Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
153101	Find All Complex Number Solutions	x^2+5x-5=0	$x^{2} + 5 x - 5 = 0$
153102	Find All Complex Number Solutions	x^2-2x-8=0	$x^{2} - 2 x - 8 = 0$
153103	Find All Complex Number Solutions	12x^2-11x=11	$12 x^{2} - 11 x = 11$
153104	Find All Complex Number Solutions	2x^2-3x-5=0	$2 x^{2} - 3 x - 5 = 0$
153105	Find All Complex Number Solutions	3x^2-2x-5=0	$3 x^{2} - 2 x - 5 = 0$
153106	Find All Complex Number Solutions	3x^2-7x+2=0	$3 x^{2} - 7 x + 2 = 0$
153107	Find All Complex Number Solutions	-4x^2-20x-25=0	$- 4 x^{2} - 20 x - 25 = 0$
153108	Find All Complex Number Solutions	-5x+12=Px+Q	$- 5 x + 12 = P x + Q$
153109	Find the Other Trig Values in Quadrant II	cot(x)=-( square root of 5)/2	$\cot (x) = - \frac{\sqrt{5}}{2}$
153110	Find the Other Trig Values in Quadrant III	tan(x)=(5 square root of 11)/11	$\tan (x) = \frac{5 \sqrt{11}}{11}$
153111	Multiply the Matrices	[[1],[-3],[2]]*[[-1],[3],[-2]]	$[\begin{array}{c} 1 \\ - 3 \\ 2 \end{array}] \cdot [\begin{array}{c} - 1 \\ 3 \\ - 2 \end{array}]$
153112	Multiply the Matrices	[[1,4],[7,1]][[2,2],[4,3]]	$[\begin{array}{c} 1 & 4 \\ 7 & 1 \end{array}] [\begin{array}{c} 2 & 2 \\ 4 & 3 \end{array}]$
153113	Multiply the Matrices	[[-1,5,0],[2,-1,3]][[-3,2,2],[5,3,-1],[3,4,-3]]	$[\begin{array}{c} - 1 & 5 & 0 \\ 2 & - 1 & 3 \end{array}] [\begin{array}{c} - 3 & 2 & 2 \\ 5 & 3 & - 1 \\ 3 & 4 & - 3 \end{array}]$
153114	Multiply the Matrices	[[1,-5],[3,-6]][[3,0],[-4,1]]	$[\begin{array}{c} 1 & - 5 \\ 3 & - 6 \end{array}] [\begin{array}{c} 3 & 0 \\ - 4 & 1 \end{array}]$
153115	Multiply the Matrices	[[1,-4,3],[1,5,3],[0,-2,4]][[-11],[16],[-10]]	$[\begin{array}{c} 1 & - 4 & 3 \\ 1 & 5 & 3 \\ 0 & - 2 & 4 \end{array}] [\begin{array}{c} - 11 \\ 16 \\ - 10 \end{array}]$
153116	Multiply the Matrices	[[1,2],[3,4]][[5,6,7],[8,9,0]]	$[\begin{array}{c} 1 & 2 \\ 3 & 4 \end{array}] [\begin{array}{c} 5 & 6 & 7 \\ 8 & 9 & 0 \end{array}]$
153117	Multiply the Matrices	[[1,3,-2],[2,0,3]][[3,0],[-2,1],[0,3]]	$[\begin{array}{c} 1 & 3 & - 2 \\ 2 & 0 & 3 \end{array}] [\begin{array}{c} 3 & 0 \\ - 2 & 1 \\ 0 & 3 \end{array}]$
153118	Multiply the Matrices	[[0,1],[-1,10]][[10,1],[-1,0]]	$[\begin{array}{c} 0 & 1 \\ - 1 & 10 \end{array}] [\begin{array}{c} 10 & 1 \\ - 1 & 0 \end{array}]$
153119	Multiply the Matrices	[[-1,0],[0,1]]*[[0,6,6,1,1,0],[0,0,1,1,9,9]]	$[\begin{array}{c} - 1 & 0 \\ 0 & 1 \end{array}] \cdot [\begin{array}{c} 0 & 6 & 6 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 9 & 9 \end{array}]$
153120	Multiply the Matrices	[[3,6,1],[2,4,0],[0,6,2]][[2],[0],[1]]	$[\begin{array}{c} 3 & 6 & 1 \\ 2 & 4 & 0 \\ 0 & 6 & 2 \end{array}] [\begin{array}{c} 2 \\ 0 \\ 1 \end{array}]$
153121	Multiply the Matrices	[[2,6,-5],[1,3,4],[-7,2,10]][[1,0,11],[-5,2,4],[-9,7,8]]	$[\begin{array}{c} 2 & 6 & - 5 \\ 1 & 3 & 4 \\ - 7 & 2 & 10 \end{array}] [\begin{array}{c} 1 & 0 & 11 \\ - 5 & 2 & 4 \\ - 9 & 7 & 8 \end{array}]$
153122	Multiply the Matrices	A=[[8,-7],[-9,8]] , B=[[8,7],[9,8]]	$A = [\begin{array}{c} 8 & - 7 \\ - 9 & 8 \end{array}]$ , $B = [\begin{array}{c} 8 & 7 \\ 9 & 8 \end{array}]$
153123	Multiply the Matrices	[[8,3],[-7,2]]*[[8,3],[-7,-6]]	$[\begin{array}{c} 8 & 3 \\ - 7 & 2 \end{array}] \cdot [\begin{array}{c} 8 & 3 \\ - 7 & - 6 \end{array}]$
153124	Multiply the Matrices	0.4[[2,3],[8,9]]	$0.4 [\begin{array}{c} 2 & 3 \\ 8 & 9 \end{array}]$
153125	Multiply the Matrices	[5*3]	$[5 \cdot 3]$
153126	Multiply the Matrices	[[5,-5,4],[1,2,1]][[1,4,2],[3,2,5],[7,-1,8]]	$[\begin{array}{c} 5 & - 5 & 4 \\ 1 & 2 & 1 \end{array}] [\begin{array}{c} 1 & 4 & 2 \\ 3 & 2 & 5 \\ 7 & - 1 & 8 \end{array}]$
153127	Multiply the Matrices	[[5,6,7],[8,9,0]][[1,2],[3,4]]	$[\begin{array}{c} 5 & 6 & 7 \\ 8 & 9 & 0 \end{array}] [\begin{array}{c} 1 & 2 \\ 3 & 4 \end{array}]$
153128	Multiply the Matrices	[[40,64,52],[60,82,76],[76,96,84]][[3.45,1.20],[3.65,1.30],[3.85,1.45]]	$[\begin{array}{c} 40 & 64 & 52 \\ 60 & 82 & 76 \\ 76 & 96 & 84 \end{array}] [\begin{array}{c} 3.45 & 1.2 \\ 3.65 & 1.3 \\ 3.85 & 1.45 \end{array}]$
153129	Multiply the Matrices	[[4],[7]]+[[8],[2]]=	$[\begin{array}{c} 4 \\ 7 \end{array}] + [\begin{array}{c} 8 \\ 2 \end{array}] =$
153130	Reduce	((x^2-2x-15)/(x-3))÷((x-5)/(x^2-9))	$\frac{x^{2} - 2 x - 15}{x - 3} \div \frac{x - 5}{x^{2} - 9}$
153131	Reduce	(16x^2-25)/(8x^2-14x+5)	$\frac{16 x^{2} - 25}{8 x^{2} - 14 x + 5}$
153132	Reduce	(20+40x)/(20x)	$\frac{20 + 40 x}{20 x}$
153133	Reduce	(36x^5y^8z^10)/(15x^5y^7z^2)	$\frac{36 x^{5} y^{8} z^{10}}{15 x^{5} y^{7} z^{2}}$
153134	Reduce	(40x^-2y^-3z^0)/(5x^2y^-4z^-2)	$\frac{40 x^{- 2} y^{- 3} z^{0}}{5 x^{2} y^{- 4} z^{- 2}}$
153135	Reduce	((6-x)/(x^2+2x-3))÷((x^2-4x-12)/(x^2+4x+3))	$\frac{6 - x}{x^{2} + 2 x - 3} \div \frac{x^{2} - 4 x - 12}{x^{2} + 4 x + 3}$
153136	Reduce	(7x-28)/(8x-32)	$\frac{7 x - 28}{8 x - 32}$
153137	Reduce	(a^2b^-1(ab^2)^3)/(a^-3b^4)	$\frac{a^{2} b^{- 1} {(a b^{2})}^{3}}{a^{- 3} b^{4}}$
153138	Reduce	(a^3b^-2c^-1)/(ab^3)	$\frac{a^{3} b^{- 2} c^{- 1}}{a b^{3}}$
153139	Find Trig Functions Using Identities	sin((3pi)/4)	$\sin (\frac{3 π}{4})$
153140	Find Trig Functions Using Identities	cos(2x)=cos(x)	$\cos (2 x) = \cos (x)$
153141	Find Trig Functions Using Identities	2cos(x)^2-cos(2x)	$2 \cos^{2} (x) - \cos (2 x)$
153142	Find Trig Functions Using Identities	cos(4x)^2-sin(4x)^2	$\cos^{2} (4 x) - \sin^{2} (4 x)$
153143	Find Trig Functions Using Identities	1/(1-cos(x))+1/(1+cos(x))	$\frac{1}{1 - \cos (x)} + \frac{1}{1 + \cos (x)}$
153144	Find the Sample Standard Deviation	7.2 , 9.1 , 5.7 , 8.5 , 10.2 , 9.9 , 11.0 , 7.7 , 6.4 , 8.9	$7.2$ , $9.1$ , $5.7$ , $8.5$ , $10.2$ , $9.9$ , $11$ , $7.7$ , $6.4$ , $8.9$
153145	Find the Sample Standard Deviation	70 , 66 , 68 , 72 , 75 , 70 , 67 , 70 , 72 , 67	$70$ , $66$ , $68$ , $72$ , $75$ , $70$ , $67$ , $70$ , $72$ , $67$
153146	Find the Sample Standard Deviation	74 , 52 , 65 , 64 , 58	$74$ , $52$ , $65$ , $64$ , $58$
153147	Find the Sample Standard Deviation	55 , 70 , 85 , 100 , 115 , 130 , 145	$55$ , $70$ , $85$ , $100$ , $115$ , $130$ , $145$
153148	Find the Sample Standard Deviation	56 , 45 , 48 , 47 , 56 , 55 , 43 , 44	$56$ , $45$ , $48$ , $47$ , $56$ , $55$ , $43$ , $44$
153149	Find the Sample Standard Deviation	5 , 8 , 12 , 15 , 17 , 12 , 14 , 7	$5$ , $8$ , $12$ , $15$ , $17$ , $12$ , $14$ , $7$
153150	Find the Sample Standard Deviation	52 , 19 , 44 , 49 , 37 , 46 , 52 , 36 , 54 , 13 , 14 , 17 , 34 , 16 , 51	$52$ , $19$ , $44$ , $49$ , $37$ , $46$ , $52$ , $36$ , $54$ , $13$ , $14$ , $17$ , $34$ , $16$ , $51$
153151	Find the Sample Standard Deviation	42 , 48 , 54 , 60 , 66 , 72 , 78	$42$ , $48$ , $54$ , $60$ , $66$ , $72$ , $78$
153152	Find the Sample Standard Deviation	25 , 22 , 21 , 26 , 37 , 24 , 26 , 22	$25$ , $22$ , $21$ , $26$ , $37$ , $24$ , $26$ , $22$
153153	Find the Sample Standard Deviation	26 , 31 , 10 , 37 , 38 , 35 , 30 , 24 , 26 , 27 , 24 , 32 , 32 , 19 , 34 , 33 , 14 , 32 , 24 , 39 , 30	$26$ , $31$ , $10$ , $37$ , $38$ , $35$ , $30$ , $24$ , $26$ , $27$ , $24$ , $32$ , $32$ , $19$ , $34$ , $33$ , $14$ , $32$ , $24$ , $39$ , $30$
153154	Find the Sample Standard Deviation	24 , 18 , 29 , 21 , 16 , 23 , 13 , 11	$24$ , $18$ , $29$ , $21$ , $16$ , $23$ , $13$ , $11$
153155	Find the Sample Standard Deviation	24 , 21 , 27 , 30 , 27 , 29 , 24	$24$ , $21$ , $27$ , $30$ , $27$ , $29$ , $24$
153156	Find the Sample Standard Deviation	4 , 13 , 5 , 6 , 9	$4$ , $13$ , $5$ , $6$ , $9$
153157	Find the Sample Standard Deviation	35 , 40 , 45 , 55 , 60	$35$ , $40$ , $45$ , $55$ , $60$
153158	Find the Sample Standard Deviation	36 , 14 , 21 , 39 , 11 , 2	$36$ , $14$ , $21$ , $39$ , $11$ , $2$
153159	Find the Sample Standard Deviation	3.7 , 8.2 , 9.9 , 11.3 , 15.6 , 17.3	$3.7$ , $8.2$ , $9.9$ , $11.3$ , $15.6$ , $17.3$
153160	Find the Sample Standard Deviation	325 , 310 , 289 , 288 , 285 , 285 , 285 , 280 , 280 , 273	$325$ , $310$ , $289$ , $288$ , $285$ , $285$ , $285$ , $280$ , $280$ , $273$
153161	Find the Sample Standard Deviation	11.99 , 8.84 , 16.98 , 9.99 , 10.45 , 10.86 , 11.99	$11.99$ , $8.84$ , $16.98$ , $9.99$ , $10.45$ , $10.86$ , $11.99$
153162	Find the Sample Standard Deviation	110 , 114 , 104 , 108 , 106	$110$ , $114$ , $104$ , $108$ , $106$
153163	Find the Sample Standard Deviation	111 , 135 , 115 , 120 , 145 , 130	$111$ , $135$ , $115$ , $120$ , $145$ , $130$
153164	Find the Sample Standard Deviation	0.3 , 0.6 , 0.9 , 1.3 , 0.4 , 0.6 , 1.2 , 1.4 , 1.1 , 0.2 , 0.2	$0.3$ , $0.6$ , $0.9$ , $1.3$ , $0.4$ , $0.6$ , $1.2$ , $1.4$ , $1.1$ , $0.2$ , $0.2$
153165	Find the Sample Standard Deviation	10 , 19 , 38 , 50 , 51	$10$ , $19$ , $38$ , $50$ , $51$
153166	Find the Sample Standard Deviation	112 , 149 , 112 , 148 , 139 , 121 , 116 , 134 , 148	$112$ , $149$ , $112$ , $148$ , $139$ , $121$ , $116$ , $134$ , $148$
153167	Find the Sample Standard Deviation	13 , 18 , 13 , 14 , 13 , 16 , 14 , 21 , 13	$13$ , $18$ , $13$ , $14$ , $13$ , $16$ , $14$ , $21$ , $13$
153168	Find the Sample Standard Deviation	138 , 151 , 169 , 142 , 176 , 155 , 132 , 177	$138$ , $151$ , $169$ , $142$ , $176$ , $155$ , $132$ , $177$
153169	Find the Sample Standard Deviation	147 , 148 , 134 , 151 , 148 , 145 , 152 , 153 , 143 , 141 , 150 , 150 , 159 , 148	$147$ , $148$ , $134$ , $151$ , $148$ , $145$ , $152$ , $153$ , $143$ , $141$ , $150$ , $150$ , $159$ , $148$
153170	Find the Sample Standard Deviation	147 , 148 , 134 , 151 , 148 , 145 , 6 , 152 , 153 , 143 , 141 , 210 , 150 , 150 , 159 , 148	$147$ , $148$ , $134$ , $151$ , $148$ , $145$ , $6$ , $152$ , $153$ , $143$ , $141$ , $210$ , $150$ , $150$ , $159$ , $148$
153171	Find the Sample Standard Deviation	18 , 19 , 23 , 17 , 19 , 15 , 14 , 24 , 21	$18$ , $19$ , $23$ , $17$ , $19$ , $15$ , $14$ , $24$ , $21$
153172	Find the Sample Standard Deviation	18 , 30 , 20 , 20 , 26	$18$ , $30$ , $20$ , $20$ , $26$
153173	Find the Sample Standard Deviation	15 , 18 , 21 , 22 , 26 , 28 , 31 , 39	$15$ , $18$ , $21$ , $22$ , $26$ , $28$ , $31$ , $39$
153174	Find Any Equation Parallel to the Line	y=5x-7	$y = 5 x - 7$
153175	Find Any Equation Parallel to the Line	y=-3x-7	$y = - 3 x - 7$
153176	Find Any Equation Parallel to the Line	y=3/4x+1	$y = \frac{3}{4} x + 1$
153177	Find Any Equation Parallel to the Line	y=-6x+3	$y = - 6 x + 3$
153178	Find the Sample Standard Deviation	8 , 10 , 12 , 14 , 16	$8$ , $10$ , $12$ , $14$ , $16$
153179	Find Any Equation Parallel to the Line	y=-1/2x-1	$y = - \frac{1}{2} x - 1$
153180	Find the Sample Standard Deviation	91 , 101 , 75 , 90 , 88 , 87 , 90 , 60	$91$ , $101$ , $75$ , $90$ , $88$ , $87$ , $90$ , $60$
153181	Find the Sample Standard Deviation	99 , 60 , 82 , 78 , 93 , 71 , 68 , 86 , 80 , 95 , 72 , 64	$99$ , $60$ , $82$ , $78$ , $93$ , $71$ , $68$ , $86$ , $80$ , $95$ , $72$ , $64$
153182	Evaluate the Piecewise Function	f(x)=3x^2+1 if -4<x<6; 6 if 6<=x<9	$f (x) = {\begin{cases} 3 x^{2} + 1 & - 4 < x < 6 \\ 6 & 6 \leq x < 9 \end{cases}$
153183	Find the Degree	cos(x)=5/6	$\cos (x) = \frac{5}{6}$
153184	Find the Square or Rectangle Area	(-1,1) , (-1,-4) , (5,-4) , (5,1)	$(- 1, 1) (- 1, - 4) (5, - 4) (5, 1)$
153185	Find Any Equation Perpendicular to the Line	y=-6x+3	$y = - 6 x + 3$
153186	Find Any Equation Perpendicular to the Line	y=3/4x+5	$y = \frac{3}{4} x + 5$
153187	Find Any Equation Perpendicular to the Line	y=4/3x-7	$y = \frac{4}{3} x - 7$
153188	Find Any Equation Perpendicular to the Line	y=2x-10	$y = 2 x - 10$
153189	Find Any Equation Perpendicular to the Line	y=4x-3	$y = 4 x - 3$
153190	Find Any Equation Perpendicular to the Line	y=1/5x+2	$y = \frac{1}{5} x + 2$
153191	Find Any Equation Perpendicular to the Line	2x+3y=5	$2 x + 3 y = 5$
153192	Find Any Equation Perpendicular to the Line	2x+5y=17	$2 x + 5 y = 17$
153193	Find Any Equation Perpendicular to the Line	5x+6y=7	$5 x + 6 y = 7$
153194	Find Any Equation Perpendicular to the Line	5x+7y=9	$5 x + 7 y = 9$
153195	Find Any Equation Perpendicular to the Line	7x=14y-8	$7 x = 14 y - 8$
153196	Find the Local Maxima and Minima	f(x)=x^3-15x^2+48x	$f (x) = x^{3} - 15 x^{2} + 48 x$
153197	Find the Local Maxima and Minima	R(x)=200x-0.4x^2	$R (x) = 200 x - 0.4 x^{2}$
153198	Find the Local Maxima and Minima	f(x)=x^3-5x	$f (x) = x^{3} - 5 x$
153199	Evaluate Using the Given Value	f(-6)=2 square root of -6	$f (- 6) = 2 \sqrt{- 6}$
153200	Evaluate Using the Given Value	f(6)=-16(6)^2+32(6)+384	$f (6) = - 16 {(6)}^{2} + 32 (6) + 384$