 11.1: z  x + y 2
 11.2: x + (y  1 ) 3
 11.3: x + [3(y + z)  y]
 11.4: x _ 2  y z + 2.5
 11.5: x + 2 y _ 2 x  z
 11.6: y _ 3 + 2xz x 2  z
 11.7: p = $1800, r = 6%, t = 4 years
 11.8: p = $31,000, r = 2 _1 2 %, t = 18 months
 11.9: w + x + z
 11.10: w + 12 z
 11.11: w(8  y)
 11.12: z(x + 1)
 11.13: w  3x + y
 11.14: 5x + 2z
 11.15: a  d bc
 11.16: a + d c
 11.17: a2c _2 d
 11.18: a  10b c2d2
 11.19: d + 4 a2 + 3
 11.20: 1  b 3c  3b
 11.21: NURSING Determine the IV flow rate for the patient described at the...
 11.22: BICYCLING Air pollution can be reduced by riding a bicycle rather t...
 11.23: GEOMETRY The formula for the area A of a circle with diameter d is ...
 11.24: GEOMETRY The formula for the volume V of a right circular cone with...
 11.25: b4  d
 11.26: (5  d)2 + a
 11.27: 5ad b
 11.28: 2b  15a 3c
 11.29: (a  c)2  2bd
 11.30: 1 c + _1 d
 11.31: Find the value of abn if n = 3, a = 2000, and b =  _1 5
 11.32: FIREWORKS Suppose you are about a mile from a fireworks display. Yo...
 11.33: MONEY In 1960, the average price of a car was about $2500. This may...
 11.34: MEDICINE A patient must take blood pressure medication that is disp...
 11.35: QB RATING The formula for quarterback efficiency rating in the Nati...
 11.36: OPEN ENDED Write an algebraic expression in which subtraction is pe...
 11.37: CHALLENGE Write expressions having values from one to ten using exa...
 11.38: REASONING Explain how to evaluate a + b[(c + d) e], if you were giv...
 11.39: Writing in Math Use the information about IV flow rates on page 6 t...
 11.40: ACT/SAT The following are the dimensions of four rectangles. Which ...
 11.41: REVIEW How many cubes that are 3 inches on each edge can be placed ...
 11.42: 9 4
 11.43: 16 4
 11.44: 100 4
 11.45: 169
 11.46:  4 47
 11.47:  25
 11.48: _4 9
 11.49: _36 49
Solutions for Chapter 11: Expressions and Formulas
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 11: Expressions and Formulas
Get Full SolutionsChapter 11: Expressions and Formulas includes 49 full stepbystep solutions. Since 49 problems in chapter 11: Expressions and Formulas have been answered, more than 53434 students have viewed full stepbystep solutions from this chapter. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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

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!).

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

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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.

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

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

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).

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

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 space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.