Beginning and Intermediate Algebra - Wallace Math Courses ...

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Use dimensional analysis to solve the following: 19) On a recent trip, Jan traveled 260 miles using 8 gallons of gas. How many miles per 1-gallon did she travel? How many yards per 1-ounce? 20) A chair lift at the Divide ski resort in Cold Springs, WY is 4806 feet long and takes 9 minutes. What is the average speed in miles per hour? How many feet per second does the lift travel? 21) A certain laser printer can print 12 pages per minute. Determine this printer’s output in pages per day, and reams per month. (1 ream = 5000 pages) 22) An average human heart beats 60 times per minute. If an average person lives to the age of 75, how many times does the average heart beat in a lifetime? 23) Blood sugar levels are measured in miligrams of gluclose per deciliter of blood volume. If a person’s blood sugar level measured 128 mg/dL, how much is this in grams per liter? 24) You are buying carpet to cover a room that measures 38 ft by 40 ft. The carpet cost S18 per square yard. How much will the carpet cost? 25) A car travels 14 miles in 15 minutes. How fast is it going in miles per hour? in meters per second? 26) A cargo container is 50 ft long, 10 ft wide, and 8 ft tall. Find its volume in cubic yards and cubic meters. 27) A local zoning ordinance says that a house’s “footprint” (area of its ground floor) cannot occupy more than 1 of the lot it is built on. Suppose you own a 4 1 acre lot, what is the maximum allowed footprint for your house in square 3 feet? in square inches? (1 acre = 43560 ft2 ) 28) Computer memory is measured in units of bytes, where one byte is enough memory to store one character (a letter in the alphabet or a number). How many typical pages of text can be stored on a 700-megabyte compact disc? Assume that one typical page of text contains 2000 characters. (1 megabyte = 1,000,000 bytes) 29) In April 1996, the Department of the Interior released a “spike flood” from the Glen Canyon Dam on the Colorado River. Its purpose was to restore the river and the habitants along its bank. The release from the dam lasted a week at a rate of 25,800 cubic feet of water per second. About how much water was released during the 1-week flood? 30) The largest single rough diamond ever found, the Cullinan diamond, weighed 3106 carats; how much does the diamond weigh in miligrams? in pounds? (1 carat - 0.2 grams) 286
Chapter 8 : Radicals 8.1 Square Roots ..........................................................................................288 8.2 Higher Roots ..........................................................................................292 8.3 Adding Radicals .....................................................................................295 8.4 Multiply and Divide Radicals ................................................................298 8.5 Rationalize Denominators ......................................................................303 8.6 Rational Exponents ................................................................................310 8.7 Radicals of Mixed Index .........................................................................314 8.8 Complex Numbers ..................................................................................318 287
Page 1 and 2:
Beginning and Intermediate Algebra
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Special thanks to: My beautiful wif
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Chapter 6: Factoring 6.1 Greatest C
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0.1 Pre-Algebra - Integers Objectiv
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Multiplication and division of inte
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45) (4)( − 6) Find each quotient.
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9 ÷ 3 3 = 21 ÷ 3 7 Our Soultion T
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Example 21. 13 6 − 9 6 4 6 2 3 Sa
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Find each quotient. 37) − 2 ÷ 7
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the expression that is to be evalua
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Solve. 1) − 6 · 4( − 1) 3) 3+(
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It will be more common in our study
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0.4 Practice - Properties of Algebr
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Chapter 1 : Solving Linear Equation
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Addition Problems To solve equation
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8x = − 24 8 8 x = − 3 Division
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1.2 Linear Equations - Two-Step Equ
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− 1 − 1 Divide both sides by
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1.3 Solving Linear Equations - Gene
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Example 63. − 3x +9=6x − 27 Not
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4[ − 2]+9=−15 +8(2) Finish mult
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1.4 Solving Linear Equations - Frac
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Example 72. � � 3 5 4 x + = 3 2
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1.5 Solving Linear Equations - Form
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Example 79. A = πr 2 +πrs for s S
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1.5 Practice - Formulas Solve each
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|x| = 5 Absolute value can be posit
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Example 90. 7+|2x − 5| =4 Notice
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1.7 Solving Linear Equations - Vari
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Once we have found the constant of
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1.7 Practice - Variation Write the
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sure. If the pressure of a certain
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Fifteen more than three times a num
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When we started with our first, sec
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1.8 Practice - Number and Geometry
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30. The perimeter of a college bask
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Our equation comes from the future
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4x + 2=102 Solve the two − step e
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years ago, the bronze plaque was on
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1.10 Solving Linear Equations - Dis
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Rate Time Distance Bob r + 2 3 Fred
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2 =t Our solution fort, she catches
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Find the distance he rode. 8. A man
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The first plan is flying 25 mph slo
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2.1 Graphing - Points and Lines Obj
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E B D F G C A Our Solution The main
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x y − 3 − 4 0 − 2 3 0 Our com
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2.2 Graphing - Slope Objective: Fin
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When mathematicians began working w
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Example 131. Find the value of x be
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9) 10) Find the slope of the line t
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y = − 2 x + 3 Our Solution 3 Iden
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2.3 Practice - Slope-Intercept Writ
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2.4 Graphing - Point-Slope Form Obj
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Find the equation of the line throu
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Write the point-slope form of the e
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m = 2 5 m = 2 5 Example 147. Slope
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2.5 Practice - Parallel and Perpend
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Chapter 3 : Inequalities 3.1 Solve
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than 4. If we have an expression su
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− 5 − 5 − 2x � 6 Divide bot
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Solve each inequality, graph each s
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As the graphs overlap, we take the
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3.2 Practice - Compound Inequalitie
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edition of a college algebra text!
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It is important to remember as we a
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Chapter 4 : Systems of Equations 4.
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ested in the point that is a soluti
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that parallel lines have the same s
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4.2 Systems of Equations - Substitu
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tion. This process is described and
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World View Note: French mathematici
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31) 2x + y = 2 3x + 7y = 14 33) x +
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6x +9y = 6 New second equation −
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Just as with graphing and substutio
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4.4 Systems of Equations - Three Va
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just the ordered pair (x, y). In th
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15x − 12y +9z = − 12 5x − 4y
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23) 3x + 3y − 2z = 13 6x + 2y −
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are given to use. This means someti
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− 0.5 − 0.5 c=17 We have c, num
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− 0.06x − 0.06y = − 240 Add e
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14) A bank contains 27 coins in dim
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4.6 Systems of Equations - Mixture
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Amount Part Total Start 40 3 120 Ad
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4(30 −n)+2.5n=105 Substitute into
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16) A certain grade of milk contain
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175
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5.1 Polynomials - Exponent Properti
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A quicker method to arrive at the s
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Example 210. Example 211. 7a 3 (2a
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5.2 Polynomials - Negative Exponent
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As we simplified our fraction we to
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5.2 Practice - Negative Exponents S
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Example 223. Convert 3.21 × 10 5 t
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5.3 Practice - Scientific Notation
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World View Note: Ada Lovelace in 18
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21) (3+b 4 )+(7+2b + b 4 ) 22) (1+6
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Just as we distribute a monomial th
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Example 243. (2x − 5)(4x 2 − 7x
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5.6 Polynomials - Multiply Special
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Be very careful when we are squarin
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5.7 Polynomials - Divide Polynomial
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3. Change the sign of the terms and
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Example 261. 2x 3 + 42 − 4x x + 3
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Chapter 6 : Factoring 6.1 Greatest
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ers using mental math, then we take
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6.1 Practice - Greatest Common Fact
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Example 273. 10ab + 15b + 4a+6 Spli
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example the binomials are (a + b) a
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6.3 Factoring - Trinomials where a
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As the past few examples illustrate
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6.3 Practice - Trinomials where a =
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Example 296. 10x 2 − 27x +5 Multi
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6.5 Factoring - Factoring Special P
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Example 306. 4x 2 + 20xy + 25y 2 Mu
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6.5 Practice - Factoring Special Pr
Page 235 and 236: Example 313. Example 314. Example 3
Page 237 and 238: 6.7 Factoring - Solve by Factoring
Page 239 and 240: 0=(2x +3)(2x − 3) One factor must
Page 241 and 242: 6.7 Practice - Solve by Factoring S
Page 243 and 244: 7.1 Rational Expressions - Reduce R
Page 245 and 246: However, if there is more than just
Page 247 and 248: 41) 8m+16 20m − 12 43) 2x2 − 10
Page 249 and 250: Example 333. 25x2 24y4 · 9y8 55x7
Page 251 and 252: Simplify each expression. 1) 8x2 9
Page 253 and 254: 7.3 Rational Expressions - Least Co
Page 255 and 256: As the above example illustrates, w
Page 257 and 258: 7.4 Rational Expressions - Add & Su
Page 259 and 260: 13 12 Our Solution The same process
Page 261 and 262: 7.4 Practice - Add and Subtract Add
Page 263 and 264: 2(12) 1(12) − 3 4 5(12) 1(12) + 6
Page 265 and 266: LCD =(x + 3)(x − 3) Multiply each
Page 267 and 268: 23) 25) 27) 29) x − 4+ 9 2x +3 x
Page 269 and 270: (20)(9)=6x Multiply 180 = 6x Divide
Page 271 and 272: 3.5 6 The man hasashadow of 3.5 fee
Page 273 and 274: 33) Kali reduced the size of a pain
Page 275 and 276: LCD will be more involved. We will
Page 277 and 278: x=5 or − 2 Our Solution World Vie
Page 279 and 280: 7.8 Rational Expressions - Dimensio
Page 281 and 282: � 435 1 �� 1 lbs = 16 435
Page 283 and 284: To focus on the process of conversi
Page 285: 7.8 Practice - Dimensional Analysis
Page 289 and 290: √ process is being able to transl
Page 291 and 292: Simplify. √ 1) 245 √ 3) 36 √
Page 293 and 294: Example 384. 3√ 54 We are working
Page 295 and 296: 8.3 Radicals - Adding Radicals Obje
Page 297 and 298: Simiplify 1) 2 5 √ + 2 5 √ + 2
Page 299 and 300: √ √ √ √ 4 50 + 6 30 − 8 3
Page 301 and 302: The previous example could have bee
Page 303 and 304: 8.5 Radicals - Rationalize Denomina
Page 305 and 306: 2x2 √ √ 10 − 6x 3x Our Soluti
Page 307 and 308: Example 408. 2 5 √ − 3 7 √ 5
Page 309 and 310: 37) 5 2 √ + 3 √ 5+5 2 √ 38) 3
Page 311 and 312: 1 (3) 4 Evaluate exponent 1 81 Our
Page 313 and 314: 8.6 Practice - Rational Exponents W
Page 315 and 316: Example 420. ab2 3√ a2 4√ b Rew
Page 317 and 318: 8.7 Practice - Radicals of Mixed In
Page 319 and 320: Example 426. Example 427. i 35 Divi
Page 321 and 322: √ Dividing with complex numbers a
Page 323 and 324: Simplify. 1) 3 − ( − 8+4i) 3) (
Page 325 and 326: Chapter 9 : Quadratics 9.1 Solving
Page 327 and 328: Example 444. + 1 +1 Add1to both sid
Page 329 and 330: 2 − 2=0 Subtract 0=0 True! It wor
Page 331 and 332: Solve. √ 1) 2x + 3 √ 3) 6x −
Page 333 and 334: x4 4√ = ± 4√ 16 Simplify roots
Page 335 and 336: 5√ 4x +1 = ± 3 Clear radical by
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9.3 Quadratics - Complete the Squar
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x2 + 5 25 x+ 3 36 � x + 5 �2 6
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Example 464. − 7 3 � 3 3 + 3 3
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9.4 Quadratics - Quadratic Formula
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x = Example 468. √ 30 ± 900 + 11
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9.4 Practice - Quadratic Formula So
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12x 2 − 17x + 6=0 Our Solution If
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9.5 Practice - Build Quadratics fro
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Example 479. a −2 − a −1 −
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12 = (x − 3) 2 or 13 =(x − 3) 2
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9.7 Quadratics - Rectangles Objecti
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Example 486. 2 Our Solution The len
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4(x 2 + 10x − 24) =0 Factor trino
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that require 24 square meters for p
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1(12x) 3 + 1(12x) x 1 1 5 + = 3 x 1
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6x +6(x − 1)=5x(x − 1) Reduce e
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16) A sink can be filled from the f
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These simultaneous product equation
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9.10 Quadratics - Revenue and Dista
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96n(n − 2) 96n(n − 2) +4n(n −
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upstream, the current will pull aga
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12) A pilot flying at a constant ra
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The above method to graph a parabol
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It is important to remember the gra
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Chapter 10 : Functions 10.1 Functio
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Example 504. Which of the following
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2x − 3 � 0 Set up an inequality
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Solve. 10.1 Practice - Function Not
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10.2 Functions - Operations on Func
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(x − 5)(x +1) (x − 5) Divide ou
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We can also evaluate a composition
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23) f(x) = x 2 − 5x g(x) = x + 5
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10.3 Functions - Inverse Functions
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(3x +6)(3 − 4x) 3 − 4x (4x+8)(3
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10.3 Practice - Inverse Functions S
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Example 530. 8 3x = 32 Rewrite 8 as
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10.4 Practice - Exponential Functio
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log3x =7 Identify base, 3, answer,
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10.5 Practice - Logarithmic Functio
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A = 25000(1.01625) 20 Evaluate expo
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The variable e is a constant simila
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j. All of the above compounded cont
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Using the diagram at right, find ea
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10.7 Practice - Trigonometric Funct
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21) 23) 25) 27) A B A 5 38 ◦ x x
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37) 39) A A 37.1 ◦ C x x C 13.1 4
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θ 17 From angle θ the given sides
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function to find the missing angle
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Find the measure of each angle indi
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27) 29) 14 A A θ C 15 7 C 14 θ B
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437
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7) 5 4 8) 4 3 9) 3 2 10) 8 3 11) 5
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54) 60v − 7 55) − 3x + 8x 2 56)
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45) 12 46) All real numbers 47) No
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15) wx 3 = 1458 16) h = 1.5 j 17) a
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1) B(4, − 3) C(1, 2) D( − 1, 4)
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1) y = 2x +5 2) y = − 6x +4 3) y
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23) x =4 24) y − 4 = 7 (x − 1)
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25) 5�x
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1) ( − 2, 4) 2) (2,4) 3) No solut
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27) 56, 144 28) 1.5, 3.5 29) 30 30)
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42) 1.2 × 10 6 5.4 1) 3 2) 7 3)
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5) 2x 3 + 4x 2 + x 2 6) 5p3 4 +4p2
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7) (b +8)(b + 4) 8) (b − 10)(b
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11) n(n − 1) 12) (5x +3)(x − 5)
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5) 3x2 2 6) 5p 2 7) 5m 8) 7 10 9) r
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7) 8) 5 24r 7x + 3y x 2 y 2 9) 15t+
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21) 0, 5 22) − 2, 5 3 23) 4,7 24)
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42) − 18xz 4x3yz3 � 4 8.3 1) 6
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16 3 √ + 4 5 √ 43 18) 19) 2 √
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8.8 1) 11 − 4i 2) − 4i 3) − 3
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√ √ 33) 4+i 39, 4 −i 39 34)
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9) ± 2, ± 4 10) 2,3, − 1 ±i 3
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1) 2) 3) 4) 5) 6) (-2,0) (0,-8) (-1
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11) 100 12) − 74 13) 1 5 14) 27 1
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10.5 1) 9 2 = 81 2) b −16 = a 3)
Page 489:
21) 51.3 ◦ 22) 45 ◦ 23) 56.4
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