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mathematics
contemporary mathematics

Contemporary Mathematics 1st Edition OpenStax - Solutions

Evaluate the function \(f(x)=-3 x+21\) at the values \(f(-2), f(-1), f(0), f(1)\), and \(f(2)\).
Use the graph shown to find the domain and the range. 10 8 6 4 2 -10-8-6-4-20 -2 2 4 -4 -6 -8 -10 9 00 8 10
Graph \(2 y=x-4\) using the intercepts.
Use the slope formula to find the slope of the line between \((1,4)\) and \((3,5)\).
Identify the slope and \(y\)-intercept of \(y-\frac{2}{3} x=1\).
Graph the line of \(y=\frac{2}{3} x+1\) using its slope and \(y\)-intercept.
Find the payment for two people.The equation \(C=4.50+15 p\), models the cost of visiting the Cat Café in San Diego for one hour. \(C\), in dollars, is the total cost and the cost per person, \(p\), is \(\$ 15\) plus a \(\$ 4.50\) reservation fee.
Find the payment for five people.The equation \(C=4.50+15 p\), models the cost of visiting the Cat Café in San Diego for one hour. \(C\), in dollars, is the total cost and the cost per person, \(p\), is \(\$ 15\) plus a \(\$ 4.50\) reservation fee.
Interpret the slope and \(C\)-intercept of the equation.The equation \(C=4.50+15 p\), models the cost of visiting the Cat Café in San Diego for one hour. \(C\), in dollars, is the total cost and the cost per person, \(p\), is \(\$ 15\) plus a \(\$ 4.50\) reservation fee.
Graph the equation.The equation \(C=4.50+15 p\), models the cost of visiting the Cat Café in San Diego for one hour. \(C\), in dollars, is the total cost and the cost per person, \(p\), is \(\$ 15\) plus a \(\$ 4.50\) reservation fee.
Solve the system of equations by graphing.\(\left\{\begin{array}{l}y-3 x=3 \\ y=-6 x+12\end{array}\right.\)
Solve the system of equations by substitution.\(\left\{\begin{array}{l}y=5 x-5 \\ -3 x+y=-3\end{array}\right.\)
Solve the systems of equations by elimination.\(\left\{\begin{array}{l}y=\frac{1}{3} x-6 \\ y=x-3\end{array}\right.\)
Anna goes to the concession stand at a movie theater. She buys 5 popcorns and 4 large sodas and pays a total of \(\$ 60\). During intermission, Isabelle goes to the concession stand. She buys 1 popcorn and 2 large sodas and pays a total of \(\$ 18\). What is the cost of one popcorn, and the cost of
Solve the systems of linear equations by graphing.\(\left\{\begin{array}{l}y>\frac{1}{3} x-1 \\ y
Write a system of inequalities to model this situation.Juliette is selling fresh lemonade and cupcakes. She sells a cup of lemonade for \(\$ 2\) and a cupcake for \(\$ 3\). She needs to make at least \(\$ 100\) to donate to the local cat sanctuary. She needs to sell at least 20 cups of lemonade.
Graph the system.Juliette is selling fresh lemonade and cupcakes. She sells a cup of lemonade for \(\$ 2\) and a cupcake for \(\$ 3\). She needs to make at least \(\$ 100\) to donate to the local cat sanctuary. She needs to sell at least 20 cups of lemonade.
Could she sell 30 cups of lemonade and 10 cupcakes and make \(\$ 100\) ?Juliette is selling fresh lemonade and cupcakes. She sells a cup of lemonade for \(\$ 2\) and a cupcake for \(\$ 3\). She needs to make at least \(\$ 100\) to donate to the local cat sanctuary. She needs to sell at least 20
Could she sell 20 cups of lemonade and 30 cupcakes and make \(\$ 100\) ?Juliette is selling fresh lemonade and cupcakes. She sells a cup of lemonade for \(\$ 2\) and a cupcake for \(\$ 3\). She needs to make at least \(\$ 100\) to donate to the local cat sanctuary. She needs to sell at least 20
Find the objective function.A toy maker makes exactly two toys out of wood; the Box \((x)\) and the Bat ( \(y\) ). He makes \(\$ 5\) per Box and \(\$ 6\) per Bat. Each Box requires 30 ounces of wood, and each Bat requires 45 ounces of wood. Today the toy maker has 270 ounces of wood available. The
Write the constraints as a system of inequalities.A toy maker makes exactly two toys out of wood; the Box \((x)\) and the Bat ( \(y\) ). He makes \(\$ 5\) per Box and \(\$ 6\) per Bat. Each Box requires 30 ounces of wood, and each Bat requires 45 ounces of wood. Today the toy maker has 270 ounces
Graph of the system of inequalities.A toy maker makes exactly two toys out of wood; the Box \((x)\) and the Bat ( \(y\) ). He makes \(\$ 5\) per Box and \(\$ 6\) per Bat. Each Box requires 30 ounces of wood, and each Bat requires 45 ounces of wood. Today the toy maker has 270 ounces of wood
Find the value of the objective function at each corner point of the graphed region.A toy maker makes exactly two toys out of wood; the Box \((x)\) and the Bat ( \(y\) ). He makes \(\$ 5\) per Box and \(\$ 6\) per Bat. Each Box requires 30 ounces of wood, and each Bat requires 45 ounces of wood.
To maximize profit, how many of each toy should the toymaker make?A toy maker makes exactly two toys out of wood; the Box \((x)\) and the Bat ( \(y\) ). He makes \(\$ 5\) per Box and \(\$ 6\) per Bat. Each Box requires 30 ounces of wood, and each Bat requires 45 ounces of wood. Today the toy maker
Objective Function \(P=6 x+11 y\).Find the value of the objective function at each corner of the graphed region. y (0,5)- (5, 3) (0, 0) (7,0) x
Objective Function \(T=5 x+3 y\)Find the value of the objective function at each corner of the graphed region. (0, 4)- (0, 0) y (5, 7) (8,5) (10, 0) x
Objective Function \(L=33 x+45 y\)Find the value of the objective function at each corner of the graphed region. y (4,8) (0, 3)- (6,3) (0, 0) x
Objective Function \(P=2 t+4 c\)Find the value of the objective function at each corner of the graphed region. C (2, 2) (4,7) (7,4) (8,0)
Objective Function \(P=2.5 a+3.75 b\)Find the value of the objective function at each corner of the graphed region. b (2,9) (0,3) (7,5) (2,0) a
Fernando builds birdbaths ( \(x\) ) and birdhouses ( \(y\) ). Fernando can make a total of 7 birdbaths and birdhouses per day. A birdbath costs \(\$ 8\) to make, while a birdhouse costs \(\$ 6\) to make. Fernando has \(\$ 48\) to spend on building materials for the day. When he sells them, Fernando
A fruit pie (p) requires 12 ounces of fruit and 15 ounces of dough; a fruit tart \((t)\) requires 4 ounces of fruit and 3 ounces of dough. There are 72 ounces of fruit and 60 ounces of dough.Write the constraint inequalities. The variables to use are given in parentheses.
One recipe for chocolate cake (c) calls for 9 ounces of chocolate chips and 4 eggs; a recipe for dark chocolate cake (d) requires 12 ounces of chocolate chips but only 3 eggs. There are 90 ounces of chocolate chips and 36 eggs.Write the constraint inequalities. The variables to use are given in
To build an outdoor bench (b), a carpenter needs 10 pieces of wood and 26 nails; to build an outdoor chair (c), the carpenter need 8 pieces of wood and 33 nails. There are 92 pieces of wood and 286 nails.Write the constraint inequalities. The variables to use are given in parentheses.
Graph of Exercise 6 Graph each of the system of inequalities from Exercises 6-9. Assume all graphs are in the first quadrant.Data from Exercises 6Fernando builds birdbaths ( \(x\) ) and birdhouses ( \(y\) ). Fernando can make a total of 7 birdbaths and birdhouses per day. A birdbath costs \(\$ 8\)
Graph of Exercise 7 Graph each of the system of inequalities from Exercises 6-9. Assume all graphs are in the first quadrant.Data from Exercises 7A fruit pie (p) requires 12 ounces of fruit and 15 ounces of dough; a fruit tart \((t)\) requires 4 ounces of fruit and 3 ounces of dough. There are 72
Graph of Exercise 8 Graph each of the system of inequalities from Exercises 6-9. Assume all graphs are in the first quadrant.Data from Exercises 8One recipe for chocolate cake (c) calls for 9 ounces of chocolate chips and 4 eggs; a recipe for dark chocolate cake (d) requires 12 ounces of chocolate
Graph of Exercise 9 Graph each of the system of inequalities from Exercises 6-9. Assume all graphs are in the first quadrant.Data from Exercises 9To build an outdoor bench (b), a carpenter needs 10 pieces of wood and 26 nails; to build an outdoor chair (c), the carpenter need 8 pieces of wood and
A restaurant sells both regular milk and chocolate milk. To make a glass of regular milk (x), it takes 16 ounces of, well, milk. To make a glass of chocolate milk ( \(y\) ), it takes 15 ounces of milk and 1 ounce of chocolate flavoring. The restaurant makes a profit of \(\$ 1.50\) per glass on
To make a package of all-beef hot dogs ( \(x\) ), a factory uses one pound of beef; to make their regular all-meat hot dogs ( \(y\) ), they use \(1 / 2\) pound of beef and \(1 / 2\) pound of pork. The profit on the package of all-beef hot dogs is \(\$ 2.40\) per pack; the profit on the all-meat hot
A toy maker makes two plastic toys, the Ring ( \(x\) ) and the Stick ( \(y\) ). The toy maker makes \(\$ 5\) per Ring and \(\$ 4\) per Stick. The Ring uses 4 feet of plastic, while the Stick uses 3 feet of plastic. Today the toy maker has 36 feet of plastic available. The toy maker also only makes
The toy maker also makes exactly two toys out of wood, the Box ( \(x\) ) and the Bat ( \(y\) ). The toy maker makes \(\$ 6\) per Box and \(\$ 7\) per Bat. Each Box requires 25 ounces of wood, and each Bat requires 40 ounces of wood. Today the toy maker has 260 ounces of wood available. The toy
Sara makes two kinds of kites out of fabric and popsicle sticks. Her Famous Flyer ( \(x\) ) needs 2 yards of fabric and 9 popsicle sticks; her Gallant Glider ( \(y\) ) needs 3 yards of fabric and 18 popsicle sticks. She makes a profit of \(\$ 4\) on the Famous Flyer and \(\$ 6\) on the Gallant
Randy's RV Storage stores two types of Recreational Vehicles (RVs), The Xtra RV (x) takes up 400 square feet of space, while the Yosemite RV ( \(y\) ) takes up 600 square feet of space. Randy has 55,000 square feet of storage space. By local law, he is only allowed to have a maximum of 100 RVs on
A Belgian chocolatier wants to introduce two new chocolate bar creations. The first chocolate bar is called Super Dark ( \(x\) ), and it consists of 90 grams of chocolate and 10 grams of sugar. The second chocolate bar is called Special Dark ( \(y\) ), containing 80 grams of chocolate and 20 grams
A juice bottler makes two kinds of specialty juices using different mixtures of pineapple ( \(x\) ) and orange ( \(y\) ) juices. A 16-ounce bottle of Island Delight has 10 ounces of pineapple juice and 6 ounces of orange juice. A 16-ounce bottle of Sun Fun has 4 ounces of pineapple juice and 12
Fernando builds birdbaths ( \(x\) ) and birdhouses ( \(y\) ). Fernando can make a total of 7 birdbaths and birdhouses per day. A birdbath costs \(\$ 8\) to make, while a birdhouse costs \(\$ 6\) to make. Fernando has \(\$ 48\) to spend on building materials for the day. When he sells them, Fernando
A farmer grows wheat ( \(x\) ) and barley ( \(y\) ) on his 500 acres of cropland. He expects to profit \(\$ 150\) per acre for wheat and \(\$ 180\) per acre for barley. The cost of raising each crop (seed, pesticide, etc.) is \(\$ 60\) per acre for wheat and \(\$ 90\) per acre for barley. The
A company is going to ship food \((x)\) and water \((y)\) to the victims of a tsunami. Each container of food will feed 8 people for a day, and each container of water will give 12 people their daily water. The food containers each weigh 30 pounds and take up 8 cubic feet of space; each container
Another company will send clothing ( \(x\) ) and medical supplies \((y)\) to the victims of the tsunami. Each container of clothing contains enough clothing for 12 people; each container of medical supplies can aid 8 people. The clothing containers each weigh 50 pounds and take up 6 cubic feet of
Juliette is 2 inches taller than her friend Vivian. Which algebraic equations represent their height? Use \(J\) for Juliette's height and \(V\) for Vivian's height.\(J=V+2\)\(V=J-2\)\(J+2=V\)\(J=V-2\)
Which options represent algebraic expressions?\[ \begin{aligned} & 2 x^{2}+3 x-1=0 \\ & 5 x+8 \\ & 2 n+3 m \\ & 5 x-7=3 x+1 \end{aligned} \]
Which expression equals \(10 x\) ?\((8 x+12 x) \div 4 x-2 x\)\(8 x+(12 x \div 4 x)-2 x\)\(8 x+12 x \div(4 x-2 x)\)\((8 x+12 x) \div(4 x-2 x)\)
Using the expression \(3 x^{2}-7 x+2\), when a certain number is put in for \(x\), the result is 50 . What is the value of \(x\) ? \(-2\)\(-3\)2 3
Which expression equals \((x-y)(x-y)\) ? Hint: Use the Distributive Property.\[ \begin{aligned} & x^{2}-y^{2} \\ & x^{2}+y^{2} \\ & x^{2}-2 x y-y^{2} \\ & x^{2}-2 x y+y^{2} \end{aligned} \]
Given the expression \(9 x^{3}+3 x^{2}-6 x\), the Distributive Property allows it to be rewritten as:\(3 x\left(3 x^{2}+x-2\right)\)\(3 x^{2}+x-2\)\(27 x^{5}-54 x^{4}\)\(27 x^{6}-54 x^{3}\)
Given the two algebraic expressions \((x+2)\) and \((x+y-5)\), the solution is \(x^{2}+x y-3 x+2 y-10\). What mathematical operation was performed on the two algebraic expressions?
Given the two algebraic expressions \(8 x^{2}-9 x+6\) and \(6 x\), the solution is \(3 x-1.5+\frac{1}{x}\). What mathematical operation was performed on the two algebraic expressions?
Is the solution strategy used in solving the linear equation correct? If it is correct, show the final step (check the solution). If it is not correct, explain why.\[ \begin{aligned} 8(x-2) & =6(x+10) \\ 8 x-16 & =6 x+60 \\ 8 x-16-6 x & =6 x+60-6 x \\ 2 x-16+\mathbf{1 6} & =60+\mathbf{1 6} \\ 2 x &
Is the solution strategy used in solving the linear equation correct? If it is correct, show the final step (check the solution). If it is not correct, explain why.\[ \begin{aligned} 7+4(2+5 x) & =3(6 x+7)-(13 x+36) \\ 7+8+20 x & =18 x+21-13 x-36 \\ 15+20 x & =5 x-15 \\ 15+20 x-\mathbf{5 x} &
Is the solution strategy used in solving the linear equation correct? If it is correct, show the final step (check the solution). If it is not correct, explain why.\(8 x+7-(2 x-9)=22-(4 x-4)\)\(8 x+7-2 x-9=22-4 x-4\)\(6 x-2=18-4 x\)\(6 x-2+4 x=18-4 x+4 x\)\(10 x-2+\mathbf{2}=18+\mathbf{2}\)\(10
Using the variable \(x\) for number of miles, write the equation that would allow you to find the total fare ( \(T\) ) using the Nice Cab Company.Use this scenario: The Nice Cab Company charges a flat rate of \(\$ 3.00\) for each fare, plus \(\$ 1.70\) per mile. A competing taxi service, the
It is 22 miles from the airport to your hotel. What would be your total fare using the Nice Cab Company?Use this scenario: The Nice Cab Company charges a flat rate of \(\$ 3.00\) for each fare, plus \(\$ 1.70\) per mile. A competing taxi service, the Enjoyable Cab Company, charges a flat rate of
Using the variable \(y\) for number of miles, write the equation that would allow you to find the total fare \((T)\) using the Enjoyable Cab Company.Use this scenario: The Nice Cab Company charges a flat rate of \(\$ 3.00\) for each fare, plus \(\$ 1.70\) per mile. A competing taxi service, the
Using the same 22 -mile trip from the airport to the hotel, how much would the total fare be for using the Enjoyable Cab Company?Use this scenario: The Nice Cab Company charges a flat rate of \(\$ 3.00\) for each fare, plus \(\$ 1.70\) per mile. A competing taxi service, the Enjoyable Cab Company,
Based on the cost of each cab ride, which cab company should you use for the trip from the airport to the hotel? Why?Use this scenario: The Nice Cab Company charges a flat rate of \(\$ 3.00\) for each fare, plus \(\$ 1.70\) per mile. A competing taxi service, the Enjoyable Cab Company, charges a
After solving the linear equation \(3(2 x-3)=12(x-3)-3(2 x-9)\), Nancy says there is no solution. Luis believes there are infinitely many solutions. Who is right?
The conversion formula between the Fahrenheit temperature scale and the Celsius temperature scale is given by this formula: \(C=\frac{5}{9}(F-32)\), where \(C\) is the temperature in degrees Celsius and \(F\) is the temperature in degrees Fahrenheit. What is the correct formula when solved for
To find a temperature on the Kelvin temperature scale, add 273 degrees to the temperature in Celsius. Which formula illustrates this?a. \(C=K+273\)b. \(K=C+273\)c. \(K=C-273\)d. \(C=K-273\)
Using the information from exercise 18 and exercise 19, which conversion formula would you use to find degrees Kelvin when given degrees Fahrenheit?a. \(K=\frac{5}{9}(F-32)+273\)b. \(K=\frac{5}{9} F+241\)c. \(K=\frac{9}{5}(F-32)+273\)d. \(K=\frac{9}{5} F+241\)
There is a fourth temperature scale, although it is not used much today. The Rankin temperature scale varies from the Fahrenheit scale by about 460 degrees. So given a temperature in Fahrenheit, add 460 degrees to get the temperature in Rankin. Which formula represents a formula to find degrees
Choose the correct interval notation for the graph.a. \([-1, \infty)\)b. \((-1,1)\)c. \((\infty, 1)\)d. \((-\infty, 1)\)e. \((-\infty,-1)\) + -1 01 + 2
Choose the correct interval notation for the graph.a. \((-5, \infty)\)b. \([-5, \infty)\)c. \([-5, \infty)\)d. \([-5,-3)\)e. \([-5,-3]\) -6 + + -5 -4-3
Choose the correct interval notation for the graph.a. \((1, \infty)\)b. \([1, \infty)\)c. \(\left[\frac{3}{2}, \infty\right)\)d. \(\left(\frac{3}{2}, \infty\right)\)e. \(\left(\infty, \frac{3}{2}\right)\) 0 1 2 3
Choose the correct interval notation for the graph.a. \((-4,3)\)b. \((3,-4)\)c. \([-\infty, \infty)\)d. \([-4,3]\)e. \([3,-4]\) -5 -4-3 -2 -1 0 + 1 2 13 3 4
\([4, \infty)\) is the solution for which inequality?a. \(4 x \geq 0\)b. \(4 x \leq 0\)c. \(6 x24\)e. \(6 x \geq 24\)
\((-\infty,-3)\) is the solution for which inequality?a. \(-6 x18\)c. \(-6 x \leq 18\)d. \(-6 x \geq 18\)e. \(-6 x \leq-18\)
\((-2, \infty)\) is the solution for which inequality?a. \(-4 x>-8\)b. \(4 x+3>-11\)c. \(4 x-3>-11\)d. \(-4 x \leq-8\)e. \(-4 x+3 \leq 5\)
\((-\infty, 9)\) is the solution for which inequality?a. \(9 x-13\)d. \(-3 x-14>-13\)e. \(-3 x \geq 27\)
Renaldo is hauling boxes of lawn chairs. Each box is the same size, 8 cubic feet. Renaldo's truck has a capacity of 764 cubic feet. How many boxes of lawn chairs can Renaldo put in his truck?a. \(8764\)e. None of these Choose the equation that best models the situation.
Bernadette babysits the neighbor's kids, making on average \(\$ 50\) a night. How many nights will she have to babysit in order to earn enough money to buy a used car, whose cost is \(\$ 8,120\) ?a. \(50
If \(a: b=c: d\), then \(b: a=d: c\) for all non-zero whole numbers \(a,b, c\), and \(d\).a. Trueb. False
If the ratio of wolves to rabbits in a national park is \(3: 5\), then the ratio of rabbits to (wolves and rabbits) is \(5: 8\).a. Trueb. False
All fractions are ratios but not all ratios are fractions.a. Trueb. False
In the following equation, \(\frac{x}{46}=\frac{20}{90}+4\), cross multiplication can be used as the first step towards solving for \(x\).a. Trueb. False
There are 16 math majors and 12 non-math majors in Ms. Kraft's class. What is not a correct way to express the ratio of math majors to non-math majors? 16:12 12:16 4:3
There are 16 math majors and 12 non-math majors in Ms. Kraft's class. What shows the ratio of math majors to all the students in Ms. Kraft's class? 16:12 12:16 16:28 28 12 None of these
One U.S. dollar is worth 0.72 British pounds. Damon is traveling to Great Britain and wishes to exchange \(\$ 450\) U.S. dollars for British pounds. How many British pounds should Damon get in return? 625 6,250 3,456 345.6 None of these
The HO scale for model trains is the most common size of model trains. This scale is \(1: 87\). If a real locomotive is 73 feet long, how long should the model locomotive be (in inches)? Round your answer to the nearest inch.
Albert's Honda Civic gets 37 miles per gallon of gasoline. The gas tank on the Civic can hold 13.5 gallons of gas. Albert is driving from Tucson, Arizona to Los Angeles, California, a distance of 485 miles. Albert thinks he can make it on one full tank of gasoline. Can he? Explain.
The average price of a gallon of regular gasoline in the California on July 1,2021 was \(\$ 4.28\) per gallon. Albert stops at a gas station in California and puts 9.5 gallons of gasoline into his Civic. How much did he pay for the gas?
Choose the correct solution to the equation \(6 y+10=12 y\).a. \(y=5\)b. \(y=-1\)c. \(y=\frac{1}{2}\)d. \(y=\frac{5}{3}\)
Choose the correct graph for \(y=3 x+5\). 10- 5 -10 -5 0 - -5 -10 y 10 5 X 10 5 10 -10 -5 0 5 10 5 -16 -x
Choose the correct equation for the graph shown:a. \(y=2 x+4\)b. \(y=\frac{1}{2} x+4\)c. \(y=-2 x+4\)d. \(y=\frac{1}{2} x+4\) 10 y 5 (0, 4) (-8, 0) -10 -5 0 5 10 -5 -10
Choose the correct graph for \(y>3 x+5\). 10 5 -10 -5 5 10 5 -10 -5 10 10 5 -X 10 5 10
Choose the correct inequality for the graph shown.a. \(y=-2 x+5\)b. \(y \leq-2 x+5\)c. \(y \geq-2 x+5\)d. \(y 10 y (0, 5) -10 -5 0 5 (4,-3) S -5. -10 10 -x
Which quadratic equation equals \((x-3)(x+5)\) ?a. \(x^{2}-15\)b. \(x^{2}-3 x+15\)c. \(x^{2}-2 x-15\)d. \(x^{2}+2 x-15\)
Which product is equal to \(x^{2}-8 x+15\) ?a. \((x-3)(x+5)\)b. \((x-3)(x-5)\)c. \((x+3)(x+5)\)d. \((x+3)(x-5)\)
The graph shown is the graph of which quadratic equation?a. \(x^{2}-x+5=0\)b. \(x^{2}-5 x+1=0\)c. \(x^{2}+6 x+5=0\)d. \(x^{2}-4 x+5=0\) 10 10 00 8 6 4 2 -10-8-6-4-20 2 2 4 -4 -6 -8 -10- 6 00 8 10 10 X
What is the solution to \(x^{2}-49=0\) ?a. \(x=7\)b. \(x=-7\)c. \(x= \pm 49\)d. \(x= \pm 7\)
\(x^{2}-5 x+5=0\) can be factored to \((x-1)(x-5)\).a. Trueb. False

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