Intermediate Algebra
19th Edition
ISBN: 9780998625720
Author: Lynn Marecek
Publisher: OpenStax College
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Textbook Question
Chapter 1.1, Problem 1.16TI
Translate the English phrase into an algebraic expression:
(a) the sum of 17y2and 19
(b) the product of 7 and y
(c) Eleven more than x
(d) Fourteen less than 11a
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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 - In the following exercises, simplify. 68....Ch. 1.2 - In the following exercises, simplify. 69....Ch. 1.2 - In the following exercises, simplify. 70....Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - In the following exercises, simplify each...Ch. 1.2 - 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Football...Ch. 1.2 - In the following exercises, solve. 136. Football...Ch. 1.2 - In the following exercises, solve. 137. Checking...Ch. 1.2 - In the following exercises, solve. 138. 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, 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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- Answersarrow_forward************* ********************************* 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_forward
- T. 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_forwardQ.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_forwardif 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_forward1.2.18. (!) Let G be the graph whose vertex set is the set of k-tuples with elements in (0, 1), with x adjacent to y if x and y differ in exactly two positions. Determine the number of components of G.arrow_forward1.2.17. (!) Let G,, be the graph whose vertices are the permutations of (1,..., n}, with two permutations a₁, ..., a,, and b₁, ..., b, adjacent if they differ by interchanging a pair of adjacent entries (G3 shown below). Prove that G,, is connected. 132 123 213 312 321 231arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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