 1.3.1: Write an algebraic expression to represent each verbal expression.
 1.3.2: Write an algebraic expression to represent each verbal expression.
 1.3.3: Write a verbal expression to represent each equation.
 1.3.4: Write a verbal expression to represent each equation.
 1.3.5: Name the property illustrated by each statement.
 1.3.6: Name the property illustrated by each statement.
 1.3.7: Solve each equation. Check your solution
 1.3.8: Solve each equation. Check your solution
 1.3.9: Solve each equation. Check your solution
 1.3.10: Solve each equation. Check your solution
 1.3.11: Solve each equation. Check your solution
 1.3.12: Solve each equation. Check your solution
 1.3.13: Solve each equation or formula for the specified variable.
 1.3.14: Solve each equation or formula for the specified variable.
 1.3.15: If 4x + 7 = 18, what is the value of 12x + 21?
 1.3.16: During the 2005 season, Vladimir Guerrero and Garret Anderson of th...
 1.3.17: Write an algebraic expression to represent each verbal expression
 1.3.18: Write an algebraic expression to represent each verbal expression
 1.3.19: Write an algebraic expression to represent each verbal expression
 1.3.20: Write an algebraic expression to represent each verbal expression
 1.3.21: Write an algebraic expression to represent each verbal expression
 1.3.22: Write an algebraic expression to represent each verbal expression
 1.3.23: Write a verbal expression to represent each equation
 1.3.24: Write a verbal expression to represent each equation
 1.3.25: Write a verbal expression to represent each equation
 1.3.26: Write a verbal expression to represent each equation
 1.3.27: Name the property illustrated by each statement
 1.3.28: Name the property illustrated by each statement
 1.3.29: Name the property illustrated by each statement
 1.3.30: Name the property illustrated by each statement
 1.3.31: Solve each equation. Check your solution
 1.3.32: Solve each equation. Check your solution
 1.3.33: Solve each equation. Check your solution
 1.3.34: Solve each equation. Check your solution
 1.3.35: Solve each equation. Check your solution
 1.3.36: Solve each equation. Check your solution
 1.3.37: Solve each equation or formula for the specified variable.
 1.3.38: Solve each equation or formula for the specified variable.
 1.3.39: Solve each equation or formula for the specified variable.
 1.3.40: Solve each equation or formula for the specified variable.
 1.3.41: Solve each equation or formula for the specified variable.
 1.3.42: Omar and Morgan arrive at Sunnybrook Lanes with $16.75. What is the...
 1.3.43: The perimeter of a regular octagon is 124 inches. Find the length o...
 1.3.44: Write an algebraic expression to represent each verbal expression
 1.3.45: Write an algebraic expression to represent each verbal expression
 1.3.46: Write this as an algebraic expression
 1.3.47: Write an equivalent expression using the Distributive Property.
 1.3.48: Write a verbal expression to represent each equation
 1.3.49: Write a verbal expression to represent each equation
 1.3.50: Solve each equation or formula for the specified variable
 1.3.51: Solve each equation or formula for the specified variable
 1.3.52: Solve each equation. Check your solution
 1.3.53: Solve each equation. Check your solution
 1.3.54: Solve each equation. Check your solution
 1.3.55: Solve each equation. Check your solution
 1.3.56: Solve each equation. Check your solution
 1.3.57: Solve each equation. Check your solution
 1.3.58: Benito spent $1837 to operate his car last year. Some of these expe...
 1.3.59: A school conference room can seat a maximum of 83 people. The princ...
 1.3.60: ChunWeis mother is 8 more than twice his age. His father is three ...
 1.3.61: A Parent Teacher Organization has raised $1800 to help pay for a tr...
 1.3.62: A trucking company is hired to deliver 125 lamps for $12 each. The ...
 1.3.63: Two designs for a soup can are shown at the right. If each can hold...
 1.3.64: The Central Pacific Company laid an average of 9.6 miles of track p...
 1.3.65: About how many miles of track did each company lay?
 1.3.66: Why do you think the Union Pacific was able to lay track so much mo...
 1.3.67: Allison is saving money to buy a video game system. In the first we...
 1.3.68: Crystal and Jamal are solving C = _5 9 (F  32) for F. Who is corre...
 1.3.69: Write a twostep equation with a solution of 7.
 1.3.70: Determine whether the following statement is sometimes, always, or ...
 1.3.71: Compare and contrast the Symmetric Property of Equality and the Com...
 1.3.72: Use the information about ERA on page 18 to find the number of earn...
 1.3.73: In triangle PQR, QS and SR are angle bisectors and angle P = 74. Ho...
 1.3.74: Which of the following best describes the graph of the equations be...
 1.3.75: Simplify each expression.
 1.3.76: Simplify each expression.
 1.3.77: Evaluate each expression if a = 3, b = 2, and c = 1.2.
 1.3.78: Evaluate each expression if a = 3, b = 2, and c = 1.2.
 1.3.79: The formula for the surface area S of a regular pyramid is S = _1 2...
 1.3.80: Identify the additive inverse for each number or expression.
 1.3.81: Identify the additive inverse for each number or expression.
 1.3.82: Identify the additive inverse for each number or expression.
 1.3.83: Identify the additive inverse for each number or expression.
Solutions for Chapter 1.3: Solving Equations
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 1.3: Solving Equations
Get Full SolutionsSince 83 problems in chapter 1.3: Solving Equations have been answered, more than 42178 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.3: Solving Equations includes 83 full stepbystep solutions. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568.

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.

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

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

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).

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

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

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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

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!).

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.