 1.4.1: Evaluate each expression if a = 4 and b = 1.5.
 1.4.2: Evaluate each expression if a = 4 and b = 1.5.
 1.4.3: Evaluate each expression if a = 4 and b = 1.5.
 1.4.4: If a meat thermometer reads 160F, write an equation to determine th...
 1.4.5: Solve the equation you wrote in Exercise 4.
 1.4.6: Ham needs to reach an internal temperature of 160F to be fully cook...
 1.4.7: Solve each equation. Check your solutions
 1.4.8: Solve each equation. Check your solutions
 1.4.9: Solve each equation. Check your solutions
 1.4.10: Solve each equation. Check your solutions
 1.4.11: Solve each equation. Check your solutions
 1.4.12: Solve each equation. Check your solutions
 1.4.13: Solve each equation. Check your solutions
 1.4.14: Solve each equation. Check your solutions
 1.4.15: Evaluate each expression if a = 5, b = 6, and c = 2.8.
 1.4.16: Evaluate each expression if a = 5, b = 6, and c = 2.8.
 1.4.17: Evaluate each expression if a = 5, b = 6, and c = 2.8.
 1.4.18: Evaluate each expression if a = 5, b = 6, and c = 2.8.
 1.4.19: Evaluate each expression if a = 5, b = 6, and c = 2.8.
 1.4.20: Evaluate each expression if a = 5, b = 6, and c = 2.8.
 1.4.21: Evaluate each expression if a = 5, b = 6, and c = 2.8.
 1.4.22: Evaluate each expression if a = 5, b = 6, and c = 2.8.
 1.4.23: Solve each equation. Check your solutions
 1.4.24: Solve each equation. Check your solutions
 1.4.25: Solve each equation. Check your solutions
 1.4.26: Solve each equation. Check your solutions
 1.4.27: Solve each equation. Check your solutions
 1.4.28: Solve each equation. Check your solutions
 1.4.29: Solve each equation. Check your solutions
 1.4.30: Solve each equation. Check your solutions
 1.4.31: Solve each equation. Check your solutions
 1.4.32: Solve each equation. Check your solutions
 1.4.33: Some say that to brew an excellent cup of coffee, you must have a b...
 1.4.34: Before an election, a company conducts a telephone survey of likely...
 1.4.35: Solve each equation. Check your solutions
 1.4.36: Solve each equation. Check your solutions
 1.4.37: Solve each equation. Check your solutions
 1.4.38: Solve each equation. Check your solutions
 1.4.39: Solve each equation. Check your solutions
 1.4.40: Solve each equation. Check your solutions
 1.4.41: Solve each equation. Check your solutions
 1.4.42: Solve each equation. Check your solutions
 1.4.43: Evaluate each expression if x = 6, y = 2.8, and z = 5
 1.4.44: Evaluate each expression if x = 6, y = 2.8, and z = 5
 1.4.45: Evaluate each expression if x = 6, y = 2.8, and z = 5
 1.4.46: A machine fills bags with about 16 ounces of sugar each. After the ...
 1.4.47: The troposphere is the layer of atmosphere closest to Earth. The av...
 1.4.48: Write an absolute value equation and graph the solution set.
 1.4.49: For Exercises 4951, determine whether each statement is sometimes, ...
 1.4.50: For Exercises 4951, determine whether each statement is sometimes, ...
 1.4.51: For Exercises 4951, determine whether each statement is sometimes, ...
 1.4.52: Use the information on page 27 to explain how an absolute value equ...
 1.4.53: Which graph represents the solution set for x  3  4 = 0? A 4 8 2 ...
 1.4.54: For a party, Lenora bought several pounds of cashews and several po...
 1.4.55: Solve each equation. Check your solution
 1.4.56: Solve each equation. Check your solution
 1.4.57: Solve each equation. Check your solution
 1.4.58: Name the property illustrated by each equation.
 1.4.59: Name the property illustrated by each equation.
 1.4.60: Write an expression to represent the area of the triangle
 1.4.61: Evaluate the expression you wrote in Exercise 60 for x = 23.
 1.4.62: Solve each equation
 1.4.63: Solve each equation
 1.4.64: Solve each equation
 1.4.65: Solve each equation
Solutions for Chapter 1.4: Solving Absolute Value Equations
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 1.4: Solving Absolute Value Equations
Get Full SolutionsCalifornia Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. Chapter 1.4: Solving Absolute Value Equations includes 65 full stepbystep solutions. Since 65 problems in chapter 1.4: Solving Absolute Value Equations have been answered, more than 44285 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions.

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

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

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

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

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

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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

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

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

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.

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.

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.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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

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