 5.7.1: Match each system of inequalities with its graph.
 5.7.2: Here is the graph of this system of inequalities: Is each point lis...
 5.7.3: Consider these two inequalities together as a system. a. Name the i...
 5.7.4: Sketch a graph showing the solution to each system.
 5.7.5: Write a system of inequalities for the solution shown on the graph.
 5.7.6: APPLICATION The cereal company from Example B decides to raise the ...
 5.7.7: APPLICATION On Kids Night, every adult admitted into a restaurant m...
 5.7.8: APPLICATION The American College of Sports Medicine considers age a...
 5.7.9: Write two inequalities that describe the shaded area below. Assume ...
 5.7.10: Write a system of inequalities to describe the shaded area on the g...
 5.7.11: Graph this system of inequalities on the same set of axes. Describe...
 5.7.12: Write a system of inequalities that defines each shaded region of p...
 5.7.13: APPLICATION Manuel has a sales job at a local furniture store. Once...
 5.7.14: Think about the number trick shown at right. a. Layla got a final n...
 5.7.15: Solve each system of equations by using a symbolic method. Check th...
 5.7.16: Mr. Diaz makes an organic weed killer by mixing 8 ounces of distill...
Solutions for Chapter 5.7: Systems of Inequalities
Full solutions for Discovering Algebra: An Investigative Approach  2nd Edition
ISBN: 9781559537636
Solutions for Chapter 5.7: Systems of Inequalities
Get Full SolutionsSince 16 problems in chapter 5.7: Systems of Inequalities have been answered, more than 3069 students have viewed full stepbystep solutions from this chapter. Discovering Algebra: An Investigative Approach was written by Patricia and is associated to the ISBN: 9781559537636. This textbook survival guide was created for the textbook: Discovering Algebra: An Investigative Approach, edition: 2. Chapter 5.7: Systems of Inequalities includes 16 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their 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.

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

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

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

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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 ().

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

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

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

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.

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

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).
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