Calculus

Precalculus: Graphical, Numerical, Algebraic | 8th Edition | ISBN: 9780321656933 | Authors: Franklin Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy, Dave Bock
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Author: Franklin Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy, Dave Bock
Publisher: Pearson
ISBN: 9780321656933
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Chapter 7 Problems

Chapter: 7 Problem: 7.1.1.164

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, find the amount of pure acid in the solution. 40 L of a 32% acid solution

Chapter: 7 Problem: 7.1.1.165

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, find the amount of pure acid in the solution. 60 mL of a 14% acid solution

Chapter: 7 Problem: 7.1.1.166

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3 and 4, find the amount of water in the solution. 50 L of a 24% acid solution

Chapter: 7 Problem: 7.1.1.167

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3 and 4, find the amount of water in the solution. 80 mL of a 70% acid solution

Chapter: 7 Problem: 7.1.1.168

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3 and 4, find the amount of water in the solution. In Exercises 5 and 6, determine which points are on the graph of the function. \(f(x)=2 x^{2}-3 x+1\) \(\begin{array}{l}\text{(a) } (-1,6)\\\text{(b) } (2,1)\end{array}\)

Chapter: 7 Problem: 7.1.1.169

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3 and 4, find the amount of water in the solution. In Exercises 5 and 6, determine which points are on the graph of the function. \(f(x)=x^{3}-4 x-1\) \(\begin{array}{l}\text{(a) } (0,-1)\\\text{(b) } (-2,-17)\end{array}\)

Chapter: 7 Problem: 7.1.1.170

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7 and 8, solve for x or y in terms of the other variables. \(y+z-w=1\)

Chapter: 7 Problem: 7.1.1.171

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7 and 8, solve for x or y in terms of the other variables. \(x-2 z+w=3\)

Chapter: 7 Problem: 7.1.1.172

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, find the inverse of the matrix.

Chapter: 7 Problem: 7.1.1.173

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, find the inverse of the matrix.

Chapter: 7 Problem: 7.1.1.174

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1 and 2, use substitution to solve the system of equations. \(\begin{aligned} x-3 y+z & =0 \\ 2 y+3 z & =1 \\ z & =-2 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.175

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1 and 2, use substitution to solve the system of equations. \(\begin{aligned} 3 x-y+2 z & =-2 \\ y+3 z & =3 \\ 2 z & =4 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.176

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 38, use Gaussian elimination to solve the system of equations. \(\begin{aligned} x-y+z & =0 \\ 2 x-3 z & =-1 \\ -x-y+2 z & =-1 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.177

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 38, use Gaussian elimination to solve the system of equations. \(\begin{aligned} 2 x-y & =0 \\ x+3 y-z & =-3 \\ 3 y+z & =8 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.178

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 38, use Gaussian elimination to solve the system of equations. \(\begin{aligned} x+y+z & =-3 \\ 4 x-y & =-5 \\ -3 x+2 y+z & =4 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.179

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 38, use Gaussian elimination to solve the system of equations. \(\begin{aligned} x+y-3 z & =-1 \\ 2 x-3 y+z & =4 \\ 3 x-7 y+5 z & =4 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.180

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 38, use Gaussian elimination to solve the system of equations. \(\begin{aligned} x+y-z & =4 \\ y+w & =-4 \\ x-y & =1 \\ x+z+w & =1 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.181

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 38, use Gaussian elimination to solve the system of equations. \(\begin{aligned} \frac{1}{2} x-y+z-w & =1 \\ -x+y+z+2 w & =-3 \\ x-z & =2 \\ y+w & =0 \end{a

Chapter: 7 Problem: 7.1.1.182

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 912, perform the indicated elementary row operation on the matrix \(\left[\begin{array}{rrr} 2 & -6 & 4 \\ 1 & 2 & -3 \\ -3 & 1 & -2 \end{array}\right]\).

Chapter: 7 Problem: 7.1.1.183

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 912, perform the indicated elementary row operation on the matrix \(\left[\begin{array}{rrr} 2 & -6 & 4 \\ 1 & 2 & -3 \\ -3 & 1 & -2 \end{array}\right]\).

Chapter: 7 Problem: 7.1.1.184

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 912, perform the indicated elementary row operation on the matrix \(\left[\begin{array}{rrr} 2 & -6 & 4 \\ 1 & 2 & -3 \\ -3 & 1 & -2 \end{array}\right]\).

Chapter: 7 Problem: 7.1.1.185

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 912, perform the indicated elementary row operation on the matrix \(\left[\begin{array}{rrr} 2 & -6 & 4 \\ 1 & 2 & -3 \\ -3 & 1 & -2 \end{array}\right]\).

Chapter: 7 Problem: 7.1.1.186

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1316, what elementary row operations applied to \(\left[\begin{array}{rrrr} -2 & 1 & -1 & 2 \\ 1 & -2 & 3 & 0 \\ 3 & 1 & -1 & 2 \end{array}\right]\) wil

Chapter: 7 Problem: 7.1.1.187

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1316, what elementary row operations applied to \(\left[\begin{array}{rrrr} -2 & 1 & -1 & 2 \\ 1 & -2 & 3 & 0 \\ 3 & 1 & -1 & 2 \end{array}\right]\) wil

Chapter: 7 Problem: 7.1.1.188

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1316, what elementary row operations applied to \(\left[\begin{array}{rrrr} -2 & 1 & -1 & 2 \\ 1 & -2 & 3 & 0 \\ 3 & 1 & -1 & 2 \end{array}\right]\) wil

Chapter: 7 Problem: 7.1.1.189

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1316, what elementary row operations applied to \(\left[\begin{array}{rrrr} -2 & 1 & -1 & 2 \\ 1 & -2 & 3 & 0 \\ 3 & 1 & -1 & 2 \end{array}\right]\) wil

Chapter: 7 Problem: 7.1.1.190

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1720, find a row echelon form for the matrix. \(\left[\begin{array}{rrr} 1 & 2 & -1 \\ 2 & 1 & 4 \\ -3 & 0 & 1 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.191

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1720, find a row echelon form for the matrix. \(\left[\begin{array}{rrr} 1 & 2 & -3 \\ -3 & -6 & 10 \\ -2 & -4 & 7 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.192

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1720, find a row echelon form for the matrix. \(\left[\begin{array}{rrrr} 1 & 2 & 3 & -4 \\ -2 & 6 & -6 & 2 \\ 3 & 12 & 6 & 12 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.193

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1720, find a row echelon form for the matrix. \(\left[\begin{array}{llll} 3 & 6 & 9 & -6 \\ 2 & 5 & 5 & -3 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.194

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, find the reduced row echelon form for the matrix. \(\left[\begin{array}{llll} 1 & 0 & 2 & 1 \\ 3 & 2 & 4 & 7 \\ 2 & 1 & 3 & 4 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.195

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, find the reduced row echelon form for the matrix. \(\left[\begin{array}{rrrrr} 1 & -2 & 2 & 1 & 1 \\ 3 & -5 & 6 & 3 & -1 \\ -2 & 4 & -3 & -2 & 5 \\ 3 & -5 & 6 & 4 & -3 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.196

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, find the reduced row echelon form for the matrix. \(\left[\begin{array}{rrrr} 1 & 2 & 3 & 1 \\ -3 & -5 & -7 & -4 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.197

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, find the reduced row echelon form for the matrix. \(\left[\begin{array}{rrrr} 3 & -6 & 3 & -3 \\ 2 & -4 & 2 & -2 \\ -3 & 6 & -3 & 3 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.198

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, write the augmented matrix corresponding to the system of equations. \(\begin{aligned} 2 x-3 y+z & =1 \\ -x+y-4 z & =-3 \\ 3 x-z & =2 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.199

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, write the augmented matrix corresponding to the system of equations. \(\begin{array}{r} 3 x-4 y+z-w=1 \\ x+z-2 w=4 \end{array}\)

Chapter: 7 Problem: 7.1.1.200

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, write the augmented matrix corresponding to the system of equations. \(\begin{aligned} 2 x-5 y+z-w & =-3 \\ x-2 z+w & =4 \\ 2 y-3 z-w & =5 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.201

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, write the augmented matrix corresponding to the system of equations. \(\begin{array}{l} 3 x-2 y=5 \\ -x+5 y=7 \end{array}\)

Chapter: 7 Problem: 7.1.1.202

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, write the system of equations corresponding to the augmented matrix. \(\left[\begin{array}{rrr} 3 & 2 & -1 \\ -4 & 5 & 2 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.203

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, write the system of equations corresponding to the augmented matrix. \(\left[\begin{array}{rrrrr} 1 & 0 & -1 & 2 & -3 \\ 2 & 1 & 0 & -1 & 4 \\ -1 & 1 & 2 & 0 & 0 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.204

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, write the system of equations corresponding to the augmented matrix. \(\left[\begin{array}{rrrr} 2 & 0 & 1 & 3 \\ -1 & 1 & 0 & 2 \\ 0 & 2 & -3 & -1 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.205

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, write the system of equations corresponding to the augmented matrix. \(\left[\begin{array}{rrrr} 2 & 1 & -2 & 4 \\ -3 & 0 & 2 & -1 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.206

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3334, solve the system of equations by finding a row echelon form for the augmented matrix. \(\begin{aligned}x-2 y+z & =8 \\ 2 x+y-3 z & =-9 \\ -3 x+y+3 z & =5 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.207

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3334, solve the system of equations by finding a row echelon form for the augmented matrix. \(\begin{aligned} 3 x+7 y-11 z & =44 \\ x+2 y-3 z & =12 \\ 4 x+9 y-13 z & =53 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.208

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3544, solve the system of equations by finding the reduced row echelon form for the augmented matrix. \(\begin{aligned} x+2 y-z & =3 \\ 3 x+7 y-3 z & =12 \\ -2 x-4 y+3 z & =-5 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.209

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3544, solve the system of equations by finding the reduced row echelon form for the augmented matrix. \(\begin{aligned} x-2 y+z & =-2 \\ 2 x-3 y+2 z & =2 \\ 4 x-8 y+5 z & =-5 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.210

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3544, solve the system of equations by finding the reduced row echelon form for the augmented matrix. \(\begin{array}{r} x+y+3 z=2 \\ 3 x+4 y+10 z=5 \\ x+2 y+4 z=3 \end{array}\)

Chapter: 7 Problem: 7.1.1.211

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3544, solve the system of equations by finding the reduced row echelon form for the augmented matrix. \(\begin{aligned} x-z & =2 \\ -2 x+y+3 z & =-5 \\ 2 x+y-z & =3 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.212

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3544, solve the system of equations by finding the reduced row echelon form for the augmented matrix. \(\begin{array}{r} x+z=2 \\ 2 x+y+z=5 \end{array}\)

Chapter: 7 Problem: 7.1.1.213

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3544, solve the system of equations by finding the reduced row echelon form for the augmented matrix. \(\begin{aligned} x+2 y-3 z & =1 \\ -3 x-5 y+8 z & =-29 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.214

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3544, solve the system of equations by finding the reduced row echelon form for the augmented matrix. \(\begin{array}{r} x+2 y=4 \\ 3 x+4 y=5 \\ 2 x+3 y=4 \end{array}\)

Chapter: 7 Problem: 7.1.1.215

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3544, solve the system of equations by finding the reduced row echelon form for the augmented matrix. \(\begin{array}{r} x+y=3 \\ 2 x+3 y=8 \\ 2 x+2 y=6 \end{array}\)

Chapter: 7 Problem: 7.1.1.216

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3544, solve the system of equations by finding the reduced row echelon form for the augmented matrix. \(\begin{array}{r} x+y-3 z=1 \\ x-z-w=2 \\ 2 x+y-4 z-w=3 \end{array}\)

Chapter: 7 Problem: 7.1.1.217

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3544, solve the system of equations by finding the reduced row echelon form for the augmented matrix. \(\begin{aligned} x-y-z+2 w & =-3 \\ 2 x-y-2 z+3 w & =-3 \\ x-2 y-z+3 w & =-6 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.218

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45 and 46, write the system of equations as a matrix equation \(A X=B\), with A as the coefficient matrix of the system. \(\begin{aligned} 2 x+5 y & =-3 \\ x-2 y & =1 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.219

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45 and 46, write the system of equations as a matrix equation \(A X=B\), with A as the coefficient matrix of the system. \(\begin{aligned} 5 x-7 y+z & =2 \\ 2 x-3 y-z & =3 \\ x+y+z & =-3 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.220

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 47 and 48, write the matrix equation as a system of equations. \(\left[\begin{array}{rr} 3 & -1 \\ 2 & 4 \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{r} -1 \\ 3 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.221

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 47 and 48, write the matrix equation as a system of equations. \(\left[\begin{array}{rrr} 1 & 0 & -3 \\ 2 & -1 & 3 \\ -2 & 3 & -4 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{r} 3 \\ -1 \\ 2 \end{array}\right]\)

Chapter: 7 Problem: 7.1.1.222

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4954, solve the system of equations by using an inverse matrix. \(\begin{aligned} 2 x-3 y & =-13 \\ 4 x+y & =-5 \end{aligned}\)

Chapter: 7 Problem: 7.1.1.223

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 49-54, solve the system of equations by using an inverse matrix. x+2y=-2 3x-4y=9

Chapter: 7 Problem: 7.1.1.224

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 49-54, solve the system of equations by using an inverse matrix. \(2 x-y+z=-6\)

Chapter: 7 Problem: 7.1.1.225

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4954, solve the system of equations by using an inverse matrix.-3x + 3y - 5z = -13 2x + y + z = 6 x + 4y - 2z = 0

Chapter: 7 Problem: 7.1.1.226

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4954, solve the system of equations by using an inverse matrix.-2x + 3y + z - 3w = -3 3x - y - z + 2w = 3 x + 2y - 3z + w = 12 2x - y + z + w = -3

Chapter: 7 Problem: 7.1.1.227

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4954, solve the system of equations by using an inverse matrix.4x - 3y + 2z - 5w = 39 -2x + y - 3w = -1 3x + 2y - z - w = 10 2x + y + 2z = 8

Chapter: 7 Problem: 7.1.1.228

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.y + z = -9 x - z = -1 2x - y = 10

Chapter: 7 Problem: 7.1.1.229

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.3x - 1.5y = -6 y - 5.5z = -2.75 1.25x + z = -2

Chapter: 7 Problem: 7.1.1.230

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.x + z + w = 1 3x + 3y + 3z + 2w = 12 2x + y + 2z = 5 x + 2y + 2z + w = 5

Chapter: 7 Problem: 7.1.1.231

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.-2x + z + w = 5 2x - 2y - z = -10 -2x + y + z = 8 x - y + w = -4

Chapter: 7 Problem: 7.1.1.232

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.x + y + 2z = -2 x - y + z = 6

Chapter: 7 Problem: 7.1.1.233

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.2x + y - z = -4 x - 2y + z = 3

Chapter: 7 Problem: 7.1.1.234

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.x + y + z + 2w = 0 x + 2y + z + w = 1 2x + y + z + 4w = -1

Chapter: 7 Problem: 7.1.1.235

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.x + y + 2z + 3w = -1 x + 2y + 2z + 5w = 0 2x + 3y + 3z + 7w = 0

Chapter: 7 Problem: 7.1.1.236

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.x + y + z + w = -1.5 2x + y + z + 2w = -3.5

Chapter: 7 Problem: 7.1.1.237

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.x + y + z + w = 5 2x + y + 4w = 6

Chapter: 7 Problem: 7.1.1.238

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.2x + 2y - z + 5w = 4 x + y + 3w = 3 y - z + 2w = -1 x + y - z + 2w = 0

Chapter: 7 Problem: 7.1.1.239

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5566, use a method of your choice to solve the system of equations.x + y + w = 2 x + 3y + z - 3w = 2 x + 4y + z - 2w = 3 x + y + w = 2

Chapter: 7 Problem: 7.1.1.240

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Curve Fitting 1-1, 32, 11, -32, 12, 02 1x2 = ax 2 + bx + c

Chapter: 7 Problem: 7.1.1.241

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Curve Fitting -2, , , -37 1-1 -112, 10, -52, 12, 192 1x2 = ax3 + bx 2 + cx + d

Chapter: 7 Problem: 7.1.1.242

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Family of Curves-1 -421 11, -22 1x2 = ax 2 + bx + c

Chapter: 7 Problem: 7.1.1.243

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Family of Curves-1 -621 10, -12, 11, 22 1x2 = ax 3 + bx 2 + cx + d

Chapter: 7 Problem: 7.1.1.244

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Population Table 7.5 gives the population (in thousands) for Richardson, TX, and Garland, TX, for several years. Use for 1980, for 1981, and so forth. (a) Find the linear regression equation for the Richardson data and superimpose its graph on a scatter plot of the data. (b) Find the linear regressio

Chapter: 7 Problem: 7.1.1.245

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Population Table 7.6 gives the population (in thousands) for Anaheim, CA, and Anchorage, AK, for several years. Use for 1970, for 1971, and so forth. (a) Find the linear regression equation for the Anaheim data and superimpose its graph on a scatter plot of the data. (b) Find the linear regression eq

Chapter: 7 Problem: 7.1.1.246

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Train Tickets At the Pittsburgh zoo, children ride a train for 25 cents, adults pay $1.00, and senior citizens 75 cents. On a given day, 1400 passengers paid a total of $740 for the rides. There were 250 more children riders than all other riders. Find the number of children, adult, and senior riders

Chapter: 7 Problem: 7.1.1.247

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Manufacturing Stewarts Metals has three silver alloys on hand. One is 22% silver, another is 30% silver, and the third is 42% silver. How many grams of each alloy is required to produce 80 grams of a new alloy that is 34% silver if the amount of 30% alloy used is twice the amount of 22% alloy used

Chapter: 7 Problem: 7.1.1.248

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Investment Monica receives an $80,000 inheritance. She invests part of it in CDs (certificates of deposit) earning 6.7% APY (annual percentage yield), part in bonds earning 9.3% APY, and the remainder in a growth fund earning 15.6% APY. She invests three times as much in the growth fund as in the oth

Chapter: 7 Problem: 7.1.1.249

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Investments Oscar invests $20,000 in three investments earning 6% APY, 8% APY, and 10% APY. He invests $9000 more in the 10% investment than in the 6% investment. How much does he have invested at each rate if he receives $1780 interest the first year?

Chapter: 7 Problem: 7.1.1.250

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Investments Morgan has $50,000 to invest and wants to receive $5000 interest the first year. He puts part in CDs earning 5.75% APY, part in bonds earning 8.7% APY, and the rest in a growth fund earning 14.6% APY. How much should he invest at each rate if he puts the least amount possible in the growt

Chapter: 7 Problem: 7.1.1.251

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Mixing Acid Solutions Simpsons Drugstore needs to prepare a 40-L mixture that is 32% acid from three solutions: a 10% acid solution, a 25% acid solution, and a 50% acid solution. How much of each solution should be used if Simpsons wants to use as little of the 50% solution as possible?

Chapter: 7 Problem: 7.1.1.252

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Loose Change Matthew has 74 coins consisting of nickels, dimes, and quarters in his coin box. The total value of the coins is $8.85. If the number of nickels and quarters is four more than the number of dimes, find how many of each coin Matthew has in his coin box.

Chapter: 7 Problem: 7.1.1.253

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Vacation Money Heather has saved $177 to take with her on the family vacation. She has 51 bills consisting of $1, $5, and $10 bills. If the number of $5 bills is three times the number of $10 bills, find how many of each bill she has

Chapter: 7 Problem: 7.1.1.254

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 8182, use inverse matrices to find the equilibrium point for the demand and supply curves.p = 20 + 10x Supply curve p = 100 - 5x demand curve

Chapter: 7 Problem: 7.1.1.255

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 8182, use inverse matrices to find the equilibrium point for the demand and supply curves.p = 30 + 24x p = 150 - 12x Demand curve Supply curve

Chapter: 7 Problem: 7.1.1.256

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Explain why adding one row to another row in a matrix is an elementary row operation.

Chapter: 7 Problem: 7.1.1.257

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Explain why subtracting one row from another row in a matrix is an elementary row operation.

Chapter: 7 Problem: 7.1.1.258

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False Every nonzero square matrix has an inverse. Justify your answer

Chapter: 7 Problem: 7.1.1.259

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The reduced row echelon form of the augmented matrix of a system of three linear equations in three variables must be of the form where a, b, c, are real numbers. Justify your answer

Chapter: 7 Problem: 7.1.1.260

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following is the determinant of the matrix ? (A) 0 (B) 4 (C) (D) 8 (E)

Chapter: 7 Problem: 7.1.1.261

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following is the augmented matrix of the system of equations (A) (B) (C) (D) (E)

Chapter: 7 Problem: 7.1.1.262

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The matrix was obtained from by an elementary row operation. Which of the following describes the elementary row operation? (A) (B) (C) (D) (E) 122R2 + R1 1-22R2 + R1 122R1 + R2 1-22R1 1-22R1 + R2 C 123 456 789 C S 123 210 789

Chapter: 7 Problem: 7.1.1.263

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following is the reduced row echelon form for the augmented matrix of ? (A) (B) (C) (D) (E)

Chapter: 7 Problem: 7.1.1.264

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Investigating the Solution of a System of 3 Linear Equations in 3 Variables Assume that the graph of a linear equation in three variables is a plane in 3-dimensional space. (You will study these in Chapter 8.) (a) Explain geometrically how such a system can have a unique solution. (b)

Chapter: 7 Problem: 7.1.1.265

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Explain why a row echelon form of a matrix is not unique. That is, show that a matrix can have two unequal row echelon forms. Give an example.

Chapter: 7 Problem: 7.1.1.266

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The roots of the characteristic polynomial of the matrix A are the eigenvalues of A (see Section 7.2, Exercises 72 and 73). Use this information in Exercises 93 and 94.Let (a) Find the characteristic polynomial of A. (b) Find the graph of (c) Find the eigenvalues of A. (d) Compare det A with the y-in

Chapter: 7 Problem: 7.1.1.267

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The roots of the characteristic polynomial of the matrix A are the eigenvalues of A (see Section 7.2, Exercises 72 and 73). Use this information in Exercises 93 and 94.Let (a) Find the characteristic polynomial of A. (b) Find the graph of (c) Find the eigenvalues of A. (d) Compare det A with the y-in

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