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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

The graphs labeled (a)–(d) in the figure represent y = 3x, y = 5x, y = (1/3)x, and y = (1/5)x, but not necessarily in that order. Which is which? Describe the process that enables you to make this
Use the graph of f to determine each of the following. Where applicable, use interval notation.a. the domain of fb. the range of fc. the x-interceptsd. the y-intercepte. interval(s) where f is
In Exercises 53–54, make a rough sketch in a rectangular coordinate system of the graphs representing the equations in each system.The system, whose graphs are a line with negative slope and a
Explain how to find the partial fraction decomposition of a rational expression with a repeated linear factor in the denominator.
In Exercises 87–88, we used the data in a bar graph to develop linear functions that modeled the percentage of never-married American females and males, ages 25–29. For this group exercise, you
In Exercises 53–54, make a rough sketch in a rectangular coordinate system of the graphs representing the equations in each system.The system, whose graphs are a line with positive slope and a
Find ln 2 using a calculator. Then calculate each of the following: 1-; 1 - + - + 3 1+1-1/2 + 1 - 1 ; .... Describe what you observe.
Explain how to find the partial fraction decomposition of a rational expression with distinct linear factors in the denominator.
Find (f ° g)(x) and (g ° f )(x).
If g(x) = Vx [√x-3 if x ≥ 3 13 - x if x < 3' find g(-1) and g(7).
Research applications of logarithmic functions as mathematical models and plan a seminar based on your group’s research. Each group member should research one of the following areas or any other
In Exercises 105–108, evaluate each expression without using a calculator.log2(log3 81)
This group exercise involves exploring the way we grow. Group members should create a graph for the function that models the percentage of adult height attained by a boy who is x years old, f(x) = 29
In Exercises 135–138, determine whether each statement makes sense or does not make sense, and explain your reasoning.I estimate that log8 16 lies between 1 and 2 because 81 = 8 and 82 = 64.
In Exercises 17–19, use the graph to determinea. The function’s domain;b. The function’s range;c. The x-intercepts, if any;d. The y-intercept, if there is one;e. Intervals on which the function
In Exercises 105–108, evaluate each expression without using a calculator.log(ln e)
Exercises 97–99 will help you prepare for the material covered in the next section.What problem do you encounter when using the switch and- solve strategy to find the inverse of f(x) = 2x ?
In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a
In Exercises 38–41, determine whether each statement makes sense or does not make sense, and explain your reasoning.According to the Blitzer Bonus on page 278, calculus studies change by analyzing
Each group member should research one situation that provides two different pricing options. These can involve areas such as public transportation options (with or without discount passes), cellphone
In all exercises, other than Φ, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 1 X 2 V 4
An important application of systems of equations arises in connection with supply and demand. As the price of a product increases, the demand for that product decreases. However, at higher prices,
Perform the operations and write the result in standard form: -20 + √-32 10
An important application of systems of equations arises in connection with supply and demand. As the price of a product increases, the demand for that product decreases. However, at higher prices,
In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system.The sum of the x-variable and the y-variable is at most 3. The y-variable added to
The graphs show per capita consumption of soda and bottled water in the United States, in gallons, from 2000 through 2015.a. Write the slope-intercept equation of the line that models soda
The graphs show changing attitudes toward gay marriage for the period from 2001 through 2015.a. Write the slope-intercept equation of the line that models the percentage of the U.S. public that
Find the partial fraction decomposition of 4x² + 5x9 3- 6x-9
In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system.The sum of the x-variable and the y-variable is at most 4. The y-variable added to
Explain how to solve a nonlinear system using the addition method. Use x2 - y2 = 5 and 3x2 - 2y2 = 19 to illustrate your explanation.
The graphs of solution sets of systems of inequalities involve finding the intersection of the solution sets of two or more inequalities. By contrast, in Exercises 71–72, you will be graphing the
Exercises 69–71 will help you prepare for the material covered in the next section.Graph x - y = 3 and (x - 2)2 + (y + 3)2 = 4 in the same rectangular coordinate system. What are the two
In Exercises 69–72, determine whether each statement makes sense or does not make sense, and explain your reasoning.Without using any algebra, it’s obvious that the nonlinear system consisting of
Exercises 69–71 will help you prepare for the material covered in the next section.Solve by the addition method: 2x + 4y = -4 (3x + 5y = -3.
In Exercises 69–72, determine whether each statement makes sense or does not make sense, and explain your reasoning.I graphed a nonlinear system that modeled the orbits of Earth and Mars, and the
In Exercises 69–70, rewrite each inequality in the system without absolute value bars. Then graph the rewritten system in rectangular coordinates. f|x ≤ 1 X y ≤ 2
Harsh, mandatory minimum sentences for drug offenses account for more than half the population in U.S. federal prisons. The bar graph shows the number of inmates in federal prisons, in thousands, for
Does x2 + y = 10 define y as a function of x?
In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system.The sum of the x-variable and the y-variable is no more than 2. The y-variable is
The bar graph indicates that fewer U.S. adults are getting married.a. Use these models to determine the year, rounded to the nearest year, when the percentage of never-married adults will be the same
Write a system of equations, one equation whose graph is a line and the other whose graph is a parabola, that has no ordered pairs that are real numbers in its solution set. Graph the equations using
68. Given f(x) = 6x + 5 and g(x) = x2 - 3x + 2, find each of the following:a. ( f ° g) (x)b. (g ° f ) (x)c. ( f ° g) (-1).
In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system.The sum of the squares of the x-variable and the y-variable is no more than 25. The
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. V/0.64
Evaluate the expression by hand. Check your result with a calculator. -3)³
Use grouping to factor the polynomial. 424 +42³ +2²+ =
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate.
Find the partial fraction decomposition for the rational expression. 3x² + x³ + 5x² - x +4 (x - 1)(x² + 1)²
Evaluate the expression by hand. Check your result with a calculator.
Use grouping to factor the polynomial. 2x³ 3x² + 2x - 3 -
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate.
Find the partial fraction decomposition for the rational expression. -x²8x² + 3x - 10 (x + 2)(x² + 4)²
Find the partial fraction decomposition for the rational expression. -1
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. VII
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. V/0.36
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate.
Use grouping to factor the polynomial. 8x³2x² + 12x - 3
Evaluate the expression by hand. Check your result with a calculator. 104
Find an exponential model f(x) that describes each situation.A sample of 152 birds decreases in number by 3.4% per week.
Find the partial fraction decomposition for the rational expression. 5x + 10x15x³+4x²+ 13x - 9 x³ + 2x²-3x
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. 16 25
Find the opposite of the polynomial. 7x³
Use grouping to factor the polynomial. 2x²x³ + 4x - 2
Evaluate the expression by hand. Check your result with a calculator. 뚜
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x) = 8(1.12)
Use grouping to factor the polynomial. 2x²5x³+ 10x - 25 -
Evaluate the expression by hand. Check your result with a calculator. 뚜
Find an exponential model f(x) that describes each situation.A mutual fund account contains $2500 and increases by 2.1% per year.
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate.
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x) = 9(1.005)*
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate.
Find the partial fraction decomposition for the rational expression. 3+5 + 3x² + 3x + рив + F2 X
Find the opposite of the polynomial. -38
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number.
Find an exponential model f(x) that describes each situation.A mutual fund account contains $2500 and increases by 2.1% per year.
Use grouping to factor the polynomial. ab - 3a + 2b - 6
Evaluate the expression by hand. Check your result with a calculator.
Find the opposite of the polynomial. 1925 - 52² + 3z
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate.
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x)= 1.5(0.35)*
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. -16
Use grouping to factor the polynomial. 2ax 6bxay + 3by -
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x)= 100(1.23)*
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. -64
Find the opposite of the polynomial. -x²-x+6 9
Find the area of the right triangle that satisfies the conditions. Approximate values to the nearest tenth when appropriate. Legs with lengths 3 feet and 6 feet
Factor the expression completely. x² + 7x + 10
Evaluate the expression by hand. Check your result with a calculator.
Find the opposite of the polynomial. 4- ? - 9
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x) = 0.55*
Find the area of the right triangle that satisfies the conditions. Approximate values to the nearest tenth when appropriate. Hypotenuse 10 inches and leg 6 inches
Factor the expression completely. x² + 3x - 10
Evaluate the expression by hand. Check your result with a calculator. 01
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. 27
Find the opposite of the polynomial. 1 - 8x + 6x²-x³
Factor the expression completely. x² + 8x + 12
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x) = 0.4*
Find the area of the right triangle that satisfies the conditions. Approximate values to the nearest tenth when appropriate. Hypotenuse 15 inches and leg 11 inches
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. 64
Use the product rule to simplify. -9 .

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