 15.1: Rewrite each expression using the Distributive Property. Then evalu...
 15.2: Rewrite each expression using the Distributive Property. Then evalu...
 15.3: Rewrite each expression using the Distributive Property. Then evalu...
 15.4: COSMETOLOGY A hair stylist cut 12 customers hair. She earned $29.95...
 15.5: Use the Distributive Property to rewrite each expression. Then find...
 15.6: Use the Distributive Property to rewrite each expression. Then find...
 15.7: Rewrite each expression using the Distributive Property. Then simpl...
 15.8: Rewrite each expression using the Distributive Property. Then simpl...
 15.9: Simplify each expression. If not possible, write simplified. 13m + m
 15.10: Simplify each expression. If not possible, write simplified. 14a 2 ...
 15.11: Simplify each expression. If not possible, write simplified. 3(x + 2x)
 15.12: Rewrite each expression using the Distributive Property. Then evalu...
 15.13: Rewrite each expression using the Distributive Property. Then evalu...
 15.14: Rewrite each expression using the Distributive Property. Then evalu...
 15.15: Rewrite each expression using the Distributive Property. Then evalu...
 15.16: Rewrite each expression using the Distributive Property. Then evalu...
 15.17: Rewrite each expression using the Distributive Property. Then evalu...
 15.18: COMMUNICATION A consultant keeps a log of all contacts she makes. I...
 15.19: OLYMPICS The table shows the average daily attendance for two venue...
 15.20: Use the Distributive Property to rewrite each expression. Then find...
 15.21: Use the Distributive Property to rewrite each expression. Then find...
 15.22: Use the Distributive Property to rewrite each expression. Then find...
 15.23: Use the Distributive Property to rewrite each expression. Then find...
 15.24: Rewrite each expression using the Distributive Property. Then simpl...
 15.25: Rewrite each expression using the Distributive Property. Then simpl...
 15.26: Rewrite each expression using the Distributive Property. Then simpl...
 15.27: Rewrite each expression using the Distributive Property. Then simpl...
 15.28: Simplify each expression. If not possible, write simplified. 2x + 9x
 15.29: Simplify each expression. If not possible, write simplified. 4b  1...
 15.30: Simplify each expression. If not possible, write simplified. 5n 2  7n
 15.31: Simplify each expression. If not possible, write simplified. 3a 2 +...
 15.32: Simplify each expression. If not possible, write simplified. 12(4 +...
 15.33: Simplify each expression. If not possible, write simplified. (3x  ...
 15.34: Write and evaluate an expression to calculate the total cost of med...
 15.35: How much would an employee expect to pay for family medical and den...
 15.36: Rewrite each expression using the Distributive Property. Then simpl...
 15.37: Rewrite each expression using the Distributive Property. Then simpl...
 15.38: Rewrite each expression using the Distributive Property. Then simpl...
 15.39: Rewrite each expression using the Distributive Property. Then simpl...
 15.40: Simplify each expression. If not possible, write simplified. 6 x 2 ...
 15.41: Simplify each expression. If not possible, write simplified. 4 y 3 ...
 15.42: Simplify each expression. If not possible, write simplified. a + _a...
 15.43: REASONING Explain why the Distributive Property is sometimes called...
 15.44: OPEN ENDED Write an expression that has five terms, three of which ...
 15.45: FIND THE ERROR Courtney and Che are simplifying 3(x + 4). Who is co...
 15.46: CHALLENGE The expression 2( + w) can be used to find the perimeter ...
 15.47: Writing in Math Use the data about video game prices on page 26 to ...
 15.48: In three months, Mayuko had 108 minutes of incoming calls on her vo...
 15.49: 49. REVIEW If each dimension of the prism is tripled, which express...
 15.50: Name the property illustrated by each statement or equation. If 7 2...
 15.51: Name the property illustrated by each statement or equation. mnp = ...
 15.52: Name the property illustrated by each statement or equation. _3 4 _...
 15.53: Name the property illustrated by each statement or equation. 32 + 2...
 15.54: PHYSICAL SCIENCE Sound travels through air at an approximate speed ...
 15.55: Evaluate each expression if a = 4, b = 6, and c = 3. ( 3b  c
 15.56: Evaluate each expression if a = 4, b = 6, and c = 3. ( 8(a  c) 2 + 3
 15.57: Evaluate each expression if a = 4, b = 6, and c = 3. ( _6ab 2(c + 5)
 15.58: PREREQUISITE SKILL Find the area of each figure.
 15.59: PREREQUISITE SKILL Find the area of each figure.
 15.60: PREREQUISITE SKILL Find the area of each figure.
Solutions for Chapter 15: The Distributive Property
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 15: The Distributive Property
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. Since 60 problems in chapter 15: The Distributive Property have been answered, more than 34341 students have viewed full stepbystep solutions from this chapter. Chapter 15: The Distributive Property includes 60 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Column space C (A) =
space of all combinations of the columns of A.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

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].

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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

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.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

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.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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