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nature of mathematics

Questions and Answers of Nature Of Mathematics

In Problems 4-13, decide whether the statement is true or false. If it is false, tell what is wrong.The matrix for the system \(\left\{\begin{array}{l}x_{1}=1 \\ x_{2}=2 \\ x_{3}=0 \\
Find the inverse of each matrix in Problems 6-7.\(\left[\begin{array}{rr}2 & 1 \\ -\frac{3}{2} & -\frac{1}{2}\end{array}ight]\\\)
Describe a procedure for finding the inverse of a square matrix.
A plane travels \(200 \mathrm{mph}\) relative to the ground while flying with a strong wind and only \(150 \mathrm{mph}\) returning against it. What is the plane's speed in still air?
Describe the addition method for solving a system of equations.
Graph the solution of each system given in Problems 5-18.a. \(\left\{\begin{array}{l}x \leq 0 \\ y \leq 0\end{array}ight.\)b. \(\left\{\begin{array}{l}x \leq 0 \\ y \geq 0\end{array}ight.\)
In Problems 4-13, decide whether the statement is true or false. If it is false, tell what is wrong.In *Row + notation, the first number listed is the target row.
Find the inverse of each matrix in Problems 6-7.\(\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{array}ight]\\\)
Describe a procedure for using the inverse of a matrix to solve a system of equations.
The demand for a product varies from 150,000 units at \(\$ 110\) per unit to 300,000 at \(\$ 20\) per unit. Also, 300,000 could be supplied at \(\$ 90\) per unit, whereas only 200,000 could be
Solve the systems in Problems 7-14 by graphing.\(\left\{\begin{array}{l}x-y=2 \\ 2 x+3 y=9\end{array}ight.\)
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ x
In Problems 4-13, decide whether the statement is true or false. If it is false, tell what is wrong.In *Row and *Row + notation, the target row is the last number listed.
Solve the systems in Problems \(8-12\) by the indicated method.By graphing: \(\left\{\begin{array}{l}2 x-y=2 \\ 3 x-2 y=1\end{array}ight.\)
What is a communication matrix?
California Instruments, a manufacturer of calculators, finds by test marketing its calculators at UCLA that 180 calculators could be sold when they were priced at \(\$ 10\), but only 20 calculators
Solve the systems in Problems 7-14 by graphing.\(\left\{\begin{array}{l}3 x-4 y=16 \\ -x+2 y=-6\end{array}ight.\)
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ x
In Problems 4-13, decide whether the statement is true or false. If it is false, tell what is wrong.If row 3 of a matrix \([A]\) is added to row 5 of \([A]\), then the correct notation is \(*
In Problems 9-16, find the indicated matrices, if possible.\[[\mathrm{A}]=\left[\begin{array}{rr}1 & 2 \\4 & 0 \\-1 & 3 \\2 & 1\end{array}ight] \quad[\mathrm{B}]=\left[\begin{array}{rr}4 & 2 \\-1 &
Solve the systems in Problems \(8-12\) by the indicated method.By addition: \(\left\{\begin{array}{l}x+3 y=3 \\ 4 x-6 y=-6\end{array}ight.\)
According to the Centers for Disease Control, the numbers of new AIDS-related cases for selected years are shown in Table 15.1.a. Plot the points represented in Table 15.1 using 2000 as the base year
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(x \geq y\)
If \(h(x)=3 x-1\), finda. \(h(0)\)b. \(h(-10)\)c. \(h(a) \)
The information is based on the spreadsheet as shown Suppose Ingredient I is made up of \(80 \%\) micoden and \(20 \%\) water, Ingredient II is made up of \(30 \%\) micoden, \(50 \%\) bixon, and \(20
The information is based on the spreadsheet as shown Suppose Ingredient I is made up of \(80 \%\) micoden and \(20 \%\) water, Ingredient II is made up of \(30 \%\) micoden, \(50 \%\) bixon, and \(20
The information is based on the spreadsheet as shown Suppose Ingredient I is made up of \(80 \%\) micoden and \(20 \%\) water, Ingredient II is made up of \(30 \%\) micoden, \(50 \%\) bixon, and \(20
A manufacturer of lapel buttons test marketed a new item at the University of California, Davis. It was found that 900 items could be sold if they were priced at \(\$ 1\), but only 300 items could be
Solve the systems in Problems 7-14 by graphing.\(\left\{\begin{array}{l}y=3 x+1 \\ x-2 y=8\end{array} \quadight.\)
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}-9
In Problems 4-13, decide whether the statement is true or false. If it is false, tell what is wrong.If row 7 of a matrix \([B]\) is multiplied by -2 and then added to row 6 of \([\mathrm{B}]\), then
Solve the systems in Problems \(8-12\) by the indicated method.By substitution: \(\left\{\begin{array}{l}y=1-2 x \\ 5 x+2 y=1\end{array}ight.\)
In Problems 9-16, find the indicated matrices, if possible.\[[\mathrm{A}]=\left[\begin{array}{rr}1 & 2 \\4 & 0 \\-1 & 3 \\2 & 1\end{array}ight] \quad[\mathrm{B}]=\left[\begin{array}{rr}4 & 2 \\-1 &
Director Ron Howard is nine years older than actor Tom Cruise. If the sum of their birth years is 3,915 , in what year was Tom Cruise born?
Solve the systems in Problems 7-14 by graphing.\(\left\{\begin{array}{l}2 x-3 y=12 \\ -4 x+6 y=18\end{array}ight.\)
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}-4 \leq x \leq-2 \\ -5 \leq y \leq 9\end{array}ight.\)
In Problems 4-13, decide whether the statement is true or false. If it is false, tell what is wrong.The notation *Row \(+(2\), [ANS], 6,3\()\) means multiply row 6 of the previous matrix by 2 and add
Solve the systems in Problems \(8-12\) by the indicated method.By Gauss-Jordan: \(\left\{\begin{array}{l}x+y+z=2 \\ x+2 y-2 z=1 \\ x+y+3 z=4\end{array}ight.\)
In Problems 9-16, find the indicated matrices, if possible.\[[\mathrm{A}]=\left[\begin{array}{rr}1 & 2 \\4 & 0 \\-1 & 3 \\2 & 1 \end{array}ight] \quad[\mathrm{B}]=\left[\begin{array}{rr}4 & 2 \\-1 &
Clint Eastwood is fifteen years older than fellow actor Goldie Hawn. If the sum of their birth years is 3,875 , in what year was Hawn born?
Solve the systems in Problems 7-14 by graphing.\(\left\{\begin{array}{l}x-6=y \\ 4 x+y=9\end{array} \quadight.\)
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}2 x+y>3 \\ 3 x-y
In Problems 4-13, decide whether the statement is true or false. If it is false, tell what is wrong.The notation \(* \operatorname{Row}+\left(3^{-1},[\mathrm{C}], 4,2ight)\) means multiply row 2 of
Solve the systems in Problems \(8-12\) by the indicated method.By using an inverse matrix: \(\left\{\begin{array}{l}2 x+y=13 \\ -\frac{3}{2} x-\frac{1}{2} y=10\end{array}ight.\)
In Problems 9-16, find the indicated matrices, if possible. See IM.\[[\mathrm{A}]=\left[\begin{array}{rr}1 & 2 \\4 & 0 \\-1 & 3 \\2 & 1 \end{array}ight] \quad[\mathrm{B}]=\left[\begin{array}{rr}4 & 2
The sum of the birth years of actresses Debra Winger and Meryl Streep is 3,904. If Debra is six years younger, in what year was she born?
Solve the systems in Problems 7-14 by graphing.\(\left\{\begin{array}{l}6 x+y=-5 \\ x+3 y=2\end{array} \quadight.\)
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}y \leq 3 x-4 \\ y \geq-2 x+5\end{array}ight.\)
In Problems 4-13, decide whether the statement is true or false. If it is false, tell what is wrong.In the notation \(* \operatorname{Row}+(3,[A], 4,5)\), the target row is 3 .
Solve the systems in Problems 13-16 by graphing, adding, substitution, Gauss-Jordan, or inverse matrix methods.\(\left\{\begin{array}{l}3 x-y=-10 \\ x+y=-2\end{array}ight.\)
The information is based on the spreadsheet as shown .Suppose Ingredient I is made up of \(80 \%\) micoden and \(20 \%\) water, Ingredient II is made up of \(30 \%\) micoden, \(50 \%\) bixon, and
In Problems 9-16, find the indicated matrices, if possible.\[[\mathrm{A}]=\left[\begin{array}{rr}1 & 2 \\4 & 0 \\-1 & 3 \\2 & 1 \end{array}\right]
Solve the systems in Problems 7-14 by graphing.\(\left\{\begin{array}{l}4 x-3 y=-1 \\ -2 x+3 y=-1\end{array}\right.\)
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}3 x-2 y \geq 6 \\ 2 x+3 y \leq 6\end{array}\right.\)
In Problems 4-13, decide whether the statement is true or false. If it is false, tell what is wrong.For the matrix \([A]=\left[\begin{array}{lll:l}0 & 7 & 8 & 3 \\ 1 & 2 & 3 &
Solve the systems in Problems 13-16 by graphing, adding, substitution, Gauss-Jordan, or inverse matrix methods.\(\left\{\begin{array}{l}x=5-3 y \\ 5 x+7 y=25\end{array}\right.\)
The information is based on the spreadsheet as shown Suppose Ingredient I is made up of \(80 \%\) micoden and \(20 \%\) water, Ingredient II is made up of \(30 \%\) micoden, \(50 \%\) bixon, and \(20
In Problems 9-16, find the indicated matrices, if possible.\[[\mathrm{A}]=\left[\begin{array}{rr}1 & 2 \\4 & 0 \\-1 & 3 \\2 & 1 \end{array}\right]
Solve the systems in Problems 7-14 by graphing.\(\left\{\begin{array}{l}3 x+2 y=5 \\ 4 x-3 y=1\end{array} \quad\right.\)
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}y-5 \leq 0 \\ y \geq 0\end{array}\right.\)
Write each system in augmented matrix form.a. \(\left\{\begin{array}{l}4 x+5 y=-16 \\ 3 x+2 y=5\end{array}\\\right.\)b. \(\left\{\begin{array}{l}x+y+z=4 \\ 3 x+2 y+z=7 \\ x-3 y+2
Solve the systems in Problems 13-16 by graphing, adding, substitution, Gauss-Jordan, or inverse matrix methods.\(\left\{\begin{array}{l}x+y+z=5 \\ x-2 y+z=-1 \\ 3 x+y-2 z=16\end{array}\right.\)
In Problems 9-16, find the indicated matrices, if possible.\[[\mathrm{A}]=\left[\begin{array}{rr}1 & 2 \\4 & 0 \\-1 & 3 \\2 & 1 \end{array}\right]
Solve the systems in Problems 15-26 by the substitution method.\(\left\{\begin{array}{l}y=3-2 x \\ 3 x+2 y=-17\end{array}\right.\)
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}x-10 \leq 0 \\ x \geq 0\end{array}\right.\)
Write a system of equations that has the given augmented matrix.a. \(\left[\begin{array}{lll:l}6 & 7 & 8 & 3 \\ 1 & 2 & 3 & 4 \\ 0 & 1 & 3 & 4\end{array}\right]
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}y-25 \leq 0 \\ y \geq 0\end{array}\right.\)
Given the matrices in Problems 16-19, perform elementary row operations to obtain a 1 in the row 1, column 1 position.\([B]=\left[\begin{array}{rrr:r}-2 & 3 & 5 & 9 \\ 1 & 0 & 2
Graph the solution of the system: \(\left\{\begin{array}{l}2 x-y+2 \leq 0 \\ 2 x-y+12 \geq 0 \\ 3 x+2 y+10>0 \\ 3 x+2 y-18<0\end{array}\right.\)
Write \([\mathrm{A}][\mathrm{X}]=[\mathrm{B}]\), if possible, for the matrices given in Problems 17-18.\([\mathrm{A}]=\left[\begin{array}{rrr}1 & 2 & 4 \\ -3 & 2 & 1 \\ 2 & 0
Solve the systems in Problems 15-26 by the substitution method.\(\left\{\begin{array}{l}y=5-3 x \\ 2 x+3 y=1\end{array} \quad\right.\)
Graph the solution of each system given in Problems 5-18.\(\left\{\begin{array}{l}x-y \geq 0 \\ y \leq 0\end{array}\right.\)
Given the matrices in Problems 16-19, perform elementary row operations to obtain a 1 in the row 1, column 1 position.\([\mathrm{C}]=\left[\begin{array}{rrr:r}2 & 4 & 10 & -12 \\ 6 &
To manufacture a certain alloy wheel, it is necessary to use \(33 \mathrm{oz}\) of metal A and \(56 \mathrm{oz}\) of metal B. It is easier for the manufacturer to buy and mix two products that come
Write \([\mathrm{A}][\mathrm{X}]=[\mathrm{B}]\), if possible, for the matrices given in Problems 17-18.\([\mathrm{A}]=\left[\begin{array}{rrr}4 & 1 & 0 \\ 3 & -1 & 2 \\ 2 & 3
Given the matrices in Problems 16-19, perform elementary row operations to obtain a 1 in the row 1, column 1 position.\([\mathrm{A}]=\left[\begin{array}{rrr:r}3 & 1 & 2 & 1 \\ 0 & 2
Solve the systems in Problems 13-16 by graphing, adding, substitution, Gauss-Jordan, or inverse matrix methods.\(\left\{\begin{array}{l}5 x+3 y=82 \\ 4 x-6 y=-10\end{array}\right.\)
The information is based on the spreadsheet as shown Suppose Ingredient I is made up of \(80 \%\) micoden and \(20 \%\) water, Ingredient II is made up of \(30 \%\) micoden, \(50 \%\) bixon, and \(20
Solve the systems in Problems 15-26 by the substitution method.\(\left\{\begin{array}{l}5 x-2 y=-19 \\ x=3 y+4\end{array}\right.\)
In Problems 9-16, find the indicated matrices, if possible.\[[\mathrm{A}]=\left[\begin{array}{rr}1 & 2 \\4 & 0 \\-1 & 3 \\2 & 1 \end{array}\right]
Sketch the graphs of the equations for \(x \geq 0\) in Problems 39-42.\(y=\left(\frac{1}{10}\right)^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(\frac{y^{2}}{16}-\frac{x^{2}}{36}=1\)
Sketch the graph of each equation in Problems 3-30.\(y=x^{2}-4\)
Sketch the requested conic sections in Problems 14-23 using the definition.A hyperbola with the distance between the foci 10 units and the difference of the distances 6 units
If \(f(x)=x^{2}+1\), finda. \(f(-3)\)b. \(f\left(\frac{1}{2}\right)\)c. \(f(b)\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(y>x\)
Sketch the graph of each equation in Problems 3-30.\(y=x^{2}+4\)
Identify the curves in Problems 24-27.a. \(2 x-y-8=0 \quad\)b. \(4 x^{2}-16 y=0\)c. \((x-1)=-2(y+2)\)
If \(g(x)=\frac{x}{2}\), finda. \(g(10)\)b. \(g(-4)\)c. \(g(3)\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(y \geq-\frac{2}{3} x\)
Sketch the graph of each equation in Problems 3-30.\(y=9-x^{2}\)
Identify the curves in Problems 24-27.a. \(2 x+y-10=0 \quad\)b. \(x^{2}+8(y-12)^{2}=16\)c. \(y^{2}-4 x+10 y+13=0\)
If \(h(x)=0.6 x\), finda. \(h(4.1)\)b. \(h(2.3)\)c. \(h\left(\frac{5}{2}\right)\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(y \leq-\frac{3}{5} x\)
Sketch the graph of each equation in Problems 3-30.\(y=-3 x^{2}+4\)
Use the vertical line test in Problems 27-32 to determine whether the curve is a function. Also state the probable domain and range. Ymin= -5 Ymax=5 Xmin=-2 Xmax=2 Xsc1=1 Ysc1=1
Identify the curves in Problems 24-27.a. \(x^{2}+y^{2}-3 y=0\)b. \(y^{2}+4 x-3 y+1=0\)c. \(x^{2}-9 y^{2}-6 x+18=0\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(y \leq \frac{4}{5} x\)
Use the vertical line test in Problems 27-32 to determine whether the curve is a function. Also state the probable domain and range. Xmin=-7.589645.. Xmax 7.5806451.... Xsc1=1 min-5 Ymax=5 Ysc1=1
Sketch the graph of each equation in Problems 3-30.\(y=2 x^{2}-3\)

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