 103.1: Solve each equation. Check your solution.
 103.2: Solve each equation. Check your solution.
 103.3: Solve each equation. Check your solution.
 103.4: GEOMETRY The surface area of a basketball is x square inches. What ...
 103.5: Solve each equation. Check your solution.
 103.6: Solve each equation. Check your solution.
 103.7: Solve each equation. Check your solution.
 103.8: Solve each equation. Check your solution.
 103.9: Solve each equation. Check your solution.
 103.10: Solve each equation. Check your solution.
 103.11: Solve each equation. Check your solution.
 103.12: Solve each equation. Check your solution.
 103.13: Solve each equation. Check your solution.
 103.14: Solve each equation. Check your solution.
 103.15: Solve each equation. Check your solution.
 103.16: Solve each equation. Check your solution.
 103.17: Solve each equation. Check your solution.
 103.18: Solve each equation. Check your solution.
 103.19: Solve each equation. Check your solution.
 103.20: Solve each equation. Check your solution.
 103.21: Solve each equation. Check your solution.
 103.22: Solve each equation. Check your solution.
 103.23: Solve each equation. Check your solution.
 103.24: Solve each equation. Check your solution.
 103.25: Solve each equation. Check your solution.
 103.26: Solve each equation. Check your solution.
 103.27: Solve each equation. Check your solution.
 103.28: Solve each equation. Check your solution.
 103.29: AVIATION For Exercises 29 and 30, use the following information. Th...
 103.30: AVIATION For Exercises 29 and 30, use the following information. Th...
 103.31: The square root of the sum of a number and 7 is 8. Find the number.
 103.32: The square root of the quotient of a number and 6 is 9. Find the nu...
 103.33: Solve each equation. Check your solution.
 103.34: Solve each equation. Check your solution.
 103.35: Solve each equation. Check your solution.
 103.36: Solve each equation. Check your solution.
 103.37: Solve each equation. Check your solution.
 103.38: Solve each equation. Check your solution.
 103.39: Solve each equation. Check your solution.
 103.40: Solve each equation. Check your solution.
 103.41: Solve each equation. Check your solution.
 103.42: Solve each equation. Check your solution.
 103.43: GEOMETRY For Exercises 4346, use the figure. The area A of a circle...
 103.44: GEOMETRY For Exercises 4346, use the figure. The area A of a circle...
 103.45: GEOMETRY For Exercises 4346, use the figure. The area A of a circle...
 103.46: GEOMETRY For Exercises 4346, use the figure. The area A of a circle...
 103.47: OCEANS For Exercises 4749, use the following information. Tsunamis,...
 103.48: OCEANS For Exercises 4749, use the following information. Tsunamis,...
 103.49: OCEANS For Exercises 4749, use the following information. Tsunamis,...
 103.50: State whether the following equation is sometimes, always, or never...
 103.51: PHYSICAL SCIENCE For Exercises 5153, use the following information....
 103.52: PHYSICAL SCIENCE For Exercises 5153, use the following information....
 103.53: PHYSICAL SCIENCE For Exercises 5153, use the following information....
 103.54: BROADCASTING For Exercises 5456, use the following information. Spo...
 103.55: BROADCASTING For Exercises 5456, use the following information. Spo...
 103.56: BROADCASTING For Exercises 5456, use the following information. Spo...
 103.57: Use a graphing calculator to solve each radical equation. Round to ...
 103.58: Use a graphing calculator to solve each radical equation. Round to ...
 103.59: Use a graphing calculator to solve each radical equation. Round to ...
 103.60: Use a graphing calculator to solve each radical equation. Round to ...
 103.61: Use a graphing calculator to solve each radical equation. Round to ...
 103.62: Use a graphing calculator to solve each radical equation. Round to ...
 103.63: REASONING Explain why it is necessary to check for extraneous solut...
 103.64: OPEN ENDED Give an example of a radical equation. Then solve the eq...
 103.65: FIND THE ERROR Alex and Victor are solving  x  5 = 2. Who is cor...
 103.66: CHALLENGE Solve h + 9  h = 3 .
 103.67: Writing in Math Use the information about skydiving on page 541 to ...
 103.68: What is the solution for this equation? x + 3  2 = 7 A 22 B 78 C 3...
 103.69: REVIEW Mr. and Mrs. Hataro are putting fresh sod onto their yard. T...
 103.70: Simplify
 103.71: Simplify
 103.72: Simplify
 103.73: Simplify
 103.74: Simplify
 103.75: Simplify
 103.76: Find each product.
 103.77: Find each product.
 103.78: Find each product.
 103.79: PHYSICAL SCIENCE A Europeanmade hot tub is advertised to have a te...
 103.80: Write each equation in standard form.
 103.81: Write each equation in standard form.
 103.82: Write each equation in standard form.
 103.83: MUSIC The table shows the number of country music radio stations in...
 103.84: PREREQUISITE SKILL Evaluate a 2 + b 2 for each value of a and b. (Les
 103.85: PREREQUISITE SKILL Evaluate a 2 + b 2 for each value of a and b. (Les
 103.86: PREREQUISITE SKILL Evaluate a 2 + b 2 for each value of a and b. (Les
 103.87: PREREQUISITE SKILL Evaluate a 2 + b 2 for each value of a and b. (Les
 103.88: PREREQUISITE SKILL Evaluate a 2 + b 2 for each value of a and b. (Les
 103.89: PREREQUISITE SKILL Evaluate a 2 + b 2 for each value of a and b. (Les
Solutions for Chapter 103: Radical Equations
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 103: Radical Equations
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1. Since 89 problems in chapter 103: Radical Equations have been answered, more than 31118 students have viewed full stepbystep solutions from this chapter. Chapter 103: Radical Equations includes 89 full stepbystep solutions.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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!).

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

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

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

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

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

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).