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mathematics
precalculus
Precalculus Concepts Through Functions A Unit Circle Approach To Trigonometry 5th Edition Michael Sullivan - Solutions
In Problems 77 – 82, determine where each rational function R is undefined. Determine whether an asymptote or a hole appears in the graph of R at such numbers. R(x) = x³ + 2x² + x x4 + x³ + 2x + 2 3
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x+4)²
In Problems 77–92, simplify each expression. 163/4
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (3x + y)(3x - y)
In Problems 75–86, perform the indicated operations and simplify the result. Leave your answer in factored form. x 2 x - 1 + x + 2 x + 1 x+1 2x3 X
On an exam, Jane solved the equation √2x + 3 − x = 0 and wrote that the solution set was {−1, 3}. Jane received 3 out of 5 points for the problem. Jane asks you why she received 3 out of 5 points. Provide an explanation.
In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. 2- 8x² 2
In Problems 11 – 68, solve each equation. 2 y + 3 + 3 y - 4 || 5 y + 6
In Problems 61–72, factor each polynomial.3x2 + 2x − 8
Use z = a + bi to show that z + z̅ = 2a and that z − z̅ = 2bi.
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3x - 1 2 3 +x
In Problems 59–68, find the value of each expression if x = 3 and y = −2. 14x - 5y|
In Problems 55–68, rationalize the denominator of each expression. Assume that all variables are positive when they appear. 5 32
In Problems 63–74, perform the indicated operations and simplify the result. Leave your answer in factored form. 3x x - 1 x - 4 18 x² - 2x + 1 2
In Problems 61 – 72, find the numbers at which f is continuous. At which numbers is f discontinuous?f (x) = −2 cos x
In Problems 11 – 68, solve each equation. 5 5z - 11 + 4 2z - 3 -3 5 - z
In Problems 49 – 66, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.(x − 3y)(−2x + y)
Use z = a + bi to show that = Z.
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2x2 3 + x
In Problems 61–72, factor each polynomial.3x2 + 10x + 8
In Problems 55–68, rationalize the denominator of each expression. Assume that all variables are positive when they appear. دریا
In Problems 59–68, find the value of each expression if x = 3 and y = −2. |3x + 2yl
In Problems 63–74, perform the indicated operations and simplify the result. Leave your answer in factored form. 3 + (x - 1)²(x + 1) 2 (x - 1)(x + 1)²
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x-7)(x + 7)
Use z = a + bi and w = c + di to show that z + w = Z + w.
In Problems 11 – 68, solve each equation. x² - 1 x + 3 x2 x² - x -3 x² + x
In Problems 61 – 72, find the numbers at which f is continuous. At which numbers is f discontinuous?f (x) = 2 tan x
In Problems 61–72, factor each polynomial.3x2 − 2x − 8
In Problems 63–74, perform the indicated operations and simplify the result. Leave your answer in factored form. 1 X 2 x + zx + 3 x3x²
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 글(x - 4) > x +8
In Problems 61–72, factor each polynomial.3x2 + 10x − 8
In Problems 69–76, rationalize the numerator of each expression. Assume that all variables are positive when they appear. √6-√15 √15
In Problems 61 – 72, find the numbers at which f is continuous. At which numbers is f discontinuous? f(x) = In x x - 3
Research the origins of complex numbers. Write a paragraph describing what you find, and present it to the class.
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + 5)²
In Problems 63–74, perform the indicated operations and simplify the result. Leave your answer in factored form. (x - 1)² 2 2 + X x + 1 -3 x³ - x2
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 1 3x +4>(x-2)
In Problems 69–76, rationalize the numerator of each expression. Assume that all variables are positive when they appear. √5 + √3 √5
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x-4)²
In Problems 63–74, perform the indicated operations and simplify the result. Leave your answer in factored form. 1 h\x + h I X
In Problems 61–72, factor each polynomial.3x2 − 10x − 8
A student multiplied √−9 and √−9 as follows:The instructor marked the problem incorrect. Why? -9. -9 = (-9)(-9) = 81 = 9
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. X IV 1 X 4
In Problems 73–78, determine what number should be added to complete the square of each expression. Then factor each expression.x2 + 10x
In Problems 69–76, rationalize the numerator of each expression. Assume that all variables are positive when they appear. x - c X-C X C
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. X > 2+ X 6
In Problems 63–74, perform the indicated operations and simplify the result. Leave your answer in factored form. 1 h[(x 1 2 + h)²
In Problems 69–76, determine which of the values (a) through (d), if any, must be excluded from the domain of the variable in each expression.(a) x = 3(b) x = 1(c) x = 0(d) x = −1 了 x2-1
In Problems 69–76, rationalize the numerator of each expression. Assume that all variables are positive when they appear. t = x x-4 √x-2
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (3x + 4)(3x - 4)
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (5x3)(5x + 3)
In Problems 75–86, perform the indicated operations and simplify the result. Leave your answer in factored form. 4 + 3- +2 al 1 +2
A civil engineer relates the thickness T, in inches, and the height H, in feet, of a square wooden pillar to its crushing load L, in tons, using the modelIf a square wooden pillar is 4 inches thick and 10 feet high, what is its crushing load? T = LH2 25
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 4≤ 2x + 2 ≤ 10
In Problems 69–76, rationalize the numerator of each expression. Assume that all variables are positive when they appear. 4-√√x-9 x - 25 x = 25
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (2x - 3)²
In Problems 75–86, perform the indicated operations and simplify the result. Leave your answer in factored form. 2 3+ x + 1 X x - 1 x + 1
The period of a pendulum is the time it takes the pendulum to make one full swing back and forth. The period T, in seconds, is given by the formulawhere l is the length, in feet, of the pendulum. In 1851, Jean-Bernard-Leon Foucault demonstrated the axial rotation of Earth using a large pendulum
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -5 ≤ 4-3x < 2
In Problems 77–92, simplify each expression. 82/3
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -3 ≤ 3-2x ≤ 9
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (3x - 4)2
In Problems 75–86, perform the indicated operations and simplify the result. Leave your answer in factored form. 1- 2- x x+1 x-1 X
In Problems 73–78, determine what number should be added to complete the square of each expression. Then factor each expression. X x2 + 3 X
In Problems 77–92, simplify each expression. 43/2
In Problems 77 – 82, determine where each rational function R is undefined. Determine whether an asymptote or a hole appears in the graph of R at such numbers. R(x) - x³ 2x² + 4x - 8 x²+x-6 -
In Problems 77–92, simplify each expression. (-27)¹/3
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + y)(x - y)
In Problems 75–86, perform the indicated operations and simplify the result. Leave your answer in factored form. x + 4 2 x x 3 x + 1 x + 1
In Problems 77 – 82, determine where each rational function R is undefined. Determine whether an asymptote or a hole appears in the graph of R at such numbers. R(x) = x³ - x² + 3x x² + 3x - 4 -
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. -3 < 2x-1
Make up a radical equation that has no solution.
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + 3y)(x - 3y)
In Problems 75–86, perform the indicated operations and simplify the result. Leave your answer in factored form. x 2 x + 1 x x-2 x + 3
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 0 < 3x + 2 < 4 2
Make up a radical equation that has an extraneous solution.
Discuss the step in the solving process for radical equations that leads to the possibility of extraneous solutions. Why is there no such possibility for linear and quadratic equations?
In Problems 67 – 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x - 5)²
The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until a sound is heard. If t1 is the time (measured in seconds) that it takes for the object to strike the water, then t1 will obey the equation s = 16t12,
In Problems 75–86, perform the indicated operations and simplify the result. Leave your answer in factored form. 1 + 1. X X
In Problems 59–94, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 0 2x6 ≤ 4
In Problems 69–76, determine which of the values (a) through (d), if any, must be excluded from the domain of the variable in each expression.(a) x = 3(b) x = 1(c) x = 0(d) x = −1 x2 + 5x – 10 x3 -
In Problems 69–76, rationalize the numerator of each expression. Assume that all variables are positive when they appear. √x-7-1 x - 8 x = 8
In Problems 73 – 76, discuss whether R is continuous at each number c. Use limits to analyze the graph of R at c. Graph R. R(x) = x² + 4x 16' x² c = -4 and c = 4 =
In Problems 49–58, perform the indicated operations and express your answer in the form a + bi. √-12
In Problems 11 – 68, solve each equation. √3t + 4 = 2
In Problems 43–48, use a graphing utility to investigate the indicated limit. Round answers to two decimal places. x³ lim x³ x3 x4 3x² + 4x - 12 3x³ + x - 3
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. 2 x + 5 5 x-5
In Problems 41–58, fill in the blank(s) to form a correct inequality statement. If x > 2, then-4x. 8.
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 2 (√x + √5)²
In Problems 45–50, use the given real number line to compute each distance.d(C, E) A B C I -4 -3 -2 -1 0 I D I 1 I 2 E | 3 I 4 5 I 6
In Problems 11 – 68, solve each equation. 3t + 4 -6
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. X x + 1 + 2x3 x - 1
In Problems 41–58, fill in the blank(s) to form a correct inequality statement. If x 5, then - 4x - 20.
In Problems 29 – 48, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form.(2x − 3)(x2 + x + 1)
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 16x4 - 2x
In Problems 11 – 68, solve each equation. √5t + 3 = -2
In Problems 43 – 54, factor each polynomial.x2 + 11x + 10
In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. 3x x - 4 + 2x x + 3
In Problems 41–58, fill in the blank(s) to form a correct inequality statement. If x-4, then-3x 12.
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