Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x3 / y-2
> Assume that a couple invests $4000 each year for 4 years in an investment that earns 8% compounded annually. What will the value of the investment be 8 years after the first amount is invested?
> Assume that a couple invests $1000 upon the birth of their daughter. Assume that the investment earns 6.8% compounded annually. What will the investment be worth on the daughter’s 18th birthday?
> Refer to the cost function in Fig. 18. Translate the task “solve C(x) = 3500 for x” into a task involving the graph of the function. C D B E A Figure 12
> If the cylinder in Exercise 6 has a volume of 54p cubic inches, find the surface area of the cylinder. Cylinder in Exercise 6: C D B E A Figure 12
> Calculate the compound amount from the given data. principal = $1500, compounded daily, 3 years, annual rate = 6%
> Calculate the compound amount from the given data. principal = $1500, compounded daily,1 year, annual rate = 6%
> Describe the domain of the function. f (x) =8x / (x - 1)(x - 2)
> Decide which curves are graphs of functions. 8 7 6 3 2 1 2 3 4 5 6 7 8 4) 1.
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 2x / √x
> Calculate the compound amount from the given data. principal = $500, compounded monthly,1 year, annual rate = 4.5%
> Calculate the compound amount from the given data. principal = $100, compounded monthly, 10 years, annual rate = 5%
> In Exercises 47–50, find the zeros of the function. (Use the specified viewing window.) f (x) = x2 - x - 2; [-4, 5] [-4, 10]
> Calculate the compound amount from the given data. principal = $20,000, compounded quarterly, 3 years, annual rate = 12%
> Calculate the compound amount from the given data. principal = $50,000, compounded quarterly, 10 years, annual rate = 9.5%
> Calculate the compound amount from the given data. principal = $700, compounded annually, 8 years, annual rate = 8%
> In Exercises 51–54, find the points of intersection of the graphs of the functions. (Use the specified viewing window.) f (x) = 2x - 1; g(x) = x2 - 2; [-4, 4] by [-6, 10]
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (x)g(x)
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) + g(x)
> A catering company estimates that, if it has x customers in a typical week, its expenses will be approximately C(x) = 550x + 6500 dollars, and its revenue will be approximately R(x) = 1200x dollars. (a) How much profit will the company earn in 1 week whe
> Calculate the compound amount from the given data. principal = $500, compounded annually, 6 years, annual rate = 6%
> Evaluate f (4). f (x) = x0
> Evaluate f (4). f (x) = x-5/2
> Sketch the graph of the function. f (x) = √(x + 1)
> Evaluate f (4). f (x) = x-1/2
> Evaluate f (4). f (x) = x3/2
> Decide which curves are graphs of functions. x = degrees Fahrenheit, y = degrees Celsius, so the points (32, 0) and (212, 100) lie on the line. 100 – 0 100 5 212 – 32 180 9 Now find b: 160 y = mx + b= 32 ㅎ = (0)+b=b: 9 5 160 Thus, y =x+32. y=-(98.6)
> When a car is moving at x miles per hour and the driver decides to slam on the brakes, the car will travel x + (1/20) x2 feet. (The general formula is f (x) = ax + bx2, where the constant a depends on the driver’s reaction time and the constant b depends
> Draw the following intervals on the number line. [ -2, √2)
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. g(x) - h(x - 3)
> Evaluate f (4). f (x) = x1/2
> Evaluate f (4). f (x) = x-1
> Evaluate f (4). f (x) = x3
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (t) - h(t)
> Evaluate f (4). f (x) = x2
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x + 5 / x – 10, g(x) = x / x + 10
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. Explain why √a/√b = √ (a/b).
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. Explain why √a * √b = √(ab).
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. √ (x/y) - √ (y/x) = √xy ( )
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. x-1/4 + 6x1/4 = x-1/4( )
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. [ f (x)]3g(x)
> Graph the following equations. y = 3x + 1
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. 2x2/3 - x-1/3 = x-1/3 ( )
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (3x2 / 2y)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x)3/2 * (x)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x)3/2 * (x)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-3x)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-4 / x3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. -x3y / -xy
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. -3x / 15x4
> Refer to the cost and revenue functions in Fig. 17. The cost of producing x units of goods is C(x) dollars and the revenue from selling x units of goods is R(x) dollars. At what level of production is the cost $1400? 1 x+ 2y = 0= y = --x= m = 2 1 2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (2x)4
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) =-x / x + 3, g(x) = x / x + 5
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. √x – 1/√x = 1/√x ( )
> Solve the equations in Exercises 39–44. 1 = 5 / x +6 / x2
> Sketch the graph of the function. f (x) = 2x2 - 1
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-3 * x7
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x5 * (y2 / x)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. √(1 + x) * (1 + x)3/2
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) + h(x)
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x3y5)4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x/y)-2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x4 / y2)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x3 * y6)1/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-1/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 1/x-3
> Solve the equations in Exercises 39–44. x + 14 / x + 4 = 5
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x / x - 8, g(x) =-x / x - 4
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. g(x) - h(x)
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x4 * y5)/ xy2
> Sketch the graph of the function. f (x) = x2 + 1
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x1/3)6
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-27x5)2/3 / x3/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (xy)6
> Use the laws of exponents to compute the numbers. (61/2)0
> Use the laws of exponents to compute the numbers. 74/3 / 71/3
> Use the laws of exponents to compute the numbers. (125 * 27)1/3
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g(g(x))
> Use the laws of exponents to compute the numbers. (8/27)2/3
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) - g(x + 1)
> Use the laws of exponents to compute the numbers. 200.5 * 50.5
> Solve the equations in Exercises 39–44. x + 2 / x – 6 = 3
> Use the laws of exponents to compute the numbers. (21/3 * 32/3)3
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = 3 / x – 6, g(x) = -2 / x - 2
> Use the laws of exponents to compute the numbers. 35/2 / 31/2
> Use the laws of exponents to compute the numbers. 104 / 54
> Describe the domain of the function. g(x) =4 / x(x + 2)
> Use the laws of exponents to compute the numbers. (94/5)5/8
> Use the laws of exponents to compute the numbers. 61/3 * 62/3
> Refer to the function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16. What is the cost of constructing a cylinder of radius 6 inches? x(8x2/3) = x/3.8x2/3
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (f (x))
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x2 / x5y
> Use the laws of exponents to compute the numbers. (31>3 * 31>6)6
> Use the laws of exponents to compute the numbers. 51/3 * 2001/3
> Compute the numbers. 1-1.2
> Refer to the function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16. How much is saved by increasing the radius from 1 inch to 3 inches? =X.X = x.x = x =-
> Solve the equations in Exercises 39–44. 21/x - x = 4
> Compute the numbers. (.01)-1.5
> Compute the numbers. (1/8)-2/3
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = 2 / x - 3, g(x) = 1 / x + 2
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) - g(x)
