 1.5.1: According to the U.S. Office of Management and Budget, the 2011 bud...
 1.5.2: In 2000, 31% of U.S. adults viewed a college education as essential...
 1.5.3: A text message plan costs $4 per month plus $0.15 per text. The mon...
 1.5.4: I purchased a computer after a 15% price reduction. If x represents...
 1.5.5: Solving a formula for a variable means rewriting the formula so tha...
 1.5.6: The first step in solving IR + Ir = E for I is to obtain a single o...
 1.5.7: 70% of what number is 224?
 1.5.8: 70% of what number is 252?
 1.5.9: One number exceeds another by 26. The sum of the numbers is 64. Wha...
 1.5.10: One number exceeds another by 24. The sum of the numbers is 58. Wha...
 1.5.11: y1 = 13x  4, y2 = 5x + 10, and y1 exceeds y2 by 2.
 1.5.12: y1 = 10x + 6, y2 = 12x  7, and y1 exceeds y2 by 3.
 1.5.13: y1 = 10(2x  1), y2 = 2x + 1, and y1 is 14 more than 8 times y2 .
 1.5.14: y1 = 9(3x  5), y2 = 3x  1, and y1 is 51 less than 12 times y2 .
 1.5.15: y1 = 2x + 6, y2 = x + 8, y3 = x, and the difference between 3 times...
 1.5.16: y1 = 2.5, y2 = 2x + 1, y3 = x, and the difference between 2 times y...
 1.5.17: Whats the last word in capital punishment? An analysis of the final...
 1.5.18: How many words are there? The bar graph shows the number of words i...
 1.5.19: In a triangle, the measure of the first angle is twice the measure ...
 1.5.20: In a triangle, the measure of the first angle is three times the me...
 1.5.21: In a triangle, the measures of the three angles are consecutive int...
 1.5.22: In a triangle, the measures of the three angles are consecutive eve...
 1.5.23: In 2000, 31% of U.S. adults viewed a college education as essential...
 1.5.24: In 2000, 45% of U.S. adults believed that most qualified students g...
 1.5.25: If this trend continues, by which year will corporations pay zero t...
 1.5.26: If this trend continues, by which year will the percentage of feder...
 1.5.27: Each day, the number of births in the world is 92 thousand less tha...
 1.5.28: Each day, the number of births in the world exceeds twice the numbe...
 1.5.29: You are choosing between two health clubs. Club A offers membership...
 1.5.30: Video Store A charges $9 to rent a video game for one week. Althoug...
 1.5.31: The bus fare in a city is $1.25. People who use the bus have the op...
 1.5.32: A discount pass for a bridge costs $30 per month. The toll for the ...
 1.5.33: In 2008, there were 13,300 students at college A, with a projected ...
 1.5.34: In 2000, the population of Greece was 10,600,000, with projections ...
 1.5.35: After a 20% reduction, you purchase a television for $336. What was...
 1.5.36: After a 30% reduction, you purchase a dictionary for $30.80. What w...
 1.5.37: Including 8% sales tax, an inn charges $162 per night. Find the inn...
 1.5.38: Including 5% sales tax, an inn charges $252 per night. Find the inn...
 1.5.39: The selling price of a refrigerator is $584. If the markup is 25% o...
 1.5.40: The selling price of a scientific calculator is $15. If the markup ...
 1.5.41: A rectangular soccer field is twice as long as it is wide. If the p...
 1.5.42: A rectangular swimming pool is three times as long as it is wide. I...
 1.5.43: The length of the rectangular tennis court at Wimbledon is 6 feet l...
 1.5.44: The length of a rectangular pool is 6 meters less than twice the wi...
 1.5.45: The rectangular painting in the figure shown measures 12 inches by ...
 1.5.46: The rectangular swimming pool in the figure shown measures 40 feet ...
 1.5.47: For an international telephone call, a telephone company charges $0...
 1.5.48: A job pays an annual salary of $33,150, which includes a holiday bo...
 1.5.49: A = lw for l (geometry)
 1.5.50: A = lw for w (geometry)
 1.5.51: A = 1 2 bh for b (geometry)
 1.5.52: A = 1 2 bh for h (geometry)
 1.5.53: I = Prt for P (finance)
 1.5.54: I = Prt for t (finance)
 1.5.55: T = D + pm for p (finance)
 1.5.56: P = C + MC for M (finance)
 1.5.57: A = 1 2 h(a + b) for a (geometry)
 1.5.58: A = 1 2 h(a + b) for b (geometry)
 1.5.59: V = 1 3 pr2 h for h (geometry)
 1.5.60: V = 1 3 pr2 h for r 2 (geometry)
 1.5.61: y  y1 = m(x  x1) for m (algebra)
 1.5.62: y2  y1 = m(x2  x1) for m (algebra)
 1.5.63: V = d1  d2 t for d1 (physics)
 1.5.64: z = x  u s for x (statistics)
 1.5.65: Ax + By = C for x (algebra)
 1.5.66: Ax + By = C for y (algebra)
 1.5.67: s = 1 2 at 2 + vt for v (physics)
 1.5.68: s = 1 2 at 2 + vt for a (physics)
 1.5.69: L = a + (n  1)d for n (algebra)
 1.5.70: L = a + (n  1)d for d (algebra)
 1.5.71: A = 2lw + 2lh + 2wh for l (geometry)
 1.5.72: A = 2lw + 2lh + 2wh for h (geometry)
 1.5.73: IR + Ir = E for I (physics)
 1.5.74: A = x1 + x2 + x3 n for n (statistics)
 1.5.75: In your own words, describe a stepbystep approach for solving alg...
 1.5.76: Write an original word problem that can be solved using a linear eq...
 1.5.77: Explain what it means to solve a formula for a variable.
 1.5.78: Did you have difficulties solving some of the problems that were as...
 1.5.79: The bar graph in Figure 1.23 on page 55 indicates a gender gap in p...
 1.5.80: Use a graphing utility to numerically or graphically verify your wo...
 1.5.81: The formula y = 31 + 2.4x models the percentage of U.S. adults, y, ...
 1.5.82: In Exercises 2526, we saw that in 1960, 23% of U.S. taxes came from...
 1.5.83: I solved the formula for one of its variables, so now I have a nume...
 1.5.84: Reasoning through a word problem often increases problemsolving sk...
 1.5.85: The hardest part in solving a word problem is writing the equation ...
 1.5.86: When traveling in Europe, the most useful form of the two CelsiusF...
 1.5.87: If I = prt, then t = I  pr
 1.5.88: If y = kx z , then z = kx y .
 1.5.89: It is not necessary to use the distributive property to solve P = C...
 1.5.90: An items price, x, reduced by 1 3 is modeled by x  1 3 .
 1.5.91: The price of a dress is reduced by 40%. When the dress still does n...
 1.5.92: Suppose that we agree to pay you 8 for every problem in this chapte...
 1.5.93: It was wartime when the Ricardos found out Mrs. Ricardo was pregnan...
 1.5.94: A thief steals a number of rare plants from a nursery. On the way o...
 1.5.95: Solve for C: V = C  C  S L N.
 1.5.96: Express in setbuilder notation and graph: (4, 0]. (Section 1.1, E...
 1.5.97: Simplify: (2 + 4) 2 + (1) 5 12 , 2 # 3  3 . (Section 1.2, Example 8)
 1.5.98: Solve: 2x 3  8 3 = x. (Section 1.4, Example 4)
 1.5.99: In parts (a) and (b), complete each statement. a. b4 # b3 = (b # b ...
 1.5.100: In parts (a) and (b), complete each statement. a. b7 b3 = b # b # b...
 1.5.101: Simplify: 1 a 1 2 b 3 .
Solutions for Chapter 1.5: Problem Solving and Using Formulas
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 1.5: Problem Solving and Using Formulas
Get Full SolutionsChapter 1.5: Problem Solving and Using Formulas includes 101 full stepbystep solutions. Since 101 problems in chapter 1.5: Problem Solving and Using Formulas have been answered, more than 45928 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

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 •

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.