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mathematics
contemporary mathematics

Contemporary Mathematics 1st Edition OpenStax - Solutions

Noe installs and configures software on home computers. He charges \(\$ 125\) per job. His monthly expenses are \(\$ 1,600\). How many jobs must he work in order to make a profit of at least \(\$ 2,400\) ?Construct a linear inequality to solve the application.
Translate the following algebraic expressions from algebra into words.1. \(12+14\)2. \((30)(5)\)3. \(64 \div 8\)4. \(x-y\)
Translate the following phrases from words into algebraic expressions.1. The difference of 47 and 192. 72 divided by 9 3. The sum of \(m\) and \(n\)4. 13 times 7
Translate the following phrases from words into algebraic expressions.1. Seven more than a number \(n\).2. A number \(n\) times itself.3. Six times a number \(n\), plus two more.4. The cost of postage is a flat rate of 10 cents for every parcel, plus 34 cents per ounce \(x\).
Translate the following sentences from words into algebraic equations.1. Two times \(x\) is 6 .2. \(n\) plus 2 is equal to \(n\) times 3 .3. The quotient of 35 and 7 is 5 .4. Sixty-seven minus \(x\) is 56 .
Use parentheses to make the following statements true.1. \(17-10+3=10\)2. \(2 \cdot 26-7=38\)3. \(8+12 \div 5-3=14\)4. \(5+2^{3} \cdot 7=91\)
1. Evaluate \(3 x+5\) when \(x=2\).2. Evaluate \(x^{2}+3 x+1\) when \(x=2\).
Add \(\left(x^{2}+4 x-9\right)+\left(3 x^{2}-x+12\right)\).
Subtract \(\left(5 x^{2}+4 x-9\right)-\left(3 x^{2}-x+12\right)\).
Simplify each expression.1. \((x-3) 5\)2. \((-3)(x+y-2)\)3. \(5^{2}(7+3)(x)\)4. \(4+x \bullet 5\)5. \((4+x) \bullet 5\)
Multiply \((4 x-9)(x+2)\).
Divide \(\left(8 x^{2}+4 x-16\right) \div(4 x)\).
Solve \(7(n-3)-8=-15\)
Solve \(9(y-2)-y=16+7 y\).
The Beaudrie family has two cats, Basil and Max. Together, they weigh 23 pounds. Basil weighs 16 pounds. How much does Max weigh?
If you join your local gym at \(\$ 10\) per month and pay \(\$ 5\) per class, how many classes can you take if your gym budget is \(\$ 75\) per month?
Write an application that can be solved using the equation \(50 x+35=185\). Then solve your application.
Solve \(3(x+4)=4 x+8-x\).
Solve \(2(x+5)=4(x+3)-2 x-2\).
Solve the formula \(d=r t\) for \(t\). This is the distance formula where \(d=\) distance, \(r=\) rate, and \(t=\) time.
Solve the formula \(A=1 / 2 b h\) for \(h\). This is the area formula of a triangle where \(A=\) area, \(b=\) base, and \(h=\) height.
Graph the inequality \(x \geq-3\) and write the solution in interval notation.
Graph the inequality \(x>-3\) and \(x
Solve \(9 y
Solve the inequality \(6 y \leq 11 y+17\), graph the solution on the number line, and write the solution in interval notation.
A teacher won a mini grant of \(\$ 4,000\) to buy tablet computers for their classroom. The tablets they would like to buy cost \(\$ 254.12\) each, including tax and delivery. What is the maximum number of tablets the teacher can buy?
The local community college charges \(\$ 113\) per credit hour. Your budget is \(\$ 1,500\) for tuition this fall semester. What number of credit hours could you take this fall?
Brenda's best friend is having a destination wedding and the event will last 3 days and 3 nights. Brenda has \(\$ 500\) in savings and can earn \(\$ 15\) an hour babysitting. She expects to pay \(\$ 350\) for airfare, \(\$ 375\) for food and entertainment, and \(\$ 60\) a night for her share of a
The Euro ( \(€\) ) is the most common currency used in Europe. Twenty-two nations, including Italy, France, Germany, Spain, Portugal, and the Netherlands use it. On June 9, 2021, 1 U.S. dollar was worth 0.82 Euros. Write this comparison as a ratio.
The gravitational pull on various planetary bodies in our solar system varies. Because weight is the force of gravity acting upon a mass, the weights of objects is different on various planetary bodies than they are on Earth. For example, a person who weighs 200 pounds on Earth would weigh only 33
You are going to take a trip to France. You have \(\$ 520\) U.S. dollars that you wish to convert to Euros. You know that 1 U.S. dollar is worth 0.82 Euros. How much money in Euros can you get in exchange for \(\$ 520\) ?
A person who weighs 170 pounds on Earth would weigh 64 pounds on Mars. How much would a typical racehorse \((1,000\) pounds) weigh on Mars? Round your answer to the nearest tenth.
A cookie recipe needs \(2 \frac{1}{4}\) cups of flour to make 60 cookies. Jackie is baking cookies for a large fundraiser; she is told she needs to bake 1,020 cookies! How many cups of flour will she need?
Isabelle has a part-time job. She kept track of her pay and the number of hours she worked on four different days, and recorded it in the table below. What is the constant of proportionality, or pay divided by hours? What does the constant of proportionality tell you in this situation? Pay $87.50
Zac runs at a constant speed: 4 miles per hour (mph). One day, Zac left his house at exactly noon (12:00 PM) to begin running; when he returned, his clock said 4:30 PM. How many miles did he run?
Joe had a job where every time he filled a bucket with dirt, he was paid \(\$ 2.50\). One day Joe was paid \(\$ 337.50\). How many buckets did he fill that day?
While driving in Canada, Mabel quickly noticed the distances on the road signs were in kilometers, not miles. She knew the constant of proportionality for converting kilometers to miles was about 0.62-that is, there are about 0.62 miles in 1 kilometer. If the last road sign she saw stated that
Figure 5.17 is an outline map of the state of Colorado and its counties. If the distance of the southern border is 380 miles, determine the scale (i.e., 1 inch = how many miles). Then use that scale to determine the approximate lengths of the other borders of the state of Colorado. Moffat Rio
Die-cast NASCAR model cars are said to be built on a scale of \(1: 24\) when compared to the actual car. If a model car is 9 inches long, how long is a real NASCAR automobile? Write your answer in feet.
Plot the following points in the rectangular coordinate system and identify the quadrant in which the point is located:1. \((-5,4)\)2. \((-3,-4)\)3. \((2,-3)\)4. \((0,-1)\)5. \(\left(3, \frac{5}{2}\right)\)
Figure 5.24 is the graph of \(y=2 x-3\).For each ordered pair, decide:I. Is the ordered pair a solution to the equation?II. Is the point on the line?A: \((0,-3)\)B: \((3,3)\)\(C:(2,-3)\)D: \((-1,-5)\) 60 y 5 y=2x-3 4 3 2- -X 2 3 4 5 6 1+ -6-5-4-3-2-1 0 1 -1 -2 -3; -5 -6 Figure 5.24 Graph of y = 2x-3
Graph the equation: \(y=\frac{1}{2} x+3\).
Gasoline costs \(\$ 3.53\) per gallon. You put 10 gallons of gasoline in your car, and pay \(\$ 35.30\). Your friend puts 15 gallons of gasoline in their car and pays \(\$ 52.95\). Your neighbor needs 5 gallons of gasoline, how much will they pay?
Determine whether each ordered pair is a solution to the inequality \(y>x+4\) :1. \((0,0)\)2. \((1,6)\)3. \((2,6)\)4. \((-5,-15)\)5. \((-8,12)\)
The boundary line shown in this graph is \(y=2 x-1\). Write the inequality shown in Figure 5.35. 7 6- 8 96 S 5 4- 3 2 6 7 7 8 -8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 m -3 -4 -5 -6- -7- L8 Figure 5.35
Graph the linear inequality \(y \geq \frac{3}{4} x-2\).
Hilaria works two part time jobs to earn enough money to meet her obligations of at least \(\$ 240\) a week. Her job in food service pays \(\$ 10\) an hour and her tutoring job on campus pays \(\$ 15\) an hour. How many hours does Hilaria need to work at each job to earn at least \(\$ 240\) ?1. Let
Multiply \((x+2)(x+3)\).
Multiply \((2 x+7)(3 x-5)\).
Factor \(x^{2}+7 x+12\).
Factor \(x^{2}-11 x+28\).
Graph \(y=x^{2}-1\) and list the solutions to the quadratic equation.
Find the solutions of \(y=x^{2}+5 x+4\) from its graph (Figure 5.49). 10 8 00 6 4 2 -10-8-6 -2, 0 2 4 -2 -4 -6 -8 -10 Figure 5.49 60 00 8 10 10 x
Solve \((x+1)(x-4)=0\).
Solve \(x^{2}+2 x-8=0\).
Solve using the square Root Property: \(x^{2}=169\).
Solve using the Square Root Property: \(144 q^{2}=25\).
Solve using the quadratic formula: \(x^{2}-6 x+5=0\).
Solve using the quadratic formula: \(2 x^{2}+9 x-5=0\).
The product of two consecutive integers is 132. Find the integers.
A rectangular garden has an area 15 square feet. The length of the garden is 2 feet more than the width. Find the length and width of the garden.
For the function \(f(x)=2 x^{2}+3 x-1\), evaluate the function.1. \(f(3)\)2. \(f(-2)\)3. \(f(a)\)
The number of unread emails in Sylvia's inbox is 75 . This number grows by 10 unread emails a day. The function\(N(t)=75+10 t\) represents the relation between the number of emails, \(N\), and the time, \(t\), measured in days. Find \(N(5)\). Explain what this result means.
Use the set of ordered pairs to determine whether the relation is a function.1. \(\{(-3,27),(-2,8),(-1,1),(0,0),(1,1),(2,8),(3,27)\}\)2. \(\{(9,-3),(4,-2),(1,-1),(0,0),(1,1),(4,2),(9,3)\}\)
Use the mapping in Figure 5.57 to determine whether the relation is a function. Name Lydia Eugene Janet Rick Marty Phone Number 321-549-3327 home 427-658-2314 cell 321-964-7324 cell 684-358-7961 home 684-369-7231 cell 798-367-8541 cell Figure 5.57
Determine whether each equation is a function. Assume \(x\) is the independent variable.1. \(2 x+y=7\)2. \(y=x^{2}+1\)3. \(x+y^{2}=3\)
Determine whether the graph (Figure 5.59) is the graph of a function applying the vertical line test. 6 y 5- 4- 3 2 1 -6-5-4-3-2-10 -1 -2 -3 -4 -5- -6 1 2 3 4 5 6 Figure 5.59 x
Determine whether the graph is the graph of a function (Figure 5.61). 6 5 4 3 2 -6-5-4-3-2-10 y x 1 2 3 4 5 6 -2 -3 -4 -5 -6 Figure 5.61
For \(\{(1,1),(2,4),(3,9),(4,16),(5,25)\}\) :1. Find the domain of the relation.2. Find the range of the relation.
Use Figure 5.63 to:1. List the ordered pairs of the relation.2. Find the domain of the relation.3. Find the range of the relation. 9 5 4 3 2. -6-5-4-3-2-1 1 0 1 2 3 4 5 6 -2 -3- -4- -5- -6 Figure 5.63
Find the \(x\)-intercept and \(y\)-intercept on the (a) and (b) graphs in Figure 5.66 . 6 55 N 2 1 -2 -8-7 -6-5-4-3-2 10 -1 - y 00 8 7 6 54 3 2 7 60 00 8 2 3 4 6 7 8 -8-7-6-5 -3-2-10 1 2 3 4 5 -2 -3 -4 -5 -6 m 7 -8 (a) (b) Figure 5.66
Find the intercepts of \(2 x+y=8\). Then graph the function using the intercepts.
Find the slope of the line shown in Figure 5.69. 7 y 6 4 3 2 1 0 1 2 3 4 5 6 7 8 1 Figure 5.69 x
Use the slope formula to find the slope of the line through the points \((-2,-3)\) and \((-7,4)\).
Identify the slope and \(y\)-intercept of the line from the equation:1. \(y=-\frac{4}{7} x-2\)2. \(x+3 y=9\)
Graph the line of the equation \(y=-x+4\) using its slope and \(y\)-intercept.
Graph: \(x=2\).
Graph: \(y=-1\).
In Figure 5.79 the \(x\)-axis on the graph represents the 120 -minute bike ride Juan went on. The \(y\)-axis represents how far away he was from his home.1. Interpret the \(x\) - and \(y\)-intercept.2. For each segment, find the slope.3. Create an interpretation of this graph (i.e., make up a story
The equation \(F=\frac{9}{5} C+32\) is used to convert temperatures from degrees Celsius \((C)\) to degrees Fahrenheit \((F)\).1. Find the Fahrenheit temperature for a Celsius temperature of \(0^{\circ}\).2. Find the Fahrenheit temperature for a Celsius temperature of \(20^{\circ}\).3. Interpret
Sam drives a delivery van. The equation \(C=0.5 d+60\) models the relation between his weekly cost, \(C\), in dollars and the number of miles, \(d\), that he drives.1. Find Sam's cost for a week when he drives 0 miles.2. Find the cost for a week when he drives 250 miles.3. Interpret the slope and
Determine whether the ordered pair is a solution to the system.\[ \left\{\begin{aligned} x-y & =-1 \\ 2 x-y & =-5 \end{aligned}\right. \]1. \((-2,-1)\)2. \((-4,-3)\)
Determine whether the ordered pair is a solution to the system\[ \left\{\begin{aligned} y & =\frac{3}{2} x+1 \\ 2 x-3 y & =7 \end{aligned}\right. \]1. \((-4,-5)\)2. \((-4,5)\)
Solve this system of linear equations by graphing.\[ \left\{\begin{array}{l} 2 x+y=7 \\ x-2 y=6 \end{array}\right. \]
Solve this system of linear equations by substitution:\[ \left\{\begin{array}{l} 2 x+y=7 \\ x-2 y=6 \end{array}\right. \]
Solve this system of linear equations by elimination:\[ \left\{\begin{array}{l} 2 x+y=7 \\ x-2 y=6 \end{array}\right. \]
Solve the system by a method of your choice:\[ \left\{\begin{aligned} y & =\frac{1}{2} x-3 \\ x-2 y & =4 \end{aligned}\right. \]
Solve the system by a method of your choice:\(\left\{\begin{aligned} y & =2 x-3 \\ -6 x+3 y & =-9\end{aligned}\right.\)
Heather has been offered two options for her salary as a trainer at the gym. Option A would pay her \(\$ 25,000\) a year plus \(\$ 15\) for each training session. Option B would pay her \(\$ 10,000\) a year plus \(\$ 40\) for each training session. How many training sessions would make the salary
Determine whether the ordered pair is a solution to the system:\[ \left\{\begin{aligned} x+4 y & \geq 10 \\ 3 x-2 y &
Use Figure 5.88 to solve the system of linear inequalities:\[ \left\{\begin{array}{l} y \geq 2 x-1 \\ y. \] 7 6- 5 4 3- 2 -7-6-5-4-3-21 0 -1 -2 -3 34 1 2 3 4 5 6 7 5+ -6- -7 Figure 5.88 -X
Solve the system by graphing:\[ \left\{\begin{array}{l} x-y>3 \\ y
Solve the system by graphing:\[ \left\{\begin{aligned} x-2 y & -4 \end{aligned}\right. \]
Solve the system by graphing:\[ \left\{\begin{array}{l} 4 x+3 y \geq 12 \\ y
Solve the system by graphing:\[ \left\{\begin{array}{l} y>\frac{1}{2} x-4 \\ x-2 y
A photographer sells their prints at a booth at a street fair. At the start of the day, they want to have at least 25 photos to display at their booth. Each small photo they display costs \(\$ 4\) and each large photo costs \(\$ 10\). They do not want to spend more than \(\$ 200\) on photos to
Miriam starts her own business, where she knits and sells scarves and sweaters out of high-quality wool. She can make a profit of \(\$ 8\) per scarf and \(\$ 10\) per sweater. Write an objective function that describes her profit.
William's factory produces two products, widgets and wadgets. It takes 24 minutes for his factory to make 1 widget, and 32 minutes for his factory to make 1 wadget. Write an objective function that describes the time it takes to make the products.
Two friends start their own business, where they knit and sell scarves and sweaters out of high-quality wool. They can make a profit of \(\$ 8\) per scarf and \(\$ 10\) per sweater. To make a scarf, 3 bags of knitting wool are needed; to make a sweater, 4 bags of knitting wool are needed. The
A factory produces two products, widgets and wadgets. It takes 24 minutes for the factory to make 1 widget, and 32 minutes for the factory to make 1 wadget. Research indicates that long-term demand for products from the factory will result in average sales of 12 widgets per day and 10 wadgets per

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