MathJaxMap['math_1'] = '2×6−36÷(7−4)2︸Start herePerform the operation within the parentheses.=2×6−36÷(3)2Perform the square.=2×6−36÷9Perform the multiplication and division from left to right.=12−4Finally, perform the subtraction.=8';
MathJaxMap['math_2'] = '128−4(2+14)7+52.128−4(2+14)7+52Working on the numerator, perform the calculation in the parentheses.=128−4(16)7+52Continuing with the numerator, perform the multiplication.=128−647+52Finishing with the numerator, perform the subtraction.=647+52Switching to the denominator, square 5 to get 25.=647+25Finishing with the denominator, compute the sum.=6432Perform the division.=2';
MathJaxMap['math_3'] = '−24=−1⋅24=−1⋅16=−16';
MathJaxMap['math_4'] = 'a(b+c)=ab+ac or a(b−c)=ab−ac';
MathJaxMap['math_5'] = '3(2x+5)=(3)(2x)+(3)(5)=6x+15';
MathJaxMap['math_6'] = '−2(x−3)=(−2)(x)−(−2)(3)=−2x+6';
MathJaxMap['math_7'] = 'ab+ac=a(b+c) or ab−ac=a(b−c)';
MathJaxMap['math_8'] = '4x+2=(2)(2x)+(2)(1)=2(2x+1)';
MathJaxMap['math_9'] = '6x2−9x=(3x)(2x)−(3x)(3)=3x(2x−3)';
MathJaxMap['math_10'] = '34−56=3⋅34⋅3−5⋅26⋅2Replace each fraction with an equivalent fraction with a denominator of 12.3⋅34⋅3−5⋅26⋅2=912−1012=9−1012=−112Since both fractions have the same denominator, subtract the numerators.−112=−112It doesn\'t matter if the "_" is in the numerator or out in front of the entire fraction.';
MathJaxMap['math_11'] = '1549×1425=15×1449×25=(5.3)×(2.7)(7.7)×(5.5)=635';
MathJaxMap['math_12'] = '516=5.6=30';
MathJaxMap['math_13'] = '12÷34=1234=12⋅43=1⋅42⋅3=2⋅22⋅3=23';
MathJaxMap['math_14'] = '1520=0.75';
MathJaxMap['math_15'] = '(0.75×100)%=75%';
MathJaxMap['math_16'] = '568,000=5.68×105';
MathJaxMap['math_17'] = '0.0028=2.8×10−3';
MathJaxMap['math_18'] = '568,000 might appear as 5.68 E5.0. 0028 might appear as 2.8 E−3.';
MathJaxMap['math_19'] = '307=3×102+0×101+7×100';
MathJaxMap['math_20'] = '1027=1×103+0×102+2×101+7×100';
MathJaxMap['math_21'] = '1×23+0×22+1×21+1×20=8+0+2+1=11';
MathJaxMap['math_22'] = '0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111…';
MathJaxMap['math_23'] = 'x̄=x1+x2+⋯+xnn.';
MathJaxMap['math_24'] = 'm=y2−y1x2−x1';
MathJaxMap['math_25'] = 'A=P(1+rt)';
MathJaxMap['math_26'] = 'n=3 and x1=2,x2=−3, and x3=5';
MathJaxMap['math_27'] = 'x̄=2+(−3)+53';
MathJaxMap['math_28'] = 'x̄=2+2(−3)+53=43';
MathJaxMap['math_29'] = '(x1,y1)=(−3,4) and (x2,y2)=(2,5)';
MathJaxMap['math_30'] = 'm=y2−y1x2−x1=5−42−(−3)';
MathJaxMap['math_31'] = '5−42−(−3)=5−42+3=15';
MathJaxMap['math_32'] = 'A=P(1+rt)=1000(1+(0.04)(5))';
MathJaxMap['math_33'] = '1000(1+(0.04)(5))Order of operations tells us tocompute the value inside theparentheses first. We begin bycomputing the multiplication thatappears in the expression insidethe parentheses.=1000(1+0.2)Next, complete the addition thatappears in the expression insidethe parentheses.=1000(1.02)Perform the multiplication.=1020';
MathJaxMap['math_34'] = 'x̄=10,x1=8,x2=12, and x3=6. We need to find x4.';
MathJaxMap['math_35'] = 'x̄=x1+x2+x3+x4n10=8+12+6+x44';
MathJaxMap['math_36'] = '10=26+x44';
MathJaxMap['math_37'] = '(4)(10)=(4)(26+x44) Multiply both sides of the equation by 4 and then simplify.40=26+x4 Subtract 26 from both sides of the equation.40−26=26+x4−26 Simplify.14=x4';
MathJaxMap['math_38'] = 'm=1/2,(x1,y1)=(1,1),(x2,y2)=(x2,3). We need to find x2.';
MathJaxMap['math_39'] = 'm=y2−y1x2−x112=3−1x2−1';
MathJaxMap['math_40'] = '12=2x2−1';
MathJaxMap['math_41'] = '12=2x2−1 To clear the fractions, multiply both sides of the equation by 2(x2−1), which is valid as long as 2(x2−1)≠0 or x2≠1.2(x2−1)12 Simplify.=2(x2−1)1x2−1x2−1=4 Add +1 to both sides of the equation.x2−1+1=4+1 Simplify.x2=5';
MathJaxMap['math_42'] = '(6−9)÷(17−5)ENTER,';
MathJaxMap['math_43'] = 'd=Cπ';
MathJaxMap['math_44'] = 'F=95C+32The original formula gives F in termsof C. Subtract 32 from both sidesof the equation.F−32=95CMultiply both sides by 59.(Noticethat 59⋅95=1.)59(F−32)=CSwitch the left and right sides of theequation for ease of reading C in terms of F.C=59(F−32)';
MathJaxMap['math_45'] = 'm=20.25nThe original formula gives m interms of n. Isolate the radicalexpression on one side of theequation by dividing both sidesby 2.m2=0.25nSquare both sides of the equationto remove the radical.(m2)2=0.25nRemove the parentheses from theleft-hand side by squaring.m24=0.25nMultiply both sides of theequation by 4n to clear thefractions.n⋅m2=4(0.25)=1Divide both sides by m2 to solvefor n.n=1m2Wenowhaveaformulawherenisgivenintermsofm.';
MathJaxMap['math_46'] = 'C=πr2The original formula gives C in termsof r. Isolate the expression raisedto a power on one side of theequation by dividing both sidesby π.Cπ=r2Raise both sides to the one-half power.(Cπ)12=(r2)12=rSwitch the left and right sides of theequation for ease of reading r interms of C.r=(Cπ)12=CπWe now have a formula in which r isgiven in terms of C.';
MathJaxMap['math_47'] = 'surface area=π(3)2+π(3)(3)2+(9)2≈117.7 in.2';
MathJaxMap['math_48'] = 'Volume=13π(3)2(9)≈84.8 in.3';
MathJaxMap['math_49'] = 'Linear EquationsNonlinear Equations2x=6x2+1=60.3(w−5)+4=6.1+0.1w3x+4=512(x+2)=37(2x−1)=4p(1−p)25=0.1';
MathJaxMap['math_50'] = '12(x+2)+37(2x−1)=4Clear the fractions:Multiply both sidesof the equation by 14,the smallest numberdivisible by both 2and 7.14(12(x+2)+37(2x−1))=14(4)Multiply each term on theleft-hand side by 14.(Use the distributive law.)14(12(x+2))+14(37(2x−1))=14[4]Perform the multiplicationsby 14.7(x+2)+6(2x−1)=56Apply the distributivelaw to remove the parentheses.7x+14+12x−6=56Simplify by combiningterms involving x andconstant terms.19x+8=56';
MathJaxMap['math_51'] = '19x+8=56Subtract 8 from both sidesof the equation.19x+8−8=56−8';
MathJaxMap['math_52'] = '19x=48';
MathJaxMap['math_53'] = '19x19=4819Divide both sides of theequation by 19, thecoefficient of x.x=4819';
MathJaxMap['math_54'] = '0.3(w−5)+4=6.1+0.1wRemove parentheses onthe left-hand side bymultiplication.0.3w−1.5+4=6.1+0.1wCombine the constantterms on the left-hand side.0.3w+2.5=6.1+0.1w';
MathJaxMap['math_55'] = '−0.3w+2.5=6.1+0.1wAdd −0.1w−2.5 to bothsides of the equation.0.3w+2.5−|0.1w−2.5=6.1+0.1w−0.1w−2.5';
MathJaxMap['math_56'] = '0.2w=3.6';
MathJaxMap['math_57'] = '0.2w0.2=3.60.2Divide both sides of theequation by the coefficient of w.w=18';
MathJaxMap['math_58'] = 'D=(x2−x1)2+(y2−y1)2';
MathJaxMap['math_59'] = 'D=(6−1)2+(5−2)2=52+32=25+9=34≈5.83';
MathJaxMap['math_60'] = 'Midpoint=2+122=172=7';
MathJaxMap['math_61'] = '(x1+x22,y1+y22)';
MathJaxMap['math_62'] = 'Midpoint=(1+62,2+52)=(72,72)';
MathJaxMap['math_63'] = 'D=(72−1)2+(72−2)2=(52)2+(32)2=344=342';
MathJaxMap['math_64'] = 'D=(1−72)2+(5−72)2=(52)2+(32)2=344=342';
MathJaxMap['math_65'] = '3(4)+2(−3)=?612+(−6)=?66=6 True';
MathJaxMap['math_66'] = '3(1)+2(1)=?63+(2)=?65=6 True';
MathJaxMap['math_67'] = '3(0)+2y=60+2y=62y=6y=3';
MathJaxMap['math_68'] = '3x+2(0)=63x+0=63x=6x=2';
MathJaxMap['math_69'] = '4x+6y=4(3+x)Remove the parenthesesby multiplying. (Use thedistributive law.)4x+6y=12+4xSubtract 4x from both sides of theequation.6y=12Divide both sides of the equationby 6, the coefficient of y.y=2';
MathJaxMap['math_70'] = '3x+2y≤12Subtract 3x from both sides of theinequality.2y≤−3x+12Divide both sides of the inequality by2, the coefficient of y.y≤−32x+6';
MathJaxMap['math_71'] = '5x−10y≤5Subtract 5x from both sides of theinequality.−10y≤5x+5Divide both sides of the inequality by−10 and reverse the direction ofthe inequality.y≥−5−10x+|5−10Simplify.y≥12x−12';
MathJaxMap['math_72'] = 'x+y=5(1)x+2y=7(2)';
MathJaxMap['math_73'] = 'x+y=5Add −x to both sides of the equation.y=−x+5Substitute−x+5 for y in equation (2).x+2(−x+5)=7';
MathJaxMap['math_74'] = 'x+2(−x+5)=7Use the distributive law to removethe parentheses.x−2x+10=7Subtract 10 from both sides of theequation.x−2x+10−10=7−10Simplify by combining terms.−x=−3Multiply both sides of the equationby−1.x=3';
MathJaxMap['math_75'] = 'x+y=5Substitute 3 for x in equation (1).3+y=5Subtract 3 from both sides of theequation.y=5−3=2';
MathJaxMap['math_76'] = 'Check (3,2) inCheck (3,2) inx+y=5x+2y=73+2=53+2(2)=?75=5 True7=7 True';
MathJaxMap['math_77'] = 'y=−x+5 (1)′y=12x+72 (2)′';
MathJaxMap['math_78'] = '2y−x=2y+2x=9';
MathJaxMap['math_79'] = '3y+2x=76y+4x=10';
MathJaxMap['math_80'] = 'y=3x+9y=−2x+1';
MathJaxMap['math_81'] = '∑i=13i2=12+22+32=14';
MathJaxMap['math_82'] = '∑i=153i=3(1)+3(2)+3(3)+3(4)+3(5)=3+6+9+12+15=45';
MathJaxMap['math_83'] = '∑i=1nkai=k∑i=1nai';
MathJaxMap['math_84'] = '∑i=153i=3∑i=15i=3(1+2+3+4+5)=3(15)=45';
MathJaxMap['math_85'] = 's=∑i=1n(xi−x̄)2n−1';
MathJaxMap['math_86'] = '3,6,9,12…';
MathJaxMap['math_87'] = '(number of terms, n2) × (first term + last term)';
MathJaxMap['math_88'] = 'Sn=∑i=1nai=n(a1+an)2';
MathJaxMap['math_89'] = 'Sn=a(rn−1r−1)';
MathJaxMap['math_90'] = 'S8=3(28−12−1)=3(256−11)=3(255)=765';
MathJaxMap['math_91'] = '(−8)2=(−8)(−8)=64';
MathJaxMap['math_92'] = 'an=a⋅a⋅a⋯a︸ntimes';
MathJaxMap['math_93'] = '25=(2)(2)(2)(2)(2)=32(−2)3=(−2)(−2)(−2)=−8(−3)4=(−3)(−3)(−3)(−3)=81';
MathJaxMap['math_94'] = 'an=b means bn=a';
MathJaxMap['math_95'] = '144=12 because 122=144';
MathJaxMap['math_96'] = '325=2 because 25=32';
MathJaxMap['math_97'] = '(3.1)(2.7)5=8.375=1.674≈1.3';
MathJaxMap['math_98'] = 's=(x1−x̄)2+(x2−x̄)2+⋯+(xn−x̄)2n−1';
MathJaxMap['math_99'] = 's=(x1−x̄)2+(x2−x̄)2+(x3−x̄)2n−1=(2−43)2+(−3−43)2+(5−43)23−1';
MathJaxMap['math_100'] = 's=(2−43)2+(−3−43)2+(5−43)23−1=(23)2+(−133)2+(113)22=49+1699+12192=29492=29418=493=13≈4.04';
MathJaxMap['math_101'] = 'a0=1,a≠0a−n=1an,a≠0';
MathJaxMap['math_102'] = '30=12−4=124=116−3−2=−(132)Order of operations tells us that powersare performed before multiplication.=−19Taking the opposite of a number isequivalent to multiplication by −1.';
MathJaxMap['math_103'] = 'a1n=an, a≥0 if n is evenamn=amn=(an)m';
MathJaxMap['math_104'] = '3612=36=6';
MathJaxMap['math_105'] = '823=(83)2=(2)2=4';
MathJaxMap['math_106'] = '823=823=643=4';
MathJaxMap['math_107'] = 'x5=1x5(x32)=x23';
MathJaxMap['math_108'] = '897=8917≈1.90(45)3=4532≈301.87';
MathJaxMap['math_109'] = 'aman=am+n';
MathJaxMap['math_110'] = '23⋅24=2⋅2⋅2︸3 times⋅2⋅2⋅2⋅2︸4 times︸7 times=23+4=27';
MathJaxMap['math_111'] = '35⋅34=35+4=39743⋅713=743+13=753';
MathJaxMap['math_112'] = 'aman=am−n,a≠0';
MathJaxMap['math_113'] = '4343=4⋅4⋅44⋅4⋅4=1 and 4343=43−3=40=14346=4⋅4⋅44⋅4⋅4⋅4⋅4⋅4=143 and 4346=43−6=4−3=143';
MathJaxMap['math_114'] = '(am)n=am×n';
MathJaxMap['math_115'] = '(23)2=23⋅23︸2 times=2⋅2⋅2︸3 times⋅2⋅2⋅2︸3 times︸2×3=6 times=22×3=26';
MathJaxMap['math_116'] = '(45)3=45×45×45︸3 times=4⋅4⋅4⋅4⋅4︸5 times×4⋅4⋅4⋅4⋅4︸5 times×4⋅4⋅4⋅4⋅4︸5 times︸3×5=15 times=415';
MathJaxMap['math_117'] = '(a+b)n≠an+bn';
MathJaxMap['math_118'] = '(x+2)2=(x+2)(x+2)Expand the square.=(x+2)(x)+(x+2)(2)Use the distributive law.=(x)(x)+(2)(x)+(x)(2)+(2)(2)Use the distributive lawa second time.=x2+4x+4Combine like terms andsimplify.';
MathJaxMap['math_119'] = 'abn=an⋅bn';
MathJaxMap['math_120'] = 'ab=nanbn';
MathJaxMap['math_121'] = '490,000=49⋅100⋅100=49⋅100⋅100=7⋅10⋅10=700';
MathJaxMap['math_122'] = '0.0036=3610,000=6⋅6100⋅100=62100⋅100=610⋅10=0.06';
MathJaxMap['math_123'] = '9x3=9x2⋅x=9x2⋅x=3xx';
MathJaxMap['math_124'] = 'a+bn≠an+bn';
MathJaxMap['math_125'] = 'logx=log10x';
MathJaxMap['math_126'] = '102+3logxApply logarithm property 2.102+3logx=102+logx3Use the rule of exponents:am+n=aman=10210logx3=100x3Apply logarithm property 1.';
MathJaxMap['math_127'] = '2x=10Take the natural logarithm ofboth sides of the equation.ln(2x)=ln(10)Use logarithm property 2[see Algebra Review VI, item E,Logarithms (page AR-26)] to movethe x in front of the logarithm.x ln(2)=ln(10)Divide both sides of the equation by ln(2).x=ln(10)ln(2)';
MathJaxMap['math_128'] = 'P(1+i)n=AWe switched the right and leftsides of the equation. Isolate theexpression with n by dividingboth sides of the equation by P.(1+i)n=APTake the natural logarithm of bothsides.ln(1+i)n=ln(Ap)Use logarithm property 2 to movethe exponent in front of the logarithm.nln(1+i)=ln(Ap)Divide both sides by ln(1+i).n=ln(Ap)ln(1+i)';
MathJaxMap['math_129'] = 'f(−3)=(−3)2=9 and f(3)=32=9';
MathJaxMap['math_130'] = 'n!=(n)(n−1)(n−2)⋯(2)(1)';
MathJaxMap['math_131'] = '5!=(5)(4)(3)(2)(1)=120';
MathJaxMap['math_132'] = '7!+7⋅6⋅5⋅4⋅3⋅1︷5!=7⋅6⋅5!=7⋅6⋅120=5040';
MathJaxMap['math_133'] = ' nPk=n!(n−k)=(n)(n−1)⋯(n−k+1)';
MathJaxMap['math_134'] = ' 5P3=5!(5−3)!=5⋅4⋅3⋅2⋅12⋅1=60';
MathJaxMap['math_135'] = ' 5P3=25!(25−4)!=25!21!=25⋅24⋅23⋅22⋅21!21!=303,606';
MathJaxMap['math_136'] = ' nCk= nPkk!=n!(n−k)!k!';
MathJaxMap['math_137'] = ' 50C3=50!(50−3)!3!=50⋅49⋅48⋅47!47!3!=50︷25⋅49⋅48︷163⋅2⋅1=25⋅49⋅16=19,600';
MathJaxMap['math_138'] = ' 25C4=25!(25−1)!4!=25⋅24⋅23⋅22⋅2121!4!=25⋅24⋅23⋅224⋅3⋅2⋅1=22⋅23⋅22=12,650 25P4=303,600 which is 4!×25C4 or 24×25C4';
MathJaxMap['math_139'] = '2×6−36÷(7−4)2';
MathJaxMap['math_140'] = '−24';
MathJaxMap['math_141'] = '−1⋅24';
MathJaxMap['math_142'] = '(5)(6)−10÷2+1';
MathJaxMap['math_143'] = '5+44−(6+8÷2)+(2)(3)';
MathJaxMap['math_144'] = '−32+2⋅3+10';
MathJaxMap['math_145'] = '5−(2+3)2+(8)(2)÷4';
MathJaxMap['math_146'] = '5−47−(−2)';
MathJaxMap['math_147'] = '5−(−3)−2−(−7)';
MathJaxMap['math_148'] = '(−5)(3)+426+32';
MathJaxMap['math_149'] = '15÷5⋅4÷6−8−6−(−5)−8÷2';
MathJaxMap['math_150'] = '3(2x+5)';
MathJaxMap['math_151'] = '3(2x+5), a=3, b=2x';
MathJaxMap['math_152'] = 'c=5';
MathJaxMap['math_153'] = '−2(x−3)';
MathJaxMap['math_154'] = '2x+4';
MathJaxMap['math_155'] = '6x2−9x';
MathJaxMap['math_156'] = '3x';
MathJaxMap['math_157'] = '3x';
MathJaxMap['math_158'] = '2(x+1)';
MathJaxMap['math_159'] = '7(2w−3)';
MathJaxMap['math_160'] = '(x+4)(−3)';
MathJaxMap['math_161'] = '3.1(2p+1.5)';
MathJaxMap['math_162'] = '5(2x+y−3)';
MathJaxMap['math_163'] = '12x−6';
MathJaxMap['math_164'] = '24x2+10x';
MathJaxMap['math_165'] = '2+4x+8x2';
MathJaxMap['math_166'] = 'mn';
MathJaxMap['math_167'] = 'm';
MathJaxMap['math_168'] = 'n(n≠0)';
MathJaxMap['math_169'] = '16';
MathJaxMap['math_170'] = '34';
MathJaxMap['math_171'] = '6=2⋅3';
MathJaxMap['math_172'] = '4=2⋅2';
MathJaxMap['math_173'] = '2⋅2⋅3=12';
MathJaxMap['math_174'] = '1549';
MathJaxMap['math_175'] = '1425';
MathJaxMap['math_176'] = '16';
MathJaxMap['math_177'] = '12÷34';
MathJaxMap['math_178'] = '635−320';
MathJaxMap['math_179'] = '(19)(34)';
MathJaxMap['math_180'] = '495';
MathJaxMap['math_181'] = '4523';
MathJaxMap['math_182'] = '25+1102';
MathJaxMap['math_183'] = '13(65−310)';
MathJaxMap['math_184'] = '215+625';
MathJaxMap['math_185'] = '2334+45';
MathJaxMap['math_186'] = '15100=0.15';
MathJaxMap['math_187'] = '313';
MathJaxMap['math_188'] = '618';
MathJaxMap['math_189'] = 'a';
MathJaxMap['math_190'] = 'b';
MathJaxMap['math_191'] = 'a';
MathJaxMap['math_192'] = 'b';
MathJaxMap['math_193'] = 'a';
MathJaxMap['math_194'] = 'b';
MathJaxMap['math_195'] = 'a÷b';
MathJaxMap['math_196'] = 'a−(whole part from Step 1)×b';
MathJaxMap['math_197'] = '95÷7';
MathJaxMap['math_198'] = '95−(13×7)';
MathJaxMap['math_199'] = 'N';
MathJaxMap['math_200'] = 'N';
MathJaxMap['math_201'] = 'N';
MathJaxMap['math_202'] = 'N';
MathJaxMap['math_203'] = '147≈12.12';
MathJaxMap['math_204'] = '147÷3=49';
MathJaxMap['math_205'] = '151≈12.28';
MathJaxMap['math_206'] = '2+3+0+1=6';
MathJaxMap['math_207'] = 'a×10n';
MathJaxMap['math_208'] = '1≤a<10';
MathJaxMap['math_209'] = 'n';
MathJaxMap['math_210'] = '10n';
MathJaxMap['math_211'] = 'n';
MathJaxMap['math_212'] = '(5.65)5';
MathJaxMap['math_213'] = '(2.8)−3';
MathJaxMap['math_214'] = '525';
MathJaxMap['math_215'] = '(8+1=9)';
MathJaxMap['math_216'] = '(4+1=5)';
MathJaxMap['math_217'] = '(9+1=10)';
MathJaxMap['math_218'] = '307=3×100+0×10+7×1';
MathJaxMap['math_219'] = '112';
MathJaxMap['math_220'] = '1111002';
MathJaxMap['math_221'] = '10110112';
MathJaxMap['math_222'] = '100011002';
MathJaxMap['math_223'] = '111112';
MathJaxMap['math_224'] = '10010012';
MathJaxMap['math_225'] = '111112';
MathJaxMap['math_226'] = 'X';
MathJaxMap['math_227'] = 'x';
MathJaxMap['math_228'] = 'x ̄';
MathJaxMap['math_229'] = 'n';
MathJaxMap['math_230'] = 'x1, x2, …, xn';
MathJaxMap['math_231'] = '(x1, y1)';
MathJaxMap['math_232'] = '(x2, y2)';
MathJaxMap['math_233'] = 'P';
MathJaxMap['math_234'] = 'r';
MathJaxMap['math_235'] = 'A';
MathJaxMap['math_236'] = 't';
MathJaxMap['math_237'] = '—3';
MathJaxMap['math_238'] = '−3,4';
MathJaxMap['math_239'] = '2−(−3)=2+3=5';
MathJaxMap['math_240'] = 'P';
MathJaxMap['math_241'] = 'P=1000';
MathJaxMap['math_242'] = 'r=0.04';
MathJaxMap['math_243'] = 't=5';
MathJaxMap['math_244'] = 'A';
MathJaxMap['math_245'] = 'A=$1020';
MathJaxMap['math_246'] = 'y';
MathJaxMap['math_247'] = '−.25';
MathJaxMap['math_248'] = '−4,8,3, and −2';
MathJaxMap['math_249'] = '(3,−6) and (5,−4)';
MathJaxMap['math_250'] = 'x';
MathJaxMap['math_251'] = '32';
MathJaxMap['math_252'] = 'x';
MathJaxMap['math_253'] = 'y';
MathJaxMap['math_254'] = '−5';
MathJaxMap['math_255'] = 'y';
MathJaxMap['math_256'] = 'P';
MathJaxMap['math_257'] = 'P';
MathJaxMap['math_258'] = 'A=l×w';
MathJaxMap['math_259'] = 'A';
MathJaxMap['math_260'] = 'l';
MathJaxMap['math_261'] = 'w';
MathJaxMap['math_262'] = '84 cm2';
MathJaxMap['math_263'] = 'C=πd';
MathJaxMap['math_264'] = 'C';
MathJaxMap['math_265'] = 'd';
MathJaxMap['math_266'] = 'd';
MathJaxMap['math_267'] = 'C';
MathJaxMap['math_268'] = 'π';
MathJaxMap['math_269'] = 'F=95C+32';
MathJaxMap['math_270'] = 'C';
MathJaxMap['math_271'] = 'm=22.25n';
MathJaxMap['math_272'] = 'n';
MathJaxMap['math_273'] = 'C=wr2 for r';
MathJaxMap['math_274'] = 'A=P(1+rt)';
MathJaxMap['math_275'] = 'P';
MathJaxMap['math_276'] = 't';
MathJaxMap['math_277'] = 'A=P(1+i)n';
MathJaxMap['math_278'] = 'P';
MathJaxMap['math_279'] = 'i';
MathJaxMap['math_280'] = 'l=w';
MathJaxMap['math_281'] = 'perimeter=2(12 ft)+2(8 ft)=40 ft';
MathJaxMap['math_282'] = '(12 ft)(8 ft)=96 ft2';
MathJaxMap['math_283'] = 'π(3)2≈28.3';
MathJaxMap['math_284'] = '117.7−28.3';
MathJaxMap['math_285'] = '89.4 in.2';
MathJaxMap['math_286'] = '144 cm2';
MathJaxMap['math_287'] = 'x';
MathJaxMap['math_288'] = '12(x+2)+37(2x−1)=4';
MathJaxMap['math_289'] = 'x';
MathJaxMap['math_290'] = 'x';
MathJaxMap['math_291'] = 'x';
MathJaxMap['math_292'] = 'x';
MathJaxMap['math_293'] = '0.3(w−5)+4=6.1+0.1w';
MathJaxMap['math_294'] = 'w';
MathJaxMap['math_295'] = 'w';
MathJaxMap['math_296'] = 'w';
MathJaxMap['math_297'] = 'x';
MathJaxMap['math_298'] = '2x=6';
MathJaxMap['math_299'] = '40−2x=19+5x';
MathJaxMap['math_300'] = '2.8−2(x−1.3)=1.6x';
MathJaxMap['math_301'] = '23x−6=4−12x';
MathJaxMap['math_302'] = '4(1−5x)=2(x−1)+6x';
MathJaxMap['math_303'] = '1−4(2x)=6−(x+6)';
MathJaxMap['math_304'] = '15(2−x)+1=110x';
MathJaxMap['math_305'] = '14x+12(x−4)=3−16(x−2)';
MathJaxMap['math_306'] = 'x';
MathJaxMap['math_307'] = 'y';
MathJaxMap['math_308'] = 'x';
MathJaxMap['math_309'] = 'y';
MathJaxMap['math_310'] = 'x';
MathJaxMap['math_311'] = 'x=3';
MathJaxMap['math_312'] = 'y';
MathJaxMap['math_313'] = 'y=2';
MathJaxMap['math_314'] = '−1';
MathJaxMap['math_315'] = '−2';
MathJaxMap['math_316'] = '−3,−1';
MathJaxMap['math_317'] = '−2';
MathJaxMap['math_318'] = '−4';
MathJaxMap['math_319'] = '−2';
MathJaxMap['math_320'] = '−2';
MathJaxMap['math_321'] = '−2';
MathJaxMap['math_322'] = '−2';
MathJaxMap['math_323'] = '−2';
MathJaxMap['math_324'] = '−4';
MathJaxMap['math_325'] = '−4';
MathJaxMap['math_326'] = '−2';
MathJaxMap['math_327'] = '−2';
MathJaxMap['math_328'] = 'x1,y1';
MathJaxMap['math_329'] = 'x2,y2';
MathJaxMap['math_330'] = '(x1,y1) and (x2,y2)';
MathJaxMap['math_331'] = 'x1';
MathJaxMap['math_332'] = 'x2';
MathJaxMap['math_333'] = 'x1+x22';
MathJaxMap['math_334'] = '102';
MathJaxMap['math_335'] = 'x1,y1';
MathJaxMap['math_336'] = 'x2,y2';
MathJaxMap['math_337'] = 'x';
MathJaxMap['math_338'] = 'y';
MathJaxMap['math_339'] = 'x';
MathJaxMap['math_340'] = 'y';
MathJaxMap['math_341'] = 'x1,y1';
MathJaxMap['math_342'] = 'x2,y2';
MathJaxMap['math_343'] = '(72,72)';
MathJaxMap['math_344'] = '(72,72)';
MathJaxMap['math_345'] = '−2,−7';
MathJaxMap['math_346'] = '−2,−7';
MathJaxMap['math_347'] = '−6,−7';
MathJaxMap['math_348'] = '−3';
MathJaxMap['math_349'] = '−6,−7';
MathJaxMap['math_350'] = '−3';
MathJaxMap['math_351'] = 'x';
MathJaxMap['math_352'] = 'y';
MathJaxMap['math_353'] = 'ax+by=c';
MathJaxMap['math_354'] = 'x';
MathJaxMap['math_355'] = 'y';
MathJaxMap['math_356'] = '−3';
MathJaxMap['math_357'] = '3x+2y=6';
MathJaxMap['math_358'] = 'x';
MathJaxMap['math_359'] = '−3';
MathJaxMap['math_360'] = 'y';
MathJaxMap['math_361'] = '3x+2y=6';
MathJaxMap['math_362'] = 'ax+by=c';
MathJaxMap['math_363'] = 'y';
MathJaxMap['math_364'] = 'x=0';
MathJaxMap['math_365'] = 'y';
MathJaxMap['math_366'] = 'x';
MathJaxMap['math_367'] = 'y=0';
MathJaxMap['math_368'] = 'x';
MathJaxMap['math_369'] = 'ax+by=c';
MathJaxMap['math_370'] = 'x';
MathJaxMap['math_371'] = 'y';
MathJaxMap['math_372'] = 'x';
MathJaxMap['math_373'] = 'y';
MathJaxMap['math_374'] = '3x+2y=6';
MathJaxMap['math_375'] = 'y';
MathJaxMap['math_376'] = 'x=0';
MathJaxMap['math_377'] = 'y';
MathJaxMap['math_378'] = 'y';
MathJaxMap['math_379'] = 'x';
MathJaxMap['math_380'] = 'y=0';
MathJaxMap['math_381'] = 'x';
MathJaxMap['math_382'] = 'x';
MathJaxMap['math_383'] = '3x+2y=6';
MathJaxMap['math_384'] = '−3';
MathJaxMap['math_385'] = 'y=b';
MathJaxMap['math_386'] = 'b';
MathJaxMap['math_387'] = 'y';
MathJaxMap['math_388'] = 'x=a';
MathJaxMap['math_389'] = 'a';
MathJaxMap['math_390'] = 'x';
MathJaxMap['math_391'] = '4x+6y=4(3+x)';
MathJaxMap['math_392'] = 'y';
MathJaxMap['math_393'] = 'x=1';
MathJaxMap['math_394'] = '4x+3y=10';
MathJaxMap['math_395'] = '4x+3y=10';
MathJaxMap['math_396'] = 'x';
MathJaxMap['math_397'] = 'y';
MathJaxMap['math_398'] = '4x+3y=10';
MathJaxMap['math_399'] = '4x−5y=2(3+x)';
MathJaxMap['math_400'] = 'ax+by=c';
MathJaxMap['math_401'] = '(2,−25)';
MathJaxMap['math_402'] = 'x';
MathJaxMap['math_403'] = 'y';
MathJaxMap['math_404'] = '6x+4y=4(2+y)';
MathJaxMap['math_405'] = '14x+2y=2(5x−3)+4x';
MathJaxMap['math_406'] = 'm=change in ychange in x′';
MathJaxMap['math_407'] = 'm=13';
MathJaxMap['math_408'] = 'x1,y1';
MathJaxMap['math_409'] = 'x2,y2';
MathJaxMap['math_410'] = 'm=y2−y1x2−x1';
MathJaxMap['math_411'] = '(x1,y1)=(1,3)';
MathJaxMap['math_412'] = '(x2,y2)=(4,0)';
MathJaxMap['math_413'] = 'm=y2−y1x2−x1=0−34−1=−33=−1';
MathJaxMap['math_414'] = 'y';
MathJaxMap['math_415'] = 'x';
MathJaxMap['math_416'] = 'y';
MathJaxMap['math_417'] = 'x';
MathJaxMap['math_418'] = '−2';
MathJaxMap['math_419'] = '−6';
MathJaxMap['math_420'] = '−2';
MathJaxMap['math_421'] = '−3,8';
MathJaxMap['math_422'] = '−5,8';
MathJaxMap['math_423'] = 'y=mx+b';
MathJaxMap['math_424'] = 'b';
MathJaxMap['math_425'] = 'y';
MathJaxMap['math_426'] = 'y=23x−1';
MathJaxMap['math_427'] = 'y';
MathJaxMap['math_428'] = 'y';
MathJaxMap['math_429'] = '0,−1';
MathJaxMap['math_430'] = '23';
MathJaxMap['math_431'] = '0,−1';
MathJaxMap['math_432'] = '0,−1';
MathJaxMap['math_433'] = 'y=−0.5x+2';
MathJaxMap['math_434'] = 'y';
MathJaxMap['math_435'] = 'x';
MathJaxMap['math_436'] = 'x=0';
MathJaxMap['math_437'] = 'x=4';
MathJaxMap['math_438'] = 'y=−0.5(4)+2=−2+2=0';
MathJaxMap['math_439'] = 'y';
MathJaxMap['math_440'] = 'y=mx+b';
MathJaxMap['math_441'] = 'Y=';
MathJaxMap['math_442'] = 'mx+b';
MathJaxMap['math_443'] = 'ZOOM6';
MathJaxMap['math_444'] = 'Xmin=&−10,Xmax=10,Ymin=−10,Ymax=10';
MathJaxMap['math_445'] = 'y=2x+5';
MathJaxMap['math_446'] = '2x+5';
MathJaxMap['math_447'] = 'y';
MathJaxMap['math_448'] = '45';
MathJaxMap['math_449'] = 'y';
MathJaxMap['math_450'] = '−3';
MathJaxMap['math_451'] = 'y=54x+2';
MathJaxMap['math_452'] = 'y';
MathJaxMap['math_453'] = 'x';
MathJaxMap['math_454'] = 'y';
MathJaxMap['math_455'] = 'y=−0.25x+5';
MathJaxMap['math_456'] = 'x';
MathJaxMap['math_457'] = 'y=mx+b';
MathJaxMap['math_458'] = 'b';
MathJaxMap['math_459'] = 'y=2.8x+3';
MathJaxMap['math_460'] = 'y=−32x+12';
MathJaxMap['math_461'] = 'Xmin=−5,Xmax=5,Ymin=−5, and Ymax=5';
MathJaxMap['math_462'] = '≤';
MathJaxMap['math_463'] = '≥';
MathJaxMap['math_464'] = '<';
MathJaxMap['math_465'] = '>';
MathJaxMap['math_466'] = '3x+2y≤12';
MathJaxMap['math_467'] = 'y';
MathJaxMap['math_468'] = 'x';
MathJaxMap['math_469'] = '≤';
MathJaxMap['math_470'] = '3(0)+2(0)≤12';
MathJaxMap['math_471'] = '0≤12';
MathJaxMap['math_472'] = 'y';
MathJaxMap['math_473'] = 'y≤mx+b';
MathJaxMap['math_474'] = '≥,≤,>, or <';
MathJaxMap['math_475'] = '3x+2y≤12';
MathJaxMap['math_476'] = 'y';
MathJaxMap['math_477'] = '0≤−32(0)+6 or 0≤6';
MathJaxMap['math_478'] = 'y=32x+6';
MathJaxMap['math_479'] = 'Y=';
MathJaxMap['math_480'] = '((−)3÷2)X,T,θ,n6';
MathJaxMap['math_481'] = 'ZOOM6';
MathJaxMap['math_482'] = 'Y=';
MathJaxMap['math_483'] = 'ENTER';
MathJaxMap['math_484'] = 'GRAPH';
MathJaxMap['math_485'] = '≤';
MathJaxMap['math_486'] = 'y: 5x−10y≤5';
MathJaxMap['math_487'] = 'y';
MathJaxMap['math_488'] = '0≥12(0)−12=−12';
MathJaxMap['math_489'] = 'y=12x−12';
MathJaxMap['math_490'] = 'x';
MathJaxMap['math_491'] = 'y';
MathJaxMap['math_492'] = '−5';
MathJaxMap['math_493'] = '4x−2y>1';
MathJaxMap['math_494'] = '2x−4y≤0';
MathJaxMap['math_495'] = '5y−10x>20';
MathJaxMap['math_496'] = '5y−10x=20';
MathJaxMap['math_497'] = '4x−2y>1';
MathJaxMap['math_498'] = '2x−4y≤0';
MathJaxMap['math_499'] = '3x−4y≥6';
MathJaxMap['math_500'] = 'y';
MathJaxMap['math_501'] = 'y(≥ or ≤) mx+b';
MathJaxMap['math_502'] = 'y≤−3x+6';
MathJaxMap['math_503'] = '3x−4y≥6';
MathJaxMap['math_504'] = 'y';
MathJaxMap['math_505'] = 'y';
MathJaxMap['math_506'] = 'x';
MathJaxMap['math_507'] = 'y';
MathJaxMap['math_508'] = 'x';
MathJaxMap['math_509'] = 'y';
MathJaxMap['math_510'] = '(1)′';
MathJaxMap['math_511'] = '(2)′';
MathJaxMap['math_512'] = 'Y=';
MathJaxMap['math_513'] = '(1)′';
MathJaxMap['math_514'] = '(2)′';
MathJaxMap['math_515'] = 'WINDOW';
MathJaxMap['math_516'] = 'Xmin=−1,Xmax=8,Xscl=1;Ymin=−1,Ymax=6,YScl=1. Press GRAPH';
MathJaxMap['math_517'] = '2nd TRACE';
MathJaxMap['math_518'] = '5';
MathJaxMap['math_519'] = 'ENTER';
MathJaxMap['math_520'] = 'ENTER';
MathJaxMap['math_521'] = 'x=3 and y=2';
MathJaxMap['math_522'] = 'x≥1,y≥2, and 3x+2y=12';
MathJaxMap['math_523'] = 'x=1,y=2, and 3x+2y=12';
MathJaxMap['math_524'] = '≤';
MathJaxMap['math_525'] = '≥';
MathJaxMap['math_526'] = 'x=1';
MathJaxMap['math_527'] = 'Y=';
MathJaxMap['math_528'] = 'x=1';
MathJaxMap['math_529'] = '2nd PRGM';
MathJaxMap['math_530'] = '4';
MathJaxMap['math_531'] = 'ENTER';
MathJaxMap['math_532'] = 'y+3x=6';
MathJaxMap['math_533'] = '2y−x=4';
MathJaxMap['math_534'] = '2y+3x=12';
MathJaxMap['math_535'] = '4y+7x=12';
MathJaxMap['math_536'] = 'x≥0,y+2x≤4, and y≥3x';
MathJaxMap['math_537'] = 'x≤6,y≥4, and y≥2x+3';
MathJaxMap['math_538'] = 'x>1,2y−x≥2,y+2x≤9';
MathJaxMap['math_539'] = 'k';
MathJaxMap['math_540'] = 'a1,a2,…,ak';
MathJaxMap['math_541'] = '∑i=13i2';
MathJaxMap['math_542'] = 'i';
MathJaxMap['math_543'] = 'i';
MathJaxMap['math_544'] = '∑i=153i';
MathJaxMap['math_545'] = '∑i=153i';
MathJaxMap['math_546'] = 'n';
MathJaxMap['math_547'] = 'x̄=x1+x2+⋯xnn';
MathJaxMap['math_548'] = 'x̄';
MathJaxMap['math_549'] = 'x̄=∑i=1nxin.';
MathJaxMap['math_550'] = 'n';
MathJaxMap['math_551'] = 's=(x1−x̄)2+(x2−x̄)2+⋯+(xn−x̄)2n−1';
MathJaxMap['math_552'] = 's';
MathJaxMap['math_553'] = '∑i=15aibi';
MathJaxMap['math_554'] = 'i';
MathJaxMap['math_555'] = 'a';
MathJaxMap['math_556'] = 'i';
MathJaxMap['math_557'] = '−5';
MathJaxMap['math_558'] = '−1';
MathJaxMap['math_559'] = 'b';
MathJaxMap['math_560'] = 'i';
MathJaxMap['math_561'] = '−3';
MathJaxMap['math_562'] = '∑i=15aibi=(2)(3)+(−5)(2)+(0)(−3)+(3)(1)+(−1)(4)=6+(−10)=6+(−10)+0+3+(−4)=−5';
MathJaxMap['math_563'] = '∑i=13i3';
MathJaxMap['math_564'] = '∑i=152i';
MathJaxMap['math_565'] = '∑i=14(2i−1)';
MathJaxMap['math_566'] = 'x1=3,x2=5, and x3=4';
MathJaxMap['math_567'] = 'x̄';
MathJaxMap['math_568'] = 's';
MathJaxMap['math_569'] = 'i';
MathJaxMap['math_570'] = 'a';
MathJaxMap['math_571'] = 'i';
MathJaxMap['math_572'] = 'b';
MathJaxMap['math_573'] = 'i';
MathJaxMap['math_574'] = '∑i=14aibi';
MathJaxMap['math_575'] = '∑i=14(ai−bi)';
MathJaxMap['math_576'] = 't1';
MathJaxMap['math_577'] = 't1=3';
MathJaxMap['math_578'] = 't0';
MathJaxMap['math_579'] = 't1';
MathJaxMap['math_580'] = 't5=15';
MathJaxMap['math_581'] = 't1';
MathJaxMap['math_582'] = 't8';
MathJaxMap['math_583'] = '3,6,9,12,15,18,21,24,…';
MathJaxMap['math_584'] = 't8=24';
MathJaxMap['math_585'] = 'tn';
MathJaxMap['math_586'] = 'n';
MathJaxMap['math_587'] = 'tn−1';
MathJaxMap['math_588'] = 'tn, and tn+1';
MathJaxMap['math_589'] = 'tn';
MathJaxMap['math_590'] = 'n';
MathJaxMap['math_591'] = 't35';
MathJaxMap['math_592'] = 't1=3⋅1';
MathJaxMap['math_593'] = 't2=3⋅2';
MathJaxMap['math_594'] = 't3=3⋅3';
MathJaxMap['math_595'] = 't4=3⋅4';
MathJaxMap['math_596'] = 'tn=3⋅n';
MathJaxMap['math_597'] = 't35=3⋅35=105';
MathJaxMap['math_598'] = 't9';
MathJaxMap['math_599'] = '2′';
MathJaxMap['math_600'] = 't1=3';
MathJaxMap['math_601'] = 't2=t1+3';
MathJaxMap['math_602'] = 't3=t2+3';
MathJaxMap['math_603'] = 't4=t3+3';
MathJaxMap['math_604'] = 't1=3';
MathJaxMap['math_605'] = 'tn=tn−1+3';
MathJaxMap['math_606'] = 'n≥2';
MathJaxMap['math_607'] = 'tn+1=tn+3 for n≥1';
MathJaxMap['math_608'] = 't9';
MathJaxMap['math_609'] = 't8=24';
MathJaxMap['math_610'] = 't9:t9=t8+3=24+3=27';
MathJaxMap['math_611'] = 't1=5';
MathJaxMap['math_612'] = 'tn=4⋅tn−1+1';
MathJaxMap['math_613'] = '5 ENTER';
MathJaxMap['math_614'] = '× 4+1 ENTER';
MathJaxMap['math_615'] = 'ENTER';
MathJaxMap['math_616'] = 'ENTER';
MathJaxMap['math_617'] = 'tn=n2−2';
MathJaxMap['math_618'] = 'n=1';
MathJaxMap['math_619'] = 't1';
MathJaxMap['math_620'] = '1 x2 − 2 ENTER';
MathJaxMap['math_621'] = '2nd ENTER';
MathJaxMap['math_622'] = '2';
MathJaxMap['math_623'] = 'ENTER';
MathJaxMap['math_624'] = '2nd ENTER';
MathJaxMap['math_625'] = '3';
MathJaxMap['math_626'] = 'ENTER';
MathJaxMap['math_627'] = 'n';
MathJaxMap['math_628'] = 'ENTER';
MathJaxMap['math_629'] = '−1,2,7,14,23';
MathJaxMap['math_630'] = 'an=12n';
MathJaxMap['math_631'] = 'b1=3';
MathJaxMap['math_632'] = 'bn=bn−1+2';
MathJaxMap['math_633'] = 'b1=3';
MathJaxMap['math_634'] = 'cn+1=3⋅cn−1';
MathJaxMap['math_635'] = 'dn=3n−2';
MathJaxMap['math_636'] = 't1=1';
MathJaxMap['math_637'] = 't2=2';
MathJaxMap['math_638'] = 'tn=tn−1+tn−2';
MathJaxMap['math_639'] = 'a';
MathJaxMap['math_640'] = 'd';
MathJaxMap['math_641'] = 'r';
MathJaxMap['math_642'] = 'a';
MathJaxMap['math_643'] = 'a+d';
MathJaxMap['math_644'] = 'a+2d';
MathJaxMap['math_645'] = 'ar2';
MathJaxMap['math_646'] = 'a+3d';
MathJaxMap['math_647'] = 'ar3';
MathJaxMap['math_648'] = '⋮';
MathJaxMap['math_649'] = '⋮';
MathJaxMap['math_650'] = '⋮';
MathJaxMap['math_651'] = 'n';
MathJaxMap['math_652'] = 'a+(n−1)d';
MathJaxMap['math_653'] = 'arn−1';
MathJaxMap['math_654'] = 'n';
MathJaxMap['math_655'] = 'a+(n−1)d';
MathJaxMap['math_656'] = 'n';
MathJaxMap['math_657'] = 'arn−1';
MathJaxMap['math_658'] = 'd=2';
MathJaxMap['math_659'] = 'r=2';
MathJaxMap['math_660'] = '3+5+7+9+11+13+15+17';
MathJaxMap['math_661'] = '4⋅20=80';
MathJaxMap['math_662'] = 'n';
MathJaxMap['math_663'] = 'n';
MathJaxMap['math_664'] = 'a1,a2,a3';
MathJaxMap['math_665'] = 'an=3+2(n−1)';
MathJaxMap['math_666'] = 'S10';
MathJaxMap['math_667'] = 'a1=3+2(1−1)=3';
MathJaxMap['math_668'] = 'a10=3+2(10−1)=21';
MathJaxMap['math_669'] = 'S10=10(3+21)2=2402=120';
MathJaxMap['math_670'] = 'a';
MathJaxMap['math_671'] = 'r';
MathJaxMap['math_672'] = 'a';
MathJaxMap['math_673'] = 'r';
MathJaxMap['math_674'] = 'n';
MathJaxMap['math_675'] = '2,−2,4,−4,6,−6';
MathJaxMap['math_676'] = '−12';
MathJaxMap['math_677'] = 'd=5';
MathJaxMap['math_678'] = 'S5';
MathJaxMap['math_679'] = 'r=4';
MathJaxMap['math_680'] = 'S15';
MathJaxMap['math_681'] = 'an=1+4(n−1)';
MathJaxMap['math_682'] = 'S5';
MathJaxMap['math_683'] = 'a=2';
MathJaxMap['math_684'] = 'r=3';
MathJaxMap['math_685'] = 'S15';
MathJaxMap['math_686'] = 'a';
MathJaxMap['math_687'] = 'a2';
MathJaxMap['math_688'] = 'a';
MathJaxMap['math_689'] = 'a';
MathJaxMap['math_690'] = 'a';
MathJaxMap['math_691'] = '(−8)2';
MathJaxMap['math_692'] = 'a3';
MathJaxMap['math_693'] = 'a';
MathJaxMap['math_694'] = 'an';
MathJaxMap['math_695'] = 'a';
MathJaxMap['math_696'] = 'n';
MathJaxMap['math_697'] = 'a';
MathJaxMap['math_698'] = 'n';
MathJaxMap['math_699'] = 'n';
MathJaxMap['math_700'] = 'a';
MathJaxMap['math_701'] = 'n';
MathJaxMap['math_702'] = '25,(−2)3';
MathJaxMap['math_703'] = '(−3)4';
MathJaxMap['math_704'] = '−4';
MathJaxMap['math_705'] = '((−)4)^2';
MathJaxMap['math_706'] = 'ENTER';
MathJaxMap['math_707'] = '(−4)2=16';
MathJaxMap['math_708'] = '−4';
MathJaxMap['math_709'] = '(−)4^2ENTER';
MathJaxMap['math_710'] = '−42=−16';
MathJaxMap['math_711'] = '−16';
MathJaxMap['math_712'] = 'a';
MathJaxMap['math_713'] = 'a';
MathJaxMap['math_714'] = 'a';
MathJaxMap['math_715'] = 'a';
MathJaxMap['math_716'] = 'an';
MathJaxMap['math_717'] = 'n';
MathJaxMap['math_718'] = 'a';
MathJaxMap['math_719'] = 'n';
MathJaxMap['math_720'] = 'a';
MathJaxMap['math_721'] = '144';
MathJaxMap['math_722'] = '325';
MathJaxMap['math_723'] = 'n';
MathJaxMap['math_724'] = 'n';
MathJaxMap['math_725'] = '(3.1)(2.7)5';
MathJaxMap['math_726'] = '−3';
MathJaxMap['math_727'] = 'n=3';
MathJaxMap['math_728'] = 'x1=2';
MathJaxMap['math_729'] = 'x2=−3';
MathJaxMap['math_730'] = 'x3=5';
MathJaxMap['math_731'] = '−3';
MathJaxMap['math_732'] = 'x̄=43';
MathJaxMap['math_733'] = 'ENTER';
MathJaxMap['math_734'] = '−3';
MathJaxMap['math_735'] = '2ndx2(for√()';
MathJaxMap['math_736'] = '((2−4÷3)∘2+';
MathJaxMap['math_737'] = '((−)3−4÷3)∘2+';
MathJaxMap['math_738'] = '(5−4÷3)∘2)÷(3−1))';
MathJaxMap['math_739'] = 'ENTER';
MathJaxMap['math_740'] = 'n';
MathJaxMap['math_741'] = 'a';
MathJaxMap['math_742'] = 'an';
MathJaxMap['math_743'] = 'n≥3';
MathJaxMap['math_744'] = 'n';
MathJaxMap['math_745'] = 'MATH5(for x)';
MathJaxMap['math_746'] = 'a';
MathJaxMap['math_747'] = 'ENTER';
MathJaxMap['math_748'] = '(−3)4';
MathJaxMap['math_749'] = '(−2)5';
MathJaxMap['math_750'] = '43';
MathJaxMap['math_751'] = '10,0004';
MathJaxMap['math_752'] = '0.0083';
MathJaxMap['math_753'] = '2500';
MathJaxMap['math_754'] = '(2.7)2+3(4.6)4';
MathJaxMap['math_755'] = 'x̄=4';
MathJaxMap['math_756'] = '(1+0.05)6';
MathJaxMap['math_757'] = '30,2−4';
MathJaxMap['math_758'] = '−3−2';
MathJaxMap['math_759'] = 'mn';
MathJaxMap['math_760'] = 'm';
MathJaxMap['math_761'] = 'n';
MathJaxMap['math_762'] = 'n>0';
MathJaxMap['math_763'] = 'man';
MathJaxMap['math_764'] = 'a≥0';
MathJaxMap['math_765'] = 'n';
MathJaxMap['math_766'] = 'a';
MathJaxMap['math_767'] = 'n';
MathJaxMap['math_768'] = 'a';
MathJaxMap['math_769'] = '3612';
MathJaxMap['math_770'] = '823';
MathJaxMap['math_771'] = 'x5';
MathJaxMap['math_772'] = '(x3)2';
MathJaxMap['math_773'] = '897';
MathJaxMap['math_774'] = '(45)3';
MathJaxMap['math_775'] = '420';
MathJaxMap['math_776'] = '5−2';
MathJaxMap['math_777'] = '(−27)13';
MathJaxMap['math_778'] = '(−27)23';
MathJaxMap['math_779'] = 'x10';
MathJaxMap['math_780'] = 'x35';
MathJaxMap['math_781'] = '0.0026';
MathJaxMap['math_782'] = '(2565)2';
MathJaxMap['math_783'] = '140';
MathJaxMap['math_784'] = 'y=c⋅ax';
MathJaxMap['math_785'] = 'x';
MathJaxMap['math_786'] = 'y=10x';
MathJaxMap['math_787'] = 'y=10x';
MathJaxMap['math_788'] = 'y=x';
MathJaxMap['math_789'] = 'y=10x';
MathJaxMap['math_790'] = 'x';
MathJaxMap['math_791'] = 'y=10x';
MathJaxMap['math_792'] = '102=100';
MathJaxMap['math_793'] = '101=10';
MathJaxMap['math_794'] = '1012=10≈3.16';
MathJaxMap['math_795'] = '100=1';
MathJaxMap['math_796'] = '−1/2';
MathJaxMap['math_797'] = '10−12=110≈0.32';
MathJaxMap['math_798'] = '−1';
MathJaxMap['math_799'] = '10−1=110=0.1';
MathJaxMap['math_800'] = '−2';
MathJaxMap['math_801'] = '10−2=1102=1100=0.01';
MathJaxMap['math_802'] = 'y=10x';
MathJaxMap['math_803'] = 'y=x';
MathJaxMap['math_804'] = 'y=10x';
MathJaxMap['math_805'] = 'y=x';
MathJaxMap['math_806'] = 'x';
MathJaxMap['math_807'] = 'y';
MathJaxMap['math_808'] = 'y=ax';
MathJaxMap['math_809'] = 'a>1';
MathJaxMap['math_810'] = 'y=4x';
MathJaxMap['math_811'] = 'x';
MathJaxMap['math_812'] = '−2.0';
MathJaxMap['math_813'] = '−1.5';
MathJaxMap['math_814'] = '−1.0';
MathJaxMap['math_815'] = '−0.5';
MathJaxMap['math_816'] = 'y=4x';
MathJaxMap['math_817'] = 'y=4x';
MathJaxMap['math_818'] = '−2';
MathJaxMap['math_819'] = 'y=ex';
MathJaxMap['math_820'] = 'y=2x';
MathJaxMap['math_821'] = 'x';
MathJaxMap['math_822'] = 'e≈2.718';
MathJaxMap['math_823'] = '2ndLN(for ex)';
MathJaxMap['math_824'] = '35⋅34';
MathJaxMap['math_825'] = '743⋅713';
MathJaxMap['math_826'] = '2523';
MathJaxMap['math_827'] = '2523=2⋅2⋅2⋅2⋅22⋅2⋅2=22';
MathJaxMap['math_828'] = '2523=25−3=22';
MathJaxMap['math_829'] = '4343';
MathJaxMap['math_830'] = '4346';
MathJaxMap['math_831'] = '(23)2';
MathJaxMap['math_832'] = '(45)3';
MathJaxMap['math_833'] = '(45)3=45×3=415';
MathJaxMap['math_834'] = '(x+2)2=x2+4';
MathJaxMap['math_835'] = 'x+2';
MathJaxMap['math_836'] = '490,000';
MathJaxMap['math_837'] = '0.0036';
MathJaxMap['math_838'] = '9x3';
MathJaxMap['math_839'] = '16+9=16+9=7';
MathJaxMap['math_840'] = '16+9=25=5';
MathJaxMap['math_841'] = '43⋅47';
MathJaxMap['math_842'] = '108104';
MathJaxMap['math_843'] = '(42)5';
MathJaxMap['math_844'] = '632⋅6−12';
MathJaxMap['math_845'] = '35⋅3';
MathJaxMap['math_846'] = '(53)−2';
MathJaxMap['math_847'] = '752712';
MathJaxMap['math_848'] = '(162)4';
MathJaxMap['math_849'] = '33310';
MathJaxMap['math_850'] = '516⋅513';
MathJaxMap['math_851'] = '6400';
MathJaxMap['math_852'] = '0.0049';
MathJaxMap['math_853'] = '64+4=64+4=8+2';
MathJaxMap['math_854'] = 'logbx';
MathJaxMap['math_855'] = 'b';
MathJaxMap['math_856'] = 'x';
MathJaxMap['math_857'] = 'logbx';
MathJaxMap['math_858'] = 'b';
MathJaxMap['math_859'] = 'x';
MathJaxMap['math_860'] = 'log39';
MathJaxMap['math_861'] = 'log381';
MathJaxMap['math_862'] = 'log39=2';
MathJaxMap['math_863'] = 'log381=4';
MathJaxMap['math_864'] = 'log39=2';
MathJaxMap['math_865'] = '32=9';
MathJaxMap['math_866'] = 'log381=4';
MathJaxMap['math_867'] = '34=81';
MathJaxMap['math_868'] = 'LOG';
MathJaxMap['math_869'] = 'log(1000)=log101000=';
MathJaxMap['math_870'] = '103=1000';
MathJaxMap['math_871'] = 'log(1000)=3';
MathJaxMap['math_872'] = 'log(10)=log1010=1 because 101=10';
MathJaxMap['math_873'] = 'log(1)=log101=0 because 100=1';
MathJaxMap['math_874'] = 'x>0';
MathJaxMap['math_875'] = 'alogax=x';
MathJaxMap['math_876'] = '10logx=x';
MathJaxMap['math_877'] = 'logaxr=rlogax';
MathJaxMap['math_878'] = 'logxr=rlogx';
MathJaxMap['math_879'] = '102+3logx';
MathJaxMap['math_880'] = 'x>0';
MathJaxMap['math_881'] = 'e';
MathJaxMap['math_882'] = 'π';
MathJaxMap['math_883'] = 'e';
MathJaxMap['math_884'] = 'logex';
MathJaxMap['math_885'] = 'e';
MathJaxMap['math_886'] = 'x';
MathJaxMap['math_887'] = 'log216';
MathJaxMap['math_888'] = 'log51';
MathJaxMap['math_889'] = 'log525';
MathJaxMap['math_890'] = 'log(110)';
MathJaxMap['math_891'] = 'log(1100)';
MathJaxMap['math_892'] = 'e';
MathJaxMap['math_893'] = '103+2logx';
MathJaxMap['math_894'] = '101−4logx';
MathJaxMap['math_895'] = 'e';
MathJaxMap['math_896'] = 'x=logex';
MathJaxMap['math_897'] = 'logx=log10x';
MathJaxMap['math_898'] = '2x=10';
MathJaxMap['math_899'] = '23=8 and 24−16';
MathJaxMap['math_900'] = 'x';
MathJaxMap['math_901'] = 'x';
MathJaxMap['math_902'] = 'x=3.32';
MathJaxMap['math_903'] = 'A=P(1+i)n';
MathJaxMap['math_904'] = 'P';
MathJaxMap['math_905'] = 'i';
MathJaxMap['math_906'] = 'n';
MathJaxMap['math_907'] = 'A';
MathJaxMap['math_908'] = 'P';
MathJaxMap['math_909'] = 'i';
MathJaxMap['math_910'] = 'A=P(1+i)n';
MathJaxMap['math_911'] = 'n';
MathJaxMap['math_912'] = 'A=P(1+i)n';
MathJaxMap['math_913'] = 'n';
MathJaxMap['math_914'] = '3x=15';
MathJaxMap['math_915'] = '2⋅5x=28';
MathJaxMap['math_916'] = '80(1.03)t=100';
MathJaxMap['math_917'] = 'A=P(1+i)n';
MathJaxMap['math_918'] = 'A=2000,P=1000, and i=0.04';
MathJaxMap['math_919'] = 'n';
MathJaxMap['math_920'] = 'x';
MathJaxMap['math_921'] = 'y';
MathJaxMap['math_922'] = 'x';
MathJaxMap['math_923'] = 'y';
MathJaxMap['math_924'] = 'f(x)';
MathJaxMap['math_925'] = 'f';
MathJaxMap['math_926'] = 'x';
MathJaxMap['math_927'] = 'f';
MathJaxMap['math_928'] = 'x';
MathJaxMap['math_929'] = 'f(x)';
MathJaxMap['math_930'] = '(a)(b)';
MathJaxMap['math_931'] = 'ab';
MathJaxMap['math_932'] = 'f(x)=x2';
MathJaxMap['math_933'] = 'x';
MathJaxMap['math_934'] = 'x';
MathJaxMap['math_935'] = 'f(x)=x2';
MathJaxMap['math_936'] = 'f(−3)';
MathJaxMap['math_937'] = 'f(3)';
MathJaxMap['math_938'] = 'f(x)';
MathJaxMap['math_939'] = '(x, f(x))';
MathJaxMap['math_940'] = '(x, x2)';
MathJaxMap['math_941'] = 'f(x)=x2';
MathJaxMap['math_942'] = '(−3, 9)';
MathJaxMap['math_943'] = '(0, 02)=(0, 0)';
MathJaxMap['math_944'] = '(2, 22)=(2, 4)';
MathJaxMap['math_945'] = 'f(x)=x';
MathJaxMap['math_946'] = 'a';
MathJaxMap['math_947'] = 'a';
MathJaxMap['math_948'] = 'f(x)=mx+b';
MathJaxMap['math_949'] = 'm=1';
MathJaxMap['math_950'] = 'b=0';
MathJaxMap['math_951'] = 'f(x)=a⋅bx';
MathJaxMap['math_952'] = 'f(x)=x2';
MathJaxMap['math_953'] = 'Y=';
MathJaxMap['math_954'] = 'Y1=';
MathJaxMap['math_955'] = 'X,T,θ,n x2';
MathJaxMap['math_956'] = 'ZOOM 6';
MathJaxMap['math_957'] = 'f(x)=x2';
MathJaxMap['math_958'] = 'f(−4)';
MathJaxMap['math_959'] = 'f';
MathJaxMap['math_960'] = 'Y1(−4)';
MathJaxMap['math_961'] = 'VARS';
MathJaxMap['math_962'] = '1';
MathJaxMap['math_963'] = '1';
MathJaxMap['math_964'] = '((−)4)ENTER';
MathJaxMap['math_965'] = 'f(x)=x3';
MathJaxMap['math_966'] = 'f(−2)';
MathJaxMap['math_967'] = 'f(x)=x3';
MathJaxMap['math_968'] = 'x';
MathJaxMap['math_969'] = 'f(x)=x2+x';
MathJaxMap['math_970'] = 'f(−2)';
MathJaxMap['math_971'] = 'f(2)';
MathJaxMap['math_972'] = 'f(x)=x2+x';
MathJaxMap['math_973'] = 'f(x)=x2+x';
MathJaxMap['math_974'] = 'f(x)=3⋅2x';
MathJaxMap['math_975'] = 'f(2)';
MathJaxMap['math_976'] = 'f(3)';
MathJaxMap['math_977'] = 'f(x)=3x+7';
MathJaxMap['math_978'] = 'f(1)';
MathJaxMap['math_979'] = 'f(4)';
MathJaxMap['math_980'] = 'n';
MathJaxMap['math_981'] = 'n';
MathJaxMap['math_982'] = 'n';
MathJaxMap['math_983'] = ' 5P3';
MathJaxMap['math_984'] = 'n';
MathJaxMap['math_985'] = 'k';
MathJaxMap['math_986'] = ' nPk';
MathJaxMap['math_987'] = '5';
MathJaxMap['math_988'] = 'MATH';
MathJaxMap['math_989'] = '4';
MathJaxMap['math_990'] = 'ENTER';
MathJaxMap['math_991'] = ' 25P4';
MathJaxMap['math_992'] = '5';
MathJaxMap['math_993'] = 'MATH';
MathJaxMap['math_994'] = '2';
MathJaxMap['math_995'] = ' nPr';
MathJaxMap['math_996'] = '4';
MathJaxMap['math_997'] = 'ENTER';
MathJaxMap['math_998'] = ' 15P5';
MathJaxMap['math_999'] = ' 30P2';
MathJaxMap['math_1000'] = ' 27P3';
MathJaxMap['math_1001'] = ' nPk';
MathJaxMap['math_1002'] = ' 50P10';
MathJaxMap['math_1003'] = 'k';
MathJaxMap['math_1004'] = 'n';
MathJaxMap['math_1005'] = ' nCk';
MathJaxMap['math_1006'] = 'n';
MathJaxMap['math_1007'] = 'k';
MathJaxMap['math_1008'] = ' 5P3=60';
MathJaxMap['math_1009'] = ' 5P3/3!=606=10';
MathJaxMap['math_1010'] = 'k';
MathJaxMap['math_1011'] = 'n';
MathJaxMap['math_1012'] = ' 25C4';
MathJaxMap['math_1013'] = ' 25P4';
MathJaxMap['math_1014'] = ' 25C4';
MathJaxMap['math_1015'] = '25';
MathJaxMap['math_1016'] = 'MATH';
MathJaxMap['math_1017'] = '3';
MathJaxMap['math_1018'] = ' nCr';
MathJaxMap['math_1019'] = '4';
MathJaxMap['math_1020'] = 'ENTER';
MathJaxMap['math_1021'] = ' 15C5';
MathJaxMap['math_1022'] = ' 30C2';
MathJaxMap['math_1023'] = ' 27C3';
MathJaxMap['math_1024'] = ' 50C10';
MathJaxMap['math_1025'] = ' nCk';
MathJaxMap['math_1026'] = ' 50C20';