 38.1: What is the greatest factor of both 54 and 45?
 38.2: Roberto began saving $3 each week for a bicycle, whichcosts $126. H...
 38.3: Gandhi was born in 1869. About how old was he when hewas assassinat...
 38.4: 29 1.2
 38.5: 3.6 216
 38.6: 5.63 1.2
 38.7: 5.376 + 0.24
 38.8: 4.75 0.6
 38.9: 216 29
 38.10: Write fortyseven hundredthsa. as a fraction.b. as a decimal number.
 38.11: Write (9 1000) + (4 10) + (3 1) in standard notation.
 38.12: Which digit is in the hundredths place in $123.45?
 38.13: The area of a square is 81 square inches. a. What is the length of ...
 38.14: What is the least common multiple of 2, 3, and 4?
 38.15: 123 223
 38.16: 32 114
 38.17: What is 34 of 45?
 38.18: 710 1110
 38.19: a. How many 23 s are in 1?b. Use the answer to part a to find the n...
 38.20: Six of the nine players got on base. What fraction of the players g...
 38.21: List the factors of 30.
 38.22: Write each percent as a reduced fraction: a. 35% b. 65%
 38.23: Round 186,282 to the nearest thousand.
 38.24: 13m 1
 38.25: 22 23 243
 38.26: Compare: 24 8 240 80
 38.27: Write 0.7 and 0.21 as fractions. Then multiply the fractions. Chang...
 38.28: Peter bought ten carrots for $0.80. What was the cost for eachcarrot?
 38.29: Which of these fractions is closest to 1? A 15 B 25 C 35 D 45
 38.30: If you know the perimeter of a square, you can find the area ofthe ...
Solutions for Chapter 38: Adding and Subtracting Decimal Numbers and Whole Numbers Squares and Square Roots
Full solutions for Saxon Math, Course 1  1st Edition
ISBN: 9781591417835
Solutions for Chapter 38: Adding and Subtracting Decimal Numbers and Whole Numbers Squares and Square Roots
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 30 problems in chapter 38: Adding and Subtracting Decimal Numbers and Whole Numbers Squares and Square Roots have been answered, more than 35729 students have viewed full stepbystep solutions from this chapter. Saxon Math, Course 1 was written by and is associated to the ISBN: 9781591417835. This textbook survival guide was created for the textbook: Saxon Math, Course 1, edition: 1. Chapter 38: Adding and Subtracting Decimal Numbers and Whole Numbers Squares and Square Roots includes 30 full stepbystep solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

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!).

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

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

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.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

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

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

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

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