Intermediate Algebra
19th Edition
ISBN: 9780998625720
Author: Lynn Marecek
Publisher: OpenStax College
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Textbook Question
Chapter 1.1, Problem 3E
In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.
3. 896
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Assume {u1, U2, us} spans R³.
Select the best statement.
A. {U1, U2, us, u4} spans R³ unless u is the zero vector.
B. {U1, U2, us, u4} always spans R³.
C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set.
D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³.
OE. {U1, U2, 3, 4} never spans R³.
F. none of the above
Assume {u1, U2, 13, 14} spans R³.
Select the best statement.
A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set.
B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector.
C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set.
D. {U1, U2, us} always spans R³.
E. {U1, U2, u3} may, but does not have to, span R³.
F. none of the above
Let H = span {u, v}. For each of the following sets of vectors determine whether H is a line or a plane.
Select an Answer
u =
3
1.
-10
8-8
-2
,v=
5
Select an Answer
-2
u =
3
4
2.
+
9
,v=
6
Chapter 1 Solutions
Intermediate Algebra
Ch. 1.1 - Is 4,962 divisible by (a) 2? (b) 3? (c) 5? (d) 6?...Ch. 1.1 - Is 3,765 divisible by (a) 2? (b) 3? (c) 5? (d) 6?...Ch. 1.1 - Find the prime factorization of 80.Ch. 1.1 - Find the prime factorization of 60.Ch. 1.1 - Find the LCM of 9 and 12 using the Prime Factors...Ch. 1.1 - Find the LCM of 18 and 24 using the Prime Factors...Ch. 1.1 - Simplify: 305+10(32) .Ch. 1.1 - Simplify: 7010+4(62) .Ch. 1.1 - Simplify: 9+53[4(9+3)].Ch. 1.1 - Simplify: 722[4(5+1)].
Ch. 1.1 - Evaluate when x=3 , (a) x2 (b) 4x (c) 3x2+4x+1 .Ch. 1.1 - Evaluate when x=6 , (a) x3 (b) 2x (c) 6x24x7 .Ch. 1.1 - Simplify: 3x2+7x+9+7x2+9x+8 .Ch. 1.1 - Simplify: 4y2+5y+2+8y2+4y+5 .Ch. 1.1 - Translate the English phrase into an algebraic...Ch. 1.1 - Translate the English phrase into an algebraic...Ch. 1.1 - Translate the English phrase into an algebraic...Ch. 1.1 - Translate the English phrase into an algebraic...Ch. 1.1 - The length of a rectangle is 7 less than the...Ch. 1.1 - The width of a rectangle is 6 less than the...Ch. 1.1 - Geoffrey has dimes and quarters in his pocket. The...Ch. 1.1 - Lauren has dimes and nickels in her purse. The...Ch. 1.1 - In the following exercises, use the divisibility...Ch. 1.1 - In the following exercises, use the divisibility...Ch. 1.1 - In the following exercises, use the divisibility...Ch. 1.1 - In the following exercises, use the divisibility...Ch. 1.1 - In the following exercises, use the divisibility...Ch. 1.1 - In the following exercises, use the divisibility...Ch. 1.1 - In the following exercises, find the prime...Ch. 1.1 - In the following exercises, find the prime...Ch. 1.1 - In the following exercises, find the prime...Ch. 1.1 - In the following exercises, find the prime...Ch. 1.1 - In the following exercises, find the prime...Ch. 1.1 - In the following exercises, find the prime...Ch. 1.1 - In the following exercises, find the least common...Ch. 1.1 - In the following exercises, find the least common...Ch. 1.1 - In the following exercises, find the least common...Ch. 1.1 - In the following exercises, find the least common...Ch. 1.1 - In the following exercises, find the least common...Ch. 1.1 - In the following exercises, find the least common...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, simplify each...Ch. 1.1 - In the following exercises, evaluate the following...Ch. 1.1 - In the following exercises, evaluate the following...Ch. 1.1 - In the following exercises, evaluate the following...Ch. 1.1 - In the following exercises, evaluate the following...Ch. 1.1 - In the following exercises, evaluate the following...Ch. 1.1 - In the following exercises, evaluate the following...Ch. 1.1 - In the following exercises, simplify the following...Ch. 1.1 - In the following exercises, simplify the following...Ch. 1.1 - In the following exercises, simplify the following...Ch. 1.1 - In the following exercises, simplify the following...Ch. 1.1 - In the following exercises, simplify the following...Ch. 1.1 - In the following exercises, simplify the following...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - In the following exercises, translate the phrases...Ch. 1.1 - Explain in your own words how to find the prime...Ch. 1.1 - Why is it important to use the order of operations...Ch. 1.1 - Explain how you identify the like terms in the...Ch. 1.1 - Explain the difference between the phrases “4...Ch. 1.2 - Fill in < ,> , or = for each of the following...Ch. 1.2 - Fill in < , > , or = for each of the following...Ch. 1.2 - Simplify: 19|114(31)| .Ch. 1.2 - Simplify: 9|84(75)| .Ch. 1.2 - Add: (a) 2+(4) (b) 2+4 (c) 2+(4) .Ch. 1.2 - Add: (a) 2+(5) (b) 2+5 (c) 2+(5) .Ch. 1.2 - Subtract: (a) 64 (b) 6(4) (c) 64 (d) 6(4) .Ch. 1.2 - Subtract: (a) 74 (b) 7(4) (c) 74 (d) 7(4) .Ch. 1.2 - Simplify: (a) 2113 and 21+(13) (b) -11 - 7 and...Ch. 1.2 - Simplify: (a) 157 and 15+(7) (b) 148 and 14+(8)...Ch. 1.2 - Simplify: 8(31)9 .Ch. 1.2 - Simplify: 12(96)14 .Ch. 1.2 - Multiply or divide: (a) 115(5) (b) 512 (c) 9(7)...Ch. 1.2 - Multiply or divide: (a) 117(3) (b) 313 (c) 7(4)...Ch. 1.2 - Simplify: (a) (3)4 (b) 34 .Ch. 1.2 - Simplify: (a) (7)2 (b) 72 .Ch. 1.2 - Simplify: (a) 12(9)(3)3 (b) 273+(5)(6) .Ch. 1.2 - Simplify: (a) 18(4)(2)3 (b) 324+(2)(7) .Ch. 1.2 - Evaluate: 3x22xy+6y2 when x=1,y=2 .Ch. 1.2 - Evaluate: 4x2xy+5y2 when x=2,y=3 .Ch. 1.2 - Translate and simplify the sum of 9 and 16 ,...Ch. 1.2 - Translate and simplify the sum of 8 and 12 ,...Ch. 1.2 - The temperature in Anchorage, Alaska one morning...Ch. 1.2 - The temperature in Denver was 6 degrees at...Ch. 1.2 - In the following exercises, fill in <, >, or = for...Ch. 1.2 - In the following exercises, fill in <, >, or = for...Ch. 1.2 - In the following exercises, fill in <, >, or = for...Ch. 1.2 - In the following exercises, fill in <, >, or = for...Ch. 1.2 - In the following exercises, simplify. 63....Ch. 1.2 - In the following exercises, simplify. 64....Ch. 1.2 - In the following exercises, simplify. 65....Ch. 1.2 - In the following exercises, simplify. 66....Ch. 1.2 - In the following exercises, simplify. 67....Ch. 1.2 - 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Checking...Ch. 1.2 - Explain why the sum of 8 and 2 is negative, but...Ch. 1.2 - Give an example from your life experience of...Ch. 1.2 - In your own words, state the rules for multiplying...Ch. 1.2 - Why is 43=(4)3 ?Ch. 1.3 - Simplify: 69120 .Ch. 1.3 - Simplify: 120192 .Ch. 1.3 - Multiply: 113(9a) .Ch. 1.3 - Multiply: 137(14b) .Ch. 1.3 - Divide: 727(3536) .Ch. 1.3 - Divide: 514(1528) .Ch. 1.3 - Simplify: a8ab6 .Ch. 1.3 - Simplify: p2pq8 .Ch. 1.3 - Add: 712+1115.Ch. 1.3 - Add: 1315+1720 .Ch. 1.3 - Simplify: (a) 3a489 (b) 3a489 .Ch. 1.3 - Simplify: (a) 4k516 (b) 4k516 .Ch. 1.3 - Simplify: 8(2)+4(3)5(2)+3 .Ch. 1.3 - Simplify: 7(1)+9(3)5(3)2 .Ch. 1.3 - Simplify: ( 1 3 )223+2 .Ch. 1.3 - Simplify: 1+42( 1 4 )2.Ch. 1.3 - Simplify: 13+123413 .Ch. 1.3 - Simplify: 231214+13 .Ch. 1.3 - Evaluate 3ab2 when a=23 and b=12 .Ch. 1.3 - Evaluate 4c3d when c=12 and d=43 .Ch. 1.3 - In the following exercises, simplify. 143. 10863Ch. 1.3 - In the following exercises, simplify. 144. 10448Ch. 1.3 - In the following exercises, simplify. 145. 120252Ch. 1.3 - In the following exercises, simplify. 146. 182294Ch. 1.3 - In the following exercises, simplify. 147. 14x221yCh. 1.3 - In the following exercises, simplify. 148. 24a32b2Ch. 1.3 - In the following exercises, simplify. 149....Ch. 1.3 - In the following exercises, simplify. 150....Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, perform the indicated...Ch. 1.3 - In the following exercises, simplify. 167. 8211235Ch. 1.3 - In the following exercises, simplify. 168. 9163340Ch. 1.3 - In the following exercises, simplify. 169.452Ch. 1.3 - In the following exercises, simplify. 170.5310Ch. 1.3 - In the following exercises, simplify. 171. m3n2Ch. 1.3 - In the following exercises, simplify. 172. 38y12Ch. 1.3 - In the following exercises, add or subtract....Ch. 1.3 - In the following exercises, add or subtract....Ch. 1.3 - In the following exercises, add or subtract. 175....Ch. 1.3 - In the following exercises, add or subtract. 176....Ch. 1.3 - In the following exercises, add or subtract. 177....Ch. 1.3 - In the following exercises, add or subtract. 178....Ch. 1.3 - In the following exercises, add or subtract. 179....Ch. 1.3 - In the following exercises, add or subtract. 180....Ch. 1.3 - In the following exercises, add or subtract. 181....Ch. 1.3 - In the following exercises, add or subtract. 182....Ch. 1.3 - In the following exercises, add or subtract. 183....Ch. 1.3 - In the following exercises, add or subtract. 184....Ch. 1.3 - In the following exercises, add or subtract. 185....Ch. 1.3 - In the following exercises, add or subtract. 186....Ch. 1.3 - In the following exercises, add or subtract. 187....Ch. 1.3 - In the following exercises, add or subtract. 188....Ch. 1.3 - In the following exercises, add or subtract. 189....Ch. 1.3 - In the following exercises, add or subtract. 190....Ch. 1.3 - In the following exercises, add or subtract. 191....Ch. 1.3 - In the following exercises, add or subtract. 192....Ch. 1.3 - In the following exercises, simplify. 193....Ch. 1.3 - In the following exercises, simplify. 194 8976...Ch. 1.3 - In the following exercises, simplify. 195. 523235Ch. 1.3 - In the following exercises, simplify. 196. 624246Ch. 1.3 - In the following exercises, simplify. 197....Ch. 1.3 - In the following exercises, simplify. 198....Ch. 1.3 - In the following exercises, simplify. 199....Ch. 1.3 - In the following exercises, simplify. 200....Ch. 1.3 - In the following exercises, simplify. 201.23+42( 2...Ch. 1.3 - In the following exercises, simplify. 202.3332( 3...Ch. 1.3 - In the following exercises, simplify. 203. 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( 3 4...Ch. 1.3 - In the following exercises, simplify. 205. 213+15Ch. 1.3 - In the following exercises, simplify. 206. 514+13Ch. 1.3 - drymlIn the following exercises, simplify. 207....Ch. 1.3 - In the following exercises, simplify. 208....Ch. 1.3 - In the following exercises, simplify. 209. 38(310)Ch. 1.3 - In the following exercises, simplify. 210. 312(59)Ch. 1.3 - In the following exercises, simplify. 211.] 38+512Ch. 1.3 - In the following exercises, simplify. 212. 18+712Ch. 1.3 - In the following exercises, simplify. 213. 715y4Ch. 1.3 - In the following exercises, simplify. 214. 38x11Ch. 1.3 - In the following exercises, simplify....Ch. 1.3 - In the following exercises, simplify. 216....Ch. 1.3 - In the following exercises, simplify. 217....Ch. 1.3 - In the following exercises, simplify. 218. 13+2534Ch. 1.3 - In the following exercises, simplify. 219. 135110Ch. 1.3 - In the following exercises, simplify. 220. 156112Ch. 1.3 - In the following exercises, simplify. 221. 3816+34Ch. 1.3 - In the following exercises, simplify. 222. 25+5834Ch. 1.3 - In the following exercises, simplify. 223....Ch. 1.3 - In the following exercises, simplify. 224....Ch. 1.3 - In the following exercises, simplify. 225....Ch. 1.3 - In the following exercises, simplify. 226....Ch. 1.3 - In the following exercises, simplify. 227....Ch. 1.3 - In the following exercises, simplify. 228....Ch. 1.3 - In the following exercises, evaluate. 229. 710w...Ch. 1.3 - In the following exercises, evaluate. 230. 512w...Ch. 1.3 - In the following exercises, evaluate. 231. 2x2y3...Ch. 1.3 - In the following exercises, evaluate. 232. 8u2v3...Ch. 1.3 - In the following exercises, evaluate. 233. a+bab...Ch. 1.3 - In the following exercises, evaluate. 234. rsr+s...Ch. 1.3 - Why do you need a common denominator to add or...Ch. 1.3 - How do you find the LCD of 2 fractions?Ch. 1.3 - Explain how you find the reciprocal of a fraction.Ch. 1.3 - Explain how you find the reciprocal of a negative...Ch. 1.4 - Round 6.582 to the nearest (a) hundredth (b) tenth...Ch. 1.4 - Round 15.2175 to the nearest (a) thousandth (b)...Ch. 1.4 - Add or subtract: (a) 4.811.69 (b) 9.5810 .Ch. 1.4 - Add or subtract: (a) 5.12318.47 (b) 37.4250 .Ch. 1.4 - Multiply: 4.5(6.107) .Ch. 1.4 - Multiply: 10.79(8.12) .Ch. 1.4 - Multiply 2.58 by (a) 10 (b) 100 (c) 1000.Ch. 1.4 - Multiply 14.2 by (a) 10 (b) 100 (c) 1000.Ch. 1.4 - Divide: 23.492(0.04) .Ch. 1.4 - Divide: 4.11(0.12) .Ch. 1.4 - Write: (a) 0.234 as a fraction (b) 78 as a...Ch. 1.4 - Write: (a) 0.024 as a fraction (b) 38 as a...Ch. 1.4 - Convert each: (a) percent to a decimal: 9%, 87%,...Ch. 1.4 - Convert each: (a) percent to a decimal: 3%, 91%,...Ch. 1.4 - Simplify: (a) 36 (b) 169 (c) 225 .Ch. 1.4 - Simplify: (a) 16 (b) 196 (c) 100 .Ch. 1.4 - Given the numbers 3,2,0.3,95,4,49 , list the (a)...Ch. 1.4 - Given numbers 25,38,1,6,121, 2.041975..., list the...Ch. 1.4 - Locate and label the following on a number line:...Ch. 1.4 - Locate and label the following on a number line:...Ch. 1.4 - Locate on the number line: (a) 0.6 (b) 0.25 .Ch. 1.4 - Locate on the number line: (a) 0.9 (b) 0.75 .Ch. 1.4 - In the following exercises, round each number to...Ch. 1.4 - In the following exercises, round each number to...Ch. 1.4 - In the following exercises, round each number to...Ch. 1.4 - In the following exercises, round each number to...Ch. 1.4 - In the following exercises, round each number to...Ch. 1.4 - In the following exercises, round each number to...Ch. 1.4 - In the following exercises, add or subtract. 245....Ch. 1.4 - In the following exercises, add or subtract. 246....Ch. 1.4 - In the following exercises, add or subtract. 247....Ch. 1.4 - In the following exercises, add or subtract. 248....Ch. 1.4 - In the following exercises, add or subtract. 249....Ch. 1.4 - In the following exercises, add or subtract. 250....Ch. 1.4 - In the following exercises, add or subtract. 251....Ch. 1.4 - In the following exercises, add or subtract. 252....Ch. 1.4 - In the following exercises, add or subtract. 253....Ch. 1.4 - In the following exercises, add or subtract. 254....Ch. 1.4 - In the following exercises, add or subtract. 255....Ch. 1.4 - In the following exercises, add or subtract. 256....Ch. 1.4 - In the following exercises, multiply. 257....Ch. 1.4 - In the following exercises, multiply. 258....Ch. 1.4 - In the following exercises, multiply. 259....Ch. 1.4 - In the following exercises, multiply. 260....Ch. 1.4 - In the following exercises, multiply. 261....Ch. 1.4 - In the following exercises, multiply. 262....Ch. 1.4 - In the following exercises, multiply. 263....Ch. 1.4 - In the following exercises, multiply. 264....Ch. 1.4 - In the following exercises, multiply. 265....Ch. 1.4 - In the following exercises, multiply. 266....Ch. 1.4 - In the following exercises, multiply. 267....Ch. 1.4 - In the following exercises, multiply. 268....Ch. 1.4 - In the following exercises, divide. 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In the following exercises, simplify. 291. 64Ch. 1.4 - In the following exercises, simplify. 292. 169Ch. 1.4 - In the following exercises, simplify. 293. 144Ch. 1.4 - In the following exercises, simplify. 294. 4Ch. 1.4 - In the following exercises, simplify. 295. 100Ch. 1.4 - In the following exercises, simplify. 296. 121Ch. 1.4 - In the following exercises, list the (a) whole...Ch. 1.4 - In the following exercises, list the (a) whole...Ch. 1.4 - In the following exercises, list the (a) whole...Ch. 1.4 - In the following exercises, list the (a) whole...Ch. 1.4 - In the following exercises, locate the numbers on...Ch. 1.4 - In the following exercises, locate the numbers on...Ch. 1.4 - In the following exercises, locate the numbers on...Ch. 1.4 - In the following exercises, locate the numbers on...Ch. 1.4 - In the following exercises, locate the numbers on...Ch. 1.4 - In the following exercises, locate the numbers on...Ch. 1.4 - In the following exercises, locate the numbers on...Ch. 1.4 - In the following exercises, locate the numbers on...Ch. 1.4 - How does knowing about U.S. money help you learn...Ch. 1.4 - When the Szetos sold their home, the selling price...Ch. 1.4 - In your own words, explain the difference between...Ch. 1.4 - Explain how the sets of numbers (counting, whole,...Ch. 1.5 - Simplify: 23r+14s+9r+15s .Ch. 1.5 - Simplify: 37m+21n+4m15n .Ch. 1.5 - Simplify: (715+58)+38 .Ch. 1.5 - Simplify: (29+712)+512 .Ch. 1.5 - Simplify: 27a+(48a)+27a .Ch. 1.5 - Simplify: 39x+(92x)+(39x) .Ch. 1.5 - Simplify: 916549169 .Ch. 1.5 - Simplify: 6171125176 .Ch. 1.5 - Simplify: (a) 0m+7 , where m7, (b) 186c0 ,where...Ch. 1.5 - Simplify: (a) 0d4 where d4 (b) 154q0 , where 154q0...Ch. 1.5 - Simplify: 4(x+2) .Ch. 1.5 - Simplify: 6(x+7) .Ch. 1.5 - Simplify: 6(56y+12) .Ch. 1.5 - Simplify: 12(13n+34) .Ch. 1.5 - Simplify: 100(0.7+0.15p) .Ch. 1.5 - Simplify: 100(0.04+0.35d) .Ch. 1.5 - Simplify: 5(23a) .Ch. 1.5 - Simplify: 7(815y) .Ch. 1.5 - Simplify: (z11) .Ch. 1.5 - Simplify: (x4) .Ch. 1.5 - Simplify: 93(x+2) .Ch. 1.5 - Simplify: 7x5(x+4) .Ch. 1.5 - Simplify: 6(x9)(x+12) .Ch. 1.5 - Simplify: 8(x1)(x+5) .Ch. 1.5 - In the following exercises, simplify. 313....Ch. 1.5 - In the following exercises, simplify. 314....Ch. 1.5 - In the following exercises, simplify. 315....Ch. 1.5 - In the following exercises, simplify. 316....Ch. 1.5 - In the following exercises, simplify. 317....Ch. 1.5 - In the following exercises, simplify. 318....Ch. 1.5 - In the following exercises, simplify. 319. 24738Ch. 1.5 - In the following exercises, simplify. 320. 361149Ch. 1.5 - In the following exercises, simplify. 321....Ch. 1.5 - In the following exercises, simplify. 322....Ch. 1.5 - In the following exercises, simplify. 323....Ch. 1.5 - In the following exercises, simplify. 324....Ch. 1.5 - In the following exercises, simplify. 325....Ch. 1.5 - In the following exercises, simplify. 326....Ch. 1.5 - In the following exercises, simplify. 327. 12(56p)Ch. 1.5 - In the following exercises, simplify. 328. 20(35q)Ch. 1.5 - 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