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mathematics
college algebra graphs and models
College Algebra 7th Edition Robert F Blitzer - Solutions
In Exercises 127–130, solve each equation by the method of your choice. x2 - 1 3x + 2 1 x + 2 5 x2 — 4 - X²
In Exercises 123–124, list all numbers that must be excluded from the domain of each rational expression. 3 2x² + 4x - 9
In Exercises 123–124, list all numbers that must be excluded from the domain of each rational expression. 7 2x² - 8x + 5
In Exercises 120–123, determine whether each statement makes sense or does not make sense, and explain your reasoning.Although I can solve by first subtracting from both sides, I find it easier to begin by multiplying both sides by 20, the least common denominator. 114 - || - UIH 3x +
If x represents a number, write an English sentence about the number that results in an inconsistent equation.
Exercises 124–127, 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 and x = 4 are equivalent. X x - 4 4 x - 4
In Exercises 115–122, find all values of x satisfying the given conditions. y₁ = x - 3, y₂ = x + 8, and y₁y2 = -30.
In Exercises 115–122, find all values of x satisfying the given conditions. Y₁ = 2x² + 5x = 4, y2 = x² + 15x - 10, and У1 - y₁ - y₂ = 0. У1
In Exercises 116–119, use your graphing utility to enter each side of the equation separately under y1 and y2. Then use the utility’s TABLE or GRAPH feature to solve the equation. x - 3 5 - 1 = x-5 4
In Exercises 116–119, use your graphing utility to enter each side of the equation separately under y1 and y2. Then use the utility’s TABLE or GRAPH feature to solve the equation. 2x + 3(x4) = 4x - 7
In Exercises 116–119, use your graphing utility to enter each side of the equation separately under y1 and y2. Then use the utility’s TABLE or GRAPH feature to solve the equation. 5x + 2(x - 1) = 3x + 10
Exercises 124–127, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.If a and b are any real numbers, then ax + b = 0 always has one number in its solution set.
Exercises 124–127, 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 3y - 1 = 11 and 3y - 7 = 5 are equivalent.
In Exercises 120–123, determine whether each statement makes sense or does not make sense, and explain your reasoning.Because x = x + 5 is an inconsistent equation, the graphs of y = x and y = x + 5 should not intersect.
Exercises 124–127, 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 -7x = x has no solution.
In Exercises 120–123, determine whether each statement makes sense or does not make sense, and explain your reasoning.The model P = -0.18n + 2.1 describes the number of pay phones, P, in millions, n years after 2000, so I have to solve a linear equation to determine the number of pay phones in
In Exercises 115–122, find all values of x satisfying the given conditions. y = 5x² + 3x and y = 2.
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [-10, 10, 1] by [-10, 10, 1] viewing rectangles and labeled (a) through (f). 2 y = x² + 6x + 9
In Exercises 115–122, find all values of x satisfying the given conditions. 2x² 3x and y = 2. y = 2x²
In Exercises 115–122, find all values of x satisfying the given conditions. Y₁ = x − 1, y₂ = x + 4, and y₁y2 = 14.
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [-10, 10, 1] by [-10, 10, 1] viewing rectangles and labeled (a) through (f). y = x² - 2x + 2
In Exercises 120–123, determine whether each statement makes sense or does not make sense, and explain your reasoning.Because I know how to clear an equation of fractions, I decided to clear the equation 0.5x + 8.3 = 12.4 of decimals by multiplying both sides by 10.
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [-10, 10, 1] by [-10, 10, 1] viewing rectangles and labeled (a) through ( f ). y = -(x + 1)² + 4
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [-10, 10, 1] by [-10, 10, 1] viewing rectangles and labeled (a) through ( f ). y = x² - 6x + 7 2
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [-10, 10, 1] by [-10, 10, 1] viewing rectangles and labeled (a) through ( f ). y = x2 — 4x — 5
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [-10, 10, 1] by [-10, 10, 1] viewing rectangles and labeled (a) through (f). y = -(x + 3)2 + 1
Solve each equation in Exercises 83–108 by the method of your choice. 3 x - 3 + 5 x - 4 x² - 20 x² - 7x + 12
Suppose you are an algebra teacher grading the following solution on an examination:You should note that 8 checks, so the solution set is {8}. The student who worked the problem therefore wants full credit. Can you find any errors in the solution? If full credit is 10 points, how many points should
Solve each equation in Exercises 83–108 by the method of your choice. 2x x - 3 + 6 x + 3 28 x² - 9
Solve each equation in Exercises 83–108 by the method of your choice. Solve each equation in Exercises 83–108 by the method of your choice. 1 X + 1 x + 3 1 4
The line graph shows the cost of inflation. What cost $10,000 in 1984 would cost the amount shown by the graph in subsequent years.Here are two mathematical models for the data shown by the graph. In each formula, C represents the cost x years after 1990 of what cost $10,000 in 1984.a. Use the
A company wants to increase the 10% peroxide content of its product by adding pure peroxide (100% peroxide). If x liters of pure peroxide are added to 500 liters of its 10% solution, the concentration, C, of the new mixture is given byHow many liters of pure peroxide should be added to produce a
Solve each equation in Exercises 83–108 by the method of your choice. 2x² - 7x = 0
What is an inconsistent equation? Give an example.
What is a conditional equation? Give an example.
Solve each equation in Exercises 83–108 by the method of your choice. 2x² + 5x = 3
The line graph shows the cost of inflation. What cost $10,000 in 1984 would cost the amount shown by the graph in subsequent years.Here are two mathematical models for the data shown by the graph. In each formula, C represents the cost x years after 1990 of what cost $10,000 in 1984.a. Use the
Solve each equation in Exercises 83–108 by the method of your choice. 1 X + 1 x + 2 1 3
What is an identity? Give an example.
Why should restrictions on the variable in a rational equation be listed before you begin solving the equation?
Explain how to find restrictions on the variable in a rational equation.
Formulas with rational expressions are often used to model learning. Many of these formulas model the proportion of correct responses in terms of the number of trials of a particular task. One such model, called a learning curve, is where P is the proportion of correct responses after x trials. If
The line graph shows the cost of inflation. What cost $10,000 in 1984 would cost the amount shown by the graph in subsequent years.Here are two mathematical models for the data shown by the graph. In each formula, C represents the cost x years after 1990 of what cost $10,000 in 1984.Use model 1 to
The line graph shows the cost of inflation. What cost $10,000 in 1984 would cost the amount shown by the graph in subsequent years.Here are two mathematical models for the data shown by the graph. In each formula, C represents the cost x years after 1990 of what cost $10,000 in 1984.Use model 1 to
Solve each equation in Exercises 83–108 by the method of your choice. 5x² = 2x3
Suppose that x liters of pure acid are added to 200 liters of a 35% acid solution.a. Write a formula that gives the concentration, C, of the new mixture.b. How many liters of pure acid should be added to produce a new mixture that is 74% acid?
Refer to the mathematical model and the bar graph on the previous page.a. According to the formula, in 2000, what percentage of U.S. college freshmen had an average grade of A in high school? Does this underestimate or overestimate the percent displayed by the bar graph? By how much?b. If trends
Solve each equation in Exercises 83–108 by the method of your choice. x² - 4x + 290
Solve each equation in Exercises 83–108 by the method of your choice. *2 6x + 13 = 0
Solve each equation in Exercises 83–108 by the method of your choice. x² = 4x - 7
Formulas with rational expressions are often used to model learning. Many of these formulas model the proportion of correct responses in terms of the number of trials of a particular task. One such model, called a learning curve, is where P is the proportion of correct responses after x trials. If
Suppose that you solve x/5 - x/2 = 1 by multiplying both sides by 20 rather than the least common denominator (namely, 10). Describe what happens. If you get the correct solution, why do you think we clear the equation of fractions by multiplying by the least common denominator?
What is a linear equation in one variable? Give an example of this type of equation.
In Exercises 89–96, solve each equation. -217- [4 - 2(1-x) + 3]} = 10 - [4x - 2(x-3)]
Solve each equation in Exercises 83–108 by the method of your choice. 3x²27 = 0
a. According to the formula, in 2010, what percentage of U.S. college freshmen had an average grade of A in high school? Does this underestimate or overestimate the percent displayed by the bar graph? By how much?b. If trends shown by the formula continue, project when 57% of U.S. college freshmen
Solve each equation in Exercises 83–108 by the method of your choice. 3x² - 12x + 12 = 0
In Exercises 89–96, solve each equation. 4x + 13 (2x [4(x-3) 5]} = 2(x - 6) -
Solve each equation in Exercises 83–108 by the method of your choice. 4x² - 16 = 0
Solve each equation in Exercises 83–108 by the method of your choice. 9 - 6x + x² = 0
In Exercises 89–96, solve each equation. 0.5(x + 2) = 0.1 + 3(0.1x + 0.3)
Solve each equation in Exercises 83–108 by the method of your choice. (2x + 7)² = 25
Explain each of the three jokes in the cartoon shown below. THE KID WHO LEARNED ABOUT MATH ON THE STREET If divide you 6,973 by 0, you die 00 Once, this guy tried to find the square root of 9, and his eyeballs turned black. This girl my brother knows found out. exactly what π equals, but she went
Contrary to popular belief, older people do not need less sleep than younger adults. However, the line graphs show that they awaken more often during the night. The numerous awakenings are one reason why some elderly individuals report that sleep is less restful than it had been in the past. Use
Solve each equation in Exercises 65–74 using the quadratic formula. I - xy = 3x²
The equations in Exercises 69–80 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2 x - 2 = 3+ x x - 2
Solve each equation in Exercises 65–74 using the quadratic formula. 4x² = 2x+7
The equations in Exercises 69–80 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. x + 2 7 || 5 x + 1 3
Solve each equation in Exercises 65–74 using the quadratic formula. 5x² 5r2 + x - 2 =0
It was wartime when the Ricardos found out Mrs. Ricardo was pregnant. Ricky Ricardo was drafted and made out a will, deciding that $14,000 in a savings account was to be divided between his wife and his child-to-be. Rather strangely, and certainly with gender bias, Ricky stipulated that if the
The equations in Exercises 69–80 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. x + 5 2 - 4 || 2x 1 - 3
In Exercises 71–74, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Some irrational numbers are not complex numbers.
Solve each equation in Exercises 65–74 using the quadratic formula. 3x² - 3x - 4 = 0 0
Solve each equation in Exercises 65–74 using the quadratic formula. x2 + 5x + 2 = 0
Suppose that we agree to pay you 8¢ for every problem in this chapter that you solve correctly and fine you 5¢ for every problem done incorrectly. If at the end of 26 problems we do not owe each other any money, how many problems did you solve correctly?
In Exercises 71–74, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.If the product of a point’s coordinates is positive, the point must be in quadrant I.
In Exercises 61–68, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 3 x - 3 X x - 3 +3
In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.When I add or subtract complex numbers, I am basically combining like terms.
In a film, the actor Charles Coburn plays an elderly “uncle” character criticized for marrying a woman when he is 3 times her age. He wittily replies, “Ah, but in 20 years time I shall only be twice her age.” How old is the “uncle” and the woman?
Solve each equation in Exercises 65–74 using the quadratic formula. x2 + 5x + 3 = 0 =
In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.I used the ordered pairs (time of day, calories that I burned) to obtain a graph that is a horizontal line.
In Exercises 61–68, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x x - 3 || 6 x - 3 +4
In Exercises 61–68, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 7 = 2x + 7
In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.By writing the imaginary number 5i, I can immediately see that 5 is the constant and i is the variable.
The price of a dress is reduced by 40%. When the dress still does not sell, it is reduced by 40% of the reduced price. If the price of the dress after both reductions is $72, what was the original price?
Explain the error in Exercises 65–66. (√-9)² = √-9. V-9 = √81 = 9
In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.I used the ordered pairs (-2, 2), (0, 0), and (2, 2) to graph a straight line.
Solve each equation in Exercises 65–74 using the quadratic formula. x² + 8x + 12 = 0
In Exercises 61–68, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 10x + 3 = 8x + 3
In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.The word imaginary in imaginary numbers tells me that these numbers are undefined.
At the north campus of a performing arts school, 10% of the students are music majors. At the south campus, 90% of the students are music majors. The campuses are merged into one east campus. If 42% of the 1000 students at the east campus are music majors, how many students did the north and south
In Exercises 61–68, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 3(x + 2) = 7 + 3x
In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.There is something wrong with my graphing utility because it is not displaying numbers along the x- and y-axes.
In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.The humor in the cartoon is based on the fact that “rational” and “real” have different meanings in mathematics and in everyday speech.
Solve each equation in Exercises 65–74 using the quadratic formula. x² + 8x + 15 = 0
Explain the error in Exercises 65–66. V−9+ V-16 = V-25 = i√25 = 5i
In Exercises 61–68, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4(x + 5) 21+ 4x =
In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.The rectangular coordinate system provides a geometric picture of what an equation in two variables looks like.
Solve each equation in Exercises 47–64 by completing the square. 3x²5x 5x – 10 = 0
Solve each equation in Exercises 47–64 by completing the square. 3x²2x2 = 0
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