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mathematics
college algebra graphs and models
College Algebra 7th Edition Robert F Blitzer - Solutions
Predict the number of tick marks on the positive x-axis and the positive y-axis. Then show the viewing rectangle on your graphing calculator. [-30, 30, 5] by [-20, 20, 5]
Make a scatterplot of the relation. {(6,8). (-4,-10), (-2,-6). (2,-5)}
Evaluate the expression for the given function f. f(a+h)-f(a) for f(x) = x - x²
Write a symbolic representation (formula) for a function g that calculates the given quantity. Then evaluate g(10) and interpret the result.The number of feet in x miles
The line graph represents the gallons of water W in a small swimming pool after x hours. (a) Evaluate W(4) and interpret your result. (b) Determine the domain D of function W and explain what it represents. (c) Determine the range R of function W and explain what it represents. Water
The table contains real data. Netflix Subscriptions (millions)(a) Determine the maximum and minimum values for each variable in the table. (b) Use your results from part (a) to find an appropriate viewing rectangle. (c) Make a scatterplot of the data. (d) Make a line graph of the data. x 2011
The table contains real data. U.S. College Students Who Study Chinese (thousands)(a) Determine the maximum and minimum values for each variable in the table. (b) Use your results from part (a) to find an appropriate viewing rectangle. (c) Make a scatterplot of the data. (d) Make a line graph of
The table contains real data. Global Vehicle Sales That Are Electric/Hybrid(a) Determine the maximum and minimum values for each variable in the table. (b) Use your results from part (a) to find an appropriate viewing rectangle. (c) Make a scatterplot of the data. (d) Make a line graph of the
The table contains real data. MySpace U.S. Advertising Revenue ($ millions)(a) Determine the maximum and minimum values for each variable in the table. (b) Use your results from part (a) to find an appropriate viewing rectangle. (c) Make a scatterplot of the data. (d) Make a line graph of the
A golf ball is hit and its vertical height/in feet above the ground after r seconds is given by h(t) = 64t - 16t2. (a) What is the initial height of the golf ball? (b) What is the height of the golf ball after 4 seconds? (c) If the golf ball spends the same amount of time going upas
When the relative humidity is 100%, air cools 5.8F for every 1-mile increase in alti- tude. Give verbal, symbolic, graphical, and numeri- cal representations of a function f that computes this change in temperature for an increase in altitude of x miles for 0 ≤ x ≤ 3.
Function P computes the percent- age of U.S. households that were food insecure during a selected year. Function P is defined by P(2007) 11.1, P (2008) = 14.6, P (2009) = 14.7. P(2010) = 14.5 and P(2015) = 14.3. (a) Write Pas a set of ordered pairs. (b) Give the domain and range of P.
As technology advances there are more and more obsolete electronic devices that need to be disposed of. The function f(x) = 40x estimates the millions of tons of electronic waste that will accumulate worldwide after x years. Evaluate f(5) and interpret the result.
If the average American always ordered the larger portion while eating out, then W(x) = 8x would estimate the resulting weight gain in pounds after x years. Evaluate W(3) and interpret the result.
Do the mean and median represent the same thing? Explain your answer and give an example.
Crutch Length Each year 15 million people have foot and ankle problems. Many times they need crutches. The formula f(x) = 0.72x + 2 calculates the appropriate crutch length in inches for a per- son with a height of x inches. (a) Find the crutch length for a person 6 feet 3 inches
The average top-loading washing machine uses about 40 gallons of water per load of clothes. Write the formula for a function W that calculates the number of gallons of water used while washing x loads of clothes. Evaluate W (30) and interpret your result.
Explain in your own words what a function is. How is a function different from a relation?
Give an example of a relation that has meaning in the real world. Give an example of an ordered pair (x, y) that is in your relation. Does the ordered pair (v. x) also have meaning? Explain your answers.
Going Green The average person uses 2200 paper napkins in one year. Write the formula for a func- tion N that calculates the number of paper napkins that the average person uses in x years. Evaluate N(3) and interpret your result.
Explain how you could use a complete numerical representation (table) for a function to determine its domain and range.
Write a symbolic representation (formula) for a function g that calculates the given quantity. Then evaluate g(10) and interpret the result.The number of quarters in x dollars
Predict the number of tick marks on the positive x-axis and the positive y-axis. Then show the viewing rectangle on your graphing calculator. Standard viewing rectangle
The graphs show the percentage of jobs in the U.S. labor force held by men and by women from 1970 through 2015. Exercises 109–110 are based on the data displayed by the graphs.The formulamodels the percentage of jobs in the U.S. labor force, p, held by men t years after 1970.a. Use the
The graphs show the percentage of jobs in the U.S. labor force held by men and by women from 1970 through 2015. Exercises 109–110 are based on the data displayed by the graphs.The formulamodels the percentage of jobs in the U.S. labor force, p, held by women t years after 1970.a. Use the
In Exercises 85–94, find all values of x satisfying the given conditions. 2x 6 (2) Y1 = 6 3 3/2 = 5/ 2x X - 3, and y₁ exceeds y2 by 6.
Solve each equation in Exercises 83–108 by the method of your choice. (3x-4)2 = 16
Solve each radical equation in Exercises 11–30. Check all proposed solutions. Vx+ 5 Vx - 3 = 2
Solve each radical equation in Exercises 11–30. Check all proposed solutions. Vx √x - 3 = x-9
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √x-5-√x - 8 = 3
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √3x + 10 = x + 4
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √x + 8 - √x - 4 = 2
Solve each radical equation in Exercises 11–30. Check all proposed solutions. V2x + 15 6 = x -
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √2x + 19 - 8 = x
Solve each radical equation in Exercises 11–30. Check all proposed solutions. V6x + 1 = x - 1
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √x + 11 = 1
Solve each radical equation in Exercises 11–30. Check all proposed solutions. x - √2x + 5 = 5
Solve each radical equation in Exercises 11–30. Check all proposed solutions. V2x + 13 = x + 7
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √3x + 18 = x
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 2x4 = 16x
In Exercises 13–17, find the x-intercepts of the graph of each equation. y = 2x2 + 26 У -
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √/20 - 8x = x
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √x + 10 = x - 2 Vx
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √x + 3 = x - 3.
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 3x4 = 81x
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 9y³ + 8 = 4y + 18y2
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 4y32y8y²
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 2x3 = 8x³ - 12x²
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 4x³ - 12x² 12x² = 9x = 9x - 27
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. x + 1 = 9x³ + 9x²
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 3x3 + 2x² = 12x + 8
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 3x4 - 48x² = 0
Exercises 137–139 will help you prepare for the material covered in the next section.Solve x + 3 4 || x - 2 3 1 4
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 5x4 - 20x² = 0
Fill in each blank so that the resulting statement is true.To solve x2 -2/3 x = 4 9by completing the square, add _______to both sides of the equation.
Solve without squaring both sides: 5 2 X || 5- V 2 X
Solve: √6x - 2 = √2x + 3-√4x - 1.
In Exercises 129–132, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The first step in solving is to square both sides, obtaining √x + 6 = x + 2
In Exercises 125–128, determine whether each statement makes sense or does not make sense, and explain your reasoning.The equation is quadratic in form, but when I reverse the variable terms and obtain the resulting equation is no longer quadratic in form. 5x3+ 11x3 +2=0
Fill in each blank so that the resulting statement is true.The fractions in the equation X/4 = 2+ X-3/3 3can be eliminated by multiplying both sides by the____________ of X/4 and X-3/3 which is_________ .
In Exercises 129–132, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The equation is equivalent to x = 6 or x = -6. 9- = |x|
In Exercises 122–124, use a graphing utility and the graph’s x-intercepts to solve each equation. Check by direct substitution. A viewing rectangle is given. -x² + 4x³ 4x² = 0 [-6, 6, 1] by [-9, 2, 1]
In Exercises 129–132, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.To solve we let √u = x. x 9√x + 14 = 0,
Exercises 137–139 will help you prepare for the material covered in the next section.Solve: -2x - 4 = x + 5.
Fill in each blank so that the resulting statement is true.The solutions of ax2 + bx + c = 0 correspond to the_____ for the graph of y = ax2 + bx + c.
In Exercises 129–132, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The equations have the same solution set. x + 4 = -5 and x + 4 = 25
Exercises 137–139 will help you prepare for the material covered in the next section.Is -1 a solution of 3 - 2x ≤ 11?
In Exercises 122–124, use a graphing utility and the graph’s x-intercepts to solve each equation. Check by direct substitution. A viewing rectangle is given. √2x + 13 [-5, 5, 1] by [-5, 5, 1] x 5 = 0
Fill in each blank so that the resulting statement is true.In 2000, 31% of U.S. adults viewed a college education as essential for success. For the period from 2000 through 2010, this percentage increased by approximately 2.4 each year. The percentage of U.S. adults who viewed a college education
In Exercises 122–124, use a graphing utility and the graph’s x-intercepts to solve each equation. Check by direct substitution. A viewing rectangle is given. x³ + 3x²x3 = 0 [-6, 6, 1] by [-6, 6, 1]
For each planet in our solar system, its year is the time it takes the planet to revolve once around the Sun. The formulaWe, of course, have 365 Earth days in our year. What is the average distance of Earth from the Sun? Use a calculator and round to the nearest million kilometers. E = 0.2x2
Use the Pythagorean Theorem to solve Exercises 113–114.Towns A and B are located 6 miles and 3 miles, respectively, from a major expressway. The point on the expressway closest to town A is 12 miles from the point on the expressway closest to town B. Two new roads are to be built from A to the
For each planet in our solar system, its year is the time it takes the planet to revolve once around the Sun. The formulaThere are approximately 88 Earth days in the year of the planet Mercury. What is the average distance of Mercury from the Sun? Use a calculator and round to the nearest million
Explain why the procedure that you explained in Exercise 120 does not apply to the equationWhat is the solution set for this equation?Data from in exercise 120Explain how to solve an equation involving absolute value. X - 21 = -3.
Describe two methods for solving this equation: x - 5√x + 4 = 0.
A basketball player’s hang time is the time spent in the air when shooting a basket. The formulamodels hang time, t, in seconds, in terms of the vertical distance of a player’s jump, d, in feet. Use this formula to solve Exercises 105–106.If hang time for a shot by a professional basketball
In Exercises 125–128, determine whether each statement makes sense or does not make sense, and explain your reasoning.When I solve an equation that is quadratic in form, it’s important to write down the substitution that I am making.
In solvingwhy is it a good idea to isolate a radical term? What if we don’t do this and simply square each side? Describe what happens. √3x + 4 V2x + 4 = 2,
In Exercises 125–128, determine whether each statement makes sense or does not make sense, and explain your reasoning.After squaring both sides of a radical equation, the only solution that I obtained was extraneous, so must be the solution set of the original equation.
In Exercises 125–128, determine whether each statement makes sense or does not make sense, and explain your reasoning.When checking a radical equation’s proposed solution, I can substitute into the original equation or any equation that is part of the solution process.
A basketball player’s hang time is the time spent in the air when shooting a basket. The formulamodels hang time, t, in seconds, in terms of the vertical distance of a player’s jump, d, in feet. Use this formula to solve Exercises 105–106.When Michael Wilson of the Harlem Globetrotters
Use the graph of the formula for hang time to solve Exercises 107–108. How is your answer to Exercise 106 shown on the graph? Data from in exercise 106 A basketball player’s hang time is the time spent in the air when shooting a basket. The formula models hang time, t, in seconds, in terms of
Solve for A:r = A 4π
Explain how to solve an equation involving absolute value.
In Exercises 103–104, list all numbers that must be excluded from the domain of each expression. x³ - 2x². x² + 3x² 9x + 18. x 3
Explain how to recognize an equation that is quadratic in form. Provide two original examples with your explanation.
Use the graph of the formula for hang time to solve Exercises 107–108. How is your answer to Exercise 105 shown on the graph? Data from in exercise 105 A basketball player’s hang time is the time spent in the air when shooting a basket. The formula models hang time, t, in seconds, in terms of
In Exercises 95–98, solve each equation. x(x - 2)³35(x - 2)² = 0
In Exercises 103–104, list all numbers that must be excluded from the domain of each expression. |x-1|-3 x + 2 - 14
Use the Pythagorean Theorem to solve Exercises 113–114.Two vertical poles of lengths 6 feet and 8 feet stand 10 feet apart. A cable reaches from the top of one pole to some point on the ground between the poles and then to the top of the other pole. Where should this point be located to use 18
What is an extraneous solution to a radical equation?
In Exercises 95–98, solve each equation. |x² + 6x + 1| = 8
Without actually solving the equation, give a general description of how to solve x3 - 5x2 - x + 5 = 0.
In Exercises 95–98, solve each equation. x(x + 1)³ 42(x + 1)² = 0 -
In Exercises 95–98, solve each equation. |x² + 2x - 36 = 12
In Exercises 89–96, solve each equation. 2(5x + 58) 10x + 4(21 3.5 - 11)
In Exercises 89–96, solve each equation. 0.7x + 0.4(20) = 0.5(x + 20)
In Exercises 85–94, find all values of x satisfying the given conditions. y₁ = (x² − 1)²³, y₂ = 2(x² − 1), and y₁ exceeds y2 by 3. - -
Solve each equation in Exercises 83–108 by the method of your choice. (2x + 3)(x + 4) = 1
If a number is decreased by 3, the principal square root of this difference is 5 less than the number. Find the number(s).
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