Jack buys 3 peaches and 2 limes, which cost \(\$ 1.50\); Jill buys 6 peaches and 5 limes, which cost \(\$ 3.45\). What is the cost of a peach? What is the cost of a lime?Translate to a system of equations and solve.
Red candies to green candies Use this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7 red. What is the ratio of the following candy colors?
Green candies to black candies Use this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7 red. What is the ratio of the following candy colors?
Yellow candies to black candies Use this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7 red. What is the ratio of the following candy colors?
Black candies to blue candies Use this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7 red. What is the ratio of the following candy colors?
Orange candies to non-orange candies Use this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7 red. What is the ratio of the following candy colors?
Yellow candies to non-yellow candies Use this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7 red. What is the ratio of the following candy colors?
Red candies to all candies Use this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7 red. What is the ratio of the following candy colors?
Pink candies to all candies Use this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7 red. What is the ratio of the following candy colors?
Candies with the letter ' \(r\) ' in their name to all candiesUse this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7 red. What is the ratio of the following
Candies with the letter ' \(r\) ' in their name to candies without the letter ' \(r\) ' in their name Use this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7
\(\frac{x}{46}=\frac{4}{8}\)Solve each proportion for the unknown variable.
\(\frac{27}{x}=\frac{3.5}{14}\)Solve each proportion for the unknown variable.
\(\frac{16}{7}=\frac{x}{14}\)Solve each proportion for the unknown variable.
\(\frac{1}{0.8}=\frac{x}{514}\)Solve each proportion for the unknown variable.
\(\frac{203}{g}=\frac{10}{22}\)Solve each proportion for the unknown variable.
\(\frac{1}{29.5}=\frac{16}{m}\)Solve each proportion for the unknown variable.
\(\frac{14}{95}=\frac{a}{19}\)Solve each proportion for the unknown variable.
\(\frac{13}{140}=\frac{s}{2961}\)Solve each proportion for the unknown variable.
\(\frac{1}{k}=\frac{69}{111}\) (Round answer to the nearest hundredth.)Solve each proportion for the unknown variable.
\(\frac{p}{1}=\frac{22}{7}\) (Round answer to the nearest hundredth.)Solve each proportion for the unknown variable.
Pet Paradise has 20 cats and 16 dogs. Animal Acres has 15 cats. How many dogs must be at Animal Acres so that Pet Paradise and Animal Acres have the same ratio of cats to dogs?
Pet Paradise has 20 cats and 16 dogs. Critter Corral has 28 dogs. How many cats must be at Critter Corral so that Pet Paradise and Critter Corral have the same ratio of cats to dogs?
A high school has 960 students. The ratio of students to high school teachers is \(16: 1\). How many high school teachers are at the school?
A high school has 960 students. The ratio of students to high school teachers is \(16: 1\). How many more teachers are needed to have a \(12: 1\) ratio at the high school of students to teachers?
One U.S. dollar is worth \(\$ 1.23\) Canadian dollars. Bernice is traveling to Canada and wants to convert \(\$ 550\) U.S. to Canadian money. How much in Canadian money should she receive?
One U.S. dollar is worth \(\$ 1.23\) Canadian dollars. Rene is traveling from Canada to the United States and wants to convert \(\$ 550\) of Canadian money to U.S. money. How much in U.S. money should he receive? Round your answer to the nearest cent.
One U.S. dollar is worth \(\$ 1.23\) Canadian dollars. What is one Canadian dollar worth in U.S. funds? Round your answer to the nearest cent.
A salad recipe needs one cup of crushed almonds. It will serve eight people. Rashida needs to make a salad to serve 20 people. How many cups of crushed almonds does she need?
A salad recipe needs one cup of crushed almonds. It will serve eight people. Elmer has 4.75 cups of crushed almonds. If he uses all of the crushed almonds he has to make this salad, how many people will it serve?
Jorge is 6 feet tall and casts a 7-foot shadow. At the same time, a nearby tree has a shadow of 56 feet. How tall is the tree?
Tony can run 4 kilometers in 30 minutes. At that rate, how far could he run in 1 hour, 45 minutes?
Kara's parent owns a restaurant. When she came in one day, they asked her to figure out how much they were spending per ounce on steak they were buying from a vendor. They had their last four receipts, but unfortunately they spilled liquid on them and some parts were unreadable. Find out how much
The scale for a map reads " 1 inch \(=250\) miles." You measure the distance on the map from Fargo, North Dakota to Winnipeg, Manitoba and get 1.44 inches. How far is it from Fargo to Winnipeg?
Hot Wheels toy cars are said to be built on a scale of \(1: 64\) when compared to the actual car. If a real car is 18 feet long, how long should the Hot Wheels toy car be (in inches)?
The Eiffel Tower in Paris, France, is 1,067 feet tall. The replica Eiffel Tower in Las Vegas, Nevada, is built on the scale of 1.976:1. How tall is the replica Eiffel Tower in Las Vegas? Round your answer to the nearest foot.
Plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.a. \((3,-1)\)b. \((-3,1)\)c. \((-2,0)\)d. \((-4,-3)\)e. \(\left(1, \frac{14}{5}\right)\)
\((0,-3)\)For each ordered pair above, decide:I. Is the ordered pair a solution to the equation?II. Is the point on the line in the given graph?\(y=\frac{1}{2} x-3\) -8-7-6-5-4-3-2-1 8 7 6 10 5 4 3 2 1 0 1 2 3 4 5 6 7 8 -1 W3 -2 3 -4 -5 -6- -7 -8
\((2,-2)\)For each ordered pair above, decide:I. Is the ordered pair a solution to the equation?II. Is the point on the line in the given graph?\(y=\frac{1}{2} x-3\) -8-7-6-5-4-3-2-1 8 7 6 10 5 4 3 2 1 0 1 2 3 4 5 6 7 8 -1 W3 -2 3 -4 -5 -6- -7 -8
\((-2,-4)\)For each ordered pair above, decide:I. Is the ordered pair a solution to the equation?II. Is the point on the line in the given graph?\(y=\frac{1}{2} x-3\) -8-7-6-5-4-3-2-1 8 7 6 10 5 4 3 2 1 0 1 2 3 4 5 6 7 8 -1 W3 -2 3 -4 -5 -6- -7 -8
\((4,1)\)For each ordered pair above, decide:I. Is the ordered pair a solution to the equation?II. Is the point on the line in the given graph?\(y=\frac{1}{2} x-3\) -8-7-6-5-4-3-2-1 8 7 6 10 5 4 3 2 1 0 1 2 3 4 5 6 7 8 -1 W3 -2 3 -4 -5 -6- -7 -8
\((0,-4)\)For each ordered pair above, decide:I. Is the ordered pair a solution to the equation?II. Is the point on the line in the given graph?\(y=x-4\) 00 8 7 10 6 5 4 3 2 1 -8-7-6-5-4-3-2-10 -2- N 1 2 3 4 5 6 7 8 -3 4. 5 10 6 -7 -8
\((3,-1)\)For each ordered pair above, decide:I. Is the ordered pair a solution to the equation?II. Is the point on the line in the given graph?\(y=x-4\) 00 8 7 10 6 5 4 3 2 1 -8-7-6-5-4-3-2-10 -2- N 1 2 3 4 5 6 7 8 -3 4. 5 10 6 -7 -8
\((2,2)\)For each ordered pair above, decide:I. Is the ordered pair a solution to the equation?II. Is the point on the line in the given graph?\(y=x-4\) 00 8 7 10 6 5 4 3 2 1 -8-7-6-5-4-3-2-10 -2- N 1 2 3 4 5 6 7 8 -3 4. 5 10 6 -7 -8

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