Algebra & Trigonometry (10th Edition)
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; Two equations are given with two unknowns and... more
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Amount invested for fund x=$0Amount invested for... more
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; Find in terms of in the first equation and ... more
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No real solutions for and ; To find the values of... more
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From the graph, is the point of intersection of ... more
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5172 pairs. ; Let the total cost be . The cost of... more
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In the fifth week, the ticket sales for the two ... more
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solution ; The solutions of equations in arbitrary... more
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substitution ; In the substitution method, one ... more
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point ; The solutions of two equations using a ... more
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break-even ; Break-even point is the point where ... more
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Fiind y in terms of x from the equation 2x+y=6 ... more
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Using the equation express in terms of and in ... more
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, ;Using a graphing utility, it can be verified ... more
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, ;Using a graphing utility, it can be verified ... more
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Using a graphing utility, it can be verified that ... more
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Using a graphing utility, it can be verified that ... more
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Using a graphing utility, it can be verified that ... more
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, ;Using a graphing utility, it can be verified ... more
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; From the first equation, , express in terms of... more
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; From the first equation, , express in terms of... more
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; From the first equation, , express in terms of... more
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; From the second equation , express in terms of... more
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. ; Number the given equations as (1) and (2) From... more
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; Number the given equations as (1) and (2)From ... more
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; Number the given equations as (1) and (2)From ... more
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; Number the given equations as (1) and (2). From... more
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The solution does not exist. ; Number the given ... more
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No solution exist. ; Number the given equations as... more
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; Let the amount in the fund be , the ... more
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; Let the amount invested in the fund and the ... more
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; Let the amount invested in the fund and the ... more
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; Let the amount invested in the fund and the ... more
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, ; From the equation for isolate . ; Substitute... more
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, ; From the equation isolate the . ; Substitute... more
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No real solution exists. ; Simplify and rewrite ... more
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; Substitute in to find .The two values of is ... more
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Make a two-column table corresponding to the and... more
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Choose some arbitrary values of and calculate the... more
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Make a two-column table corresponding to the and... more
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; Follow the steps below to draw the graph of .... more
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, ; Follow the steps below to draw the graph of .... more
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, ; Follow the steps below to draw the graph of .... more
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No solution. ; Follow the steps below to draw the ... more
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No solution. ; Follow the steps below to draw the ... more
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, ; Follow the steps below to draw the graph of .... more
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, ; Follow the steps below to draw the graph of .... more
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; Follow the steps below to solve the system of ... more
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Approximately . ; Follow the steps below to solve ... more
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Approximately . ; Follow the steps below to solve ... more
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;Approximately Approximately ; Follow the steps ... more
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;The algebraic method is chosen over the graphical... more
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and The substitution method is a simpler method ... more
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No Solution. ; The graphical method is the better ... more
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, and ; ; The graphical method is the better ... more
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; ; The graphical method is the better choice in... more
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and ; ; The graphical method is the better choice ... more
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and ; ; The graphical method is the better choice ... more
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and ; ; The graphical method is the better choice... more
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; The total cost of producing units is given by... more
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; The total cost of producing units is given by... more
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16667 sales. ; Let be the payment and be the ... more
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and ; Graph the equation of demand and supply ... more
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The error occurred while solving the second ... more
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; Let the width be , so, the length will be .It ... more
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; Let the length be , so, the width will be It ... more
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or ; Let the length be , so the width is .It is... more
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and ; Let the height of the triangle be and the... more
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False.Any one variable can be solved to get the ... more
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True;If the system has the equation of circle and ... more
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When the system of equations are inconsistentAlso... more
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; The pair of equations observed is . Add both ... more
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; Multiply the equation with the constant 3, i.e... more
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. ; Multiply the equation with the constant 5, ... more
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; Since the coefficients of the system of the ... more
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No solution and inconsistent ; The given pair of ... more
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No solution and inconsistent in nature. ; The ... more
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Infinitely many solutions, ; The given pair of ... more
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Approximately Approximately . ; Let and be the ... more
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; Substitute for the price per unit in the ... more
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Elimination. ; The elimination method is a ... more
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Equivalent. ; An equivalent system will have the ... more
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Consistent. ; If a system of equations has only ... more
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Equilibrium point. ; The demand, supply, and ... more
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, ; The graphs are labeled in the figure using the... more
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, ; The graphs are labeled in the figure using the... more
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; Multiply the equation with 2 and subtract it ... more
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; The graphs are labeled in the figure using the ... more
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No solution. ; To solve the system of equation, ... more
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No solution. ; The graphs are labeled in figure ... more
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Infinite solution. ; The graphs are labeled in the... more
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Infinite solution. ; The graphs are labelled using... more
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To verify the solution, substitute and in the ... more
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To verify the solution substitute, and in the ... more
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To verify the solution, substitute and in the ... more
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To verify the solution, substitute and in the ... more
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To verify the solution, substitute and in the ... more
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To verify the solution substitute and in the ... more
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To verify the solution substitute and in the ... more
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To verify the solution substitute and in the ... more
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To verify the solution substitute and in the ... more
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To verify the solution substitute and in the ... more
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;Check the values of and that satisfy both ... more
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To verify the solution substitute and in the ... more
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No Solution. ; The given pair of equations are .... more
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No Solution. ; The given pair of equations are .... more
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Infinite number of solutions, ; The given pair of ... more
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Infinite number of solutions, ; The given pair of ... more
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Check the values of and that satisfy both ... more
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;Substitute 1 for and 7 for in the equation and... more
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On dividing the equation by -2, is obtained. The... more
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;If in one of the equations any variable and ... more
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;If in one of the equations any variable and ... more
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;If in one of the equations any variable and ... more
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;If in one of the equations any variable and ... more
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;If in one of the equations, any variable and ... more
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;If in one of the equation any variable and ... more
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; According to the distance formula, , and it can... more
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Speed of the first plane: Speed of the second ... more
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Caloric content of a cheeseburger: Caloric content... more
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The amount of vitamin C in one-eighth ounce of ... more
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; At the equilibrium, demand is equal to supply. ... more
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; At the equilibrium, demand is equal to supply. ... more
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; At the equilibrium, demand is equal to supply. ... more
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; At the equilibrium, demand is equal to supply. ... more
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; Let be the amount invested in a bond with ... more
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; Let be the amount invested in a bond with ... more
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; Solve the simplified equation for and by ... more
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Solve the system of linear equations for and then... more
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True ; Two lines are said to be parallel if and ... more
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No ; Solving a system of equations does not always... more
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-4 ; Calculate the value of from the first ... more
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-2 ; Calculate the value of from the second ... more
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No; consistent equations can either overlap and ... more
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Substitution ; First substitute the value of from... more
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. The solution does not appear in any portion of ... more
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The solution does not appear in any portion of ... more
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; Each equation among the system of two equations... more
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; Each equation among the system of two equations... more
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; The row-echelon form of the system of equations... more
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; The outline of Gaussian elimination is that the... more
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; The system of equations is brought into the row... more
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No solution ; The system of equations is brought ... more
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, where is any real number. ; The system of ... more
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, where is any real number. ; The system of ... more
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The values of , , and are -32, 20, and 100, ... more
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; The points are substituted in the equation ... more
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Row–echelon ; The row–echelon form is the modified... more
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Ordered triple ; Instead of writing the value of ... more
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Gaussian ; Gaussian elimination is a systematic ... more
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Row operation ; Any equation in a system of ... more
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Nonsquare ; A nonsquare system is defined to be ... more
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Position ; The position equation describes the ... more
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; Back substitute the third equation's value in... more
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; Back substitute the third equation's value in... more
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; Back substitute the third equation's value in... more
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; Back substitute the third equation's value in... more
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; Back substitute the third equation's value in... more
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; Back substitute the third equation's value in... more
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First step is to convert the system into row-... more
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First step is to convert the system into row ... more
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;Substitute and in both equations and to ... more
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;Substitute and in both equations and to ... more
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;Substitute and in both equations and to ... more
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;Substitute and in both equations and to ... more
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Substitute , , and in the equations , and to ... more
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;Substitute and in the equations , and to ... more
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;Substitute and in the equations ,, and to ... more
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;Substitute and in the equations ,, and to ... more
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Inconsistent system with no solution. ; To ... more
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Inconsistent system with no solution. ; To ... more
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;Substitute , and in the equations to verify the ... more
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;Substitute and in the equations ,, and to ... more
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;Substitute ,, and in the equations ,, and to ... more
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;Substitute ,, and in the equations ,, and to ... more
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Inconsistent system with no solution. ; Number the... more
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;Substitute and in the equations , , and to ... more
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;Substitute ,, and in the equations , to verify ... more
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The equations have infinitely many solutions of ... more
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The equations have infinitely many solutions of ... more
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The equations have infinitely many solutions of ... more
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; Given equations can be assigned numbers for ... more
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; Given equations can be assigned numbers for ... more
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; Here the equations are Equation can be ... more
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; Here the equations are Multiply equation by 5 ... more
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; Here the equations are Multiply equation ... more
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; Here the equations are Multiply equation by 2 ... more
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; General equation for the position of the object... more
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; The general equation for the position of the ... more
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The generalised equation of the parabola is .Which... more
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; The generalised equation of a parabola is ,... more
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The generalised equation of a parabola is Which ... more
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The generalised equation of a parabola is .Which ... more
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; The generalised equation of a parabola is .... more
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; The generalised equation of a parabola is .... more
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; The generalised equation of a circle is . ... more
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; The generalised equation of a circle is . Which... more
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; The generalised equation of a circle is Which ... more
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; The generalised equation of a circle is . ... more
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Leading coefficient of the third equation is not ... more
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, , and . ; Suppose pound for brand , pound for ... more
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at at at ; Let , and ; now, write the equations... more
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Television: 30Radio: 10Newspaper: 20 ; Let the ... more
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, and ; According to the law of the triangle and ... more
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,, and ; According to the law of the triangle and ... more
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, and ; Define the variables, , .Form the ... more
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,, and ; Write the system of equations in the ... more
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, , and ; Write the system of equations in the ... more
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, and . ; Write the system of equations in the ... more
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, and . ; Form equations from the given data; ... more
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. ; Find the value of from the given equation... more
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and . ; Let be equation (1), be equation (2), ... more
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For a unique solution in the linear equation ... more
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For an inconsistent linear equation system, there ... more
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No ; Apply the Gaussian elimination method to ... more
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. ; The points , , and will satisfy . as it ... more
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. ; If the ordered triple is a solution of the ... more
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. ; If the ordered triple is a solution of the ... more
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. ; If the ordered triple is a solution of the ... more
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\[ \begin{aligned}x+5y&=6\\2x-10y&=4\\x+2z&=5\end{... more
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; Factorize the denominator (since the expression... more
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; Convert the improper expression into a proper ... more
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; Take as a common term from the denominator of... more
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; Separate each factor of the denominator with a ... more
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; The denominator has repeated linear and ... more
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Partial fraction decomposition ; Any rational ... more
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Improper ; An expression in which the degree of ... more
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Partial fraction ; Any rational expression can be ... more
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Basic equation ; After multiplying with the least ... more
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The least common denominator is . ; The least ... more
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; Factorize the denominator since the expression ... more
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; The denominator is factorized. ; Separate each ... more
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; The denominator has repeated linear factors ; ... more
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; The denominator has repeated linear factors.... more
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; Simplify the denominator by factoring it. ; The... more
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; Factorize the denominator. Note that the ... more
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; Factorize the denominator. Note that the ... more
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. ; Factorize the denominator and simplify the ... more
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; Factorize the denominator of the rational ... more
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; Factorize the denominator of the rational ... more
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; Factorize the denominator to simplify the ... more
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; Simplify the denominator by factoring it. ; ... more
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; Factorize the denominator and simplify. ; ... more
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. ; Simplify the denominator by factoring it. ; ... more
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; Factorize the denominator and simplify. ; ... more
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; Factorize the denominator to simplify. ; ... more
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; Factorize the denominator to simplify. ; ... more
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. ; Factorize the denominator and simplify. ; . ; ... more
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; Factorize the denominator to simplify. ; ... more
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; Factorize the denominator to simplify. ; ... more
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; Factorize the denominator to simplify. ; ... more
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; The given expression is a proper fraction, so ... more
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; The given expression is a proper fraction, so ... more
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; The given expression is a proper fraction; ... more
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; The given expression is a proper fraction, so ... more
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. ; The given expression is a proper fraction, so ... more
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; The given expression is a proper fraction; ... more
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; The given expression is a proper fraction; ... more
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; The given expression is a proper fraction; ... more
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; The given expression is a proper fraction; ... more
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; The given expression is a proper fraction; ... more
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; The given expression is a proper fraction; ... more
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; The expression is proper; therefore, when ... more
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; The expression is proper; therefore, when ... more
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; This rational expression is improper; therefore... more
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; This rational expression is improper; therefore... more
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; This rational expression is improper; therefore... more
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; This rational expression is improper; therefore... more
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; Expand the denominator . This rational ... more
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; Expand the denominator . This rational ... more
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; This rational expression is improper; so, ... more
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; Divide the numerator by the denominator to find... more
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; Simplify the denominator of the expression to ... more
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; The expression is simplified as a partial ... more
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; Simplify the denominator of the expression by ... more
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; Simplify the denominator of the expression by ... more
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; The expression is simplified as a partial ... more
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; The expression is simplified as a partial ... more
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; The rational expression is improper. Therefore... more
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; The rational expression is improper. Therefore... more
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p000400.570.57601.121.12802.672.67 ; The ... more
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The partial decomposition is The rational ... more
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The fraction is improper and for an improper ... more
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The degrees could be equal.An example of a partial... more
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As the expression is an improper rational ... more
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Distinct linear factors:If the expression is ... more
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The given inequality is represented by the shaded ... more
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The inequality is .represents the vertical line ... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Consumer surplus: Producer surplus: ; The demand ... more
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; Let represent the number of units of nutrients ... more
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solution ; The inequality has two variables and If... more
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graph ; An inequality contains an uncountable ... more
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solution ; A system of inequalities contains two ... more
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solution set ; The solution set represents a ... more
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Follow the below steps to sketch the graph,Convert... more
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Follow the below steps to sketch the graph,Make a ... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Draw the ... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Replace the sign with equal to and rewrite the ... more
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Replace the sign with equal to and rewrite the ... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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Follow these steps to construct a graph:Make a two... more
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; From the graph, it is observed that the ... more
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; From the graph, it is observed that equation of... more
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; The graph is a parabola of the form since is ... more
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; This is a graph of the circle, with equation ... more
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Draw the axis and axis and set the boundary ... more
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Draw the x-axis and the y-axis and set the ... more
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Draw the axis and axis and set the boundary ... more
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Draw the x-axis and the y-axis and set the ... more
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Draw the x axis and the y axis and set the ... more
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Draw the x axis and the y axis and set the ... more
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Draw the x axis and the y axis and set the ... more
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The given system of inequalities is .Divide the ... more
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Draw the axis and the axis and set the boundary ... more
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Draw the axis and the axis and set the boundary ... more
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Draw the axis and the axis and set the boundary ... more
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Draw the axis and the axis and set the boundary ... more
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Draw the axis and the axis and set the boundary ... more
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Draw the axis and the axis and set the boundary ... more
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Plot the graph of the system of inequalities using... more
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Plot the graph of the system of inequalities using... more
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Plot the graph of the system of inequalities using... more
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Plot the graph of the system of inequalities using... more
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Plot the graph of the system of inequalities using... more
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Plot the graph of the system of inequalities using... more
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; It is observed that the line is passing the two... more
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; The equation of a line crossing two points and... more
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; The shaded region is bounded by two lines and a... more
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; The shaded area is bounded by two lines and a ... more
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; There will be four sides of the rectangle and ... more
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; There are four sides of the parallelogram and ... more
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; The triangle has three sides and each side ... more
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; The triangle has three sides and each side ... more
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; Assume that and are the amounts in two ... more
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; Assume to be the number of reserved seats and ... more
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. ; Assume the number of tables to be and the ... more
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; Assume and as the number of laptops of model A ... more
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TrueThe solution region of the inequality is a ... more
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FalseThe point , which belongs to the solution ... more
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Take any test point below the line and above the ... more
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The points on the lines are and . The equation of... more
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The maximum value of is , and this occurs when... more
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The maximum value of is , and this occurs when... more
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The maximum value of is 96, and this occurs when... more
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30 ; Draw the graphs of the given function , on ... more
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. 1050 boxes of chocolate-covered creams and 150 ... more
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3 bottles of brand and 2 bottles of brand . ; Let... more
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Optimization ; To maximize the gain or minimize ... more
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linear programming ; Linear programming is an ... more
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objective ; Using the objective function, the ... more
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constraints ; Constraints are equations or ... more
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inside ; Feasible solutions are the set of all the... more
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Vertex. ; The vertex of a feasible region has the ... more
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The maximum value of is 20 occurring at .The ... more
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The maximum value of is 32 occuring at .The ... more
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The maximum value of is 26 occuring at and ... more
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The maximum value is 31 occurring at and minimum ... more
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The maximum value is 740 at and minimum value is ... more
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The maximum value is 36000 at and and minimum ... more
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The maximum value of is 24; it occurs at and The ... more
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The maximum value of is 80; it occurs at The ... more
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No maximum value;The minimum value of is 35; it ... more
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No maximum value;The minimum value of is 20; it ... more
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The maximum value of is 180; it occurs at The ... more
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Minimum at : 0The maximum, 84, occurs at any point... more
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Minimum at : 7.2Maximum at : 60 ; Consider the ... more
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Maximum at : 20The minimum, 0, occurs at any point... more
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Minimum at : 0Maximum at : 25 ; Consider the ... more
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Minimum at : 0Maximum at : ; The shaded region is... more
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Minimum at : 0Maximum at : ; The shaded region is... more
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Minimum at : 0Maximum at : 42 ; The shaded region... more
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Minimum at : 10No maximum ; Consider the ... more
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Minimum at : 29No maximum ; The shaded region is ... more
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No minimum Maximum at : 7 ; The shaded region is ... more
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Minimum at : -7No maximum ; The shaded region is... more
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Minimum at : 0The maximum, 5, occurs at any point ... more
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The solution region is unbounded.Minimum at : 2No ... more
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The constraint is extraneous.Minimum at : -... more
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The solution region is unbounded.Minimum at : 0No ... more
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The feasible set is empty. ; Consider the ... more
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Minimum at : 0The maximum, 4, occurs at any point ... more
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Consider the inequalities of the constraints as ... more
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Consider the inequalities of the constraints as ... more
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230 units of the model,45 units of the model,... more
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Optimum profit: 570000Optimum number of model : ... more
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Number of bottles of brand : 2Number of bottles of... more
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The minimum number of hours needed for and are ... more
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The maximum revenue is .Optimal number of audits: ... more
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The maximum revenue is .The optimal number of ... more
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Crop : Crop : Yield : ; Let the number of acres ... more
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Optimal number of crop : Optimal number of crop... more
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TV ads: Newspaper ads: ; Let the TV ad minutes be... more
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Optimal investment for type Optimal investment for... more
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True;The maximum value of an objective function ... more
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False, as the minimum value depends on the ... more
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True, because all the points between the vertices... more
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; When an objective function has a maximum value ... more
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;Substitute 1 for and in the equation and to ... more
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;Substitute -3 for and in the equation and to ... more
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;Substitute for and 5 for in the equation and... more
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; The system of equations is given byFrom ... more
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; The system of equations is given byFrom ... more
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, ; The system of equations is given by From ... more
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; The system of equations is given as From ... more
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; The system of equations is given as From ... more
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; The system of equations is given by From ... more
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; The system of equations is given by Substitute ... more
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The system of equations if given by Write the ... more
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The system of equations is given by Write the ... more
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, ; The system of equations is given by Write ... more
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; The system of equations is given by Write ... more
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(0,-2) ; The system of equations is given by Set... more
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; The system of equations is given by Set , , , ... more
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No real solution. ; The system of equations is ... more
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(9.678,-0.839) ; The system of equations is given ... more
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Males will exceed females after of age. ; The ... more
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More than . ; Consider the total annual salary to ... more
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; Consider the length and breadth of the ... more
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; Consider the length and the breadth of the ... more
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; The system of equations is given by.To equalize... more
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; To solve the equations, both equations must ... more
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; Since the coefficients are equal in both the ... more
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; To solve the equations, both the equations must... more
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; Multiply the equation by 4 to make the ... more
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No solution ; Multiply the equation by 4 to make ... more
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; At the equilibrium point, demand and supply ... more
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; At the equilibrium point, demand and supply ... more
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x=2,y=-4, and z=-5 ; Substitute in the equation... more
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; Substitute in the equation to solve for . ; ... more
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; Subtract the equation from to eliminate the ... more
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; Subtract the equations and from to eliminate... more
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; Subtract the equations and from to ... more
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Inconsistent system with no solution ; Add the ... more
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; Multiply the equation by 2 and subtract it ... more
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; Add the equations , and to eliminate the ... more
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, ; Multiply the equation by so that ... more
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z=a, y=5a+6, and x=2-3a ; Multiply the equation ... more
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y=2x^2+x-5 ; In the equation of the parabola , ... more
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y=3x^2+11x-14 ; In the equation of the parabola , ... more
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Equation of the circle is .Input the points , , ... more
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Input the points , , and using a graphic utility... more
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,, and ; Total amount of chemical A is , chemical... more
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There are 2 par 3 holes, 14 par 4 holes, and 2 par... more
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The first investment is , the second investment is... more
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The first investment is , the second investment is... more
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; Find the system of equations for the vertical ... more
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; Find the system of equations for the vertical ... more
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; Find the factors for the denominator by taking... more
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; Find the factors for the denominator by ... more
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; Find the factors for the denominator . ; ... more
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; The given function is .Here, the expression ... more
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Check:Substitute in :Substitute in :Hence, ... more
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Check:Substitute in :Substitute in :Hence, ... more
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Check:Substitute to the left-hand side:Substitute... more
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Check:Substitute to the left-hand side:Substitute... more
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Check:Substitute to the left-hand side of ... more
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Check:Substitute to the left-hand side of ... more
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Check:Substitute to the left-hand side of ... more
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Check:Substitute to the left-hand side of ... more
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For plotting an inequality, draw a line , which is... more
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For plotting an inequality, draw a line , which is... more
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For plotting an inequality, take and find the ... more
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For plotting an inequality, take and find the ... more
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For plotting an inequality, graph the equation , ... more
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For plotting an inequality, graph the equation , ... more
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For plotting an inequality, take and find the ... more
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For plotting an inequality, take and find the ... more
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For plotting an inequality, take and find the ... more
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For plotting an inequality, take and find the ... more
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For plotting an inequality, take and find the ... more
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For plotting an inequality, take and find the ... more
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For plotting an inequality, graph the equations ... more
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For plotting an inequality, take and find the ... more
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; There will be four sides to the rectangle and ... more
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; There will be three sides to the triangle and ... more
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The number of items of products and denoted by ... more
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The equations and are plotted by calculating ... more
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; Multiply the equations /(1.4x-y=17/) and /(0.8x... more
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The equations and are plotted by calculating ... more
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The equations and are plotted by calculating ... more
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72; 0; ; The number of haircuts given by the ... more
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False. The inequality also satisfies , therefore ... more
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False. The repeated linear factor should have an ... more
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; The ordered pair is a solution of the given ... more
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; The ordered pair is a solution of the given ... more
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; The ordered pair is a solution of the given ... more
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; The ordered pair is a solution of the given ... more
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; The ordered triple satisfies the first ... more
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; The ordered triple satisfies the first ... more
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; The ordered triple satisfies the first ... more
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; The ordered triple satisfies the first ... more
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A system of linear equations that does not have ... more
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The graph consists of parallel lines that do not ... more
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(-4,-5) ; Consider the first equation . and solve... more
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, ; The given system of equations is solved using ... more
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, ; , ; Consider the second equation and solve ... more
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, ; Find the and intercepts of the equations ... more
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, and , ; Find the and intercepts of the ... more
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. ; Substitute different values of in the two ... more
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; Multiply the equation by 5 and by 4 to make ... more
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, , ; The system of equations is converted into ... more
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No solutions ; The system of equations is ... more
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; As the expression is proper, rewrite the ... more
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; As the expression is proper, rewrite the ... more
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; The expression is improper. Divide the ... more
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; As the expression is proper, factor the ... more
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The graph of the inequalities is sketched by ... more
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The graph of the inequalities is sketched by ... more
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The graph of the inequalities is sketched by ... more
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is the minimum is the maximum ; The graph of the ... more
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at at ; Let the amount invested in the first ... more
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; Since the parabola passes through the points... more
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Model I: Model II: Optimal profit: ; Let the ... more
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Draw a circle of radius 10 and the lines and The ... more
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; Two equations have an infinite number of ... more
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. ; Since the equations and represent the ... more
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\mathrm{10.1\;ft}\mathrm{252.75\;ft} ; Since the ... more
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. ; Let the weight of a carbon atom be and the ... more
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; Let the cost of cable be and the cost of 1 ... more
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, , ; is a solution of the equations , , and .... more
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; Consider the system of equation:The system has ... more
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; Consider the system of equation:The system has ... more
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