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mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
In Problems 19–54, solve each inequality algebraically.x4 > 1
In Problems 19–54, solve each inequality algebraically. x < 9x2
In Problems 25–32, use the given zero to find the remaining zeros of each polynomial function. f(x) = x² − 7x³ + 14x² − 38x − 60; zero:1 + 3i
In Problems 31–42, graph each polynomial function f by following Steps 1 through 5.f(x) = 4x - x3
In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then use Descartes’ Rule of Signs to determine how many positive and how many negative real zeros each polynomial function may have. Do not attempt to find the zeros. [− x + - + p^ - s* = (x)f
In Problems 29 and 30, use Descartes’ Rule of Signs to determine how many positive and negative real zeros each polynomial function may have. Do not attempt to find the zeros.f(x) = -6x5 + x4 + 5x3 + x + 1
In Problems 31–42, graph each polynomial function f by following Steps 1 through 5. Steps for Graphing a Polynomial Function STEP 1: Determine the end behavior of the graph of the function. STEP 2: Find the x- and y-intercepts of the graph of the function. STEP 3: Determine the real zeros of the
In Problems 37 and 38, find bounds on the real zeros of each polynomial function.f(x) = x3 - x2 - 4x + 2
Problems 50–59 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Given f(x) as (-²). 2, 2x³7x+1, find f
In Problems 31–42, graph each polynomial function f by following Steps 1 through 5. Steps for Graphing a Polynomial Function STEP 1: Determine the end behavior of the graph of the function. STEP 2: Find the x- and y-intercepts of the graph of the function. STEP 3: Determine the real zeros of the
In Problems 31–42, graph each polynomial function f by following Steps 1 through 5. Steps for Graphing a Polynomial Function STEP 1: Determine the end behavior of the graph of the function. STEP 2: Find the x- and y-intercepts of the graph of the function. STEP 3: Determine the real zeros of the
In Problems 37 and 38, find bounds on the real zeros of each polynomial function. f(x) = 2x³7x² 2x³7x²10x + 35
In Problems 31–42, graph each polynomial function f by following Steps 1 through 5. Steps for Graphing a Polynomial Function STEP 1: Determine the end behavior of the graph of the function. STEP 2: Find the x- and y-intercepts of the graph of the function. STEP 3: Determine the real zeros of the
In Problems 31–42, graph each polynomial function f by following Steps 1 through 5. Steps for Graphing a Polynomial Function STEP 1: Determine the end behavior of the graph of the function. STEP 2: Find the x- and y-intercepts of the graph of the function. STEP 3: Determine the real zeros of the
In Problems 45–56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. T(x) +3 x¹ - 1
In Problems 7–50, follow Steps 1 through 7. Steps for Graphing a Rational Function R STEP 1: Factor the numerator and denominator of R. Find the domain of the rational function. STEP 2: Write R in lowest terms. STEP 3: Find and plot the intercepts of the graph. Use multiplicity to determine the
In Problems 7–50, follow Steps 1 through 7. Steps for Graphing a Rational Function R STEP 1: Factor the numerator and denominator of R. Find the domain of the rational function. STEP 2: Write R in lowest terms. STEP 3: Find and plot the intercepts of the graph. Use multiplicity to determine the
In Problems 79–84, use the Intermediate Value Theorem to show that each polynomial function has a real zero in the given interval. f(x) = 3x³ - 10x + 9; [-3, -2]
Problems 79–88 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. - 15(* = ³). fl 4 If f(x) = 4x + 3, find
In Problems 79–84, use the Intermediate Value Theorem to show that each polynomial function has a real zero in the given interval. f(x) = x³ x² + 7x²³7x² 18x + 18; [1.4, 1.5]
Factor each polynomial completely. 2p² - 5pq +3q²
Solve each equation. V6+ 2x − 1 = √7 - 2x
Evaluate each exponential. (-243) 2/5
Perform the indicated operations, and express each answer in simplest form. Assume that all variables represent positive real numbers. 6 EA
Simplify. Assume that all variables represent positive real numbers. 13 V 49
Solve. x + 1 x-3 || 4 x - 3 +6
Find each root. -32
Multiply, and then simplify each product. Assume that all variables represent positive real numbers. (1 + EA + 6A) (1 - EA)
Add or subtract to simplify each radical expression. Assume that all variables represent positive real numbers. 7914€ + EAS
Add or subtract to simplify each radical expression. Assume that all variables represent positive real numbers. 3√x²y²-2V/64x²y²
Evaluate each exponential.491/2
Perform the indicated operations. -8.84 (-3.46)
Based on the discussion and examples of this section, give the first step to solve each equation. Do not actually solve. 14 X =x-5
Match each quadratic function in parts (a)–(d) with its graph from choices A–D. (a) f(x) = (x + 2)² - 1 (b) f(x) = (x + 2)² + 1 (c) f(x) = (x - 2)² - 1 (d) f(x) = (x - 2)² + 1 A. C. V X B. D. T A X x
Solve each equation or inequality. V = r²+ R²h for R
The solution set of the inequality x2 + x - 12 < 0 is the interval (-4, 3). Without actually performing any work, give the solution set of the inequality x² + x - 12 ≥ 0.
Solve each equation or inequality. 3t²6t= -4
Decide whether the zero-factor property, the square root property, or the quadratic formula is most appropriate for solving each quadratic equation. Do not actually solve.(2x + 3)2 = 4
One patron wrote the quadratic formula, as shown here, on a wall at the Cadillac Bar in Houston, Texas. Was this correct? If not, correct it. x = -b√b² - 4ac 2a
Perform the indicated operations. ~ 10
Based on the discussion and examples of this section, give the first step to solve each equation. Do not actually solve. V1 + x + x = 5
In solving a formula that has the specified variable in the denominator, what is the first step?
Solve 5x2 + 13x = 6 using the zero-factor property.
How can we determine just by looking at the equation of a parabola whether it has a vertical or a horizontal axis?
Match each quadratic function in parts (a)–(d) with its graph from choices A–D. (a) f(x) = x² + 2 (b) f(x)=x²-2 (c) f(x) = (x + 2)² - (d) f(x) = -(x - 2)² A. C. ⠀⠀ 14 IN N 2 ........ X B. D. +2. ..ol. N E X X
Solve each equation using the square root property or completing the square.t2 = 121
A student solved 5x2 - 5x + 1 = 0 incorrectly as follows.Give the correct solution set. X = X = || -(-5) ± √(-5)² - 4(5) (1) 2(5) 5 ± √5 10 1 2 + √5
Decide whether the zero-factor property, the square root property, or the quadratic formula is most appropriate for solving each quadratic equation. Do not actually solve.4x2 - 3x = 1
Perform the indicated operations. |-12| + |13|
Solve each equation or inequality. (3x + 11)² = 7
Explain how to determine whether to include or to exclude endpoints when solving a quadratic or higher-degree inequality.
What is the first step in solving a formula like gw2 = 2r for w?
Based on the discussion and examples of this section, give the first step to solve each equation. Do not actually solve. (x² + x)² − 8(x² + x) + 12 = 0
Why can’t the graph of a quadratic function be a parabola with a horizontal axis?
Solve each equation using the square root property or completing the square.t2 = 54
Solve each equation using the square root property or completing the square.p2 = 3
Decide whether the zero-factor property, the square root property, or the quadratic formula is most appropriate for solving each quadratic equation. Do not actually solve.x2 + 5x - 8 = 0
In each exercise, the graph of a quadratic function ƒ is given. Use the graph to find the solution set of each equation or inequality. (a) x² - 4x + 3 = 0 (b) x² - 4x + 3 > 0 (c) x² - 4x + 3
Solve each equation using the square root property or completing the square. (7x + 3)² = 25
Match each quadratic function in Column I with the description of the parabola that is its graph in Column II. I (a) f(x) = (x-4)² - 2 (b) f(x) = (x - 2)² - 4 (c) f(x) = (x + 4)² + 2 (d) f(x)=(x-4)² - 2 (e) f(x) = (x - 2)² - 4 == (f) f(x) = (x-4)² + 2 - II A. Vertex (2, -4), opens down B.
Solve each equation using the square root property or completing the square. (2x + 5)² = 100
Solve each equation or inequality. S = Id² k for d
What is the first step in solving a formula like gw2 = kw + 24 for w?
Based on the discussion and examples of this section, give the first step to solve each equation. Do not actually solve. 3x=V16-10x
How can we determine the number of x-intercepts of the graph of a quadratic function without graphing the function?
In each exercise, the graph of a quadratic function ƒ is given. Use the graph to find the solution set of each equation or inequality. (a) 3x² + 10x8 = 0 (b) 3x²+ 10x - 8≥0 (c) 3x² + 10x -8
For the quadratic function ƒ(x) = a(x - h)2 + k, in what quadrant is the vertex if the values of h and k are as follows? (a) h> 0, k>0 (c) h0 (b) h> 0, k
Solve each equation using the square root property or completing the square. (3x - 2)² = -25
Decide whether the zero-factor property, the square root property, or the quadratic formula is most appropriate for solving each quadratic equation. Do not actually solve.2x2 + 3x = 1
A student incorrectly claimed that the equation 2x2 - 5 = 0 cannot be solved using the quadratic formula because there is no first-degree x-term. Give the values of a, b, and c for this equation.
Study this incorrect “solution.”Solution set: {4, -1} Give the correct solution set. x = √3x +4 x² = 3x + 4 x² 3x4=0 (x4) (x + 1) = 0 x -4 = 0 x = 4 or x + 1 = 0 or x = -1
Perform the indicated operations.Find 6% of 12.
Solve each equation or inequality. (8x-7)² ≥-1
Why is it particularly important to check all proposed solutions to an applied problem against the information in the original problem?
If the vertex of the graph of a quadratic function is (1, -3), and the graph opens down, how many x-intercepts does the graph have?
Solve each equation using the square root property or completing the square.x2 + 2x = 4
Decide whether the zero-factor property, the square root property, or the quadratic formula is most appropriate for solving each quadratic equation. Do not actually solve.3x2 = 2 - 5x
Use the quadratic formula to solve each equation. x2 - 8x + 15 = 0
Perform the indicated operations.Simplify 3 - 6(42 - 8).
Decide whether the zero-factor property, the square root property, or the quadratic formula is most appropriate for solving each quadratic equation. Do not actually solve.x2 = 5
In each exercise, the graph of a quadratic function ƒ is given. Use the graph to find the solution set of each equation or inequality. (a) x² + 3x + 10 = 0 (b) x² + 3x + 10 ≥ 0 (c) x² + 3x + 10 ≤0 F y 10 10 0. f(x) = -x² + 3x + 10 X
For each triangle, solve for m in terms of the other variables (where m > 0). m 90° n P
Which equations have a graph that is a vertical parabola? A horizontal parabola? A. y = -x² + 20x + 80 C. x + 1 = (y + 2)² B. x = 2y² + 6y + 5 D. f(x) = (x-4)²
Solve each equation using the square root property or completing the square. x² + 4x = 15
Identify the vertex of each parabola. f(x) = -3x²
LetList the elements of S that are elements of each set.(a) Integers (b) Rational numbers (c) Real numbers (d) Complex numbers 32 S = {-3, -2, -√3, 0, 0.7, V12, V−8, 7, 33³}.
Study this incorrect “solution.”Solution set:Give the correct solution set. 2(x - 1)² - 3(x-1) + 1 = 0 2u²3u + 1 = 0 (2u - 1)(u - 2u - 1 = 0 U 1) = 0 1 2 or u − 1 = 0 or u = 1
Solve each equation or inequality. 2x - √x = 6
Solve each equation using the quadratic formula.2x2 - 3x - 1 = 0
In each exercise, the graph of a quadratic function ƒ is given. Use the graph to find the solution set of each equation or inequality. (a) (b) (c) -3 2x² - x + 15 = 0 2x²-x+ 15 ≥ 0 2x² - x + 15 ≤ 0 10 .0 f(x) = -2x²-x + 15 X
For each triangle, solve for m in terms of the other variables (where m > 0). " ዘ 90° P
Identify the vertex of each parabola. f(x) = -4x²
Which of the equations in Exercise 5 represent functions?Data from in Exercise 5Which equations have a graph that is a vertical parabola? A horizontal parabola? A. y = -x² + 20x + 80 C. x + 1 = (y + 2)² B. x = 2y² + 6y + 5 D. f(x) = (x-4)²
Solve each equation using the square root property or completing the square. 2x²-3x = -1
Use the quadratic formula to solve each equation. x2 + 3x - 28 = 0
Solve each equation or inequality. x48x² = -1
Solve each equation or inequality. 7-(4+3t) + 2t = −6(t− 2) - 5
Solve each equation. Check the solutions. 14 x -= x - 5
Solve each inequality, and graph the solution set. (x + 1)(x - 5) > 0
Solve each equation using the quadratic formula.3t2 - 4t = -5
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