Elementary Algebra
17th Edition
ISBN: 9780998625713
Author: Lynn Marecek, MaryAnne Anthony-Smith
Publisher: OpenStax - Rice University
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Chapter 6.4, Problem 6.109TI
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You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methods
Plane II is spanned by the vectors:
- (2) · P² - (4)
P1=2
P21
3
Subspace W is spanned by the vectors:
2
W1
- (9) ·
1
W2
1
= (³)
Chapter 6 Solutions
Elementary Algebra
Ch. 6.1 - Determine whether each polynomial is a monomial,...Ch. 6.1 - Determine whether each polynomial is a monomial,...Ch. 6.1 - Find the degree of the following polynomials: (a)...Ch. 6.1 - Find the degree of the following polynomials: (a)...Ch. 6.1 - Add: 12q2+9q2 .Ch. 6.1 - Add: 15c2+8c2 .Ch. 6.1 - Subtract: 8m(5m) .Ch. 6.1 - Subtract: 15z3(5z3) .Ch. 6.1 - Add: 8y2+3z23y2 .Ch. 6.1 - Add: 3m2+n27m2 .
Ch. 6.1 - Simplify: m2n28m2+4n2 .Ch. 6.1 - Simplify: pq26p5q2 .Ch. 6.1 - Find the sum: (7x24x+5)+(x27x+3) .Ch. 6.1 - Find the sum: (14y2+6y4)+(3y2+8y+5) .Ch. 6.1 - Find the difference: (8x2+3x19)(7x214) .Ch. 6.1 - Find the difference: (9b25b4)(3b25b7) .Ch. 6.1 - Subtract: (5z26z2) from (7z2+6z4) .Ch. 6.1 - Subtract: (x25x8) from (6x2+9x1) .Ch. 6.1 - Find the sum: (3x24xy+5y2)+(2x2xy) .Ch. 6.1 - Find the sum: (2x23xy2y2)+(5x23xy) .Ch. 6.1 - Find the difference: (a2+b2)(a2+5ab6b2) .Ch. 6.1 - Find the difference: (m2+n2)(m27mn3n2) .Ch. 6.1 - Simplify: (x3x2y)(xy2+y)+(x2y+xy2) .Ch. 6.1 - Simplify: (p3p2q)(pq2+q3)(p2q+pq2) .Ch. 6.1 - Evaluate: 3x2+2x15 when (a)x=3 (b)x=5 (c)x=0Ch. 6.1 - Evaluate: 5z2z4 when (a) z=2 (b) z=0 (c) z=2Ch. 6.1 - The polynomial 16t2+250 gives the height of a ball...Ch. 6.1 - The polynomial 16t2+250 gives the height of a ball...Ch. 6.1 - The polynomial 6x2+15xy gives the cost, in...Ch. 6.1 - The polynomial 6x2+15xy gives the cost, in...Ch. 6.1 - In the following exercises, determine if each of...Ch. 6.1 - In the following exercises, determine if each of...Ch. 6.1 - In the following exercises, determine if each of...Ch. 6.1 - In the following exercises, determine if each of...Ch. 6.1 - In the following exercises, determine the degree...Ch. 6.1 - In the following exercises, determine the degree...Ch. 6.1 - In the following exercises, determine the degree...Ch. 6.1 - In the following exercises, determine the degree...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, add or subtract the...Ch. 6.1 - 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In the following exercises, add or subtract the...Ch. 6.1 - In the following exercises, evaluate each...Ch. 6.1 - In the following exercises, evaluate each...Ch. 6.1 - In the following exercises, evaluate each...Ch. 6.1 - In the following exercises, evaluate each...Ch. 6.1 - In the following exercises, evaluate each...Ch. 6.1 - In the following exercises, evaluate each...Ch. 6.1 - In the following exercises, evaluate each...Ch. 6.1 - In the following exercises, evaluate each...Ch. 6.1 - Fuel Efficiency The fuel efficiency (in miles per...Ch. 6.1 - Stopping Distance The number of feet it takes for...Ch. 6.1 - Rental Cost The cost to rent a rug cleaner for d...Ch. 6.1 - Height of Projectile The height (in feet) of an...Ch. 6.1 - Temperature Conversion The temperature in degrees...Ch. 6.1 - Using your own words, explain the difference...Ch. 6.1 - Using your own words, explain the difference...Ch. 6.1 - Ariana thinks the sum 6y2+5y4 is 11y6 . What is...Ch. 6.1 - Jonathan thinks that 13 and 1x are both monomials....Ch. 6.2 - Simplify: (a) 63 (b) 151 (c) (37)2 (d) (0.43)2Ch. 6.2 - Simplify: (a) 25 (b) 211 (c) (25)3 (d) (0.218)2 .Ch. 6.2 - Simplify: (a) (3)4 (b) 34 .Ch. 6.2 - Simplify: (a) (13)2 (b) 132 .Ch. 6.2 - Simplify: b9b8 .Ch. 6.2 - Simplify: x12x4 .Ch. 6.2 - Simplify: (a) 553 (b) 4949 .Ch. 6.2 - Simplify: (a) 7678 (b) 101010Ch. 6.2 - Simplify: (a) p5p (b) y14y29 .Ch. 6.2 - Simplify: (a) zz7 (b) b15b34.Ch. 6.2 - Simplify: x6x4x8 .Ch. 6.2 - Simplify: b5b9b5Ch. 6.2 - Simplify: (a) (b7)5 (b) (54)3 .Ch. 6.2 - Simplify: (a) (z6)9 (b) (37)7Ch. 6.2 - Simplify: (a) (12y)2 (b) (2wx)5 .Ch. 6.2 - Simplify: (a) (5wx)3 (b) (3y)3 .Ch. 6.2 - Simplify: (a) (a4)5(a7)4 (b) (2c4d2)3 .Ch. 6.2 - Simplify: (a) (3x6y7)4 (b) (q4)5(q3)3 .Ch. 6.2 - Simplify: (a) (5n)2(3n10) (b) (c4d2)5(3cd5)4 .Ch. 6.2 - Simplify: (a) (a3b2)6(4ab3)4 (b) (2x)3(5x7) .Ch. 6.2 - Multiply: (5y7)(7y4) .Ch. 6.2 - Multiply: (6b4)(9b5) .Ch. 6.2 - Multiply: (25a4b3)(15ab3) .Ch. 6.2 - Multiply: (23r5s)(12r6s7) .Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - 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In the following exercises, simplify each...Ch. 6.2 - In the following exercises, simplify each...Ch. 6.2 - Email Kate emails a flyer to ten of her friends...Ch. 6.2 - Salary Jamal’s boss gives him a 3% raise every...Ch. 6.2 - Clearance A department store is clearing out...Ch. 6.2 - Depreciation Once a new car is driven away from...Ch. 6.2 - Use the Product Property for Exponents to explain...Ch. 6.2 - Explain why 53=(5)3 but 54(5)4 .Ch. 6.2 - Jorge thinks (12)2 is 1. What is wrong with his...Ch. 6.2 - Explain why x3x5 is x8 , and not x15 .Ch. 6.3 - Multiply: 5(x+7) .Ch. 6.3 - Multiply: 3(y+13) .Ch. 6.3 - Multiply: x(x7) .Ch. 6.3 - Multiply: d(d11) .Ch. 6.3 - Multiply: 5x(x+4y) .Ch. 6.3 - Multiply: 2p(6p+r) .Ch. 6.3 - Multiply: 3y(5y2+8y7) .Ch. 6.3 - Multiply: 4x2(2x23x+5) .Ch. 6.3 - Multiply: 4x(3x25x+3) .Ch. 6.3 - Multiply: 6a3(3a22a+6) .Ch. 6.3 - Multiply: (x+8)p .Ch. 6.3 - Multiply: (a+4)p .Ch. 6.3 - Multiply: (x+8)(x+9) .Ch. 6.3 - Multiply: (5x+9)(4x+3) .Ch. 6.3 - Multiply: (3b+5)(4b+6) .Ch. 6.3 - Multiply: (a+10)(a+7) .Ch. 6.3 - Multiply: (5y+2)(6y3) .Ch. 6.3 - Multiply: (3c+4)(5c2) .Ch. 6.3 - Multiply: (a+7)(ab) .Ch. 6.3 - Multiply: (x+5)(xy) .Ch. 6.3 - Multiply using the FOIL method: (x+6)(x+8) .Ch. 6.3 - Multiply using the FOIL method: (y+17)(y+3) .Ch. 6.3 - Multiply: (x7)(x+5) .Ch. 6.3 - Multiply: (b3)(b+6) .Ch. 6.3 - Multiply: (3x+7)(5x2) .Ch. 6.3 - Multiply: (4y+5)(4y10) .Ch. 6.3 - Multiply: (10cd)(c6) .Ch. 6.3 - Multiply: (7xy)(2x5) .Ch. 6.3 - Multiply: (x2+6)(x8) .Ch. 6.3 - Multiply: (y2+7)(y9) .Ch. 6.3 - Multiply: (2ab+5)(4ab4) .Ch. 6.3 - Multiply: (2xy+3)(4xy5) .Ch. 6.3 - Multiply using the Vertical Method: (5m7)(3m6) .Ch. 6.3 - Multiply using the Vertical Method: (6b5)(7b3) .Ch. 6.3 - Multiply using the Distributive Property:...Ch. 6.3 - Multiply using the Distributive Property:...Ch. 6.3 - Multiply using the Vertical Method: (y3)(y25y+2) .Ch. 6.3 - Multiply using the Vertical Method: (x+4)(2x23x+5)...Ch. 6.3 - In the following exercises, multiply. 173. 4(w+10)Ch. 6.3 - In the following exercises, multiply. 174. 6(b+8)Ch. 6.3 - In the following exercises, multiply. 175. 3(a+7)Ch. 6.3 - In the following exercises, multiply. 176. 5(p+9)Ch. 6.3 - In the following exercises, multiply. 177. 2(x7)Ch. 6.3 - In the following exercises, multiply. 178. 7(y4)Ch. 6.3 - In the following exercises, multiply. 179. 3(k4)Ch. 6.3 - In the following exercises, multiply. 180. 8(j5)Ch. 6.3 - In the following exercises, multiply. 181. q(q+5)Ch. 6.3 - In the following exercises, multiply. 182. k(k+7)Ch. 6.3 - In the following exercises, multiply. 183. b(b+9)Ch. 6.3 - In the following exercises, multiply. 184. y(y+3)Ch. 6.3 - In the following exercises, multiply. 185. x(x10)Ch. 6.3 - In the following exercises, multiply. 186. p(p15)Ch. 6.3 - In the following exercises, multiply. 187....Ch. 6.3 - In the following exercises, multiply. 188....Ch. 6.3 - In the following exercises, multiply. 189....Ch. 6.3 - In the following exercises, multiply. 190. 9m(m11)Ch. 6.3 - In the following exercises, multiply. 191....Ch. 6.3 - In the following exercises, multiply. 192....Ch. 6.3 - In the following exercises, multiply. 193....Ch. 6.3 - In the following exercises, multiply. 194....Ch. 6.3 - In the following exercises, multiply. 195....Ch. 6.3 - In the following exercises, multiply. 196....Ch. 6.3 - In the following exercises, multiply. 197....Ch. 6.3 - In the following exercises, multiply. 198....Ch. 6.3 - In the following exercises, multiply. 199....Ch. 6.3 - In the following exercises, multiply. 200....Ch. 6.3 - In the following exercises, multiply. 201....Ch. 6.3 - In the following exercises, multiply. 202....Ch. 6.3 - In the following exercises, multiply. 203....Ch. 6.3 - In the following exercises, multiply. 204....Ch. 6.3 - In the following exercises, multiply. 205. (2m9)mCh. 6.3 - In the following exercises, multiply. 206. (8j1)jCh. 6.3 - In the following exercises, multiply. 207. (w6)8Ch. 6.3 - In the following exercises, multiply. 208. (k4)5Ch. 6.3 - In the following exercises, multiply. 209. 4(x+10)Ch. 6.3 - In the following exercises, multiply. 210. 6(y+8)Ch. 6.3 - In the following exercises, multiply. 211. 15(r24)Ch. 6.3 - In the following exercises, multiply. 212. 12(v30)Ch. 6.3 - In the following exercises, multiply. 213. 3(m+11)Ch. 6.3 - In the following exercises, multiply. 214. 4(p+15)Ch. 6.3 - In the following exercises, multiply. 215. 8(z5)Ch. 6.3 - In the following exercises, multiply. 216. 3(x9)Ch. 6.3 - In the following exercises, multiply. 217. u(u+5)Ch. 6.3 - In the following exercises, multiply. 218. q(q+7)Ch. 6.3 - In the following exercises, multiply. 219. n(n23n)Ch. 6.3 - In the following exercises, multiply. 220. s(s26s)Ch. 6.3 - In the following exercises, multiply. 221....Ch. 6.3 - In the following exercises, multiply. 222....Ch. 6.3 - In the following exercises, multiply. 223....Ch. 6.3 - In the following exercises, multiply. 224....Ch. 6.3 - In the following exercises, multiply. 225....Ch. 6.3 - In the following exercises, multiply. 226....Ch. 6.3 - In the following exercises, multiply. 227....Ch. 6.3 - In the following exercises, multiply. 228....Ch. 6.3 - In the following exercises, multiply. 229....Ch. 6.3 - In the following exercises, multiply. 230....Ch. 6.3 - In the following exercises, multiply. 231....Ch. 6.3 - In the following exercises, multiply. 232....Ch. 6.3 - In the following exercises, multiply. 233....Ch. 6.3 - In the following exercises, multiply. 234....Ch. 6.3 - In the following exercises, multiply. 235. (2y9)yCh. 6.3 - In the following exercises, multiply. 236. (8b1)bCh. 6.3 - In the following exercises, multiply the following...Ch. 6.3 - In the following exercises, multiply the following...Ch. 6.3 - In the following exercises, multiply the following...Ch. 6.3 - In the following exercises, multiply the following...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply the...Ch. 6.3 - In the following exercises, multiply using (a) the...Ch. 6.3 - In the following exercises, multiply using (a) the...Ch. 6.3 - In the following exercises, multiply using (a) the...Ch. 6.3 - In the following exercises, multiply using (a) the...Ch. 6.3 - In the following exercises, multiply. Use either...Ch. 6.3 - In the following exercises, multiply. Use either...Ch. 6.3 - In the following exercises, multiply. Use either...Ch. 6.3 - In the following exercises, multiply. Use either...Ch. 6.3 - In the following exercises, multiply. Use either...Ch. 6.3 - In the following exercises, multiply. Use either...Ch. 6.3 - In the following exercises, multiply. Use either...Ch. 6.3 - In the following exercises, multiply. Use either...Ch. 6.3 - In the following exercises, multiply. Use either...Ch. 6.3 - In the following exercises, multiply. Use either...Ch. 6.3 - In the following exercises, multiply. 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Multiply the following:...Ch. 6.3 - Multiply the following:...Ch. 6.3 - Multiply the following: (x4)(x4)(y1)(y1)(z7)(z7)...Ch. 6.4 - Multiply: (x+9)2 .Ch. 6.4 - Multiply: (y+11)2 .Ch. 6.4 - Multiply: (x9)2 .Ch. 6.4 - Multiply: (p13)2 .Ch. 6.4 - Multiply: (6x+3)2 .Ch. 6.4 - Multiply: (4x+9)2 .Ch. 6.4 - Multiply: (2cd)2 .Ch. 6.4 - Multiply: (4x5y)2 .Ch. 6.4 - Multiply: (2x2+1)2 .Ch. 6.4 - Multiply: (3y3+2)2 .Ch. 6.4 - Multiply: (x5)(x+5) .Ch. 6.4 - Multiply: (w3)(w+3) .Ch. 6.4 - Multiply: (6x+5)(6x5) .Ch. 6.4 - Multiply: (2x+7)(2x7) .Ch. 6.4 - Multiply: (7+4x)(74x) .Ch. 6.4 - Multiply: (92y)(9+2y) .Ch. 6.4 - Find the product: ( 4p7q )( 4p+7q )Ch. 6.4 - Find the product: (3xy)(3x+y) .Ch. 6.4 - Find the product: (xy6)(xy+6) .Ch. 6.4 - Find the product: (ab9)(ab+9) .Ch. 6.4 - Find the product: (3x24y3)(3x2+4y3) .Ch. 6.4 - Find the product: Find the product:...Ch. 6.4 - Choose the appropriate pattern and use it to find...Ch. 6.4 - Choose the appropriate pattern and use it to find...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, square each binomial...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, multiply each pair of...Ch. 6.4 - In the following exercises, find each product....Ch. 6.4 - In the following exercises, find each product....Ch. 6.4 - In the following exercises, find each product....Ch. 6.4 - In the following exercises, find each product....Ch. 6.4 - Mental math You can use the product of conjugates...Ch. 6.4 - Mental math You can use the binomial squares...Ch. 6.4 - How do you decide which pattern to use?Ch. 6.4 - Why does (a+b)2result in a trinomial. but...Ch. 6.4 - Marta did the following work on her homework...Ch. 6.4 - Use the order of operations to show that (3+5)2is...Ch. 6.5 - Simplify: (a) x15x10 (b) 61465Ch. 6.5 - Simplify: (a) y43y37 (b) 1015107Ch. 6.5 - Simplify: (a) x18x22 (b) 12151230Ch. 6.5 - Simplify: (a) m7m15 (b) 98919Ch. 6.5 - Simplify: (a) b19b11 (b) z5z11Ch. 6.5 - Simplify: (a) p9p17 (b) w13w9Ch. 6.5 - Simplify: (a) 150 (b) m0Ch. 6.5 - Simplify: (a) k0 (b) 290Ch. 6.5 - Simplify: (a) (11z)0 (b) (11pq3)0 .Ch. 6.5 - Simplify: (a) (6d)0 (b) (8m2n3)0Ch. 6.5 - Simplify: (a) (58)2 (b) (p 10)4 (c) (mn)4 .Ch. 6.5 - Simplify: (a) (13)3 (b) ( 2q)3 (c) (wx)4Ch. 6.5 - Simplify: (m5)4m7 .Ch. 6.5 - Simplify: (k2)6k7Ch. 6.5 - Simplify: n12(n3)4 .Ch. 6.5 - Simplify: x15(x3)5Ch. 6.5 - Simplify: ( r 5 r 3 )4Ch. 6.5 - Simplify: ( v 6 v 4 )3Ch. 6.5 - Simplify: ( a 3 b 2 )4Ch. 6.5 - Simplify: ( q 7 r 5 )3Ch. 6.5 - Simplify: ( 7 x 3 9y)2Ch. 6.5 - Simplify: ( 3 x 4 7y)2 .Ch. 6.5 - Simplify: (a2)3(a2)4(a4)5Ch. 6.5 - Simplify: (p3)4(p5)3(p7)6Ch. 6.5 - Simplify: (3r3)2(r3)7(r3)3Ch. 6.5 - Simplify: (2x4)5(4x3)2(x3)5Ch. 6.5 - Find the quotient: 42y96y3 .Ch. 6.5 - Find the quotient: 48z88z2 .Ch. 6.5 - Find the quotient: 72a7b38a12b4Ch. 6.5 - Find the quotient: 63c8d37c12d2 .Ch. 6.5 - Find the quotient: 16a7b624ab8Ch. 6.5 - Find the quotient: 27p4q745p12qCh. 6.5 - Find the quotient: 28x5y1449x9y12Ch. 6.5 - Find the quotient: 30m5n1148m10n14 .Ch. 6.5 - Find the quotient: (6a4b5)(4a2b5)12a5b8Ch. 6.5 - Find the quotient: (12x6y9)(4x5y8)12x10y12Ch. 6.5 - In the following exercises, simplify. 356. (a)...Ch. 6.5 - In the following exercises, simplify. 357. (a)...Ch. 6.5 - In the following exercises, simplify. 358. (a)...Ch. 6.5 - In the following exercises, simplify. 359. (a)...Ch. 6.5 - In the following exercises, simplify. 360. (a)...Ch. 6.5 - In the following exercises, simplify. 361. (a)...Ch. 6.5 - In the following exercises, simplify. 362. (a) bb9...Ch. 6.5 - In the following exercises, simplify. 363. (a) xx7...Ch. 6.5 - In the following exercises, simplify. 364. (a) 20º...Ch. 6.5 - In the following exercises, simplify. 365. (a) 13...Ch. 6.5 - In the following exercises, simplify. 366. (a) 27...Ch. 6.5 - In the following exercises, simplify. 367. (a) 15...Ch. 6.5 - In the following exercises, simplify. 368. (a)...Ch. 6.5 - In the following exercises, simplify. 369. (a)...Ch. 6.5 - In the following exercises, simplify. 370. (a)...Ch. 6.5 - In the following exercises, simplify. 371. (a)...Ch. 6.5 - In the following exercises, simplify. 372. (a)...Ch. 6.5 - In the following exercises, simplify. 373. (a)...Ch. 6.5 - In the following exercises, simplify. 343. (a)...Ch. 6.5 - In the following exercises, simplify. 375. (a)...Ch. 6.5 - In the following exercises, simplify. 376. (a) (a...Ch. 6.5 - In the following exercises, simplify. 377. (a) (x...Ch. 6.5 - In the following exercises, simplify. 378. (a2)3a4Ch. 6.5 - In the following exercises, simplify. 379. (p3)4p5Ch. 6.5 - In the following exercises, simplify. 380....Ch. 6.5 - wIn the following exercises, simplify. 381....Ch. 6.5 - In the following exercises, simplify. 382. u6(u3)2Ch. 6.5 - In the following exercises, simplify. 383....Ch. 6.5 - In the following exercises, simplify. 384....Ch. 6.5 - In the following exercises, simplify. 385. n8(n6)4Ch. 6.5 - In the following exercises, simplify. 386. ( p 9 p...Ch. 6.5 - In the following exercises, simplify. 387. ( q 8 q...Ch. 6.5 - In the following exercises, simplify. 388. ( r 2 r...Ch. 6.5 - In the following exercises, simplify. 389. ( m 4 m...Ch. 6.5 - In the following exercises, simplify. 390. (p r 11...Ch. 6.5 - In the following exercises, simplify. 391. (a b 6...Ch. 6.5 - In the following exercises, simplify. 392. ( w 5 x...Ch. 6.5 - In the following exercises, simplify. 393. ( y 4 z...Ch. 6.5 - In the following exercises, simplify. 394. ( 2 j 3...Ch. 6.5 - In the following exercises, simplify. 395. ( 3 m 5...Ch. 6.5 - In the following exercises, simplify. 396. ( 3 c 2...Ch. 6.5 - In the following exercises, simplify. 397. ( 5 u 7...Ch. 6.5 - In the following exercises, simplify. 398. ( k 2 k...Ch. 6.5 - In the following exercises, simplify. 399. ( j 2 j...Ch. 6.5 - In the following exercises, simplify. 400....Ch. 6.5 - In the following exercises, simplify. 401....Ch. 6.5 - In the following exercises, simplify. 402....Ch. 6.5 - In the following exercises, simplify. 403....Ch. 6.5 - In the following exercises, simplify. 404....Ch. 6.5 - In the following exercises, simplify. 405....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - In the following exercises, divide the monomials....Ch. 6.5 - (a) 24a5+2a5 (b) 24a52a5 (c) 24a52a5 (d) 24a52a5Ch. 6.5 - (a) 15n10+3n10 (b) 15n103n10 (c) 15n103n10 (d)...Ch. 6.5 - (a) p4p6 (b) (p4)6Ch. 6.5 - (a) q5q3 (b) (q5)3Ch. 6.5 - (a) y3y (b) yy3Ch. 6.5 - (a) z6z5 (b) z5z6Ch. 6.5 - (8x5)(9x)6x3Ch. 6.5 - (4y)(12y7)8y2Ch. 6.5 - 27a73a3+54a99a5Ch. 6.5 - 32c114c5+42c96c3Ch. 6.5 - 32y58y2+60y105y7Ch. 6.5 - 48x66x435x97x7Ch. 6.5 - 63r6s39r4s272r2s26sCh. 6.5 - 56y4z57y3z345y2z25yCh. 6.5 - Memory One megabyte is approximately 106 bytes....Ch. 6.5 - Memory One gigabyte is approximately 109 bytes....Ch. 6.5 - Jennifer thinks the quotient a24a6 simplifies to...Ch. 6.5 - Maurice simplifies the quotient d7d by writing...Ch. 6.5 - When Drake simplified 30 and (3)0 he got the same...Ch. 6.5 - Robert thinks x0 simplifies to 0. What would you...Ch. 6.6 - Find the quotient: 8z2+244Ch. 6.6 - Find the quotient: 18z2279Ch. 6.6 - Find the quotient: (27b233b2)3bCh. 6.6 - Find the quotient: (25y355y2)5y .Ch. 6.6 - Find the quotient: 25y215y5Ch. 6.6 - Find the quotient: 42b218b6Ch. 6.6 - Find the quotient: 60d7+24d54d3Ch. 6.6 - Find the quotient: 216p748p56p3Ch. 6.6 - Find the quotient: (32a2b16ab2)(8ab) .Ch. 6.6 - Find the quotient: (48a8b436a6b5)(6a3b3) .Ch. 6.6 - Find the quotient: 40x3y2+24x2y216x2y38x2yCh. 6.6 - Find the quotient: 35a4b2+14a4b242a2b47a2b2Ch. 6.6 - Find the quotient: 18c2+6c96cCh. 6.6 - Find the quotient: 10d25d25dCh. 6.6 - Find the quotient: (y2+10y+21)(y+3) .Ch. 6.6 - Find the quotient: (m2+9m+20)(m+4)Ch. 6.6 - Find the quotient: (2x23x20)(x4) .Ch. 6.6 - Find the quotient: (3x216x12)(x6) .Ch. 6.6 - Find the quotient: (x3+5x2+8x+6)(x+2) .Ch. 6.6 - Find the quotient: (2x3+8x2+x8)(x+1) .Ch. 6.6 - Find the quotient: (x3+3x+14)(x+2) .Ch. 6.6 - Find the quotient: (x43x31000)(x+5) .Ch. 6.6 - Find the quotient: (x364)(x4) .Ch. 6.6 - Find the quotient: 25x38)(5x2) .Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - In the following exercises, divide each polynomial...Ch. 6.6 - Average cost Pictures Plus produces digital...Ch. 6.6 - Handshakes At a company meeting, every employee...Ch. 6.6 - James divides 48y+6 4 by 6 this way : 48y+66=48y ....Ch. 6.6 - Divide 10x2+x122x and explain with words how you...Ch. 6.7 - Simplify: (a) 23 (b) 107Ch. 6.7 - Simplify: (a) 32 (b) 104Ch. 6.7 - Simplify: (a) 1p8 (b) 143 .Ch. 6.7 - Simplify: (a) 1q7 (b) 124 .Ch. 6.7 - Simplify: (a) (23)4 (b) ( 6mn)2 .Ch. 6.7 - Simplify: (a) (35)3 (b) (a 2b)4Ch. 6.7 - Simplify: (a) 52 (b) 52 (c) (15)2 (d) (15)2Ch. 6.7 - Simplify: (a) (7)2 (b) 72 (c) (17)2 (d) (17)2Ch. 6.7 - Simplify: (a) 631 (b) (63)1Ch. 6.7 - Simplify: (a) 822 (b) (82)2Ch. 6.7 - Simplify: (a) y7 (b) (z3)5Ch. 6.7 - Simplify: (a) p9 (b) (q4)6 .Ch. 6.7 - Simplify: (a) 8p1 (b) (8p)1 (c) (8p)1 .Ch. 6.7 - Simplify: (a) 11q1 (b) (11q)1 (c) (11q)1 (c)...Ch. 6.7 - Simplify: (a) (x3)x7 (b) y7y2 (c) z4z5Ch. 6.7 - Simplify: (a) a1a6 (b) b8b4 (c) c8c7 .Ch. 6.7 - Simplify: (p6q2)(p9q1)Ch. 6.7 - Simplify: (r5s3)(r7s5)Ch. 6.7 - Simplify: (3u5v7)(4u4v2) .Ch. 6.7 - Simplify: (6c6d4)(5c2d1)Ch. 6.7 - Simplify: (4x4)2Ch. 6.7 - Simplify: (2b3)4 .Ch. 6.7 - Simplify: (8a4)2 .Ch. 6.7 - Simplify: (2c4)3Ch. 6.7 - Simplify: x8x3 .Ch. 6.7 - Simplify: y8y6 .Ch. 6.7 - Write in scientific notation: 96,000.Ch. 6.7 - Write in scientific notation: 48,300.Ch. 6.7 - Write in scientific notation: 0.0078.Ch. 6.7 - Write in scientific notation: 0.0 129.Ch. 6.7 - Convert to decimal form: 1.3103 .Ch. 6.7 - Convert to decimal form: 9.25104 .Ch. 6.7 - Convert to decimal form: 1.2104 .Ch. 6.7 - Convert to decimal form: 7.5102 .Ch. 6.7 - Multiply (3106)(2108) . Write answers in decimal...Ch. 6.7 - Multiply (3102)(3101) . Write answers in decimal...Ch. 6.7 - Divide 81042101 . Write answers in decimal form.Ch. 6.7 - Divide 81024102 . Write answers in decimal form.Ch. 6.7 - In the following exercises, simplify. 500. (a) 42...Ch. 6.7 - In the following exercises, simplify. 501. (a) 34...Ch. 6.7 - In the following exercises, simplify. 502. (a) 53...Ch. 6.7 - In the following exercises, simplify. 503. (a) 28...Ch. 6.7 - In the following exercises, simplify. 504. (a) 1c5...Ch. 6.7 - In the following exercises, simplify. 505. (a) 1c5...Ch. 6.7 - In the following exercises, simplify. 506. (a)...Ch. 6.7 - In the following exercises, simplify. 507. (a) 1t9...Ch. 6.7 - In the following exercises, simplify. 508. (a)...Ch. 6.7 - In the following exercises, simplify. 509. (a) (3...Ch. 6.7 - In the following exercises, simplify. 510. (a)...Ch. 6.7 - In the following exercises, simplify. 511. (a)...Ch. 6.7 - In the following exercises, simplify. 512. (a)...Ch. 6.7 - In the following exercises, simplify. 513. (a)...Ch. 6.7 - In the following exercises, simplify. 514. (a) 33...Ch. 6.7 - In the following exercises, simplify. 515. (a) 53...Ch. 6.7 - In the following exercises, simplify. 516. (a) 351...Ch. 6.7 - In the following exercises, simplify. 517. (a) 251...Ch. 6.7 - In the following exercises, simplify. 518. (a) 452...Ch. 6.7 - In the following exercises, simplify. 519. (a) 342...Ch. 6.7 - In the following exercises, simplify. 520. (a) m4...Ch. 6.7 - In the following exercises, simplify. 521. (a) b5...Ch. 6.7 - In the following exercises, simplify. 522. (a) p10...Ch. 6.7 - In the following exercises, simplify. 523. (a) s8...Ch. 6.7 - In the following exercises, simplify. 524. (a) 7n1...Ch. 6.7 - In the following exercises, simplify. 525. (a) 6r1...Ch. 6.7 - In the following exercises, simplify. 526. (a)...Ch. 6.7 - In the following exercises, simplify. 527. (a)...Ch. 6.7 - In the following exercises, simplify. 528. (a)...Ch. 6.7 - In the following exercises, simplify. 529. (a)...Ch. 6.7 - In the following exercises, simplify. 530. (a)...Ch. 6.7 - In the following exercises, simplify. 531. (a)...Ch. 6.7 - In the following exercises, simplify. 532. p5p2p4Ch. 6.7 - In the following exercises, simplify. 533. x4x2x3Ch. 6.7 - In the following exercises, simplify. 534....Ch. 6.7 - In the following exercises, simplify. 535....Ch. 6.7 - In the following exercises, simplify. 536....Ch. 6.7 - In the following exercises, simplify. 537....Ch. 6.7 - In the following exercises, simplify. 538....Ch. 6.7 - In the following exercises, simplify. 539....Ch. 6.7 - In the following exercises, simplify. 540....Ch. 6.7 - In the following exercises, simplify. 541....Ch. 6.7 - In the following exercises, simplify. 542. (5x2)2Ch. 6.7 - In the following exercises, simplify. 543. (4y3)3Ch. 6.7 - In the following exercises, simplify. 544. (3z3)2Ch. 6.7 - In the following exercises, simplify. 545. (2p5)2Ch. 6.7 - In the following exercises, simplify. 546. t9t3Ch. 6.7 - In the following exercises, simplify. 547. n5n2Ch. 6.7 - In the following exercises, simplify. 548. x7x3Ch. 6.7 - In the following exercises, simplify. 549. y5y10Ch. 6.7 - In the following exercises, write each number in...Ch. 6.7 - In the following exercises, write each number in...Ch. 6.7 - In the following exercises, write each number in...Ch. 6.7 - In the following exercises, write each number in...Ch. 6.7 - In the following exercises, write each number in...Ch. 6.7 - In the following exercises, write each number in...Ch. 6.7 - In the following exercises, write each number in...Ch. 6.7 - In the following exercises, write each number in...Ch. 6.7 - In the following exercises, write each number in...Ch. 6.7 - In the following exercises, write each number in...Ch. 6.7 - In the following exercises, convert each number to...Ch. 6.7 - In the following exercises, convert each number to...Ch. 6.7 - In the following exercises, convert each number to...Ch. 6.7 - In the following exercises, convert each number to...Ch. 6.7 - In the following exercises, convert each number to...Ch. 6.7 - In the following exercises, convert each number to...Ch. 6.7 - In the following exercises, multiply. Write your...Ch. 6.7 - In the following exercises, multiply. Write your...Ch. 6.7 - In the following exercises, multiply. Write your...Ch. 6.7 - In the following exercises, multiply. Write your...Ch. 6.7 - In the following exercises, multiply. Write your...Ch. 6.7 - In the following exercises, multiply. Write your...Ch. 6.7 - In the following exercises, multiply. Write your...Ch. 6.7 - In the following exercises, multiply. Write your...Ch. 6.7 - The population of the United States on July 4,...Ch. 6.7 - The population of the world on July 4, 2010 was...Ch. 6.7 - The average width of a human hair is 0.0018...Ch. 6.7 - The probability of winning the 2010 Megamillions...Ch. 6.7 - In 2010, the number of Facebook users each day who...Ch. 6.7 - At the start of 2012, the US federal budget had a...Ch. 6.7 - The concentration of carbon dioxide in the...Ch. 6.7 - The width of a proton is 1105 of the width of an...Ch. 6.7 - Health care costs The Centers for Medicare and...Ch. 6.7 - Coin production In 1942, the U.S. Mint produced...Ch. 6.7 - Distance The distance between Earth and one of the...Ch. 6.7 - Debt At the end of fiscal year 2015 the gross...Ch. 6.7 - (a) Explain the meaning of the exponent in the...Ch. 6.7 - When you convert a number from decimal notation to...Ch. 6 - In the following exercises, determine if each of...Ch. 6 - In the following exercises, determine if each of...Ch. 6 - In the following exercises, determine the degree...Ch. 6 - In the following exercises, determine the degree...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, add or subtract the...Ch. 6 - In the following exercises, evaluate each...Ch. 6 - In the following exercises, evaluate each...Ch. 6 - In the following exercises, evaluate each...Ch. 6 - In the following exercises, evaluate each...Ch. 6 - In the following exercises, simplify. 610. 104Ch. 6 - In the following exercises, simplify. 611. 171Ch. 6 - In the following exercises, simplify. 612. 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