Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
42201	Find the Cosine Given the Point	(-1/5,1/3)	$(- \frac{1}{5}, \frac{1}{3})$
42202	Factor over the Complex Numbers	4-2i	$4 - 2 i$
42203	Factor over the Complex Numbers	8i	$8 i$
42204	Factor over the Complex Numbers	x^3+27	$x^{3} + 27$
42205	Convert to Interval Notation	(49x^2-81)/(x^2-64)<=0	$\frac{49 x^{2} - 81}{x^{2} - 64} \leq 0$
42206	Convert to Interval Notation	(x^2+2x-8)/(x^2-16)<0	$\frac{x^{2} + 2 x - 8}{x^{2} - 16} < 0$
42207	Convert to Interval Notation	(x^2+9x+20)/(x^2-x-20)>=0	$\frac{x^{2} + 9 x + 20}{x^{2} - x - 20} \geq 0$
42208	Convert to Interval Notation	(x-2)(x-3)(x-9)<=0	$(x - 2) (x - 3) (x - 9) \leq 0$
42209	Convert to Interval Notation	(x+7)/(x-19)>=1	$\frac{x + 7}{x - 19} \geq 1$
42210	Convert to Interval Notation	(x-1)(x-2)(x-3)<=0	$(x - 1) (x - 2) (x - 3) \leq 0$
42211	Convert to Interval Notation	(x-4)(x-5)(x-8)>=0	$(x - 4) (x - 5) (x - 8) \geq 0$
42212	Convert to Interval Notation	(x-7)/(x+2)>=0	$\frac{x - 7}{x + 2} \geq 0$
42213	Convert to Interval Notation	x^3+4x^2>=x+4	$x^{3} + 4 x^{2} \geq x + 4$
42214	Convert to Interval Notation	x^3>=5x^2	$x^{3} \geq 5 x^{2}$
42215	Convert to Interval Notation	x(x+2)^2(x-3)<=0	$x {(x + 2)}^{2} (x - 3) \leq 0$
42216	Convert to Interval Notation	6x-2x^2>0	$6 x - 2 x^{2} > 0$
42217	Convert to Interval Notation	3x^3-48x<x^2-16	$3 x^{3} - 48 x < x^{2} - 16$
42218	Convert to Interval Notation	2x^3-5x^2<=-4x+21	$2 x^{3} - 5 x^{2} \leq - 4 x + 21$
42219	Convert to Interval Notation	\|6-4x\|>=20	$\| 6 - 4 x \| \geq 20$
42220	Convert to Interval Notation	x>-3/(x-4)	$x > - \frac{3}{x - 4}$
42221	Convert to Interval Notation	x>12	$x > 12$
42222	Convert to Interval Notation	x<=15-2x^2	$x \leq 15 - 2 x^{2}$
42223	Solve Using the Quadratic Formula	4x^2+16x+19=0	$4 x^{2} + 16 x + 19 = 0$
42224	Solve Using the Quadratic Formula	3x^2=9x-11	$3 x^{2} = 9 x - 11$
42225	Find the Vertex	y^2-8y+8x+16=0	$y^{2} - 8 y + 8 x + 16 = 0$
42226	Find the Vertex	y^2=6x	$y^{2} = 6 x$
42227	Find the Vertex	x^2=56y	$x^{2} = 56 y$
42228	Find the Vertex	y^2+4x-2y+21=0	$y^{2} + 4 x - 2 y + 21 = 0$
42229	Find the Vertex	x^2-2x+3y-5=0	$x^{2} - 2 x + 3 y - 5 = 0$
42230	Find the Vertex	(x+5)^2=-12(y-6)	${(x + 5)}^{2} = - 12 (y - 6)$
42231	Find the Vertex	(x-2)^2=4(y-3)	${(x - 2)}^{2} = 4 (y - 3)$
42232	Find the Vertex	(y-4)^2=20(x+2)	${(y - 4)}^{2} = 20 (x + 2)$
42233	Find the Vertex	(y-9)^2=-4(x-2)	${(y - 9)}^{2} = - 4 (x - 2)$
42234	Find the Vertex	(y-2)^2=12(x+1)	${(y - 2)}^{2} = 12 (x + 1)$
42235	Find Trig Functions Using Identities	(-5/13,12/13)	$(- \frac{5}{13}, \frac{12}{13})$
42236	Expand Using Pascal's Triangle	(x-3y)^5	${(x - 3 y)}^{5}$
42237	Expand Using Pascal's Triangle	(x-2y)^4	${(x - 2 y)}^{4}$
42238	Expand Using Pascal's Triangle	(x-2)^10	${(x - 2)}^{10}$
42239	Expand Using Pascal's Triangle	(x+3)^6	${(x + 3)}^{6}$
42240	Expand Using Pascal's Triangle	(x+2y)^6	${(x + 2 y)}^{6}$
42241	Expand Using Pascal's Triangle	(1/3x+y^2)^3	${(\frac{1}{3} x + y^{2})}^{3}$
42242	Find the Discriminant	-x^2+1x-7=0	$- x^{2} + 1 x - 7 = 0$
42243	Find the Trig Value	sin(x)=1/2	$\sin (x) = \frac{1}{2}$
42244	Evaluate the Function	f(x)=x^2+3	$f (x) = x^{2} + 3$
42245	Solve the Matrix Equation	[[5,4],[-3,2]]x=[[10],[-16]]	$[\begin{array}{c} 5 & 4 \\ - 3 & 2 \end{array}] x = [\begin{array}{c} 10 \\ - 16 \end{array}]$
42246	Find the Center	((x+3)^2)/16+((y-1)^2)/4=1	$\frac{{(x + 3)}^{2}}{16} + \frac{{(y - 1)}^{2}}{4} = 1$
42247	Find the Center	y^2+6y-8x-31=0	$y^{2} + 6 y - 8 x - 31 = 0$
42248	Find the Center	9x^2+4y^2-18x+8y-23=0	$9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0$
42249	Find the Center	3y^2-2y+x+1=0	$3 y^{2} - 2 y + x + 1 = 0$
42250	Find the Center	(x^2)/81+(y^2)/49=1	$\frac{x^{2}}{81} + \frac{y^{2}}{49} = 1$
42251	Write as y=mx+b	f(x)=3x+4x-5	$f (x) = 3 x + 4 x - 5$
42252	Write in Standard Form	4x^2+4y^2-24x+32y+36=0	$4 x^{2} + 4 y^{2} - 24 x + 32 y + 36 = 0$
42253	Write in Standard Form	4x^2+y^2+126x+2y+433=0	$4 x^{2} + y^{2} + 126 x + 2 y + 433 = 0$
42254	Write in Standard Form	4x^2+3y^2-32x+12y+64=0	$4 x^{2} + 3 y^{2} - 32 x + 12 y + 64 = 0$
42255	Write in Standard Form	4x^2+25y^2+16x-150y+141=0	$4 x^{2} + 25 y^{2} + 16 x - 150 y + 141 = 0$
42256	Write in Standard Form	4x^2-9y^2+8x+40=0	$4 x^{2} - 9 y^{2} + 8 x + 40 = 0$
42257	Write in Standard Form	4x^2-16x+16y+32=0	$4 x^{2} - 16 x + 16 y + 32 = 0$
42258	Write in Standard Form	36x^2+49y^2-216x+98y-1391=0	$36 x^{2} + 49 y^{2} - 216 x + 98 y - 1391 = 0$
42259	Write in Standard Form	36x^2+100y^2-72x+200y-3464=0	$36 x^{2} + 100 y^{2} - 72 x + 200 y - 3464 = 0$
42260	Write in Standard Form	3x^2+y^2+18x-2y-8=0	$3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0$
42261	Write in Standard Form	25x^2-16y^2+100x+96y=444	$25 x^{2} - 16 y^{2} + 100 x + 96 y = 444$
42262	Write in Standard Form	25x^2-9y^2-100y-72y-269=0	$25 x^{2} - 9 y^{2} - 100 y - 72 y - 269 = 0$
42263	Write in Standard Form	2y^2+12y-x+2=0	$2 y^{2} + 12 y - x + 2 = 0$
42264	Write in Standard Form	(x-1)^2+(y-5)^2=49	${(x - 1)}^{2} + {(y - 5)}^{2} = 49$
42265	Write in Standard Form	-16x^2+4y^2-160x-32y-400=0	$- 16 x^{2} + 4 y^{2} - 160 x - 32 y - 400 = 0$
42266	Write in Standard Form	16x^2-9y^2+128x-54y+31=0	$16 x^{2} - 9 y^{2} + 128 x - 54 y + 31 = 0$
42267	Write in Standard Form	12x^2+20y^2-12x+40y-37=0	$12 x^{2} + 20 y^{2} - 12 x + 40 y - 37 = 0$
42268	Write in Standard Form	10y^2-20x^2+60y+160x-225=0	$10 y^{2} - 20 x^{2} + 60 y + 160 x - 225 = 0$
42269	Write in Standard Form	9x^2-4y^2-18x-8y-31=0	$9 x^{2} - 4 y^{2} - 18 x - 8 y - 31 = 0$
42270	Write in Standard Form	9x^2-4y^2-36x-24y-36=0	$9 x^{2} - 4 y^{2} - 36 x - 24 y - 36 = 0$
42271	Write in Standard Form	9y^2-16x^2-18y-135=0	$9 y^{2} - 16 x^{2} - 18 y - 135 = 0$
42272	Write in Standard Form	r=11	$r = 11$
42273	Write in Standard Form	9x^2-y^2+54x+10y+55=0	$9 x^{2} - y^{2} + 54 x + 10 y + 55 = 0$
42274	Write in Standard Form	4y^2-24y-2x^2+20x=22	$4 y^{2} - 24 y - 2 x^{2} + 20 x = 22$
42275	Write in Standard Form	64x^2+100y^2-256x+400y-5744=0	$64 x^{2} + 100 y^{2} - 256 x + 400 y - 5744 = 0$
42276	Write in Standard Form	64x^2+100y^2-512x+200y-5276=0	$64 x^{2} + 100 y^{2} - 512 x + 200 y - 5276 = 0$
42277	Write in Standard Form	6x^2+24x+2y-10=0	$6 x^{2} + 24 x + 2 y - 10 = 0$
42278	Write in Standard Form	-9x^2+25y^2-90x+100y-350=0	$- 9 x^{2} + 25 y^{2} - 90 x + 100 y - 350 = 0$
42279	Write in Standard Form	x^2+7y^2-12x-13=0	$x^{2} + 7 y^{2} - 12 x - 13 = 0$
42280	Write in Standard Form	x^2+2xy+y^2+x-y-4=0	$x^{2} + 2 x y + y^{2} + x - y - 4 = 0$
42281	Write in Standard Form	x^2+y^2+6x-4y-3=0	$x^{2} + y^{2} + 6 x - 4 y - 3 = 0$
42282	Write in Standard Form	x^2+y^2-8y=0	$x^{2} + y^{2} - 8 y = 0$
42283	Write in Standard Form	y^2-4y-4x^2+8x-4=0	$y^{2} - 4 y - 4 x^{2} + 8 x - 4 = 0$
42284	Write in Standard Form	y^2-4y-4x=0	$y^{2} - 4 y - 4 x = 0$
42285	Write in Standard Form	y^2-4y-8x+20=0	$y^{2} - 4 y - 8 x + 20 = 0$
42286	Write in Standard Form	x+8=2(y-5)^2	$x + 8 = 2 {(y - 5)}^{2}$
42287	Write in Standard Form	x=17(y-8)^2+9	$x = 17 {(y - 8)}^{2} + 9$
42288	Write in Standard Form	y^2+2y+8x-15=0	$y^{2} + 2 y + 8 x - 15 = 0$
42289	Write in Standard Form	y^2+4x-16y+48=0	$y^{2} + 4 x - 16 y + 48 = 0$
42290	Find the x and y Intercepts	x=-y^2-8y-22	$x = - y^{2} - 8 y - 22$
42291	Find the x and y Intercepts	x^2+y^2-2x-4y-31=0	$x^{2} + y^{2} - 2 x - 4 y - 31 = 0$
42292	Find the x and y Intercepts	x^2+y^2-4x=0	$x^{2} + y^{2} - 4 x = 0$
42293	Find the x and y Intercepts	2x^2+2y^2-16x+4y-16=0	$2 x^{2} + 2 y^{2} - 16 x + 4 y - 16 = 0$
42294	Identify the Sequence	1 , -1/2 , 1/4 , -1/8	$1$ , $- \frac{1}{2}$ , $\frac{1}{4}$ , $- \frac{1}{8}$
42295	Identify the Sequence	18 , 16 , 14 , 12	$18$ , $16$ , $14$ , $12$
42296	Write as a Single Logarithm	4^(x+4)=5^(2x+5)	$4^{x + 4} = 5^{2 x + 5}$
42297	Identify the Sequence	40 , -10 , 5/2 , -5/8 , 5/32	$40$ , $- 10$ , $\frac{5}{2}$ , $- \frac{5}{8}$ , $\frac{5}{32}$
42298	Identify the Sequence	400 , 100 , 25 , 6.25	$400$ , $100$ , $25$ , $6.25$
42299	Write as a Single Logarithm	natural log of 6+5 natural log of x+9 natural log of x^2+9	$\ln (6) + 5 \ln (x) + 9 \ln (x^{2} + 9)$
42300	Write as a Single Logarithm	2( log of 2x- log of y)-( log of 3+2 log of 5)	$2 (\log (2 x) - \log (y)) - (\log (3) + 2 \log (5))$