Elementary Algebra
17th Edition
ISBN: 9780998625713
Author: Lynn Marecek, MaryAnne Anthony-Smith
Publisher: OpenStax - Rice University
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Textbook Question
Chapter 2.7, Problem 504E
Safety A child’s height, h, must be at least 57 inches for the child to safely ride in the front seat of a car. Write this as an inequality.
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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.
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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.)
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☐ B.
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☐ C.
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D.
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☐ E.
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☐ F.
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Chapter 2 Solutions
Elementary Algebra
Ch. 2.1 - Is y=43 a solution of 9y+2=6y+3 ?Ch. 2.1 - Is y=75 a solution of 5y+3=10y4 ?Ch. 2.1 - Solve: x+19=27 .Ch. 2.1 - Solve: x+16=34 .Ch. 2.1 - Solve: n61=75 .Ch. 2.1 - Solve: p41=73 .Ch. 2.1 - Solve: p23=56 .Ch. 2.1 - Solve: q12=56 .Ch. 2.1 - Solve: b0.47=2.1 .Ch. 2.1 - Solve: c0.93=4.6 .
Ch. 2.1 - Solve: 8y47y7=4 .Ch. 2.1 - Solve: 6z+55z4=3 .Ch. 2.1 - Solve: 5(p3)4p=10 .Ch. 2.1 - Solve: 4(q+2)3q=8 .Ch. 2.1 - Solve: 4(2h3)7h=6(h2)6(h1) .Ch. 2.1 - Solve: 2(5x+2)9x=3(x2)3(x4) .Ch. 2.1 - Translate and solve: Ten more than x is equal to...Ch. 2.1 - Translate and solve: Twelve less than x is equal...Ch. 2.1 - Translate and solve: The difference of 4x and 3x...Ch. 2.1 - Translate and solve: The difference of 7a and 6a...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - 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How do...Ch. 2.1 - What is the first step in your solution to the...Ch. 2.2 - Solve: 3y=41 .Ch. 2.2 - Solve: 4z=55 .Ch. 2.2 - Solve: a7=42 .Ch. 2.2 - Solve: b6=24 .Ch. 2.2 - Solve: k=8 .Ch. 2.2 - Solve: g=3 .Ch. 2.2 - Solve: 25n=14 .Ch. 2.2 - Solve: 56y=15 .Ch. 2.2 - Solve: 925=45z .Ch. 2.2 - Solve: 56=83r .Ch. 2.2 - Solve: 1827=15c9c3c .Ch. 2.2 - Solve: 1822=12xx4x .Ch. 2.2 - Solve: 4(q2)8=24 .Ch. 2.2 - Solve: 6(r2)12=30 .Ch. 2.2 - Translate and solve: The number 132 is the product...Ch. 2.2 - Translate and solve: The number 117 is the product...Ch. 2.2 - Translate and solve: n divided by 7 is equal to 21...Ch. 2.2 - Translate and solve: n divided by 8 is equal to 56...Ch. 2.2 - Translate and solve: The quotient of q and 8 is...Ch. 2.2 - Translate and solve: The quotient of p and 9 is...Ch. 2.2 - Translate and solve: Two-fifths of f is 16.Ch. 2.2 - Translate and solve: Three-fourths of f is 21.Ch. 2.2 - Translate and solve: The sum of five-eighths and x...Ch. 2.2 - Translate and solve: The sum of three-fourths and...Ch. 2.2 - Translate and solve: Arianna bought a 24-pack of...Ch. 2.2 - Translate and solve: At JB’s Bowling Alley, 6...Ch. 2.2 - Translate and solve: The annual property tax on...Ch. 2.2 - Translate and solve: Stella planted 14 flats of...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - 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Solve: 3p14=5p .Ch. 2.3 - Solve: 8m+9=5m .Ch. 2.3 - Solve: 12j=4j+32 .Ch. 2.3 - Solve: 8h=4h+12 .Ch. 2.3 - Solve: 12x+8=6x+2 .Ch. 2.3 - Solve: 9y+4=7y+12 .Ch. 2.3 - Solve: 8q5=4q+7 .Ch. 2.3 - Solve: 7n3=n+3 .Ch. 2.3 - Solve: 2a2=6a+18 .Ch. 2.3 - Solve: 4k1=7k+17 .Ch. 2.3 - Solve: 78x12=18x2 .Ch. 2.3 - Solve: 76y+11=16y+8 .Ch. 2.3 - Solve: 2.8x+12=1.4x9 .Ch. 2.3 - Solve: 3.6y+8=1.2y4 .Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - 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How...Ch. 2.4 - Solve: 5(x+3)=35 .Ch. 2.4 - Solve: 6(y4)=18 .Ch. 2.4 - Solve: (y+8)=2 .Ch. 2.4 - Solve: (z+4)=12 .Ch. 2.4 - Solve: 2(m4)+3=1 .Ch. 2.4 - Solve: 7(n3)8=15 .Ch. 2.4 - Solve: 13(6u+3)=7u .Ch. 2.4 - Solve: 23(9x12)=8+2x .Ch. 2.4 - Solve: 123(4j+3)=17 .Ch. 2.4 - Solve: 68(k2)=10 .Ch. 2.4 - Solve: 6(p3)7=5(4p+3)12 .Ch. 2.4 - Solve: 8(q+1)5=3(2q4)1 .Ch. 2.4 - Solve: 6[42(7y1)]=8(138y) .Ch. 2.4 - Solve: 12[15(4z1)]=3(24+11z) .Ch. 2.4 - Solve: 0.55(100n+8)=0.6(85n+14) .Ch. 2.4 - Solve: 0.15(40m120)=0.5(60m+12) .Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - 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- 3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forwardFind the perimeter and areaarrow_forward
- 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 abovearrow_forwardAssume {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 abovearrow_forwardLet 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= 6arrow_forward
- 3. Let M = (a) - (b) 2 −1 1 -1 2 7 4 -22 Find a basis for Col(M). Find a basis for Null(M).arrow_forwardSchoology X 1. IXL-Write a system of X Project Check #5 | Schx Thomas Edison essay, x Untitled presentation ixl.com/math/algebra-1/write-a-system-of-equations-given-a-graph d.net bookmarks Play Gimkit! - Enter... Imported Imported (1) Thomas Edison Inv... ◄›) What system of equations does the graph show? -8 -6 -4 -2 y 8 LO 6 4 2 -2 -4 -6 -8. 2 4 6 8 Write the equations in slope-intercept form. Simplify any fractions. y = y = = 00 S olo 20arrow_forwardEXERCICE 2: 6.5 points Le plan complexe est rapporté à un repère orthonormé (O, u, v ).Soit [0,[. 1/a. Résoudre dans l'équation (E₁): z2-2z+2 = 0. Ecrire les solutions sous forme exponentielle. I b. En déduire les solutions de l'équation (E2): z6-2 z³ + 2 = 0. 1-2 2/ Résoudre dans C l'équation (E): z² - 2z+1+e2i0 = 0. Ecrire les solutions sous forme exponentielle. 3/ On considère les points A, B et C d'affixes respectives: ZA = 1 + ie 10, zB = 1-ie 10 et zc = 2. a. Déterminer l'ensemble EA décrit par le point A lorsque e varie sur [0, 1. b. Calculer l'affixe du milieu K du segment [AB]. C. Déduire l'ensemble EB décrit par le point B lorsque varie sur [0,¹ [. d. Montrer que OACB est un parallelogramme. e. Donner une mesure de l'angle orienté (OA, OB) puis déterminer pour que OACB soit un carré.arrow_forward
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