$course$/top/Default for MSII/Test#10 $course$/top/Default for MSII/Test#10/L71- Pythagorean Theorem L71 Pythagorean Theorem (b) var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false, grid:false, boundingbox: [-.25,1.25,1.25,-.25], showCopyright: false, showNavigation: false, keepAspectRatio: true}); var p1=board.create('point',[{Xa},{Ya}],{name:"",size:"0",fixed:true,showInfobox:false}); var p2=board.create('point',[{Xa},0],{name:"",size:"0",fixed:true,showInfobox:false}); var p0=board.create('point',[0,0],{name:"",size:"0",fixed:true,showInfobox:false}); var poly=board.create('polygon',[p0,p1,p2],{strokecolor:'magenta',fillColor:'magenta',fillOpacity:'1'}); var t1=board.create('text',[{Xa}+.1,{Ya}/2,"b"],{fontSize:'20'}); var t2=board.create('text',[{Xa}/2,-0.1,"{l2}"],{fontSize:'20'}); var t3=board.create('text',[{Xa}/2,{Ya}/2,"{hy}"],{anchorX:'right',anchorY:'bottom',fontSize:'20'}); ]]>

The triangle is a right triangle.		Use the Pythagorean Theorem to determine the length of the 'missing' side.
a² + b² = c²		a={l2} b=____ c={hy}
({l2})² + b² = ({hy})²		Substitute the known amounts
({l2})² + b² = ({hy})²		Determine the squares of the numbers: ({l2})² = ({l2})({l2}) = {=l2l2} ({hy})² = ({hy})({hy}) = {=hyhy}
{=l2l2} + b² = {=hyhy} -{=l2l2} -{=l2l2}		Subtract {=l2*l2} from both sides
b² = {=(hyhy) - (l2l2)}		Simplify
$\sqrt{b^2}$ = $\sqrt{{=(hyhy) - (l2l2)}}$		Take the Square root of both sides.
b = {l1}		Simplify (The length is measured on a ruler, therefore it is a positive answer.)

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. triplet={[3,4,5],[5,12,13],[8,15,17],[6,8,10],[9,12,15],[15,20,25],[12,16,20]}; triplet=[6,8,10]; l1=triplet[0]; l2=triplet[1]; hy=triplet[2]; theta=asin(l1/hy); Xa=cos(theta); Ya=sin(theta); abc 0 1 0 1 l1 _err == 0 1 1 b={_0}

]]> L71- Pythagorean Theorem (a) var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false, grid:false, boundingbox: [-.25,1.25,1.25,-.25], showCopyright: false, showNavigation: false, keepAspectRatio: true}); var p1=board.create('point',[{Xa},{Ya}],{name:"",size:"0",fixed:true,showInfobox:false}); var p2=board.create('point',[{Xa},0],{name:"",size:"0",fixed:true,showInfobox:false}); var p0=board.create('point',[0,0],{name:"",size:"0",fixed:true,showInfobox:false}); var poly=board.create('polygon',[p0,p1,p2],{strokecolor:'black',fillColor:'navy',fillOpacity:'1'}); var t1=board.create('text',[{Xa}+.1,{Ya}/2,"b"],{fontSize:'20'}); var t2=board.create('text',[{Xa}/2,-0.1,"{l2}"],{fontSize:'20'}); var t3=board.create('text',[{Xa}/2,{Ya}/2,"{hy}"],{anchorX:'right',anchorY:'bottom',fontSize:'20'}); ]]> The triangle is a right triangle. Use the Pythagorean Theorem to
determine the length of the 'missing' side. a² + b² = c²
a=____
b={l2}
c={hy}

b² + ({l2})² = ({hy})² Substitute the known amounts b² + ({l2})² = ({hy})²
Determine the squares of the numbers:
({l2})² = ({l2})({l2}) = {=l2*l2}
({hy})² = ({hy})({hy}) = {=hy*hy}

b² + {=l2*l2} = {=hy*hy}
-{=l2*l2} -{=l2*l2}
Subtract {=l2*l2} from both sides b² = {=(hy*hy) - (l2*l2)} Simplify $\sqrt{b^2}$ = $\sqrt{{=(hy*hy) - (l2*l2)}}$ Take the Square root of both sides. b = {l1}
Simplify (The length is measured
on a ruler, therefore it is a positive answer.)

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. triplet={[3,4,5],[5,12,13],[8,15,17],[6,8,10],[9,12,15],[15,20,25],[12,16,20]}; triplet= [8,15,17]; l1=triplet[0]; l2=triplet[1]; hy=triplet[2]; theta=asin(l1/hy); Xa=cos(theta); Ya=sin(theta); abc 0 1 0 1 l1 _err == 0 1 1 Determine the length of the missing side of the triangle.
b={_0}

]]> L71-Pythagorean Theorem (hy) var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false, grid:false, boundingbox: [-.25,1.25,1.25,-.25], showCopyright: false, showNavigation: false, keepAspectRatio: true}); var p1=board.create('point',[{Xa},{Ya}],{name:"",size:"0",fixed:true,showInfobox:false}); var p2=board.create('point',[{Xa},0],{name:"",size:"0",fixed:true,showInfobox:false}); var p0=board.create('point',[0,0],{name:"",size:"0",fixed:true,showInfobox:false}); var poly=board.create('polygon',[p0,p1,p2],{strokeColor:'orange',fillColor:'orange',fillOpacity:'1'}); var t1=board.create('text',[{Xa}+.1,{Ya}/2,"{l1}"],{fontSize:'20'}); var t2=board.create('text',[{Xa}/2,-0.1,"{l2}"],{fontSize:'20'}); var t3=board.create('text',[{Xa}/2,{Ya}/2,"c"],{anchorX:'right',anchorY:'bottom',fontSize:'20'}); ]]>

The triangle is a right triangle.		Use the Pythagorean Theorem to determine the length of the 'missing' side.
a² + b² = c²		a={l2} b={l1} c=___
({l2})² + ({l1})² = c²		Substitute the known amounts
({l2})² + ({l1})² = c²		Determine the squares of the numbers: ({l2})² = ({l2})({l2}) = {=l2l2} ({l1})² = ({l1}) ({l1}) = {=l1l1}
{=l2l2} + {=l1l1} = c²		Add {=l2l2} + {=l1l1}
{=l2l2+l1l1} = c²		Simplify
$\sqrt{{sums}}$ = $\sqrt{c^2}$		Take the Square root of both sides.
{hy} = c		Simplify (The length is measured on a ruler, therefore it is a positive answer.)

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. triplet={[3,4,5],[5,12,13],[8,15,17],[6,8,10],[9,12,15],[15,20,25],[12,16,20]}; triplet=[20,15,25]; l1=triplet[0]; l2=triplet[1]; hy=triplet[2]; theta=asin(l1/hy); Xa=cos(theta); Ya=sin(theta); sums=l2*l2+l1*l1; abc 0 1 0 1 hy _err == 0 1 1 c={_0}

]]> $course$/top/Default for MSII/Test#10/L72- Volume of Rectangular Prisms L72- Volume of cubes var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false, grid:false, boundingbox: [-2,8,8,-2], showCopyright: false, showNavigation: false, keepAspectRatio: true}); var p0=board.create('point',[0,0],{name:"",size:"0",fixed:true,showInfobox:false}); var p1=board.create('point',[0,{w}],{name:"",size:"0",fixed:true,showInfobox:false}); var p2=board.create('point',[{l},{w}],{name:"",size:"0",fixed:true,showInfobox:false}); var p3=board.create('point',[{l},0],{name:"",size:"0",fixed:true,showInfobox:false}); var p4=board.create('point',[{l}/2,{w}/2],{name:"",size:"0",fixed:true,showInfobox:false}); var p5=board.create('point',[{l}/2,3*{w}/2],{name:"",size:"0",fixed:true,showInfobox:false}); var p6=board.create('point',[3*{l}/2,3*{w}/2],{name:"",size:"0", fixed:true,showInfobox:false}); var p7=board.create('point',[3*{l}/2,{w}/2],{name:"",size:"0",fixed:true,showInfobox:false}); var poly1=board.create('polygon',[p0,p1,p2,p3],{strokeColor:'black', fillColor:'{color}', fillOpacity:'.3'}); var poly2=board.create('polygon',[p1,p5,p6,p2],{strokeColor:'black', fillColor:'{color}', fillOpacity:'.5'}); var poly3=board.create('polygon',[p3,p2,p6,p7],{strokeColor:'black', fillColor:'{color}', fillOpacity:'.7'}); varl1=board.create('line',[p5,p4],{strokeColor:'black',dash:'2',straightFirst:false,straightLast:false}); varl1=board.create('line',[p4,p7],{strokeColor:'black',dash:'2',straightFirst:false,straightLast:false}); varl1=board.create('line',[p4,p0],{strokeColor:'black',dash:'2',straightFirst:false,straightLast:false}); var tl=board.create('text',[{l}/2,-.1,"{s} {units}"],{anchorX:'left',anchorY:top,fontSize:'20'}); var t2=board.create('text',[-.1,{w}/2,"{s} {units}"],{anchorX:'right',fontSize:'20'}); var t3=board.create('text',[5*{l}/4,{w}/4,"{s} {units}"],{anchorX:'left',anchorY:'top',fontSize:'20'}); ]]>

V = s³		Formula for Volume
V=({s})³		Substitute the known values s= {s} {units}
V = ({s})({s})({s})		Multiply ({s})({s})({s})
V = {volume} {unit[2]}		Write the Units

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. 23 none 0 1 0 2 [volume,volUnit] _err == 0 1 1

Volume={_0}

{_1:unit}

]]> L72- Volume of Rectangular Prisms var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false, grid:false, boundingbox: [-2,8,8,-2], showCopyright: false, showNavigation: false, keepAspectRatio: true}); var p0=board.create('point',[0,0],{name:"",size:"0",fixed:true,showInfobox:false}); var p1=board.create('point',[0,{w}],{name:"",size:"0",fixed:true,showInfobox:false}); var p2=board.create('point',[{l},{w}],{name:"",size:"0",fixed:true,showInfobox:false}); var p3=board.create('point',[{l},0],{name:"",size:"0",fixed:true,showInfobox:false}); var p4=board.create('point',[{l}/2,{w}/2],{name:"",size:"0",fixed:true,showInfobox:false}); var p5=board.create('point',[{l}/2,3*{w}/2],{name:"",size:"0",fixed:true,showInfobox:false}); var p6=board.create('point',[3*{l}/2,3*{w}/2],{name:"",size:"0", fixed:true,showInfobox:false}); var p7=board.create('point',[3*{l}/2,{w}/2],{name:"",size:"0",fixed:true,showInfobox:false}); var poly1=board.create('polygon',[p0,p1,p2,p3],{strokeColor:'black', fillColor:'{color}', fillOpacity:'.3'}); var poly2=board.create('polygon',[p1,p5,p6,p2],{strokeColor:'black', fillColor:'{color}', fillOpacity:'.5'}); var poly3=board.create('polygon',[p3,p2,p6,p7],{strokeColor:'black', fillColor:'{color}', fillOpacity:'.7'}); varl1=board.create('line',[p5,p4],{strokeColor:'black',dash:'2',straightFirst:false,straightLast:false}); varl1=board.create('line',[p4,p7],{strokeColor:'black',dash:'2',straightFirst:false,straightLast:false}); varl1=board.create('line',[p4,p0],{strokeColor:'black',dash:'2',straightFirst:false,straightLast:false}); var tl=board.create('text',[{l}/2,-.1,"{dl} {units}"],{anchorX:'left',anchorY:top,fontSize:'20'}); var t2=board.create('text',[-.1,{w}/2,"{dw} {units}"],{anchorX:'right',fontSize:'20'}); var t3=board.create('text',[5*{l}/4,{w}/4,"{dh} {units}"],{anchorX:'left',anchorY:'top',fontSize:'20'}); ]]>

V = lwh		Formula for Volume
V=({dl})({dw})({dh})		Substitute the known values l= {dl} {units} w= {dw} {units} h= {dh} {units}
V = ({=dl*dw})({dh})		Multiply ({dl})({dw})
V = {volume} {unit[2]}		Multiply ({=dl*dw})({dh})

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. 23 none 0 1 0 2 [volume,volUnit] _err == 0 1 1 Volume={_0}{_1:unit}]]> $course$/top/Default for MSII/Test#10/L73- Transversal and Parallel Lines L73- transversal Parallel Lines {vp0}{vp1} is parallel to {vp2}{vp3}. line {pi0}{pi1} intersects the parallel lines. <{=angles[randAngles[0]]} = {=degrees[randAngles[0]]}^o

]]> 2 0.33 0 1 degrees[randAngles[3]] 1 1 <{=angles[randAngles[3]]}={_0}^o

]]> L73- transversal-FIND x-supplementary angles line {pl1Name} is parallel to line {pl2Name}.

<{Ang}={a}x+{b} and <{AngAns}={c}x+{d}		given
<{Ang} and <{AngAns} are supplementary		The angles add to 180^o
{a}x+{b} + {c}x+{d} = 180
{a}x + {c}x +{b}+{d} = 180		To simplify, combine the like terms {a}x + {c}x = {=a+c}x +{b}+{d} = {=b+d}
{=a+c}x + {=b+d} = 180 -{=b+d} -{=b+d}		Subtract {=b+d} from both sides
{=a+c}x = {=180-(b+d)} {=a+c} {=a+c}		Divide both sides by {=a+c}
x = {x}		The value of x.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. angle={.5:2.7:.05}; vStart={0:18:1}; x={1:30:1}; a={-5,-4,-3,-2,2,3,4,5}; c={-4,-3,-2,2,3}; axPb={30:90:1}; randAngles={[2,1],[2,4],[2,5],[2,8],[3,1],[3,4],[3,5],[3,8],[6,1],[6,4],[6,5],[6,8],[7,1],[7,4],[7,5],[7,8]}; abc 0 1 0 1 x 1 1 The value of x = {_0}
]]> L73- transversal-FIND x2-supplementary angles line {pl1Name} is parallel to line {pl2Name}.

<{Ang}={a}x+{b} and <{AngAns}={c}x+{d}		given
<{Ang} and <{AngAns} are supplementary		The angles add to 180^o
{a}x+{b} + {c}x+{d} = 180
{a}x + {c}x +{b}+{d} = 180		To simplify, combine the like terms {a}x + {c}x = {=a+c}x +{b}+{d} = {=b+d}
{=a+c}x + {=b+d} = 180 -{=b+d} -{=b+d}		Subtract {=b+d} from both sides
{=a+c}x = {=180-(b+d)} {=a+c} {=a+c}		Divide both sides by {=a+c}
x = {x}		The value of x.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. vStart={0:18:1}; x={1:30:1}; a={-5,-4,-3,-2,2,3,4,5}; c={-4,-3,-2,2,3}; cxPd={30:90:1}; randAngles={[2,1],[2,4],[2,5],[2,8],[3,1],[3,4],[3,5],[3,8],[6,1],[6,4],[6,5],[6,8],[7,1],[7,4],[7,5],[7,8]}; abc 0 1 0 1 x 1 1 The value of x = {_0}
]]> L73- transversal-FIND xANG-supplementary angles line {pl1Name} is parallel to line {pl2Name}.

<{Ang}={a}x+{b} and <{AngAns}={c}x+{d}		given
<{Ang} and <{AngAns} are supplementary		The angles add to 180^o
{a}x+{b} + {c}x+{d} = 180
{a}x + {c}x +{b}+{d} = 180		To simplify, combine the like terms {a}x + {c}x = {=a+c}x +{b}+{d} = {=b+d}
{=a+c}x + {=b+d} = 180 -{=b+d} -{=b+d}		Subtract {=b+d} from both sides 180 - {=b+d} = {=180-(b+d)}
{=a+c}x = {=180-(b+d)} {=a+c} {=a+c}		Divide both sides by {=a+c} {=180-(b+d)} ÷ {=a+c} = {x}
x = {x}		The value of x.

]]> 1 1 0 1 degrees[randomAng] _err == 0 1 1 Calculate the measure of <{=1+randomAng}.

<{=1+randomAng} = {_0}^o

]]> <{Ang}={a}x+{b}
({a})({x})+{b}
{=a*x}+{b}
{=axPb} Substitute x={x} to determine the measure of <{Ang} <{AngAns}={c}x+{d}
({c})({x})+{d}
{=c*x}+{d}
{=cxPd} Substitute x={x} to determine the measure of <{AngAns} Use the angle relationships to determine the value of each angle. var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false, grid:false, boundingbox: [-1.25,1.25,1.25,-1.25], showCopyright: false, showNavigation: false, keepAspectRatio: true}); var p1a=board.create('point',[{Xa},{Ya}],{ name:"{l1Name}", size:"0", fixed:true, showInfobox:false}); var p1b=board.create('point',[{Xb},{Yb}],{ name:"", size:"0", fixed:true, showInfobox:false}); var p0=board.create('point',[{Xpi0},{Ypi0}],{name:"",size:"0",fixed:true,showInfobox:false}); var p1=board.create('point',[{Xpi1},{Ypi1}],{name:"",size:"0",fixed:true,showInfobox:false}); var line1=board.create('line',[p1a,p1b],{firstArrow:true,lastArrow:true}); var pl0=board.create('point',[-1,0.25],{name:"{pl1Name}",size:"0",fixed:true,showInfobox:false}); var pl1=board.create('point',[1,0.25],{name:"",size:"0",fixed:true,showInfobox:false}); var pl2=board.create('point',[-1,-0.25],{name:"{pl2Name}",size:"0",fixed:true,showInfobox:false}); var pl3=board.create('point',[1,-0.25],{name:"",size:"0",fixed:true,showInfobox:false}); var pline1=board.create('line',[pl0,pl1],{firstArrow:true,lastArrow:true}); var pline2=board.create('line',[pl2,pl3],{firstArrow:true,lastArrow:true}); var tA1=board.create('text',[{Xpi0}-.25,{Ypi0}+.1,"{ang1}"],{fontSize:20,strokeColor:'blue'}); var tA2=board.create('text',[{Xpi0}+.25,{Ypi0}+.1,"{ang2}"],{fontSize:20,strokeColor:'red'}); var tA3=board.create('text',[{Xpi0}-.25,{Ypi0}-.1,"{ang3}"],{fontSize:20,strokeColor:'red'}); var tA4=board.create('text',[{Xpi0}+.25,{Ypi0}-.1,"{ang4}"],{fontSize:20,strokeColor:'blue'}); var tA5=board.create('text',[{Xpi1}-.25,{Ypi1}+.1,"{ang5}"],{fontSize:20,strokeColor:'blue'}); var tA6=board.create('text',[{Xpi1}+.2,{Ypi1}+.1,"{ang6}"],{fontSize:20,strokeColor:'red'}); var tA7=board.create('text',[{Xpi1}-.25,{Ypi1}-.1,"{ang7}"],{fontSize:20,strokeColor:'red'}); var tA8=board.create('text',[{Xpi1}+.2,{Ypi1}-.1,"{ang8}"],{fontSize:20,strokeColor:'blue'}); ]]> L73- transversal-FIND xANG-supplementary angles line {pl1Name} is parallel to line {pl2Name}.

<{Ang}={a}x+{b} and <{AngAns}={c}x+{d}		given
<{Ang} and <{AngAns} are supplementary		The angles add to 180^o
{a}x+{b} + {c}x+{d} = 180
{a}x + {c}x +{b}+{d} = 180		To simplify, combine the like terms {a}x + {c}x = {=a+c}x +{b}+{d} = {=b+d}
{=a+c}x + {=b+d} = 180 -{=b+d} -{=b+d}		Subtract {=b+d} from both sides 180 - {=b+d} = {=180-(b+d)}
{=a+c}x = {=180-(b+d)} {=a+c} {=a+c}		Divide both sides by {=a+c} {=180-(b+d)} ÷ {=a+c} = {x}
x = {x}		The value of x.

]]> 1 1 0 1 degrees[randomAng] _err == 0 1 1 Calculate the measure of <{=1+randomAng}.

<{=1+randomAng} = {_0}^o

<{Ang}={a}x+{b} and <{AngAns}={c}x+{d}		given
<{Ang} and <{AngAns} are supplementary		The angles add to 180^o
{a}x+{b} + {c}x+{d} = 180
{a}x + {c}x +{b}+{d} = 180		To simplify, combine the like terms {a}x + {c}x = {=a+c}x +{b}+{d} = {=b+d}
{=a+c}x + {=b+d} = 180 -{=b+d} -{=b+d}		Subtract {=b+d} from both sides 180 - {=b+d} = {=180-(b+d)}
{=a+c}x = {=180-(b+d)} {=a+c} {=a+c}		Divide both sides by {=a+c} {=180-(b+d)} ÷ {=a+c} = {x}
x = {x}		The value of x.

]]> 1 1 0 1 degrees[randomAng] _err == 0 1 1 Calculate the measure of <{=1+randomAng}.

<{=1+randomAng} = {_0}^o

]]> <{Ang}={a}x+{b}
({a})({x})+{b}
{=a*x}+{b}
{=axPb} Substitute x={x} to determine the measure of <{Ang} <{AngAns}={c}x+{d}
({c})({x})+{d}
{=c*x}+{d}
{=cxPd} Substitute x={x} to determine the measure of <{AngAns} Use the angle relationships to determine the value of each angle. var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false, grid:false, boundingbox: [-1.25,1.25,1.25,-1.25], showCopyright: false, showNavigation: false, keepAspectRatio: true}); var p1a=board.create('point',[{Xa},{Ya}],{ name:"{l1Name}", size:"0", fixed:true, showInfobox:false}); var p1b=board.create('point',[{Xb},{Yb}],{ name:"", size:"0", fixed:true, showInfobox:false}); var p0=board.create('point',[{Xpi0},{Ypi0}],{name:"",size:"0",fixed:true,showInfobox:false}); var p1=board.create('point',[{Xpi1},{Ypi1}],{name:"",size:"0",fixed:true,showInfobox:false}); var line1=board.create('line',[p1a,p1b],{firstArrow:true,lastArrow:true}); var pl0=board.create('point',[-1,0.25],{name:"{pl1Name}",size:"0",fixed:true,showInfobox:false}); var pl1=board.create('point',[1,0.25],{name:"",size:"0",fixed:true,showInfobox:false}); var pl2=board.create('point',[-1,-0.25],{name:"{pl2Name}",size:"0",fixed:true,showInfobox:false}); var pl3=board.create('point',[1,-0.25],{name:"",size:"0",fixed:true,showInfobox:false}); var pline1=board.create('line',[pl0,pl1],{firstArrow:true,lastArrow:true}); var pline2=board.create('line',[pl2,pl3],{firstArrow:true,lastArrow:true}); var tA1=board.create('text',[{Xpi0}-.25,{Ypi0}+.1,"{ang1}"],{fontSize:20,strokeColor:'blue'}); var tA2=board.create('text',[{Xpi0}+.25,{Ypi0}+.1,"{ang2}"],{fontSize:20,strokeColor:'red'}); var tA3=board.create('text',[{Xpi0}-.25,{Ypi0}-.1,"{ang3}"],{fontSize:20,strokeColor:'red'}); var tA4=board.create('text',[{Xpi0}+.25,{Ypi0}-.1,"{ang4}"],{fontSize:20,strokeColor:'blue'}); var tA5=board.create('text',[{Xpi1}-.25,{Ypi1}+.1,"{ang5}"],{fontSize:20,strokeColor:'blue'}); var tA6=board.create('text',[{Xpi1}+.2,{Ypi1}+.1,"{ang6}"],{fontSize:20,strokeColor:'red'}); var tA7=board.create('text',[{Xpi1}-.25,{Ypi1}-.1,"{ang7}"],{fontSize:20,strokeColor:'red'}); var tA8=board.create('text',[{Xpi1}+.2,{Ypi1}-.1,"{ang8}"],{fontSize:20,strokeColor:'blue'}); ]]> $course$/top/Default for MSII/Test#10/L74- Variables on both sides of the Equation L74- ax+b=c + dx find x (integers-positive x) {a}x + {b} = {c} + {d}x

]]> {a}x + {b} = {c} + {d}x Given -{d}x - {d}x Move the Variable terms to the left {aMd}x + {b} = {c} Simplify: {a}x - {d}x = {=a-d}x {aMd}x + {b} = {c} Make a box around the variable term.
(I changed mine to orange because I can not make a box.) -{b} -{b} Subtract {b} from both sides.
{b} - {b} Cancels out. {aMd}x = {cMb} Simplify: {c}-{b} = {=c-b}
$\frac{{aMd}}{{aMd}}$x = $\frac{{cMb}}{{aMd}}$
Divide both sides by {aMd} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. a={-5,-4,-3,-2,-1,2,3,4,5,6}; d={3,2,4,-2,-3,-4}; b={1:15:1}; x={1:10:1}; a=(a==d)?a+1:a; aX=a*x; dX=d*x; aMd=a-d; c=a*x+b-d*x; cMb=c-b; none 0 1 0 1 x _err == 0 1 1 x = {_0}

]]> L74- ax+b=c + dx find x (integers-positive x) {a}x + {b} = {c} + {d}x

]]> TL74- ax+b +ex=dx + c find x (integers-positive x) {a}x + {b} + {e}x = {d}x + {c}

]]> {a}x + {b} + {e}x = {d}x + {c} Given {a}x + {e}x + {b} = {d}x + {c} Combine the variable terms on the left {=a+e}x + {b} = {d}x + {c} {a}x + {e}x = {=a+e}x
{signD}x {signD}x Move the Variable terms to the left {aPeMd}x + {b} = {c} Simplify: {=e+a}x - {d}x = {=aPeMd}x {aPeMd}x + {b} = {c} Make a box around the variable term.
(I changed mine to orange because I can not make a box.) -{b} -{b} Subtract {b} from both sides.
{b} - {b} Cancels out. {aPeMd}x = {cMb} Simplify: {c}-{b} = {=c-b}
$\frac{{aPeMd}}{{aPeMd}}$x = $\frac{{cMb}}{{aPeMd}}$
Divide both sides by {aPeMd} x = {x}
Simplify ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. a={-5,-4,-3,-2,-1,2,3,4,5,6}; d={3,2,4,-2,-3,-4}; e={2,3,4,5}; b={1:15:1}; x={1:10:1}; 0,join("","+",abs(d)),join("","-",abs(d)));]]> none 0 1 0 1 x _err == 0 1 1 x = {_0}

]]> TL74- ax+b= dx find x (integers-positive x) {a}x + {b} = {d}x

]]> {a}x + {b} = {d}x Given {signA}x {signA}x Move the Variable terms to the right {b} = {dMa}x Simplify: {d}x {signA}x = {=d-a}x $\frac{{b}}{{dMa}}$ = $\frac{{dMa}x}{{dMa}}$ Divide both sides by {dMa} {x} = x Simplify. ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. a={-5,-4,-3,-2,-1,2,3,4,5,6}; d={3,2,4,-2,-3,-4}; x={1:10:1}; none 0 1 0 1 x _err == 0 1 1 x = {_0}

]]> TL74- ax+ex=b=dx + c find x (integers-positive x) (copy) {a}x + {e}x + {b} = {d}x + {c}

]]> {a}x + {e}x + {b} = {d}x + {c} Given {a}x + {e}x + {b} = {d}x + {c} Combine the variable terms on the left {=a+e}x + {b} = {d}x + {c} {a}x + {e}x = {=a+e}x
{signD}x {signD}x Move the Variable terms to the left {aPeMd}x + {b} = {c} Simplify: {=e+a}x - {d}x = {=aPeMd}x {aPeMd}x + {b} = {c} Make a box around the variable term.
(I changed mine to orange because I can not make a box.) -{b} -{b} Subtract {b} from both sides.
{b} - {b} Cancels out. {aPeMd}x = {cMb} Simplify: {c}-{b} = {=c-b}
$\frac{{aPeMd}}{{aPeMd}}$x = $\frac{{cMb}}{{aPeMd}}$
Divide both sides by {aPeMd} x = {x}
Simplify ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. a={-5,-4,-3,-2,-1,2,3,4,5,6}; d={3,2,4,-2,-3,-4}; e={2,3,4,5}; b={1:15:1}; x={1:10:1}; 0,join("","+",abs(d)),join("","-",abs(d)));]]> none 0 1 0 1 x _err == 0 1 1 x = {_0}

]]> TL74- ax=c + dx find x (integers-positive x) {a}x = {c} + {d}x

]]> {a}x = {c} + {d}x Given {signD}x {signD}x Move the Variable terms to the left {aMd}x = {c} Simplify: {a}x {signD}x = {=a-d}x $\frac{{aMd}x}{{aMd}}$ = $\frac{{c}}{{aMd}}$ Divide both sides by {aMd} x = {x} {c} ÷ {aMd} = {x} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. a={-5,-4,-3,-2,-1,2,3,4,5,6}; d={3,2,4,-2,-3,-4}; x={1:10:1}; none 0 1 0 1 x _err == 0 1 1 x = {_0}

]]> $course$/top/Default for MSII/Test#10/L73- Transversal and Parallel Lines/L73-Transversal Angles L73- transversal-alternate exterior line {pl1Name} is parallel to line {pl2Name}.

]]> L73- transversal-alternate interior line {pl1Name} is parallel to line {pl2Name}.

]]> L73- transversal-corresponding angles line {pl1Name} is parallel to line {pl2Name}.

]]> 2 1 0 1 corAngAns[randAngles[2]] _err == 0 1 1 <{=corAng[randAngles[2]]} is a corresponding angle to <{_0}

]]> $course$/top/Default for MSII/Test#10/L75- Estimating Square Roots and Rounding Decimals L75- Square roots estimate to tenth Estimate the decimal equivalent of $ \sqrt{num} $ to the nearest tenth.

]]> First decide on the nearest whole number squares.

$\sqrt{num}$ is between {low} and {high}.

{low}² = {=pow(low,2)}

{high}² = {=pow(high,2)}

Second determine the number to the tenth it is closest to.

{=ans-.1}² = {=pow(ans-.1,2)} {num}-{=pow(ans-.1,2)} = {=round(num-pow(ans-.1,2),2)}

{=ans}² = {=pow(ans,2)} {num}-{=pow(ans,2)} = {=round(num-pow(ans,2),2)}

{=ans+.1}² = {=pow(ans+.1,2)} {num}-{=pow(ans+.1,2)} = {=round(num-pow(ans+.1,2),2)}

$\sqrt{num}$ to the nearest tenth is {ans}.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. num={20:230}; 2 =",pow(low,2)); for (i:[1:10]){ FB=join("",FB,"
",low+.1*i,"² =",pow(low+.1*i,2)); } FB=join("",FB,"
",high,"² =",pow(high,2)); ]]> abc 0 1 0 1 ans _err == 0 1 1 $ \sqrt{num} $ ≈ {_0}

]]> L75-Round Repeating Decimals Round {whole}. {repeat} to {places} decimal places. ]]>

{whole}.	{repeat}	= {num}
{display}			To round to {places} decimal places, underline the number in the {ordPlace} place. Look to the right at {lookAt}. If it is 5 or more, round up. If it is less than 5, round down.
{ans}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. whole={2:1000:1}; repeat={101:199:2}; places={2:8}; num=whole+(repeat/1000)+(repeat/1000000)+(repeat/1000000000); ans=round(num,places); abc 0 1 0 1 ans _err == 0 1 1 L75-Round Repeating Decimals Round {whole}. {repeat} to {places} decimal places. ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. whole={2:1000:1}; repeat={101:199:2}; places={2:8}; num=whole+(repeat/1000)+(repeat/1000000)+(repeat/1000000000); ans=round(num,places); abc 0 1 0 1 ans _err == 0 1 1 L75-Round Repeating Decimals Round {whole}. {repeat} to {places} decimal places. ]]>

{whole}.	{repeat}	= {num}
{display}			To round to {places} decimal places, underline the number in the {ordPlace} place. Look to the right at {lookAt}. If it is 5 or more, round up. If it is less than 5, round down.
{ans}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. whole={2:1000:1}; repeatA={1:10:1}; repeatB={1:10:1}; repeatC={1:10:1}; places={2:8}; ")); lookAt=pick(curPlace==places+1,lookAt,join("",repeatA)); display=pick(curPlace==places+1,display,join("",display,"")); display=join("",display,repeatA); display=pick(curPlace==places,display,join("",display,"")); display=pick(curPlace==places+1,display,join("",display,"")); curPlace=curPlace+1; display=pick(curPlace==places,display,join("",display,"")); lookAt=pick(curPlace==places+1,lookAt,join("",repeatB)); display=pick(curPlace==places+1,display,join("",display,"")); display=join("",display,repeatB); display=pick(curPlace==places,display,join("",display,"")); display=pick(curPlace==places+1,display,join("",display,"")); curPlace=curPlace+1; display=pick(curPlace==places,display,join("",display,"")); lookAt=pick(curPlace==places+1,lookAt,join("",repeatC)); display=pick(curPlace==places+1,display,join("",display,"")); display=join("",display,repeatC); display=pick(curPlace==places,display,join("",display,"")); display=pick(curPlace==places+1,display,join("",display,"")); curPlace=curPlace+1; } ordinals=["zero","first","second","third","fourth","fifth", "sixth","seventh","eighth", "ninth","tenth", "eleventh","twelfth"]; ordPlace=ordinals[places]; ]]> abc 0 1 0 1 ans _err == 0 1 1 $course$/top/Default for MSII/Test#10/L76- Exponents with Signed Numbers L76-(base)Exponent Simplify:

]]> ({base})^{exponent}=({base})({base}) = {ans}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. base={-20:-1,1:20}; exponent=2; ans=pow(base,exponent); abc 0 1 0 1 ans _err == 0 1 1 ({base})^{exponent}

]]> L76-(negative base) Exponent + a Simplify: {ques}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T}
]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. base={-20:-1:1}; a={1:25:1}; ",exponent," + ",a); FB1=join("","(",base,")^",exponent," + ",a); FB1T="given"; FB2=join("","(",base,")(",base,") + ",a); FB2T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB3=join("",pow(base,2),"+ ",a,"=",ans); FB3T=join("","combine ",pow(base,2)," and (",a,")");]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-(negative base) Exponent - a Simplify: {ques}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T}
]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. base={-20:-1:1}; a={1:25:1}; ",exponent," - ",a); FB1=join("","(",base,")^",exponent," - ",a); FB1T="given"; FB2=join("","(",base,")(",base,") - ",a); FB2T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB3=join("",pow(base,2),"- ",a,"=",ans); FB3T=join("","combine ",pow(base,2)," and ",a);]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-(var negative base) Exponent Simplify: {ques}, when {var} = {base}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T} {FB4} {FB4T} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. ",exponent,""); FB1=join("",var,"^",exponent,""); FB1T="given"; FB2=join("","(",base,")^",exponent,""); FB2T=join("","Substitute the value of ",var,"
Put parentheses around the substitution!"); FB3=join("","(",base,")(",base,")"); FB3T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB4=ans; FB4T=join("",ques," = ",ans);]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-(var negative base) Exponent + var1 Simplify: {ques}, when {var} = {base}, and {var1} = {a}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T} {FB4} {FB4T} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. ",exponent," + ",var1); FB1=join("",var,"^",exponent," + ",var1); FB1T="given"; FB2=join("","(",base,")^",exponent," + (",a,")"); FB2T=join("","Substitute the value of ",var,"=",base,"and ",var1,"=",a,"
Put parentheses around the substitution!"); FB3=join("","(",base,")(",base,") + (",a,")"); FB3T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB4=join("",pow(base,2),"+ (",a,")=",ans); FB4T=join("","combine ",pow(base,2)," and (",a,")");]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-(var positive base) Exponent Simplify: {ques}, when {var} = {base}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T} {FB4} {FB4T} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. ",exponent,""); FB1=join("",var,"^",exponent,""); FB1T="given"; FB2=join("","(",base,")^",exponent,""); FB2T=join("","Substitute the value of ",var); FB3=join("","(",base,")(",base,")"); FB3T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB4=ans; FB4T=join("",ques," = ",ans);]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-a+(negative base) Exponent Simplify: {ques}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T}
]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. base={1:20:1}; a={-25:25:1}; ",exponent,""); FB1=join("",a,"+",base,"^",exponent,""); FB1T="given"; FB2=join("",a,"+","(",base,")(",base,")"); FB2T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB3=join("",a,"+",pow(base,2),"=",ans); FB3T=join("","combine ",a," and ",pow(base,2));]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-a+(negative base) Exponent Simplify: {ques}

]]> L76-a+(var negative base) Exponent Simplify: {ques}, when {var} = {base}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T} {FB4} {FB4T} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. ",exponent,""); FB1=join("",a,"+",var,"^",exponent,""); FB1T="given"; FB2=join("",a,"+","(",base,")^",exponent,""); FB2T=join("","Substitute the value of ",var,"
Put parentheses around the substitution!"); FB3=join("",a,"+","(",base,")(",base,")"); FB3T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB4=join("",a,"+",pow(base,2),"=",ans); FB4T=join("","combine ",a," and ",pow(base,2));]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-a-(negative base) Exponent Simplify: {ques}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T}
]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. base={1:20:1}; a={-25:25:1}; ",exponent,""); FB1=join("",a,"-",base,"^",exponent,""); FB1T="given"; FB2=join("",a,"-","(",base,")(",base,")"); FB2T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB3=join("",a,"-",pow(base,2),"=",ans); FB3T=join("","combine ",a," and -",pow(base,2));]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-a-(var negative base) Exponent Simplify: {ques}, when {var} = {base}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T} {FB4} {FB4T} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. ",exponent,""); FB1=join("",a,"-",var,"^",exponent,""); FB1T="given"; FB2=join("",a,"-","(",base,")^",exponent,""); FB2T=join("","Substitute the value of ",var,"
Put parentheses around the substitution!"); FB3=join("",a,"-","(",base,")(",base,")"); FB3T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB4=join("",a,"-",pow(base,2),"=",ans); FB4T=join("","combine ",a," and -",pow(base,2));]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-Neg(base) Exponent Simplify:

]]> -{base}^{exponent}= - ({base})({base}) = {ans}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. base={1:20}; exponent=2; ans=-1*pow(base,exponent); abc 0 1 0 1 ans _err == 0 1 1 -{base}^{exponent}

]]> L76-neg(var negative base) Exponent + var1 Simplify: {ques}, when {var} = {base}, and {var1} = {a}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T} {FB4} {FB4T} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. ",exponent," + ",var1); FB1=join("","-",var,"^",exponent," + ",var1); FB1T="given"; FB2=join("","-(",base,")^",exponent," + (",a,")"); FB2T=join("","Substitute the value of ",var,"=",base,"and ",var1,"=",a,"
Put parentheses around the substitution!"); FB3=join("","-(",base,")(",base,") + (",a,")"); FB3T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB4=join("","-",pow(base,2),"+ (",a,")=",ans); FB4T=join("","combine ","-",pow(base,2)," and (",a,")");]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-negative (var negative base) Exponent Simplify: {ques}, when {var} = {base}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T} {FB4} {FB4T} {FB5} {FB5T} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. ",exponent,""); FB1=join("","-",var,"^",exponent,""); FB1T="given"; FB2=join("","-(",base,")^",exponent,""); FB2T=join("","Substitute the value of ",var); FB3=join("","-(",base,")(",base,")"); FB3T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB4=join("","-(",abs(ans),")"); FB4T=join("","(",base,")(",base,")=",ans," Now multiply ",abs(ans)," by -1"); FB5=ans; FB5T=join("",ques," = ",ans);]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> L76-negative (var positive base) Exponent Simplify: {ques}, when {var} = {base}

]]> L76-var1+(var negative base) Exponent Simplify: {ques}, when {var} = {base}, and {var1} = {a}

]]> {FB1} {FB1T} {FB2} {FB2T} {FB3} {FB3T} {FB4} {FB4T} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. ",exponent,""); FB1=join("",var1,"+",var,"^",exponent,""); FB1T="given"; FB2=join("",a,"+","(",base,")^",exponent,""); FB2T=join("","Substitute the value of ",var,"=",base,"and ",var1,"=",a,"
Put parentheses around the substitution!"); FB3=join("",a,"+","(",base,")(",base,")"); FB3T=join("","The exponent dictates how many times we multiply the base ",base, " times itself. The exponent is a 2"); FB4=join("",a,"+",pow(base,2),"=",ans); FB4T=join("","combine ",a," and ",pow(base,2));]]> abc 0 1 0 1 ans _err == 0 1 1 {ques} = {_0}

]]> $course$/top/Default for MSII/Test#10/L76- Exponents with Signed Numbers/L76-Expressions with Signed bases squared L76-(var negative base) Exponent Simplify: {ques}, when {var} = {base}