Elementary Algebra
17th Edition
ISBN: 9780998625713
Author: Lynn Marecek, MaryAnne Anthony-Smith
Publisher: OpenStax - Rice University
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Textbook Question
Chapter 10.3, Problem 134E
In the following exercises, determine the number of solutions to each
134.
(a) 25p2+10p+1=0
(b) 7q2−3q−6=0
(c) 7y2+2y+8=0
(d) 25z2−60z+36=0
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Chapter 10 Solutions
Elementary Algebra
Ch. 10.1 - Solve: x2=81 .Ch. 10.1 - Solve: y2=121 .Ch. 10.1 - Solve: x250=0 .Ch. 10.1 - Solve: y227=0 .Ch. 10.1 - Solve: 2x2=98 .Ch. 10.1 - Solve: 3z2=108 .Ch. 10.1 - Solve: c2+12=0 .Ch. 10.1 - Solve: d2+81=0 .Ch. 10.1 - Solve: 12x2+4=24 .Ch. 10.1 - Solve: 34y23=18 .
Ch. 10.1 - Solve: 5r22=34 .Ch. 10.1 - Solve: 3t2+6=70 .Ch. 10.1 - Solve: (q+5)2=1 .Ch. 10.1 - Solve: (r3)2=25 .Ch. 10.1 - Solve: (a3)2=18 .Ch. 10.1 - Solve: (b+2)2=40 .Ch. 10.1 - Solve: (x13)2=59 .Ch. 10.1 - Solve: (y34)2=716 .Ch. 10.1 - Solve: (a5)2+4=24 .Ch. 10.1 - Solve: (b3)28=24 .Ch. 10.1 - Solve: (3r+4)2=8 .Ch. 10.1 - Solve: (3r+4)2=8 .Ch. 10.1 - Solve: x26x+9=12 .Ch. 10.1 - Solve: y2+12y+36=32 .Ch. 10.1 - Solve: 9m212m+4=25 .Ch. 10.1 - Solve: 16n2+40n+25=4 .Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve the following...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - In the following exercises, solve using the Square...Ch. 10.1 - Paola has enough mulch to cover 48 square feet....Ch. 10.1 - Kathy is drawing up the blueprints for a house she...Ch. 10.1 - Explain why the equation x2+12=8 has no solution.Ch. 10.1 - Explain why the equation y2+8=12 has two...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Complete the square to make a perfect square...Ch. 10.2 - Solve c2+4c=5 by completing the square.Ch. 10.2 - Solve d2+10d=9 by completing the square.Ch. 10.2 - Solve r24r=12 by completing the square.Ch. 10.2 - Solve t210t=11 by completing the square.Ch. 10.2 - Solve y210y=35 by completing the square.Ch. 10.2 - Solve z2+8z=19 by completing the square.Ch. 10.2 - Solve x216x=16 by completing the square.Ch. 10.2 - Solve y2+8y=11 by completing the square.Ch. 10.2 - Solve a2+4a+9=30 by completing the square.Ch. 10.2 - Solve b2+8b4=16 by completing the square.Ch. 10.2 - Solve p2=5p+9 by completing the square.Ch. 10.2 - Solve q2=7q3 by completing the square.Ch. 10.2 - Solve (c2)(c+8)=7 by completing the square.Ch. 10.2 - Solve (d7)(d+3)=56 by completing the square.Ch. 10.2 - Solve 2m2+16m8=0 by completing the square.Ch. 10.2 - Solve 4n224n56=8 by completing the square.Ch. 10.2 - Solve 3r22r=21 by completing the square.Ch. 10.2 - Solve 4t2+2t=20 by completing the square.Ch. 10.2 - Solve 4x2+3x=12 by completing the square.Ch. 10.2 - Solve 5y2+3y=10 by completing the square.Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, complete the square to...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - In the following exercises, solve by completing...Ch. 10.2 - 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Solve b2+10b+24=0 by using the Quadratic Formula.Ch. 10.3 - Solve 2p2+8p+5=0 by using the Quadratic Formula.Ch. 10.3 - Solve 5q211q+3=0 by using the Quadratic Formula.Ch. 10.3 - Solve 3m2+12m+7=0 by using the Quadratic Formula.Ch. 10.3 - Solve 5n2+4n4=0 by using the Quadratic Formula.Ch. 10.3 - Solve 4a23a+8=0 by using the Quadratic Formula.Ch. 10.3 - Solve 5b2+2b+4=0 by using the Quadratic Formula.Ch. 10.3 - Solve x(x+2)5=0 by using the Quadratic Formula.Ch. 10.3 - Solve y(3y1)2=0 by using the Quadratic Formula.Ch. 10.3 - Solve 14c213c=112 by using the Quadratic Formula.Ch. 10.3 - Solve 19d212d=12 by using the Quadratic Formula.Ch. 10.3 - Solve r2+10r+25=0 by using the Quadratic Formula.Ch. 10.3 - Solve 25t240t=16 by using the Quadratic Formula.Ch. 10.3 - Determine the number of solutions to each...Ch. 10.3 - Determine the number of solutions to each...Ch. 10.3 - Identify the most appropriate method to use to...Ch. 10.3 - Identify the most appropriate method to use to...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - In the following exercises, solve by using the...Ch. 10.3 - 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In the following exercises, determine the number...Ch. 10.3 - In the following exercises, identify the most...Ch. 10.3 - In the following exercises, identify the most...Ch. 10.3 - In the following exercises, identify the most...Ch. 10.3 - In the following exercises, identify the most...Ch. 10.3 - A flare is fired straight up from a ship at sea....Ch. 10.3 - An architect is designing a hotel lobby. She wants...Ch. 10.3 - Solve the equation x2+10x=200 (a) by completing...Ch. 10.3 - Solve the equation 12y2+23y=24 (a) by completing...Ch. 10.4 - The product of two consecutive odd integers is 99....Ch. 10.4 - The product of two consecutive odd integers is...Ch. 10.4 - Find the dimensions of a triangle whose width is...Ch. 10.4 - If a triangle that has an area of 110 square feet...Ch. 10.4 - The sun casts a shadow from a flag pole. The...Ch. 10.4 - The distance between opposite corners of a...Ch. 10.4 - The length of a 200 square foot rectangular...Ch. 10.4 - A rectangular tablecloth has an area of 80 square...Ch. 10.4 - An arrow is shot from the ground into the air at...Ch. 10.4 - A man throws a ball into the air with a velocity...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - In the following exercises, solve by using methods...Ch. 10.4 - 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Find the intercepts of the parabola y=x24x5 .Ch. 10.5 - Find the intercepts of the parabola y=x212x36 .Ch. 10.5 - Find the intercepts of the parabola y=9x2+12x+4 .Ch. 10.5 - Graph the parabola y=x2+2x8 .Ch. 10.5 - Graph the parabola y=x28x+12 .Ch. 10.5 - Graph the parabola y=3x2+12x12 .Ch. 10.5 - Graph the parabola y=25x2+10x+1 .Ch. 10.5 - Graph the parabola y=2x26x+5 .Ch. 10.5 - Graph the parabola y=2x21 .Ch. 10.5 - Graph the parabola y=5x2+10x+3 .Ch. 10.5 - Graph the parabola y=3x26x+5 .Ch. 10.5 - Find the maximum or minimum value of the quadratic...Ch. 10.5 - Find the maximum or minimum value of the quadratic...Ch. 10.5 - The quadratic equation h=16t2+128t+32 is used to...Ch. 10.5 - A toy rocket shot upward from the ground at a rate...Ch. 10.5 - In the following exercises, graph: 163. y=x2+3Ch. 10.5 - In the following exercises, graph: 164. y=x2+1Ch. 10.5 - In the following exercises, determine if the...Ch. 10.5 - In the following exercises, determine if the...Ch. 10.5 - In the following exercises, determine if the...Ch. 10.5 - 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Use any...Ch. 10 - Use the discriminant to determine the number of...Ch. 10 - Use the discriminant to determine the number of...Ch. 10 - Solve by factoring, the Square Root Property, or...Ch. 10 - Solve by factoring, the Square Root Property, or...Ch. 10 - For each parabola, find (a) which ways it opens,...Ch. 10 - For each parabola, find (a) which ways it opens,...Ch. 10 - For each parabola, find (a) which ways it opens,...Ch. 10 - For each parabola, find (a) which ways it opens,...Ch. 10 - For each parabola, find (a) which ways it opens,...Ch. 10 - Graph the following parabolas by using intercepts,...Ch. 10 - Graph the following parabolas by using intercepts,...Ch. 10 - Solve. 342. A water balloon is launched upward at...
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- ************* ********************************* Q.1) Classify the following statements as a true or false statements: a. If M is a module, then every proper submodule of M is contained in a maximal submodule of M. b. The sum of a finite family of small submodules of a module M is small in M. c. Zz is directly indecomposable. d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M. e. The Z-module has two composition series. Z 6Z f. Zz does not have a composition series. g. Any finitely generated module is a free module. h. If O→A MW→ 0 is short exact sequence then f is epimorphism. i. If f is a homomorphism then f-1 is also a homomorphism. Maximal C≤A if and only if is simple. Sup Q.4) Give an example and explain your claim in each case: Monomorphism not split. b) A finite free module. c) Semisimple module. d) A small submodule A of a module N and a homomorphism op: MN, but (A) is not small in M.arrow_forwardI need diagram with solutionsarrow_forwardT. Determine the least common denominator and the domain for the 2x-3 10 problem: + x²+6x+8 x²+x-12 3 2x 2. Add: + Simplify and 5x+10 x²-2x-8 state the domain. 7 3. Add/Subtract: x+2 1 + x+6 2x+2 4 Simplify and state the domain. x+1 4 4. Subtract: - Simplify 3x-3 x²-3x+2 and state the domain. 1 15 3x-5 5. Add/Subtract: + 2 2x-14 x²-7x Simplify and state the domain.arrow_forward
- Q.1) Classify the following statements as a true or false statements: Q a. A simple ring R is simple as a right R-module. b. Every ideal of ZZ is small ideal. very den to is lovaginz c. A nontrivial direct summand of a module cannot be large or small submodule. d. The sum of a finite family of small submodules of a module M is small in M. e. The direct product of a finite family of projective modules is projective f. The sum of a finite family of large submodules of a module M is large in M. g. Zz contains no minimal submodules. h. Qz has no minimal and no maximal submodules. i. Every divisible Z-module is injective. j. Every projective module is a free module. a homomorp cements Q.4) Give an example and explain your claim in each case: a) A module M which has a largest proper submodule, is directly indecomposable. b) A free subset of a module. c) A finite free module. d) A module contains no a direct summand. e) A short split exact sequence of modules.arrow_forwardListen ANALYZING RELATIONSHIPS Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) <0. y Af -2 1 2 4x a. The function is increasing when and decreasing whenarrow_forwardBy forming the augmented matrix corresponding to this system of equations and usingGaussian elimination, find the values of t and u that imply the system:(i) is inconsistent.(ii) has infinitely many solutions.(iii) has a unique solutiona=2 b=1arrow_forward
- if a=2 and b=1 1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2 2)Find a matrix C such that (B − 2C)-1=A 3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)arrow_forwardWrite the equation line shown on the graph in slope, intercept form.arrow_forward1.2.15. (!) Let W be a closed walk of length at least 1 that does not contain a cycle. Prove that some edge of W repeats immediately (once in each direction).arrow_forward
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