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Questions and Answers of College Algebra

Find the distance between each pair of points. (x + y, y) and (x - y, x)
Match each equation with the correct graph. (a) (x-3)² + (y-2)² = 25 (b) (x-3)² + (y + 2)² = 25 (c) (x + 3)² + (y-2)² = 25 (d) (x + 3)² + (y + 2)² = 25 A. C. 2 X B. D. 2 JIT ATT X
Find the equation of a circle satisfying the given conditions. Center: (-4, 3); radius: 2
A circle can be drawn on a piece of poster board by fastening one end of a string with a thumbtack, pulling the string taut with a pencil, and tracing a curve, as shown in the figure. Explain why
Find the equation of a circle satisfying the given conditions. Center: (0, 0); radius: 12
Find the equation of a circle satisfying the given conditions. Center: (0, 0); radius: 9
Find the equation of a circle satisfying the given conditions. Center: (-8,-5); radius: V5
Find the equation of a circle satisfying the given conditions. Center: (-12, 13); radius: V7
Graph each circle. Identify the center and the radius. (x+3)² + (y-2)² = 9
Graph each circle. Identify the center and the radius. (x - 2)² + (y - 3)² = 4
A Panasonic Smart Viera E50 LCD HDTV has a rectangular screen with a 36.5-in. width. Its height is 20.8 in. What is the length of the diagonal of the screen to the nearest tenth of an inch? 20.8
The length of the diagonal of a box is given bywhere L, W, and H are, respectively, the length, width, and height of the box. Find the length of the diagonal D of a box that is 4 ft long, 2 ft wide,
Graph each circle. Identify the center and the radius. 91 = z(+4) + z(I − x) -
In the study of sound, one version of the law of tensions isIf F1 = 300, F2 = 60, and ƒ2 = 260, find ƒ1 to the nearest unit. F₁ f₁ = √₂√√√ F₂²
Graph each circle. Identify the center and the radius. (x+4)² + (y + 1)² = 25
Graph each circle. Identify the center and the radius. x2 + y2 = 9
Graph each circle. Identify the center and the radius. x2 + y2 = 4
The illumination I, in foot-candles, produced by a light source is related to the distance d, in feet, from the light source by the equationwhere k is a constant. If k = 640, how far from the light
Tom owns a condominium in a high rise building on the shore of Lake Michigan, and has a beautiful view of the lake from his window. He discovered that he can find the number of miles to the horizon
Graph each circle. Identify the center and the radius. x2 + y2 = 16
Graph each circle. Identify the center and the radius. x2 + y2 = 25
Tom owns a condominium in a high rise building on the shore of Lake Michigan, and has a beautiful view of the lake from his window. He discovered that he can find the number of miles to the horizon
Heron’s formula for finding the area A of a triangle with sides a, b, and c iswhere s is the semi perimeter, andConsider the triangle, and work Exercises in order.The lengths of the sides of the
List all of the following sets to which each number belongs. A number may belong to more than one set.√2 real numbers pure imaginary numbers nonreal complex numbers complex numbers
Add or subtract as indicated. 7 t-2 6 12 t² - 2t 3 t
Multiply or divide as indicated. (8y - 16) - Зу - 6 10
Write each number as a product of a real number and i. Simplify all radical expressions. -V-196
Determine whether each equation represents direct, inverse, joint, or combined variation. y 6x st
Add or subtract as indicated. 5 x - 2 + 1 X + 2 x² - 2x
Graph the rational functionGive the equations of the vertical and horizontal asymptotes. f(x) = -2 x + 1
Multiply or divide as indicated. (y²-4). 8 2-y
Multiply or divide as indicated. (22 – 1) · 1 1-z
Multiply or divide as indicated. 4x 20 5x 2x 10 7x³
Add or subtract as indicated. 5x X x - 3 2 + X + 6 x² - 3x
Add or subtract as indicated. 3x x+1 + 4 x - 1 6 x² - 1
Multiply or divide as indicated. x³ + y³ 3 2x + 2y x² - y² 2x - 2y
Add or subtract as indicated. 5 x + 2 + 2 x² - 2x + 4 60 x³ + 8
Add or subtract as indicated. 3 2 x²5x + 6 x² - 4x + 4
Add or subtract as indicated. 3 x² + 4x + 4 + 7 x2+5x+6
Multiply or divide as indicated. a³ b3 a²2-b² 2a 2b 2a + 2b -
Multiply or divide as indicated. 8x³ - 27 2x + 6 2x² - 18 8x² + 12x + 18
Add or subtract as indicated. 2 m² - 4m + 4 + 3 m² + m - 6
Match each part of a rule for a special product in Column I with the part it equals in Column II. Assume that A and B represent positive real numbers. II A. x - y B. x + 2y√x + y² C. x - y² D. x
Match each expression in Column I with the equivalent choice in Column II.31/2 A. -4 C. √3 E. -3 G. 4 I. 6 II B. 8 D. -√6 F. √6 H. -2 J. Not a real number
Add or subtract as indicated. 5 x² + 6x + 9 2 x² + 4x + 3
Match each part of a rule for a special product in Column I with the part it equals in Column II. Assume that A and B represent positive real numbers. II A. x - y B. x + 2y√x + y² C. x - y² D. x
Find each square root. (a) √25 (b) √81 (c) √144
Match each expression in Column I with the equivalent choice in Column II.(-27)1/3 A. -4 C. √3 E. -3 G. 4 I. 6 II B. 8 D. -√6 F. √6 H. -2 J. Not a real number
Give the reason why each radical is not simplified. 2 5
Check each equation to see if the given value for x is a solution. √3x + 18 x = 0 (a) 6 (b) -3
Choose the correct response.Which difference can be simplified without first simplifying the individual radical expressions? A. √81 - V18 C. 47-97 B. 8-16 D. √75 - V12
List all of the following sets to which each number belongs. A number may belong to more than one set.-7i real numbers pure imaginary numbers nonreal complex numbers complex numbers
Match each part of a rule for a special product in Column I with the part it equals in Column II. Assume that A and B represent positive real numbers. II A. x - y B. x + 2y√x + y² C. x - y² D. x
List all of the following sets to which each number belongs. A number may belong to more than one set. real numbers pure imaginary numbers nonreal complex numbers complex numbers
Choose the correct response.Which sum can be simplified without first simplifying the individual radical expressions? A. V50 + V32 C. 32-√108 B. 3√6 +9√6 D. V6 - √192
Check each equation to see if the given value for x is a solution. V8x32x 3 2 (a) - (b) 2
Find each square root. (a) V0.25 (b) V0.81 (c) √1.44
Give the reason why each radical is not simplified. 15,
Choose the correct response.Which is the greatest perfect square factor of 128?A. 12 B. 16 C. 32 D. 64
When approximating √19 to three decimal places, a student incorrectly rounded as follows.Give the correct approximation. V 19 V19 4.358 ≈ 4.358898944
Match each expression in Column I with the equivalent choice in Column II.-161/2 A. -4 C. √3 E. -3 G. 4 I. 6 II B. 8 D. -√6 F. √6 H. -2 J. Not a real number
Check each equation to see if the given value for x is a solution. V3x - 3 - x + 1 = 0 - x 1 (a) 1 (b) 4
Choose the correct response.Which radical can be simplified? A. V21 B. V48 C. V12 D. V10
A student incorrectly gave the differenceHer teacher did not give her any credit for this answer. 28-4√2 as 24√2.
Give the reason why each radical is not simplified. 94XA
Check each equation to see if the given value for x is a solution. √x+2-√9x-2=-2√x-1 (a) 2 (b) 7
Match each expression in Column I with the equivalent choice in Column II.(-25)1/2 A. -4 C. √3 E. -3 G. 4 I. 6 II B. 8 D. -√6 F. √6 H. -2 J. Not a real number
Choose the correct response. Which radical cannot be simplified? A. V 30 B. 27a²b C. 25 81 D. 5/0 2
Give the reason why each radical is not simplified. 5 10
A student incorrectly claimed that √16 = 8. Evaluate √16 correctly.
Match each part of a rule for a special product in Column I with the part it equals in Column II. Assume that A and B represent positive real numbers. II A. x - y B. x + 2y√x + y² C. x - y² D. x
List all of the following sets to which each number belongs. A number may belong to more than one set. real numbers pure imaginary numbers nonreal complex numbers complex numbers
Match each expression in Column I with the equivalent choice in Column II.(-32)1/5 A. -4 C. √3 E. -3 G. 4 I. 6 II B. 8 D. -√6 F. √6 H. -2 J. Not a real number
Choose the correct response.Which one of the following is not equal to(Do not use calculator approximations.) 2|5 31
Choose the correct response. Which one of the following is not equal to√1/2? (Do not use calculator approximations.) A. V0.5 B. 4 C. 3 D. √4 V16
Add or subtract to simplify each radical expression. Assume that all variables represent positive real numbers. V36-V100
A student solved the following equation and claimed that 9 is a solution of the equation.He received no credit for his answer. Give the correct solution set. √x = -3
Match each part of a rule for a special product in Column I with the part it equals in Column II. Assume that A and B represent positive real numbers. II A. x - y B. x + 2y√x + y² C. x - y² D. x
Perform the indicated operations, and express each answer in simplest form. Assume that all variables represent positive real numbers. 6√10 - 12V/10
Match each expression in Column I with the equivalent choice in Column II. Answers may be used once, more than once, or not at all.-√16 A. 3 C. 2 E. -4 II B. -2 D. -3 F. Not a real number
Match each expression in Column I with the equivalent choice in Column II.(-32)2/5 A. -4 C. √3 E. -3 G. 4 I. 6 II B. 8 D. -√6 F. √6 H. -2 J. Not a real number
Add or subtract to simplify each radical expression. Assume that all variables represent positive real numbers. V25 - V81
List all of the following sets to which each number belongs. A number may belong to more than one set. real numbers pure imaginary numbers nonreal complex numbers complex numbers
Multiply, and then simplify each product. Assume that all variables represent positive real numbers. V6(3 + √2)
A student solved the following equation and obtained the proposed solutions x = -3 and x = 6.She gave { -3, 6} as the solution set. Give the correct solution set. V3x + 18 x =
Add or subtract to simplify each radical expression. Assume that all variables represent positive real numbers. 6√10+2√10
Decide whether each expression is equal to 1, -1, i, or -i. V-1
Match each expression in Column I with the equivalent choice in Column II. Answers may be used once, more than once, or not at all.√-16 A. 3 C. 2 E. -4 II B. -2 D. -3 F. Not a real number
Perform the indicated operations, and express each answer in simplest form. Assume that all variables represent positive real numbers. √(√7 -√₂)
Match each expression in Column I with the equivalent choice in Column II.43/2 A. -4 C. √3 E. -3 G. 4 I. 6 II B. 8 D. -√6 F. √6 H. -2 J. Not a real number
Perform the indicated operations, and express each answer in simplest form. Assume that all variables represent positive real numbers. (1-√3)(2 + √6)
A student multiplied incorrectly as follows.Give the correct product. V13. √5 || = V13.5 || = V65
Match each expression in Column I with the equivalent choice in Column II. Answers may be used once, more than once, or not at all.3√ -27 A. 3 C. 2 E. -4 II B. -2 D. -3 F. Not a real number
Solve each equation. Vx-2=3
Add or subtract to simplify each radical expression. Assume that all variables represent positive real numbers. 5√6 +4√6
Match each expression in Column I with the equivalent choice in Column II. Answers may be used once, more than once, or not at all.5√ -32 A. 3 C. 2 E. -4 II B. -2 D. -3 F. Not a real number
Multiply, and then simplify each product. Assume that all variables represent positive real numbers. V10(5 +√3) 5+
Match each expression in Column I with the equivalent choice in Column II.62/4 A. -4 C. √3 E. -3 G. 4 I. 6 II B. 8 D. -√6 F. √6 H. -2 J. Not a real number
Perform the indicated operations, and express each answer in simplest form. Assume that all variables represent positive real numbers. V50 V98+ V72
Solve each equation. Vx+1=7

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