 64.1: Graph the solution set of each compound inequality.
 64.2: Graph the solution set of each compound inequality.
 64.3: Solve each compound inequality. Then graph the solution set.
 64.4: Solve each compound inequality. Then graph the solution set.
 64.5: Solve each compound inequality. Then graph the solution set.
 64.6: Solve each compound inequality. Then graph the solution set.
 64.7: BIKES The recommended air pressure for the tires of a mountain bike...
 64.8: Graph the solution set of each compound inequality.
 64.9: Graph the solution set of each compound inequality.
 64.10: Graph the solution set of each compound inequality.
 64.11: Graph the solution set of each compound inequality.
 64.12: Graph the solution set of each compound inequality.
 64.13: Graph the solution set of each compound inequality.
 64.14: Solve each compound inequality. Then graph the solution set.
 64.15: Solve each compound inequality. Then graph the solution set.
 64.16: Solve each compound inequality. Then graph the solution set.
 64.17: Solve each compound inequality. Then graph the solution set.
 64.18: Solve each compound inequality. Then graph the solution set.
 64.19: Solve each compound inequality. Then graph the solution set.
 64.20: Solve each compound inequality. Then graph the solution set.
 64.21: Solve each compound inequality. Then graph the solution set.
 64.22: Solve each compound inequality. Then graph the solution set.
 64.23: Solve each compound inequality. Then graph the solution set.
 64.24: ANALYZE TABLES The Fujita Scale (Fscale) is the official classific...
 64.25: BIOLOGY Each type of fish thrives in a specific range of temperatur...
 64.26: Write a compound inequality for each graph.
 64.27: Write a compound inequality for each graph.
 64.28: Write a compound inequality for each graph.
 64.29: Write a compound inequality for each graph.
 64.30: Write a compound inequality for each graph.
 64.31: Write a compound inequality for each graph.
 64.32: Solve each compound inequality. Then graph the solution set.
 64.33: Solve each compound inequality. Then graph the solution set.
 64.34: Solve each compound inequality. Then graph the solution set.
 64.35: Solve each compound inequality. Then graph the solution set.
 64.36: HEALTH About 20% of the time you sleep is spent in rapid eye moveme...
 64.37: FUNDRAISING Rashid is selling potted flowers for his schools fund...
 64.38: Define a variable, write an inequality, and solve each problem. The...
 64.39: Define a variable, write an inequality, and solve each problem. The...
 64.40: Define a variable, write an inequality, and solve each problem. The...
 64.41: Define a variable, write an inequality, and solve each problem. The...
 64.42: HEARING For Exercises 4244, use the table.
 64.43: HEARING For Exercises 4244, use the table.
 64.44: HEARING For Exercises 4244, use the table.
 64.45: RESEARCH Use the Internet or other resource to find the altitudes i...
 64.46: In Lesson 63, you learned how to use a graphing calculator to find...
 64.47: OPEN ENDED Create an example of a compound inequality containing an...
 64.48: REASONING Formulate a compound inequality to represent $7 is less t...
 64.49: CHALLENGE Select compound inequalities that represent the values of...
 64.50: Writing in Math Use the information about the roller coaster on pag...
 64.51: REVIEW Ten pounds of fresh tomatoes make about 15 cups of cooked to...
 64.52: What is the solution set of the inequality 7 < x + 2 < 4? F 5 < x...
 64.53: REVIEW The scatterplot below shows the number of hay bales used by ...
 64.54: MONEY In the summer, Richard earns $200 per month at his parttime ...
 64.55: Solve each inequality. Check your solution.
 64.56: Solve each inequality. Check your solution.
 64.57: Solve each inequality. Check your solution.
 64.58: Solve each inequality. Check your solution.
 64.59: Solve. Assume that y varies directly as x.
 64.60: Solve. Assume that y varies directly as x.
 64.61: PREREQUISITE SKILL Solve each equation.
 64.62: PREREQUISITE SKILL Solve each equation.
 64.63: PREREQUISITE SKILL Solve each equation.
 64.64: PREREQUISITE SKILL Solve each equation.
 64.65: PREREQUISITE SKILL Solve each equation.
 64.66: PREREQUISITE SKILL Solve each equation.
 64.67: PREREQUISITE SKILL Solve each equation.
 64.68: PREREQUISITE SKILL Solve each equation.
Solutions for Chapter 64: Solving Compound Inequalities
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 64: Solving Compound Inequalities
Get Full SolutionsChapter 64: Solving Compound Inequalities includes 68 full stepbystep solutions. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1. Since 68 problems in chapter 64: Solving Compound Inequalities have been answered, more than 35309 students have viewed full stepbystep solutions from this chapter.

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.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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!).

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

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.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

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

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)ยท(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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

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.

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.