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Elementary Algebra 2e

Review Exercises

Elementary Algebra 2eReview Exercises
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Key Terms
    13. Key Concepts
    14. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Key Terms
    12. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index

Review Exercises

10.1 Solve Quadratic Equations Using the Square Root Property

In the following exercises, solve using the Square Root Property.

213.

x2=100x2=100

214.

y2=144y2=144

215.

m240=0m240=0

216.

n280=0n280=0

217.

4a2=1004a2=100

218.

2b2=722b2=72

219.

r2+32=0r2+32=0

220.

t2+18=0t2+18=0

221.

43v2+4=2843v2+4=28

222.

23w220=3023w220=30

223.

5c2+3=195c2+3=19

224.

3d26=433d26=43

In the following exercises, solve using the Square Root Property.

225.

(p5)2+3=19(p5)2+3=19

226.

(q+4)2=9(q+4)2=9

227.

(u+1)2=45(u+1)2=45

228.

(z5)2=50(z5)2=50

229.

(x14)2=316(x14)2=316

230.

(y23)2=29(y23)2=29

231.

(m7)2+6=30(m7)2+6=30

232.

(n4)250=150(n4)250=150

233.

(5c+3)2=−20(5c+3)2=−20

234.

(4c1)2=−18(4c1)2=−18

235.

m26m+9=48m26m+9=48

236.

n2+10n+25=12n2+10n+25=12

237.

64a2+48a+9=8164a2+48a+9=81

238.

4b228b+49=254b228b+49=25

10.2 Solve Quadratic Equations Using Completing the Square

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

239.

x2+22xx2+22x

240.

y2+6yy2+6y

241.

m28mm28m

242.

n210nn210n

243.

a23aa23a

244.

b2+13bb2+13b

245.

p2+45pp2+45p

246.

q213qq213q

In the following exercises, solve by completing the square.

247.

c2+20c=21c2+20c=21

248.

d2+14d=−13d2+14d=−13

249.

x24x=32x24x=32

250.

y216y=36y216y=36

251.

r2+6r=−100r2+6r=−100

252.

t212t=−40t212t=−40

253.

v214v=−31v214v=−31

254.

w220w=100w220w=100

255.

m2+10m4=−13m2+10m4=−13

256.

n26n+11=34n26n+11=34

257.

a2=3a+8a2=3a+8

258.

b2=11b5b2=11b5

259.

(u+8)(u+4)=14(u+8)(u+4)=14

260.

(z10)(z+2)=28(z10)(z+2)=28

261.

3p218p+15=153p218p+15=15

262.

5q2+70q+20=05q2+70q+20=0

263.

4y26y=44y26y=4

264.

2x2+2x=42x2+2x=4

265.

3c2+2c=93c2+2c=9

266.

4d22d=84d22d=8

10.3 Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

267.

4x25x+1=04x25x+1=0

268.

7y2+4y3=07y2+4y3=0

269.

r2r42=0r2r42=0

270.

t2+13t+22=0t2+13t+22=0

271.

4v2+v5=04v2+v5=0

272.

2w2+9w+2=02w2+9w+2=0

273.

3m2+8m+2=03m2+8m+2=0

274.

5n2+2n1=05n2+2n1=0

275.

6a25a+2=06a25a+2=0

276.

4b2b+8=04b2b+8=0

277.

u(u10)+3=0u(u10)+3=0

278.

5z(z2)=35z(z2)=3

279.

18p215p=12018p215p=120

280.

25q2+310q=11025q2+310q=110

281.

4c2+4c+1=04c2+4c+1=0

282.

9d212d=−49d212d=−4

In the following exercises, determine the number of solutions to each quadratic equation.

283.
  1. 9x26x+1=09x26x+1=0
  2. 3y28y+1=03y28y+1=0
  3. 7m2+12m+4=07m2+12m+4=0
  4. 5n2n+1=05n2n+1=0
284.
  1. 5x27x8=05x27x8=0
  2. 7x210x+5=07x210x+5=0
  3. 25x290x+81=025x290x+81=0
  4. 15x28x+4=015x28x+4=0

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation.

285.
  1. 16r28r+1=016r28r+1=0
  2. 5t28t+3=95t28t+3=9
  3. 3(c+2)2=153(c+2)2=15
286.
  1. 4d2+10d5=214d2+10d5=21
  2. 25x260x+36=025x260x+36=0
  3. 6(5v7)2=1506(5v7)2=150
10.4 Solve Applications Modeled by Quadratic Equations

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.

287.

Find two consecutive odd numbers whose product is 323.

288.

Find two consecutive even numbers whose product is 624.

289.

A triangular banner has an area of 351 square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and length of the base.

290.

Julius built a triangular display case for his coin collection. The height of the display case is six inches less than twice the width of the base. The area of the of the back of the case is 70 square inches. Find the height and width of the case.

291.

A tile mosaic in the shape of a right triangle is used as the corner of a rectangular pathway. The hypotenuse of the mosaic is 5 feet. One side of the mosaic is twice as long as the other side. What are the lengths of the sides? Round to the nearest tenth.

The image shows a rectangular pathway with a right inlaid in the lower left corner. The right angle of the triangle overlays the lower left corner of the rectangle. The left leg of the right triangle overlays the left side of the rectangle and the hypotenuse of the right triangle runs from the upper left corner of the rectangle to a point on the bottom of the rectangle.
292.

A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice the width. What is the length of the plywood’s diagonal? Round to the nearest tenth.

293.

The front walk from the street to Pam’s house has an area of 250 square feet. Its length is two less than four times its width. Find the length and width of the sidewalk. Round to the nearest tenth.

294.

For Sophia’s graduation party, several tables of the same width will be arranged end to end to give a serving table with a total area of 75 square feet. The total length of the tables will be two more than three times the width. Find the length and width of the serving table so Sophia can purchase the correct size tablecloth. Round answer to the nearest tenth.

The image shows four rectangular tables placed side by side to create one large table.
295.

A ball is thrown vertically in the air with a velocity of 160 ft/sec. Use the formula h=−16t2+v0th=−16t2+v0t to determine when the ball will be 384 feet from the ground. Round to the nearest tenth.

296.

A bullet is fired straight up from the ground at a velocity of 320 ft/sec. Use the formula h=−16t2+v0th=−16t2+v0t to determine when the bullet will reach 800 feet. Round to the nearest tenth.

10.5 Graphing Quadratic Equations in Two Variables

In the following exercises, graph by plotting point.

297.

Graph y=x22y=x22

298.

Graph y=x2+3y=x2+3

In the following exercises, determine if the following parabolas open up or down.

299.

y=−3x2+3x1y=−3x2+3x1

300.

y=5x2+6x+3y=5x2+6x+3

301.

y=x2+8x1y=x2+8x1

302.

y=−4x27x+1y=−4x27x+1

In the following exercises, find the axis of symmetry and the vertex.

303.

y=x2+6x+8y=x2+6x+8

304.

y=2x28x+1y=2x28x+1

In the following exercises, find the x- and y-intercepts.

305.

y=x24x+5y=x24x+5

306.

y=x28x+15y=x28x+15

307.

y=x24x+10y=x24x+10

308.

y=−5x230x46y=−5x230x46

309.

y=16x28x+1y=16x28x+1

310.

y=x2+16x+64y=x2+16x+64

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

311.

y=x2+8x+15y=x2+8x+15

312.

y=x22x3y=x22x3

313.

y=x2+8x16y=x2+8x16

314.

y=4x24x+1y=4x24x+1

315.

y=x2+6x+13y=x2+6x+13

316.

y=−2x28x12y=−2x28x12

317.

y=−4x2+16x11y=−4x2+16x11

318.

y=x2+8x+10y=x2+8x+10


In the following exercises, find the minimum or maximum value.

319.

y=7x2+14x+6y=7x2+14x+6

320.

y=−3x2+12x10y=−3x2+12x10

In the following exercises, solve. Rounding answers to the nearest tenth.

321.

A ball is thrown upward from the ground with an initial velocity of 112 ft/sec. Use the quadratic equation h=−16t2+112th=−16t2+112t to find how long it will take the ball to reach maximum height, and then find the maximum height.

322.

A daycare facility is enclosing a rectangular area along the side of their building for the children to play outdoors. They need to maximize the area using 180 feet of fencing on three sides of the yard. The quadratic equation A=−2x2+180xA=−2x2+180x gives the area, AA, of the yard for the length, xx, of the building that will border the yard. Find the length of the building that should border the yard to maximize the area, and then find the maximum area.

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