 Chapter 1.1: Ten less than twice a number
 Chapter 1.2: Four more than the product of six and a number
 Chapter 1.3: The quotient of nine and a number, increased by half of the number
 Chapter 1.4: x2  7x + 4, for x = 10
 Chapter 1.5: 6 + 2(x  8) 3 , for x = 11
 Chapter 1.6: x4  (x  y), for x = 2 and y = 1
 Chapter 1.7: {x x is a natural number less than 3}
 Chapter 1.8: {x x is an integer greater than 4 and less than 2}
 Chapter 1.9: 0 {x x is a natural number}
 Chapter 1.10: 2 {x x is a rational number}
 Chapter 1.11: 1 3 {x x is an irrational number}
 Chapter 1.12: 5 6 2
 Chapter 1.13: 7 3
 Chapter 1.14: 7 7
 Chapter 1.15: The bar graph shows the percentage of U.S. adults who received a fl...
 Chapter 1.16: (2, 3]
 Chapter 1.17: [1.5, 2]
 Chapter 1.18: (1, )
 Chapter 1.19: 9.7
 Chapter 1.20: 5.003
 Chapter 1.21: 0
 Chapter 1.22: 2.4 + (5.2)
 Chapter 1.23: 6.8 + 2.4
 Chapter 1.24: 7  (20)
 Chapter 1.25: (3)(20)
 Chapter 1.26:  3 5  a 1 2 b
 Chapter 1.27: a 2 7 b a 3 10 b
 Chapter 1.28: 4(3)(2)(10)
 Chapter 1.29: (2) 4
 Chapter 1.30: 25
 Chapter 1.31:  2 3 , 8 5
 Chapter 1.32: 35 5
 Chapter 1.33: 54.6 6
 Chapter 1.34: Find x if x = 7.
 Chapter 1.35: 11  [17 + (3)]
 Chapter 1.36: a 1 2 b 3 # 24
 Chapter 1.37: 3[4  (6  8)]
 Chapter 1.38: 82  36 , 32 # 4  (7)
 Chapter 1.39: (2) 4 + (3) 2 22  (21)
 Chapter 1.40: (7  9) 3  (4) 2 2 + 2(8) , 4
 Chapter 1.41: 4  (3  8) 2 + 3 , 6 # 42
 Chapter 1.42: 5(2x  3) + 7x
 Chapter 1.43: 5x + 7x2  4x + 2x2
 Chapter 1.44: 3(4y  5)  (7y + 2)
 Chapter 1.45: 8  2[3  (5x  1)]
 Chapter 1.46: 6(2x  3)  5(3x  2)
 Chapter 1.47: (1, 3)
 Chapter 1.48: (2, 5)
 Chapter 1.49: (0, 6)
 Chapter 1.50: y = 2x  2
 Chapter 1.51: y = x2  3
 Chapter 1.52: y = x
 Chapter 1.53: y = x  2
 Chapter 1.54: What does a [20, 40, 10] by [5, 5, 1] viewing rectangle mean? Dra...
 Chapter 1.55: What percentage of Americans who are 75 have Alzheimers disease?
 Chapter 1.56: What age represents 50% prevalence of Alzheimers disease?
 Chapter 1.57: Describe the trend shown by the graph.
 Chapter 1.58: Select the graph that best illustrates the following description: A...
 Chapter 1.59: 2x  5 = 7
 Chapter 1.60: 5x + 20 = 3x
 Chapter 1.61: 7(x  4) = x + 2
 Chapter 1.62: 1  2(6  x) = 3x + 2
 Chapter 1.63: 2(x  4) + 3(x + 5) = 2x  2
 Chapter 1.64: 2x  4(5x + 1) = 3x + 17
 Chapter 1.65: 2x 3 = x 6 + 1
 Chapter 1.66: x 2  1 10 = x 5 + 1 2
 Chapter 1.67: 2x 3 = 6  x 4
 Chapter 1.68: x 4 = 2 + x  3 3
 Chapter 1.69: 3x + 1 3  13 2 = 1  x 4
 Chapter 1.70: 7x + 5 = 5(x + 3) + 2x
 Chapter 1.71: 7x + 13 = 4x  10 + 3x + 23
 Chapter 1.72: 7x + 13 = 3x  10 + 2x + 23
 Chapter 1.73: 4(x  3) + 5 = x + 5(x  2)
 Chapter 1.74: (2x  3)2  3(x + 1) = (x  2)4  3(x + 5)
 Chapter 1.75: In 2010, the average U.S. household had approximately 2.9 televisio...
 Chapter 1.76: Although you want to choose a career that fits your interests and a...
 Chapter 1.77: One angle of a triangle measures 10 more than the second angle. The...
 Chapter 1.78: Without changes, the graphs show projections for the amount being p...
 Chapter 1.79: You are choosing between two texting plans. One plan has a monthly ...
 Chapter 1.80: After a 20% price reduction, a cordless phone sold for $48. What wa...
 Chapter 1.81: A salesperson earns $300 per week plus 5% commission of sales. How ...
 Chapter 1.82: The length of a rectangular field is 6 yards less than triple the w...
 Chapter 1.83: In 2005, there were 14,100 students at college A, with a projected ...
 Chapter 1.84: V = 1 3 Bh for h
 Chapter 1.85: y  y1 = m(x  x1) for x
 Chapter 1.86: E = I(R + r) for R
 Chapter 1.87: C = 5F  160 9 for F
 Chapter 1.88: s = vt + gt 2 for g
 Chapter 1.89: T = gr + gvt for g
 Chapter 1.90: (3x7 )(5x6 )
 Chapter 1.91: x2 y5
 Chapter 1.92: 32 x4 y7
 Chapter 1.93: (x3 ) 6
 Chapter 1.94: (7x3 y) 2
 Chapter 1.95: 16y3 2y10
 Chapter 1.96: (3x4 )(4x11 )
 Chapter 1.97: 12x7 4x3
 Chapter 1.98: 10a5 b6 20a3 b11
 Chapter 1.99: (3xy4 )(2x2 ) 3
 Chapter 1.100: 22 + 1 2 x0
 Chapter 1.101: (5x2 y4 ) 3
 Chapter 1.102: (3x4 y2 )(2x5 y3 )
 Chapter 1.103: 3xy3 5x3 y4 2
 Chapter 1.104: 20x2 y3 10x5 y6 3
 Chapter 1.105: 7.16 * 106
 Chapter 1.106: 1.07 * 104
 Chapter 1.107: 41,000,000,000,000
 Chapter 1.108: 0.00809
 Chapter 1.109: (4.2 * 1013 )(3 * 106 )
 Chapter 1.110: 5 * 106 20 * 108
 Chapter 1.111: The human body contains approximately 3.2 * 104 microliters of bloo...
Solutions for Chapter Chapter 1: Algebra, Mathematical Models, and Problem Solving
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter Chapter 1: Algebra, Mathematical Models, and Problem Solving
Get Full SolutionsSince 111 problems in chapter Chapter 1: Algebra, Mathematical Models, and Problem Solving have been answered, more than 40265 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Chapter Chapter 1: Algebra, Mathematical Models, and Problem Solving includes 111 full stepbystep solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.