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study help
mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
Let a and b represent real numbers.(a) What is the conjugate of a + bi?(b) If we multiply a + bi by its conjugate, we obtain ______+______ , which is always a real number.
Solve each formula for the specified variable. r = A 77 for A
Find the area of the trapezoid. Give the answer as a simplified radical. √24 in. √72 in. √288 in.
Simplify. Assume that all variables represent positive real numbers. V18m2
Simplify each root. √x15
Simplify each expression. Assume that all variables represent positive real numbers. 2:3/4 25/4.2-2
Divide. Give answers in standard form. 2 1-i
Find the equation of a circle satisfying the given conditions. Center (0, 0), r = 11
Solve each formula for the specified variable. V = 2K m for K
Find the perimeter of each triangle. y 0 (-3,-3) (2, 6).. TH (6,2) X
Find the distance between the points (-4, 7) and (10, 6).
Simplify. Assume that all variables represent positive real numbers. 9 3 32
Divide. Give answers in standard form. 2 1 + i
Simplify. Assume that all variables represent positive real numbers. √144x³y⁹
Simplify each expression. Assume that all variables represent positive real numbers. (x1/42/5) 20 x²
Find the equation of a circle satisfying the given conditions. Center (-2, 4), r = 3
Simplify. Assume that all variables represent positive real numbers. √169s5+10
Simplify each root. mº
Solve each formula for the specified variable. V = 2K m for m
Find the perimeter of each triangle. (-2,-4) y 0 (1, 3) ITTT (1,-2). FA X
Divide. Give answers in standard form. 8i 2 + 2i
Simplify each expression. Assume that all variables represent positive real numbers. p.² SI (ERS SA-¹) ST
Solve each formula for the specified variable. r = Mm F for M
Simplify. Assume that all variables represent positive real numbers. 12p 以
Simplify each root. √x30
Simplify. Assume that all variables represent positive real numbers. V121,6
Find the equation of a circle satisfying the given conditions. Center (-1, -3), r = 5 −1,
Simplify each expression. Assume that all variables represent positive real numbers. (x2/3)2 (x²) 7/3
Perform the indicated operations. Assume that all variables represent positive real numbers. 8√80-3√45
Divide. Give answers in standard form. -8i 1 + i
Perform the indicated operations. Assume that all variables represent positive real numbers. 2√8-3√50
Perform the indicated operations. Assume that all variables represent positive real numbers. -√27y + 2√75y
Perform the indicated operations. Assume that all variables represent positive real numbers. 2V54m³ +5V96m³
Perform the indicated operations. Assume that all variables represent positive real numbers. 3√54 +5√16
Multiply, and then simplify. (3√2+1)(2√2-3)
Perform the indicated operations. Assume that all variables represent positive real numbers. -6√32 + 512
Simplify. Assume that all variables represent positive real numbers. V13x7y8
Multiply, and then simplify. (√3+1)(√3-2)
Multiply, and then simplify. (√13-√2)²
Multiply, and then simplify. (√7+ √5)(√7 - √5)
Why does the equation x2 + y2 = -1 have no points on its graph?
Simplify. Assume that all variables represent positive real numbers. V64a¹5b12
Multiply, and then simplify. (6+ZAE-DA) (E+ZA)
Rationalize each denominator. Assume that all variables represent positive real numbers. E19- /2
Multiply, and then simplify. (4y - 1)(√4y + 3)
Rationalize each denominator. Assume that all variables represent positive real numbers. 31 7p Vy
Rationalize each denominator. Assume that all variables represent positive real numbers. 11 8
Rationalize each denominator. Assume that all variables represent positive real numbers. √6 √5
Rationalize each denominator. Assume that all variables represent positive real numbers. 1 √2+√7
Rationalize each denominator. Assume that all variables represent positive real numbers. -5 √6-3
Rationalize each denominator. Assume that all variables represent positive real numbers. 3 9 25
Write each quotient in lowest terms. 2-2V/5 8
Rationalize each denominator. Assume that all variables represent positive real numbers. 3 108m³ n³
Solve each equation. V8x + 9 = 5
Solve each equation. V2x-3-3=0
Write each quotient in lowest terms. -18 + V27 6
Solve each equation. 3√x - √10x-9 =
Solve each equation. x² + 3x + 7 = x + 2
Replace a with 3 and b with 4 to show that, in general, Va² + b² = a + b.
Solve each equation. √7x + 1 = x + 1
The following expression occurs in a standard problem in trigonometry.Show that it simplifies toThen verify, using a calculator approximation. 1 V2 √3 2 1 1 √2 2
Carpenters stabilize wall frames with a diagonal brace, as shown in the figure. The length of the brace is given bySolve this formula for H. L -W- H
Solve each equation. Vx+2- Vx-3 = 1
Solve each equation. 5x - 1 = W3x-2 -
Solve each equation. V1 - 2x -x 13 = 0 -
Solve each equation. Vr-1+2=0
Solve each equation. XZA=L+XA 2x
Carpenters stabilize wall frames with a diagonal brace, as shown in the figure. The length of the brace is given byIf the bottom of the brace is attached 9 ft from the corner and the brace is 12 ft long, how far up the corner post should it be nailed? Give the answer to the nearest tenth of a foot.
Simplify. Assume that all variables represent positive real numbers. EA ZA
In calculus, it is sometimes desirable to rationalize the numerator. To rationalize a numerator, we multiply the numerator and the denominator by the conjugate of the numerator. For example,Rationalize each numerator. Assume that all variables represent positive real numbers. 6-√2 (6-√2)(6+
Simplify. Assume that all variables represent positive real numbers. 3. V/4
Write each number as a product of a real number and i. Simplify. V-200
Simplify. Assume that all variables represent positive real numbers. XA. X^
Perform the indicated operations. Give answers in standard form. V-5. V-7
Perform the indicated operations. Give answers in standard form. -25. V-81
Perform the indicated operations. Give answers in standard form. √-72 V-8
Perform the indicated operations. Give answers in standard form. (-2+5i) + (-8-7i)
Perform the indicated operations. Give answers in standard form. (5+4i)(-9-3i)
Heron’s formula for finding the area A of a triangle with sides a, b, and c iswhere s is the semiperimeter, andConsider the triangle, and work Exercises in order.Use Heron’s formula to find the area of the entire triangle. Write it as a simplified radical. A = √s(sa) (s — b) (s — c), - -
Perform the indicated operations. Give answers in standard form. (6 - 2i)²
Perform the indicated operations. Give answers in standard form. (2 + 3i)(1 - i)
Perform the indicated operations. Give answers in standard form. 3-i 2+i
Find the equation of a circle satisfying the given conditions. Center: (5,-2); radius: 4
A student incorrectly solved the following equation as shown.Solve correctly and give the solution set. x² - x - 2 = 4 (x-2)(x + 1) = 4 or x + 1 = 4 or x = 3 x - 2 = 4 x = 6
Find the distance between each pair of points. (-2.9, 18.2) and (2.1, 6.2)
Find each power of i.i11
Find each power of i.i36
Find each power of i.i-10
Find each power of i.i-8
A student was asked to solve the quadratic equation x2 = 16 and did not get full credit for the solution set {4}. Give the correct solution set.
Use the zero-factor property to solve each equation.x2 + 3x + 2 = 0
Use the zero-factor property to solve each equation.x2 + 8x + 15 = 0
Use the zero-factor property to solve each equation.3x2 + 8x - 3 = 0
Use the zero-factor property to solve each equation.2x2 + x - 6 = 0
Use the zero-factor property to solve each equation.5x2 - 7x - 6 = 0
Use the zero-factor property to solve each equation.2x2 - 5x - 3 = 0
Use the zero-factor property to solve each equation.x2 - 6x = -8
Use the zero-factor property to solve each equation.x2 - 10x = -24
Use the zero-factor property to solve each equation.2x2 = 9x - 4
Use the zero-factor property to solve each equation.5x2 = 11x - 2
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