PREALGEBRA
15th Edition
ISBN: 9781938168994
Author: OpenStax
Publisher: OpenStax
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Textbook Question
Chapter 2, Problem 451PT
In the following exercises, translate each phrase into an algebraic expression.
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Assume {u1, U2, u3, u4} does not span R³.
Select the best statement.
A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set.
B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³.
C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set.
D. {u1, U2, u3} cannot span R³.
E. {U1, U2, u3} spans R³ if u̸4 is the zero vector.
F. none of the above
Select the best statement.
A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors
are distinct.
n
B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0
excluded spans Rª.
○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n
vectors.
○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors
spans Rn.
E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn.
F. none of the above
Which of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.)
☐ A.
{
7
4
3
13
-9
8
-17
7
☐ B.
0
-8
3
☐ C.
0
☐
D.
-5
☐ E.
3
☐ F.
4
TH
Chapter 2 Solutions
PREALGEBRA
Ch. 2.1 - Translate from algebra to words. 18+11 (b) (27)(9)...Ch. 2.1 - Translate from algebra to words. 4719 (b) 729 (c)...Ch. 2.1 - Translate from algebra to words. 1427 (b) 1928 (c)...Ch. 2.1 - Translate from algebra to words. 1915 (b) 7=125...Ch. 2.1 - Use Figure 2.2 to fill in the appropriate symbol....Ch. 2.1 - Use Figure 2.2 to fill in the appropriate symbol....Ch. 2.1 - Determine if each is an expression or an equation:...Ch. 2.1 - Determine if each is an expression or an equation:...Ch. 2.1 - Write each expression in exponential form:...Ch. 2.1 - Write each expression in exponential form:...
Ch. 2.1 - Write each exponential expression in expanded...Ch. 2.1 - Write each exponential expression in expanded...Ch. 2.1 - Simplifư: 53 (b) 17Ch. 2.1 - Simplify: 72 (b) 05Ch. 2.1 - Simplify the expressions: 1252 (b) (125)2Ch. 2.1 - Simplify the expressions: 8+39 (b) (8+3)9Ch. 2.1 - Simplify: 4273Ch. 2.1 - Simplify: 1234Ch. 2.1 - Simplify: 305+10(32)Ch. 2.1 - Simplify: 7010+4(62)Ch. 2.1 - Simplify: 9+53[4(9+3)]Ch. 2.1 - Simplify: 722[4(5+1)]Ch. 2.1 - Simplify: 32+242+43Ch. 2.1 - Simplify: 62535+82Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, translate from...Ch. 2.1 - In the following exercises, determine if each is...Ch. 2.1 - In the following exercises, determine if each is...Ch. 2.1 - In the following exercises, determine if each is...Ch. 2.1 - In the following exercises, determine if each is...Ch. 2.1 - In the following exercises, determine if each is...Ch. 2.1 - In the following exercises, determine if each is...Ch. 2.1 - In the following exercises, determine if each is...Ch. 2.1 - In the following exercises, write in exponential...Ch. 2.1 - In the following exercises, write in exponential...Ch. 2.1 - In the following exercises, write in exponential...Ch. 2.1 - In the following exercises, write in exponential...Ch. 2.1 - In the following exercises, write in expanded...Ch. 2.1 - In the following exercises, write in expanded...Ch. 2.1 - In the following exercises, write in expanded...Ch. 2.1 - In the following exercises, write in expanded...Ch. 2.1 - In the following exercises, simplify. 39. (a) 3+85...Ch. 2.1 - In the following exercises, simplify. (a) 2+63 (b)...Ch. 2.1 - In the following exercises, simplify. 2312(95)Ch. 2.1 - In the following exercises, simplify. 3218(115)Ch. 2.1 - In the following exercises, simplify. 38+52Ch. 2.1 - In the following exercises, simplify. 47+35Ch. 2.1 - In the following exercises, simplify. 2+8(6+1)Ch. 2.1 - In the following exercises, simplify. 4+6(3+6)Ch. 2.1 - In the following exercises, simplify. 412/8Ch. 2.1 - In the following exercises, simplify. 236/6Ch. 2.1 - In the following exercises, simplify. 6+10/2+2Ch. 2.1 - In the following exercises, simplify. 9+12/3+4Ch. 2.1 - In the following exercises, simplify. (6+10)(2+2)Ch. 2.1 - In the following exercises, simplify. (9+12)(3+4)Ch. 2.1 - In the following exercises, simplify. 204+65Ch. 2.1 - In the following exercises, simplify. 333+82Ch. 2.1 - In the following exercises, simplify. 20(4+6)5Ch. 2.1 - In the following exercises, simplify. 33(3+8)2Ch. 2.1 - In the following exercises, simplify. 42+52Ch. 2.1 - In the following exercises, simplify. 32+72Ch. 2.1 - In the following exercises, simplify. (4+5)2Ch. 2.1 - In the following exercises, simplify. (3+7)2Ch. 2.1 - In the following exercises, simplify. 3(1+96)42Ch. 2.1 - In the following exercises, simplify. 5(2+84)72Ch. 2.1 - In the following exercises, simplify. 2[1+3(102)]Ch. 2.1 - In the following exercises, simplify. 5[2+4(32)]Ch. 2.1 - Basketball In the 2014 NBA playoffs, the San...Ch. 2.1 - Elevation In Colorado there are more than 50...Ch. 2.1 - Explain the difference between an expression and...Ch. 2.1 - Why is it important to use the order of operations...Ch. 2.2 - Evaluate: y+4when (a) y=6 (b) y=15Ch. 2.2 - Evaluate: a5When (a) a=9 (b) a=17Ch. 2.2 - Evaluate: 8x3,when (a) x=2 (b) x=1Ch. 2.2 - Evaluate: 4y4,when y=3(b) y=5Ch. 2.2 - Evaluate: x2when x=8.Ch. 2.2 - Evaluate: x3when x=6.Ch. 2.2 - Evaluate: 2xWhen x=6.Ch. 2.2 - Evaluate: 3xWhen x=4.Ch. 2.2 - Evaluate: 2x+5y4when x=11and ? y=3Ch. 2.2 - Evaluate: 5x2y9when x=7and y=8Ch. 2.2 - Evaluate: 3x2+4x+1when x=3.Ch. 2.2 - Evaluate: 6x24x7when x=2.Ch. 2.2 - Identify all terms in the given expression, and...Ch. 2.2 - Identify all terms in the given expression, and...Ch. 2.2 - Identify the like terms in the list or the...Ch. 2.2 - Identify the like terms in the list or the...Ch. 2.2 - Simplify: 7x+9+9x+8Ch. 2.2 - Simplify: 5y+2+8y+4y+5Ch. 2.2 - Simplify: 3x2+9x+x2+5xCh. 2.2 - Simplify: 11y2+8y+y2+7yCh. 2.2 - Translate the given word phrase into an algebraic...Ch. 2.2 - Translate the given word phrase into an algebraic...Ch. 2.2 - Translate the given word phrase into an algebraic...Ch. 2.2 - Translate each word phrase into an algebraic...Ch. 2.2 - Translate each word phrase into an algebraic...Ch. 2.2 - Translate each word phrase into an algebraic...Ch. 2.2 - The length of a rectangle s 5inches less than the...Ch. 2.2 - The width of a rectangle is 2meters greater than...Ch. 2.2 - Geoffrey has dimes and quarters in his pocket. 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TRY IT :: 2.68 Solve: 27=n14Ch. 2.3 - TRY IT :: 2.69 Translate the sentence into an...Ch. 2.3 - TRY IT :: 2.70 Translate the sentence into an...Ch. 2.3 - TRY IT :: 2.71 Translate the sentence into an...Ch. 2.3 - TRY IT :: 2.72 Translate the sentence into an...Ch. 2.3 - TRY IT :: 2.73 Translate the given sentence into...Ch. 2.3 - TRY IT :: 2.74 Translate the given sentence into...Ch. 2.3 - TRY IT :: 2.75 Translate and solve: Seven more...Ch. 2.3 - TRY IT :: 2.76 Translate and salve: Eleven more...Ch. 2.3 - TRY IT :: 2.77 Translate and solve: The difference...Ch. 2.3 - TRY IT :: 2.78 Translate and solve: The difference...Ch. 2.3 - In the following exercises, determine whether each...Ch. 2.3 - âIn the following exercises, determine whether...Ch. 2.3 - In the following exercises, determine whether each...Ch. 2.3 - In the following exercises, determine whether each...Ch. 2.3 - In the following exercises, determine whether each...Ch. 2.3 - In the following exercises, determine whether each...Ch. 2.3 - 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Then make up a...Ch. 2.4 - TRY IT :: 2.79 Determine whether each number is a...Ch. 2.4 - TRY IT :: 280 Determine whether each number is a...Ch. 2.4 - TRY lT :: 2.81 Determine whether each number is a...Ch. 2.4 - TRY IT :: 282 determine whether each number is a...Ch. 2.4 - TRY IT :: Determine whether each number is a...Ch. 2.4 - TRY IT :: 2.84 Determine whether each number is a...Ch. 2.4 - TRY IT :: 2.85 Determine whether each number is a...Ch. 2.4 - TRY IT :: 286 Determine whether each number is a...Ch. 2.4 - TRY IT :: 2.87 Determine whether the given number...Ch. 2.4 - TRY IT :: 2.88 Determine whether the given number...Ch. 2.4 - TRY IT :: 2.89 Determine whether the given number...Ch. 2.4 - TRY IT :: 2.90 Determine whether the given number...Ch. 2.4 - TRY IT :: 2.91 Find all the factors of the given...Ch. 2.4 - TRY IT :: 2.92 Find all the factors of the given...Ch. 2.4 - TRY IT :: 2.93 Identify the number as prime or...Ch. 2.4 - TRY IT :: 2.94 Identify the number as prime or...Ch. 2.4 - In the following exercises, list all the multiples...Ch. 2.4 - In the following exercises, list all the multiples...Ch. 2.4 - In the following exercises, list all the multiples...Ch. 2.4 - In the following exercises, list all the multiples...Ch. 2.4 - In the following exercises, list all the multiples...Ch. 2.4 - In the following exercises, list all the multiples...Ch. 2.4 - In the following exercises, list all the multiples...Ch. 2.4 - In the following exercises, list all the multiples...Ch. 2.4 - In the following exercises, list all the multiples...Ch. 2.4 - In the following exercises, list all the multiples...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, use the divisibility...Ch. 2.4 - In the following exercises, find all the factors...Ch. 2.4 - In the following exercises, find all the factors...Ch. 2.4 - In the following exercises, find all the factors...Ch. 2.4 - In the following exercises, find all the factors...Ch. 2.4 - In the following exercises, find all the factors...Ch. 2.4 - In the following exercises, find all the factors...Ch. 2.4 - In the following exercises, find all the factors...Ch. 2.4 - In the following exercises, find all the factors...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - In the following exercises, determine if the given...Ch. 2.4 - Banking. Frank’s grandmother gave him $100 at his...Ch. 2.4 - Banking In March, Gina opened a Christmas club...Ch. 2.4 - If a number is divisible by 2 and by 3, why is it...Ch. 2.4 - What is the difference between prime numbers and...Ch. 2.5 - TRY IT :: 2.95 Find the prime factorization using...Ch. 2.5 - TRY IT :: 2.96 Find the prime factorization using...Ch. 2.5 - TRY IT :: 2.97 Find the prime factorization using...Ch. 2.5 - TRY IT :: 2.98 Find the prime factorization using...Ch. 2.5 - TRY IT :: 2.99 Find the prime factorization using...Ch. 2.5 - TRY IT :: 2.100 Find the prime factorization using...Ch. 2.5 - TRY IT :: 2.101 Find the prime factorization using...Ch. 2.5 - TRY IT :: 2.102 Find the prime factorization using...Ch. 2.5 - TRY IT :: 2.103 Find the least common multiple...Ch. 2.5 - TRY IT :: 2.104 Find the least common multiple...Ch. 2.5 - TRY IT :: 2.105 Find the LCM using the prime...Ch. 2.5 - TRY IT :: 2.106 Find the LCM using the prime...Ch. 2.5 - TRY IT :: 2.107 Find the LCM using the prime...Ch. 2.5 - TRY IT :: 2.108 Find the LCM using the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - In the following exercises, find the prime...Ch. 2.5 - 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