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nature of mathematics
Questions and Answers of
Nature Of Mathematics
Given the matrices in Problems 20-23, perform elementary row operations to obtain zeros under the 1 in the first column. Answers may vary.\([C]=\left[\begin{array}{rrr:r}1 & 2 & 4 & 1 \\ -2 & 5 & 0 &
Find the inverse of each matrix in Problems 21-26, if it exists.\(\left[\begin{array}{rr}8 & 6 \\ -2 & 4\end{array}ight]\)
Suppose a car rental agency gives the following choices:Option A: \(\$ 30 /\) day plus 40\& per mile Option B: Flat $50/day (unlimited miles)At what mileage are both rates the same if you rent the
Solve the systems in Problems 15-26 by the substitution method.\(\left\{\begin{array}{l}\frac{x}{3}-y=7 \\ x+\frac{y}{2}=7\end{array}ight.\)
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}-5
Given the matrices in Problems 20-23, perform elementary row operations to obtain zeros under the 1 in the first column. Answers may vary.\([D]=\left[\begin{array}{rrr:r}1 & 5 & 3 & 2 \\ 2 & 3 & -1 &
Find the inverse of each matrix in Problems 21-26, if it exists.\(\left[\begin{array}{rrr}1 & 0 & 2 \\ 2 & 1 & 0 \\ 0 & -2 & 9\end{array}ight]\)
The supply for a certain commodity is linear and determined to be\[p=0.005 n+12\]whereas the demand is linear with\[p=150-0.01 n\]where \(p\) is the price and \(n\) is the number of items. What is
Solve the systems in Problems 15-26 by the substitution method.\(\left\{\begin{array}{l}3 t_{1}+5 t_{2}=1,541 \\ t_{2}=2 t_{1}+160\end{array}ight.\)
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}y \geq \frac{3}{4} x-4 \\ y \leq-\frac{3}{4} x+11 \\ x \geq 6\end{array}ight.\)
Given the matrices in Problems 24-27, perform elementary row operations to obtain a 1 in the second row, second column without changing the entries in the first
Find the inverse of each matrix in Problems 21-26, if it exists.\(\left[\begin{array}{rrr}6 & 1 & 20 \\ 1 & -1 & 0 \\ 0 & 1 & 3\end{array}ight]\)
Suppose a car rental agency gives the following options:Option A: \(\$ 40\) per day plus \(50 otin\) per mile Option B: Flat \(\$ 60\) per day with unlimited mileage At what mileage are both rates
Solve the systems in Problems 15-26 by the substitution method.\(\left\{\begin{array}{l}x=-7 y-3 \\ 2 x+5 y=3\end{array}ight.\)
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}y \geq \frac{3}{2} x+3 \\ y \leq \frac{3}{2} x+6 \\ 3 \leq y \leq 6\end{array}ight.\)
Given the matrices in Problems 24-27, perform elementary row operations to obtain a 1 in the second row, second column without changing the entries in the first
Find the inverse of each matrix in Problems 21-26, if it exists.\(\left[\begin{array}{llll}1 & 0 & 0 & 1 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 2 & 0 & 1 & 0\end{array}ight]\)
A certain item has a linear supply curve\[p=0.0005 n-3\]and a linear demand\[p=8-0.0006 n\]where \(p\) is the price and \(n\) is the number of items. What is the equilibrium point \((p, n)\) ?
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}5 x+2 y \leq 30 \\ 5 x+2 y \geq 20 \\ x \geq 0 \\ y \geq 0\end{array}ight.\)
Solve the systems in Problems 15-26 by the substitution method.\(\left\{\begin{array}{l}x=3 y-4 \\ 5 x-4 y=-9\end{array}ight.\)
Given the matrices in Problems 24-27, perform elementary row operations to obtain a 1 in the second row, second column without changing the entries in the first
Find the inverse of each matrix in Problems 21-26, if it exists.\(\left[\begin{array}{llll}0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 1 & 3 & 0 \\ 2 & 4 & 0 & 0\end{array}ight]\)
There are six more dimes than quarters in a container. How many of each coin is there if the total value is \(\$ 3.75\) ?
Solve the systems in Problems 15-26 by the substitution method.\(\left\{\begin{array}{l}x+3 y=0 \\ x=5 y+16\end{array}ight.\)
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}5 x-2 y+30 \geq 0 \\ 5 x-2 y+20 \leq 0 \\ x \leq 0 \\ y \geq 0\end{array}ight.\)
Given the matrices in Problems 24-27, perform elementary row operations to obtain a 1 in the second row, second column without changing the entries in the first
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}4 x-7 y=-2 \\ -x+2 y=1\end{array}ight.\)
A box contains \(\$ 8.40\) in quarters and dimes. The number of quarters is twice the number of dimes. How many of each type of coin is in the box?
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}x+y=16 \\ x-y=10\end{array}ight.\)
Given the matrices in Problems 28-31, perform elementary row operations to obtain a zero (or zeros) above and below the 1 in the second column without changing the entries in the first
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}4 x-7 y=-65 \\ -x+2 y=18\end{array}ight.\)
A canoeist rows downstream in \(1 \frac{1}{2} \mathrm{hr}\) and back upstream in \(3 \mathrm{hr}\). What is the rate of the current if the canoeist rows 9 miles in each direction?
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}x+y=560 \\ x-y=490\end{array}ight.\)
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}x+y-9 \leq 0 \\ x+y+3 \geq 0 \\ x-y \leq 7 \\ y-x \leq 5\end{array}ight.\)
Given the matrices in Problems 28-31, perform elementary row operations to obtain a zero (or zeros) above and below the 1 in the second column without changing the entries in the first
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}4 x-7 y=48 \\ -x+2 y=-13\end{array}ight.\)
Charles Bronson was born nine years before another movie hard guy, Clint Eastwood. If the sum of their years of birth is 3,851, in what year was Eastwood born?
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}x+y=6 \\ x-2 y=12\end{array}ight.\)
Given the matrices in Problems 28-31, perform elementary row operations to obtain a zero (or zeros) above and below the 1 in the second column without changing the entries in the first column. [c]= 6
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ x+y \leq 9 \\ 2 x-3 y \geq-6 \\ x-y \leq 3\end{array}ight.\)
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}4 x-7 y=2 \\ -x+2 y=3\end{array}ight.\)
A plane makes a 660-mile flight with the wind in \(2 \frac{1}{2}\) hours. Returning against the wind takes 3 hours. Find the wind speed.
Given the matrices in Problems 28-31, perform elementary row operations to obtain a zero (or zeros) above and below the 1 in the second column without changing the entries in the first column. [D] =
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}3 x+y=13 \\ x-2 y=9\end{array}ight.\)
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ x+y \leq 8 \\ y \leq 4 \\ x \leq 6\end{array}ight.\)
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}4 x-7 y=5 \\ -x+2 y=4\end{array}ight.\)
Matt Damon is six years younger than Sandra Bullock. The sum of their years of birth is 3,934 . In what year was Matt born?
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}6 r-4 s=10 \\ 2 s=3 r-5\end{array}ight.\)
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}2 x+y \leq 8 \\ y \leq 5 \\ x-y \leq 2 \\ 3 x-y \geq 5\end{array}ight.\)
Given the matrices in Problems 32-35, perform elementary row operations to obtain a 1 in the third row, third column without changing the entries in the first two
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}4 x-7 y=-3 \\ -x+2 y=8\end{array}ight.\)
You have a \(24 \%\) silver alloy and some pure silver. How much of each must be mixed to obtain \(100 \mathrm{oz}\) of \(43 \%\) silver?
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}3 u+2 v=5 \\ 4 v=10-6 u\end{array}ight.\)
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}2 x+3 y \leq 30 \\ 3 x+2 y \geq 20 \\ x \geq 0 \\ y \geq 0\end{array}ight.\)
Given the matrices in Problems 32-35, perform elementary row operations to obtain a 1 in the third row, third column without changing the entries in the first two
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}8 x+6 y=12 \\ -2 x+4 y=-14\end{array}ight.\)
How much water must be added to a gallon of \(80 \%\) antifreeze to obtain a \(60 \%\) mixture?
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}3 a_{1}+4 a_{2}=-9 \\ 5 a_{1}+7 a_{2}=-14\end{array}ight.\)
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}2 x-3 y+30 \geq 0 \\ 3 x-2 y+20 \leq 0 \\ x \leq 0 \\ y \geq 0\end{array}ight.\)
Given the matrices in Problems 32-35, perform elementary row operations to obtain a 1 in the third row, third column without changing the entries in the first two
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}8 x+6 y=16 \\ -2 x+4 y=18\end{array}ight.\)
How much antifreeze must be added to a gallon of \(60 \%\) antifreeze to obtain an \(80 \%\) mixture?
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}5 s_{1}+2 s_{2}=23 \\ 2 s_{1}+7 s_{2}=34\end{array}ight.\)
Graph the solution of each system given in Problems 21-34.\(\left\{\begin{array}{l}x+y-10 \leq 0 \\ x+y+4 \geq 0 \\ x-y \leq 6 \\ y-x \leq 4\end{array}ight.\)
Given the matrices in Problems 32-35, perform elementary row operations to obtain a 1 in the third row, third column without changing the entries in the first two
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}8 x+6 y=-6 \\ -2 x+4 y=-26\end{array}ight.\)
The area of Texas is 208,044 square miles greater than that of Florida. Their combined area is 316,224 square miles. What is the area of each state?
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}s+t=12 \\ s-2 t=-4\end{array}ight.\)
Find the corner points for the set of feasible solutions for the constraints given in Problems 35-46.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ 2 x+y \leq 12 \\ x+2 y \leq 9\end{array}ight.\)
Given the matrices in Problems 36-39, perform elementary row operations to obtain zeros above and below the 1 in the third column without changing the entries in the first or second
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}8 x+6 y=-28 \\ -2 x+4 y=18\end{array}ight.\)
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}2 u-3 v=16 \\ 5 u+2 v=21\end{array}ight.\)
Find the corner points for the set of feasible solutions for the constraints given in Problems 35-46.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ 2 x+5 y \leq 20 \\ 2 x+y \leq 12\end{array}ight.\)
Given the matrices in Problems 36-39, perform elementary row operations to obtain zeros above and below the 1 in the third column without changing the entries in the first or second
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}8 x+6 y=-26 \\ -2 x+4 y=12\end{array}ight.\)
Forty-two coins have a total value of \(\$ 9.50\). If the coins are all nickels and quarters, how many are quarters?
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}2 x+5 y=7 \\ 2 x+6 y=14\end{array}ight.\)
Given the matrices in Problems 36-39, perform elementary row operations to obtain zeros above and below the 1 in the third column without changing the entries in the first or second columns. [c] =
Find the corner points for the set of feasible solutions for the constraints given in Problems 35-46.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ 3 x+2 y \leq 12 \\ x+2 y \leq 8\end{array}ight.\)
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}8 x+6 y=-36 \\ -2 x+4 y=-2\end{array}ight.\)
A collection of coins has a value of \(\$ 4.76\). There is the same number of nickels and dimes, but there are four fewer pennies than nickels or dimes. How many pennies are in the collection if
Solve the systems in Problems \(27-38\) by the addition method.\(\left\{\begin{array}{l}5 x+4 y=5 \\ 15 x-2 y=8\end{array}ight.\)
Given the matrices in Problems 36-39, perform elementary row operations to obtain zeros above and below the 1 in the third column without changing the entries in the first or second columns. [D] =
Find the corner points for the set of feasible solutions for the constraints given in Problems 35-46.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ x \leq 10 \\ y \leq 8 \\ 3 x+2 y \geq
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}2 x+3 y=9 \\ x-6 y=-3\end{array}ight.\)
A bunch of change contains nickels, dimes, and quarters. There is the same number of dimes and quarters, and there are eight more nickels than either dimes or quarters. How many dimes are there if
Solve the systems in Problems 39-56 for all real solutions, using any suitable method.\(\left\{\begin{array}{l}x+y=7 \\ x-y=-1\end{array}ight.\)
Find the corner points for the set of feasible solutions for the constraints given in Problems 35-46.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ x+y \leq 8 \\ y \leq 4 \\ x \leq
Solve the systems in Problems \(40-57\) by the Gauss-Jordan method.\(\left\{\begin{array}{l}x+y=7 \\ x-y=-1\end{array}ight.\)
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}2 x+3 y=2 \\ x-6 y=16\end{array}ight.\)
A box contains \(\$8.40\) in nickels, dimes, and pennies. How many of each type of coin is in the box if the number of dimes is six less than twice the number of pennies, and there is an equal number
Solve the systems in Problems 39-56 for all real solutions, using any suitable method.\(\left\{\begin{array}{l}x-y=8 \\ x+y=2\end{array}ight.\)
Find the corner points for the set of feasible solutions for the constraints given in Problems 35-46.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ x+y \geq 6 \\ -2 x+y \geq-16 \\ y \leq
Find the corner points for the set of feasible solutions for the constraints given in Problems 35-46.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ 3 x+2 y \leq 8 \\ x+5 y \leq 8\end{array}ight.\)
Solve the systems in Problems \(40-57\) by the Gauss-Jordan method.\(\left\{\begin{array}{l}x-y=8 \\ x+y=2\end{array}ight.\)
Sherlock Holmes was called in as a consultant to solve the Great Bank Robbery. 2006 The American Historical Theatre, Inc... www.americanhistoricaltheatre.org He was told that the thief had made away
Solve the systems in Problems 27-54 by solving the corresponding matrix equation with an inverse, if possible.\(\left\{\begin{array}{l}2 x+3 y=2 \\ x-6 y=-14\end{array}ight.\)
Solve the systems in Problems 39-56 for all real solutions, using any suitable method.\(\left\{\begin{array}{l}-x+2 y=2 \\ 4 x-7 y=-5\end{array}ight.\)
Find the corner points for the set of feasible solutions for the constraints given in Problems 35-46.\(\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ x \leq 8 \\ y \geq 2 \\ x+y \leq 10 \\ x \leq 3
Solve the systems in Problems \(40-57\) by the Gauss-Jordan method.\(\left\{\begin{array}{l}-x+2 y=2 \\ 4 x-7 y=-5\end{array}ight.\)
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