Pathways To Math Literacy (looseleaf)
Pathways To Math Literacy (looseleaf)
2nd Edition
ISBN: 9781259985607
Author: David Sobecki Professor, Brian A. Mercer
Publisher: McGraw-Hill Education
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Fundamentals of Trigonometric Identities
Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.
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Textbook Question
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Chapter 4.1, Problem 3A

A formula for the nth triangular number n 2 ( 1 n − ( − 1 ) ) ; is this simplifies to n ( n + 2 ) 2

A formula for the nth square number is n 2 ( 2 n − ( 0 ) ) ; this simplifies to n 2 .

A formula for the nth pentagonal number n 2 ( 3 n − ( 1 ) ) ; is this doesn't simplify. Sigh.

Using inductive reasoning, a formula for the nth hexagonal number is n 2 ( _ _ n − ( _ _ ) ) . (Hint: Look at the pattern in the missing numbers for the previous three formulas.)

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Chapter 4 Solutions

Pathways To Math Literacy (looseleaf)

Ch. 4.1 - Prob. 1PSQCh. 4.1 - Prob. 2PSQCh. 4.1 - What do you think the word reasoning means?Ch. 4.1 - How many handshakes would there be if there were...Ch. 4.1 - Connect each pair of dots with a line to indicate...Ch. 4.1 - Fill in the table with the results youve already...Ch. 4.1 - In Questions 46, find a counterexample to prove...Ch. 4.1 - In Questions 46, find a counterexample to prove...Ch. 4.1 - In Questions 46, find a counterexample to prove...Ch. 4.1 - The numbers illustrated here are called triangular...
Ch. 4.1 - This pattern should look familiar. . . . If it...Ch. 4.1 - The next triangle is called Pascals triangle in...Ch. 4.1 - Heres a clever number trick. Pick any number you...Ch. 4.1 - Starting with a number n, multiply that number by...Ch. 4.1 - Now add 40 to the result of Question 1.Ch. 4.1 - Next, divide the result of Question 2 by 4. Be...Ch. 4.1 - Subtract 10 from the result of Question 3.Ch. 4.1 - Now subtract the original number n. What is the...Ch. 4.1 - Pretend that youre one of the nine justices: How...Ch. 4.1 - Choose one other justice. How many hands does he...Ch. 4.1 - If we number the justices from 1 through 9, this...Ch. 4.1 - This result doesnt match the answer we got using...Ch. 4.1 - Conclusion: The number of handshakes needed for...Ch. 4.1 - After failing the first two tests in math class,...Ch. 4.1 - Marlene was having a hard time keeping up with...Ch. 4.1 - In spite of his friends pleas, Mark tried to drive...Ch. 4.1 - My favorite professional team started off the new...Ch. 4.1 - A polygon is a closed geometric figure with three...Ch. 4.1 - Prob. 2DYGICh. 4.1 - Prob. 3DYGICh. 4.1 - Look back at the Did You Get It 1, where we...Ch. 4.1 - Describe the difference between inductive and...Ch. 4.1 - Describe a time in your life that you used...Ch. 4.1 - Prob. 3RCh. 4.1 - Use inductive reasoning to find the fifth square...Ch. 4.1 - Use inductive reasoning to find the fifth...Ch. 4.1 - A formula for the nth triangular number n2(1n(1));...Ch. 4.1 - Use the formulas from Question 3 to complete this...Ch. 4.1 - In Questions 5 and 6, find a counterexample that...Ch. 4.1 - In Questions 5 and 6, find a counterexample that...Ch. 4.1 - In Questions 710, decide if inductive or deductive...Ch. 4.1 - In Questions 710, decide if inductive or deductive...Ch. 4.1 - In Questions 710, decide if inductive or deductive...Ch. 4.1 - In Questions 710, decide if inductive or deductive...Ch. 4.2 - Compute the square root exactly without using a...Ch. 4.2 - Compute the square root exactly using a calculator...Ch. 4.2 - Approximate the square root to two decimal places...Ch. 4.2 - Find the distance between points A and B, and...Ch. 4.2 - While on vacation last year, my wife and I bought...Ch. 4.2 - What do you think the sign in the picture means?Ch. 4.2 - Whats the change in elevation over a 1-mile...Ch. 4.2 - Complete the following table of common square...Ch. 4.2 - Notice that the diagram on page 471 is a right...Ch. 4.2 - In order to solve your equation to find the...Ch. 4.2 - How much farther would you drive on that road than...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - Suppose that we know that the distance between...Ch. 4.2 - How does the distance between points P and Q...Ch. 4.2 - The lower illustration also shows points P, Q, M,...Ch. 4.2 - Based on the scale provided on the two-dimensional...Ch. 4.2 - Illustrate the grade of each trail by drawing a...Ch. 4.2 - Use the Pythagorean theorem to estimate the true...Ch. 4.2 - The road sign at the beginning of this lesson is...Ch. 4.2 - How far would you actually drive in covering that...Ch. 4.2 - Estimate the distance by plotting the two given...Ch. 4.2 - Prob. 10GCh. 4.2 - The steepest road in America is Canton Avenue in...Ch. 4.2 - Waipio Road in Hawaii is actually steeper than the...Ch. 4.2 - Grids are often used at crime scenes to help in...Ch. 4.2 - What does the Pythagorean theorem say? When can...Ch. 4.2 - Why cant you just find the distance between two...Ch. 4.2 - Name one thing you learned or discovered in this...Ch. 4.2 - Estimate the elevation of point A.Ch. 4.2 - If points X and Y are 5,100 m apart looking...Ch. 4.2 - How far would you walk along the trail from point...Ch. 4.2 - An archaeological dig is marked with a rectangular...Ch. 4.2 - Using proprietary software hacked from the NSA, I...Ch. 4.2 - I was also able to use my software (allegedly) to...Ch. 4.2 - If the highway department put up a sign on each...Ch. 4.3 - In a pie chart, one sector represents a data value...Ch. 4.3 - Use a calculator to find an approximate value for...Ch. 4.3 - Prob. 3PSQCh. 4.3 - Prob. 4PSQCh. 4.3 - Prob. 5PSQCh. 4.3 - Prob. 6PSQCh. 4.3 - Prob. 1LOCh. 4.3 - Prob. 2GCh. 4.3 - Prob. 6GCh. 4.3 - Prob. 7GCh. 4.3 - Prob. 2CCh. 4.3 - Prob. 3CCh. 4.3 - Write a sentence describing exactly what your...Ch. 4.3 - Among all respondents to the survey, 30% supported...Ch. 4.3 - Prob. 6CCh. 4.3 - Prob. 7CCh. 4.3 - What if the folks from Public Policy Polling who...Ch. 4.3 - Prob. 9CCh. 4.3 - Prob. 10CCh. 4.3 - Prob. 11CCh. 4.3 - Prob. 12CCh. 4.3 - Prob. 13CCh. 4.3 - Prob. 14CCh. 4.3 - Prob. 17CCh. 4.3 - Prob. 18CCh. 4.3 - Prob. 2DYGICh. 4.3 - Prob. 3DYGICh. 4.3 - Prob. 1RCh. 4.3 - Prob. 2RCh. 4.3 - Prob. 3RCh. 4.3 - A stats class was interested in determining the...Ch. 4.3 - A stats class was interested in determining the...Ch. 4.3 - A stats class was interested in determining the...Ch. 4.3 - If surveying more students keeps the percentage at...Ch. 4.3 - Suppose that the campus in Questions 14 is a small...Ch. 4.3 - The FPC acts as a multiplier: To get the adjusted...Ch. 4.3 - Without referring to any formulas, describe what...Ch. 4.4 - The force required to move an object varies...Ch. 4.4 - More fun with physics: The direct variation...Ch. 4.4 - For the equation y=200x, fill in the table of...Ch. 4.4 - Make a scatter plot using your table from Question...Ch. 4.4 - Think about the direct variation that we studied...Ch. 4.4 - For each mode of travel, find how long it will...Ch. 4.4 - The speed doubles when going from jogging (5...Ch. 4.4 - The speed doubles when going from bus (20 mi/hr)...Ch. 4.4 - The speed is cut in half when going from bus (20...Ch. 4.4 - The speed is divided by four when going from...Ch. 4.4 - Does time depend on speed in this problem, or does...Ch. 4.4 - Graph the values in your table and connect them...Ch. 4.4 - Use your graph to estimate the time it would take...Ch. 4.4 - Use your graph to estimate the speed needed to...Ch. 4.4 - (This one will impress your instructor.) Find an...Ch. 4.4 - Use your equation to find how long it would take...Ch. 4.4 - When you exchange currency, the value of currency...Ch. 4.4 - When you drive a certain distance, the time it...Ch. 4.4 - In Questions 35, write an equation of variation...Ch. 4.4 - In Questions 35, write an equation of variation...Ch. 4.4 - In Questions 35, write an equation of variation...Ch. 4.4 - The gross pay P for working a certain hourly job...Ch. 4.4 - The number of days d it takes for a construction...Ch. 4.4 - The weight of an object on Mars varies directly as...Ch. 4.4 - The weight of an object on Mars varies directly as...Ch. 4.4 - Use your equation from Question 9 to fill in the...Ch. 4.4 - Suppose that a second excursion to Mars happens,...Ch. 4.4 - On the next trip advances in lightweight materials...Ch. 4.4 - When a wheel rolls along, the number of times it...Ch. 4.4 - The wheels on my Explorer have a circumference of...Ch. 4.4 - Use your equation from Question 14 to complete the...Ch. 4.4 - What happens to the number of revolutions if the...Ch. 4.4 - What happens to the number of revolutions if the...Ch. 4.4 - The amount of time it takes to boil a pan of water...Ch. 4.4 - Prob. 2DYGICh. 4.4 - Write a variation equation using constant k for...Ch. 4.4 - Refer back to Did You Get It 3. With a stove set...Ch. 4.4 - Prob. 5DYGICh. 4.4 - Type a short answer to each question. Describe the...Ch. 4.4 - Prob. 3RCh. 4.4 - Prob. 4RCh. 4.4 - The UV (ultraviolet light) index is a measure of...Ch. 4.4 - Write a general variation equation relating the...Ch. 4.4 - According to CBS News online Consumer Tips, at a...Ch. 4.4 - How long would it take to get a sunburn when the...Ch. 4.4 - Fill in the blank with either directly or...Ch. 4.4 - According to the North American Newsprint...Ch. 4.4 - Fill in the blank with either directly or...Ch. 4.4 - A child was struck by a car in a crosswalk. 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What is meant by the phrase...Ch. 4.8 - Prob. 2RCh. 4.8 - Describe the process we developed for multiplying...Ch. 4.8 - Prob. 4RCh. 4.8 - What questions do you have about this lesson?Ch. 4.8 - Recall that revenue is price times number of units...Ch. 4.8 - It costs the manufacturer C=0.12x2+14x+570 dollars...Ch. 4.8 - Find the profit made if 10 grills are sold per...Ch. 4.8 - Find the profit made for sales of 100 and 250...Ch. 4.8 - Use a calculator or computer program to graph the...Ch. 4.8 - Whats the largest profit the company can make from...Ch. 4.8 - Suppose that one month the company runs a...Ch. 4.8 - Write and multiply out the revenue equation in...Ch. 4.8 - Find the new profit equation using your revenue...Ch. 4.8 - Graph this new profit equation and see what effect...Ch. 4.9 - Identify all x values that make the output of each...Ch. 4.9 - Prob. 2PSQCh. 4.9 - Prob. 3PSQCh. 4.9 - Prob. 1LOCh. 4.9 - Perform the multiplication: 57=Ch. 4.9 - Prob. 2GCh. 4.9 - If the volume in the YouTube window is set at half...Ch. 4.9 - If the volume in the YouTube window is set at half...Ch. 4.9 - If the volume in the YouTube window is set all the...Ch. 4.9 - To get the overall volume, we _______ the...Ch. 4.9 - Prob. 7GCh. 4.9 - Prob. 8GCh. 4.9 - Prob. 9GCh. 4.9 - Prob. 10GCh. 4.9 - Prob. 11GCh. 4.9 - Prob. 12GCh. 4.9 - For the polynomial P(x)=(x1)(x+5), find each...Ch. 4.9 - Use the table and graph provided for...Ch. 4.9 - Prob. 3CCh. 4.9 - Prob. 4CCh. 4.9 - y(x)=(x+5)(x+4)(x2) Zeros: x intercepts:Ch. 4.9 - Perform the multiplication: (x+2)(x+12). DO NOT...Ch. 4.9 - When you multiply two binomials, youll always get...Ch. 4.9 - What you did in Question 6 was quite literally the...Ch. 4.9 - What product would give us x2? Write your answers...Ch. 4.9 - One pair of numbers that could give us a constant...Ch. 4.9 - Think of another pair of numbers with product 6,...Ch. 4.9 - How can you get y2 as a product? Set up...Ch. 4.9 - Prob. 13CCh. 4.9 - Find a pair of numbers from your list that you can...Ch. 4.9 - Now try one more factoring problem. Dont let the...Ch. 4.9 - Prob. 16CCh. 4.9 - If the current yield per tree is 800, and will go...Ch. 4.9 - If the current yield per tree is 800, and will go...Ch. 4.9 - Prob. 19CCh. 4.9 - Prob. 20CCh. 4.9 - Prob. 21CCh. 4.9 - Prob. 1DYGICh. 4.9 - Prob. 2DYGICh. 4.9 - Prob. 3DYGICh. 4.9 - Prob. 4DYGICh. 4.9 - Prob. 1RCh. 4.9 - Prob. 2RCh. 4.9 - If they add x one-dollar increments to the cover...Ch. 4.9 - If they add x one-dollar increments, how many...Ch. 4.9 - Write a function R(x) that describes the average...Ch. 4.9 - Find R(0) and describe what it means.Ch. 4.9 - Find the x intercepts of your function and...Ch. 4.9 - If all has gone well, the graph of your revenue...Ch. 4.9 - From what height is the ball thrown? (Hint: How...Ch. 4.9 - Factor the polynomial t22t3.Ch. 4.9 - Using your answer to Question 8, find the zeros of...Ch. 4.10 - For f(x)=1.3x2+5x10,findf(0),f(60),andf(330).Ch. 4.10 - Evaluate the formula for a=6.2andb=12.1...Ch. 4.10 - When selling x units of a certain product, a...Ch. 4.10 - For the price function in Question 3, find the...Ch. 4.10 - What information do you think we would need about...Ch. 4.10 - For the equation describing Giancarlo Stantons...Ch. 4.10 - Use the quadratic formula to find the two...Ch. 4.10 - One of the solutions provides the length of the...Ch. 4.10 - What is the significance of the other solution in...Ch. 4.10 - Whats the connection between the solutions of the...Ch. 4.10 - Prob. 6CCh. 4.10 - Use the vertex formula to find the first...Ch. 4.10 - Prob. 8CCh. 4.10 - Prob. 9CCh. 4.10 - Prob. 1GCh. 4.10 - Use the quadratic formula to find the zeros of the...Ch. 4.10 - Find the number of units that provides the maximum...Ch. 4.10 - Prob. 5GCh. 4.10 - Prob. 6GCh. 4.10 - Prob. 7GCh. 4.10 - Prob. 1DYGICh. 4.10 - Prob. 2DYGICh. 4.10 - Prob. 3DYGICh. 4.10 - Prob. 4DYGICh. 4.10 - What is the quadratic formula used for? Why is...Ch. 4.10 - What types of applied problems can be solved using...Ch. 4.10 - Use a calculator or spreadsheet to make a table of...Ch. 4.10 - Find the vertex of the parabola using the formula...Ch. 4.10 - Explain what each coordinate of the vertex means.Ch. 4.10 - Find the intercepts for the function.Ch. 4.10 - Explain what each intercept means.Ch. 4.10 - Describe when the ball is headed upward, and when...Ch. 4.10 - The function d(t)=49.2t describes the horizontal...Ch. 4.10 - The distance for golf shots is traditionally...Ch. 4.10 - How high was the ball at the time it was hit?Ch. 4.10 - Find the solutions to the equation...Ch. 4.10 - The home run fence is 19 feet high at the point...Ch. 4.11 - Find an exponential function of best fit for the...Ch. 4.11 - Find the correlation coefficient for the...Ch. 4.11 - Prob. 3PSQCh. 4.11 - Find the vertex of the parabola for each quadratic...Ch. 4.11 - Do you think that data can be modeled by a...Ch. 4.11 - Prob. 1GCh. 4.11 - Prob. 2GCh. 4.11 - Prob. 3GCh. 4.11 - Prob. 4GCh. 4.11 - Now try your best to ignore the scatter plot and...Ch. 4.11 - Prob. 6GCh. 4.11 - Prob. 7GCh. 4.11 - Prob. 8GCh. 4.11 - Prob. 9GCh. 4.11 - In case youre not wet enough already, were going...Ch. 4.11 - Find a best fit model for the new data, and write...Ch. 4.11 - Why do you think the bottle didnt drain at a...Ch. 4.11 - In the table, use your equation of best fit to...Ch. 4.11 - Find the quadratic equation of best fit for the...Ch. 4.11 - How much does the model predict the company would...Ch. 4.11 - Find the residuals for your quadratic model in Did...Ch. 4.11 - Would you change your answer to Question 0 at the...Ch. 4.11 - Prob. 2RCh. 4.11 - Prob. 3RCh. 4.11 - Prob. 4RCh. 4.11 - The table shows data describing a batted ball in a...Ch. 4.11 - How far away from home plate did the ball land?Ch. 4.11 - How high did it go?Ch. 4.11 - Did the ball reach its highest point exactly...Ch. 4.11 - The Home Run Tracker data actually describes where...Ch. 4.11 - Find the value of r2 and the residuals for your...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Multiplying factors in an expression will give...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - Carefully read through the list of terminology...Ch. 4 - In Questions 1 and 2, determine whether the type...Ch. 4 - In Questions 1 and 2, determine whether the type...Ch. 4 - A roller coaster is being built to include a...Ch. 4 - What would the length of the actual track be in...Ch. 4 - With the origin at Champaign, the coordinates for...Ch. 4 - A recent news article reported that according to a...Ch. 4 - For Questions 8 and 9: In conducting a survey of...Ch. 4 - For Questions 8 and 9: In conducting a survey of...Ch. 4 - For Questions 1013: While running for city...Ch. 4 - For Questions 1013: While running for city...Ch. 4 - For Questions 1013: While running for city...Ch. 4 - For Questions 1013: While running for city...Ch. 4 - Thinking in terms of exponential growth, what...Ch. 4 - Write an exponential growth function that...Ch. 4 - For the function in Question 15, find f(4) and...Ch. 4 - Thinking in terms of exponential decay, what...Ch. 4 - Write an exponential decay function that describes...Ch. 4 - For the function in Question 18, find f(4) and...Ch. 4 - The graph shows the number of bacteria over a...Ch. 4 - The amount of money in an investment account has...Ch. 4 - The amount of money in an investment account has...Ch. 4 - The amount of money in an investment account has...Ch. 4 - The graph shows the daily profit y in dollars of...Ch. 4 - The graph shows the daily profit y in dollars of...Ch. 4 - The graph shows the daily profit y in dollars of...Ch. 4 - The graph shows the daily profit y in dollars of...Ch. 4 - For Questions 2837, refer to the following: From...Ch. 4 - For Questions 2837, refer to the following: From...Ch. 4 - For Questions 2837, refer to the following: From...Ch. 4 - For Questions 2837, refer to the following: From...Ch. 4 - For Questions 2837, refer to the following: From...Ch. 4 - For Questions 2837, refer to the following: From...Ch. 4 - For Questions 2837, refer to the following: From...Ch. 4 - For Questions 2837, refer to the following: From...Ch. 4 - According to the baseball tracking system...Ch. 4 - According to the baseball tracking system...Ch. 4 - According to the baseball tracking system...Ch. 4 - In Questions 4148, simplify each expression by...Ch. 4 - In Questions 4148, simplify each expression by...Ch. 4 - In Questions 4148, simplify each expression by...Ch. 4 - In Questions 4148, simplify each expression by...Ch. 4 - In Questions 4148, simplify each expression by...Ch. 4 - In Questions 4148, simplify each expression by...Ch. 4 - In Questions 4148, simplify each expression by...Ch. 4 - In Questions 4148, simplify each expression by...Ch. 4 - Prob. 49LORCh. 4 - Prob. 50LORCh. 4 - In Question 49-52, factor each trinomial. 2x2+x6Ch. 4 - In Question 49-52, factor each trinomial. 3x24x15Ch. 4 - Solve the equation x27x+10=0 using the quadratic...
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