 1.5.1: Graph the inequality: x 2.
 1.5.2: True or False 5 7 3
 1.5.3: If each side of an inequality is multiplied by a(n) number, then th...
 1.5.4: A(n) , denoted consists of all real numbers x for whicha x b.
 1.5.5: The state that the sense, or direction, of an inequality remains th...
 1.5.6: In 69, assume thata 6 b c 6 0.True or Falsea + c 6 b + c
 1.5.7: In 69, assume thata 6 b c 6 0.True or Falsea  c 6 b  c
 1.5.8: In 69, assume thata 6 b c 6 0.True or Falseac 7 bc
 1.5.9: In 69, assume thata 6 b c 6 0.True or Falsea c 6 b c
 1.5.10: True or FalseThe square of any real number is always nonnegative.
 1.5.11: In 1116, express the graph shown in blue using interval notation.Al...
 1.5.12: In 1116, express the graph shown in blue using interval notation.Al...
 1.5.13: In 1116, express the graph shown in blue using interval notation.Al...
 1.5.14: In 1116, express the graph shown in blue using interval notation.Al...
 1.5.15: In 1116, express the graph shown in blue using interval notation.Al...
 1.5.16: In 1116, express the graph shown in blue using interval notation.Al...
 1.5.17: In 1722, an inequality is given.Write the inequality obtained by: (...
 1.5.18: In 1722, an inequality is given.Write the inequality obtained by: (...
 1.5.19: In 1722, an inequality is given.Write the inequality obtained by: (...
 1.5.20: In 1722, an inequality is given.Write the inequality obtained by: (...
 1.5.21: In 1722, an inequality is given.Write the inequality obtained by: (...
 1.5.22: In 1722, an inequality is given.Write the inequality obtained by: (...
 1.5.23: In 2330, write each inequality using interval notation, and illustr...
 1.5.24: In 2330, write each inequality using interval notation, and illustr...
 1.5.25: In 2330, write each inequality using interval notation, and illustr...
 1.5.26: In 2330, write each inequality using interval notation, and illustr...
 1.5.27: In 2330, write each inequality using interval notation, and illustr...
 1.5.28: In 2330, write each inequality using interval notation, and illustr...
 1.5.29: In 2330, write each inequality using interval notation, and illustr...
 1.5.30: In 2330, write each inequality using interval notation, and illustr...
 1.5.31: In 3138, write each interval as an inequality involving x, and illu...
 1.5.32: In 3138, write each interval as an inequality involving x, and illu...
 1.5.33: In 3138, write each interval as an inequality involving x, and illu...
 1.5.34: In 3138, write each interval as an inequality involving x, and illu...
 1.5.35: In 3138, write each interval as an inequality involving x, and illu...
 1.5.36: In 3138, write each interval as an inequality involving x, and illu...
 1.5.37: In 3138, write each interval as an inequality involving x, and illu...
 1.5.38: In 3138, write each interval as an inequality involving x, and illu...
 1.5.39: In 3952, fill in the blank with the correct inequality symbol If x ...
 1.5.40: In 3952, fill in the blank with the correct inequality symbol If x ...
 1.5.41: In 3952, fill in the blank with the correct inequality symbol If x ...
 1.5.42: In 3952, fill in the blank with the correct inequality symbol If x ...
 1.5.43: In 3952, fill in the blank with the correct inequality symbol If x ...
 1.5.44: In 3952, fill in the blank with the correct inequality symbol If x ...
 1.5.45: In 3952, fill in the blank with the correct inequality symbol If x ...
 1.5.46: In 3952, fill in the blank with the correct inequality symbol If x ...
 1.5.47: In 3952, fill in the blank with the correct inequality symbol If x ...
 1.5.48: In 3952, fill in the blank with the correct inequality symbol If x ...
 1.5.49: In 3952, fill in the blank with the correct inequality symbol If 2x...
 1.5.50: In 3952, fill in the blank with the correct inequality symbol If 3x...
 1.5.51: In 3952, fill in the blank with the correct inequality symbol If  ...
 1.5.52: In 3952, fill in the blank with the correct inequality symbol If  ...
 1.5.53: In 5388,solve each inequality. Express your answer using set notati...
 1.5.54: In 5388,solve each inequality. Express your answer using set notati...
 1.5.55: In 5388,solve each inequality. Express your answer using set notati...
 1.5.56: In 5388,solve each inequality. Express your answer using set notati...
 1.5.57: In 5388,solve each inequality. Express your answer using set notati...
 1.5.58: In 5388,solve each inequality. Express your answer using set notati...
 1.5.59: In 5388,solve each inequality. Express your answer using set notati...
 1.5.60: In 5388,solve each inequality. Express your answer using set notati...
 1.5.61: In 5388,solve each inequality. Express your answer using set notati...
 1.5.62: In 5388,solve each inequality. Express your answer using set notati...
 1.5.63: In 5388,solve each inequality. Express your answer using set notati...
 1.5.64: In 5388,solve each inequality. Express your answer using set notati...
 1.5.65: In 5388,solve each inequality. Express your answer using set notati...
 1.5.66: In 5388,solve each inequality. Express your answer using set notati...
 1.5.67: In 5388,solve each inequality. Express your answer using set notati...
 1.5.68: In 5388,solve each inequality. Express your answer using set notati...
 1.5.69: In 5388,solve each inequality. Express your answer using set notati...
 1.5.70: In 5388,solve each inequality. Express your answer using set notati...
 1.5.71: In 5388,solve each inequality. Express your answer using set notati...
 1.5.72: In 5388,solve each inequality. Express your answer using set notati...
 1.5.73: In 5388,solve each inequality. Express your answer using set notati...
 1.5.74: In 5388,solve each inequality. Express your answer using set notati...
 1.5.75: In 5388,solve each inequality. Express your answer using set notati...
 1.5.76: In 5388,solve each inequality. Express your answer using set notati...
 1.5.77: In 5388,solve each inequality. Express your answer using set notati...
 1.5.78: In 5388,solve each inequality. Express your answer using set notati...
 1.5.79: In 5388,solve each inequality. Express your answer using set notati...
 1.5.80: In 5388,solve each inequality. Express your answer using set notati...
 1.5.81: In 5388,solve each inequality. Express your answer using set notati...
 1.5.82: In 5388,solve each inequality. Express your answer using set notati...
 1.5.83: In 5388,solve each inequality. Express your answer using set notati...
 1.5.84: In 5388,solve each inequality. Express your answer using set notati...
 1.5.85: In 5388,solve each inequality. Express your answer using set notati...
 1.5.86: In 5388,solve each inequality. Express your answer using set notati...
 1.5.87: In 5388,solve each inequality. Express your answer using set notati...
 1.5.88: In 5388,solve each inequality. Express your answer using set notati...
 1.5.89: In 8998, find a and b.If1 6 x 6 1, a 6 x + 4 6 b
 1.5.90: In 8998, find a and b.If3 6 x 6 2, a 6 x  6 6 b.
 1.5.91: In 8998, find a and b.If2 6 x 6 3, a 6 4x 6 b
 1.5.92: In 8998, find a and b.If4 6 x 6 0, x 6 b.
 1.5.93: In 8998, find a and b.If0 6 x 6 4, a 6 2x + 3 6 b.
 1.5.94: In 8998, find a and b.If3 6 x 6 3, a 6 1  2x 6 b.
 1.5.95: In 8998, find a and b.If3 6 x 6 0, 6 b
 1.5.96: In 8998, find a and b.If2 6 x 6 4, 6 b
 1.5.97: In 8998, find a and b.If6 6 3x 6 12, 6 b.
 1.5.98: In 8998, find a and b.If0 6 2x 6 6, 6 b.
 1.5.99: What is the domain of the variable in the expression23x + 6?
 1.5.100: What is the domain of the variable in the expression28 + 2x?
 1.5.101: A young adult may be defined as someone older than 21, but less tha...
 1.5.102: Middleaged may be defined as being 40 or more and less than 60. Ex...
 1.5.103: Life Expectancy The Social Security Administration determined that ...
 1.5.104: General Chemistry For a certain ideal gas, the volume V (in cubic c...
 1.5.105: Real Estate A real estate agent agrees to sell an apartment complex...
 1.5.106: Sales Commission A used car salesperson is paid a commission of $25...
 1.5.107: Federal Tax Withholding The percentage method of withholding for fe...
 1.5.108: loss, the American College of Sports Medicine (ACSM) recommends 200...
 1.5.109: Electricity Rates Commonwealth Edison Companys charge for electrici...
 1.5.110: Water Bills The Village of Oak Lawn charges homeowners $37.62 per q...
 1.5.111: Markup of a New Car The markup over dealers cost of a new car range...
 1.5.112: IQ Tests A standard intelligence test has an average score of 100.A...
 1.5.113: Computing Grades In your Economics 101 class, you have scores of 68...
 1.5.114: Light Foods For food products to be labeled light, the U.S. Food an...
 1.5.115: Arithmetic Mean If show that The number is called the arithmetic me...
 1.5.116: Refer to 115. Show that the arithmetic mean of a and b is equidista...
 1.5.117: Geometric Mean If show that The number is called the geometric mean...
 1.5.118: Refer to 115 and 117. Show that the geometric mean of a and b is le...
 1.5.119: Harmonic Mean For let h be defined by Show that The number h is cal...
 1.5.120: Refer to 115, 117, and 119. Show that the harmonic mean of a and b ...
 1.5.121: nother Reciprocal Property Prove that if , then 0 6 1 b 6 1 a . 0 6...
 1.5.122: Make up an inequality that has no solution. Make up one that has ex...
 1.5.123: The inequality has no real solution. Explain whyx2 + 1 6 5
 1.5.124: Do you prefer to use inequality notation or interval notation to ex...
 1.5.125: How would you explain to a fellow student the underlying reason for...
Solutions for Chapter 1.5: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 1.5
Get Full SolutionsAlgebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. Chapter 1.5 includes 125 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Since 125 problems in chapter 1.5 have been answered, more than 57685 students have viewed full stepbystep solutions from this chapter.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

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.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

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

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.