Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
41401	Find the Number of Possibilities	1-(6 permute 4)/(8 permute 6)	$1 - \frac{{}_{6}P_{4}}{{}_{8}P_{6}}$
41402	Convert to Interval Notation	x^3+5x^2-25x<=125	$x^{3} + 5 x^{2} - 25 x \leq 125$
41403	Identify the Conic	9x^2+4xy+5y^2-40=0	$9 x^{2} + 4 x y + 5 y^{2} - 40 = 0$
41404	Find the Roots (Zeros)	f(x)=8x^4-72x^3+144x^2	$f (x) = 8 x^{4} - 72 x^{3} + 144 x^{2}$
41405	Find the Roots (Zeros)	f(x)=x^2+2x-2	$f (x) = x^{2} + 2 x - 2$
41406	Find the Vertex	(y-2)^2=4(x+3)	${(y - 2)}^{2} = 4 (x + 3)$
41407	Find the Vertex	x^2+16x-2y+46=0	$x^{2} + 16 x - 2 y + 46 = 0$
41408	Find the Vertex	x^2+6x+3y-12=0	$x^{2} + 6 x + 3 y - 12 = 0$
41409	Find the Vertex	y^2=32x	$y^{2} = 32 x$
41410	Find the Quadrant of the Angle	90 degrees	$90 °$
41411	Solve for m	(m^2+3m-18)/(m^2+7m+12)-1/(m+3)=1	$\frac{m^{2} + 3 m - 18}{m^{2} + 7 m + 12} - \frac{1}{m + 3} = 1$
41412	Solve for b	\|5b-4\|=11	$\| 5 b - 4 \| = 11$
41413	Solve for b	(2pi)/b=8	$\frac{2 π}{b} = 8$
41414	Find the Center and Radius	4x^2+y^2+8x-5=0	$4 x^{2} + y^{2} + 8 x - 5 = 0$
41415	Find the Center and Radius	x^2+y^2+10x-14y+58=0	$x^{2} + y^{2} + 10 x - 14 y + 58 = 0$
41416	Find the Center and Radius	x^2+y^2-6y+1=0	$x^{2} + y^{2} - 6 y + 1 = 0$
41417	Find the Domain	square root of x^2-4x-5	$\sqrt{x^{2} - 4 x - 5}$
41418	Convert to a Simplified Fraction	square root of 13	$\sqrt{13}$
41419	Convert from Degrees to Radians	59 degrees	$59 °$
41420	Find the Domain and Range	x^2=3y	$x^{2} = 3 y$
41421	Find the Domain and Range	y=x^2-4x-5	$y = x^{2} - 4 x - 5$
41422	Write in Standard Form	4x^2+16y^2+8x+160y+340=0	$4 x^{2} + 16 y^{2} + 8 x + 160 y + 340 = 0$
41423	Write in Standard Form	3x^2+24x-2y^2-16y+4=0	$3 x^{2} + 24 x - 2 y^{2} - 16 y + 4 = 0$
41424	Write in Standard Form	-25x^2+y^2-100x-125=0	$- 25 x^{2} + y^{2} - 100 x - 125 = 0$
41425	Write in Standard Form	-16x^2+9y^2+64x-18y-199=0	$- 16 x^{2} + 9 y^{2} + 64 x - 18 y - 199 = 0$
41426	Write in Standard Form	16x^2+288y+36y^2=0	$16 x^{2} + 288 y + 36 y^{2} = 0$
41427	Write in Standard Form	10y^2-20x^2+60y+160x-255=0	$10 y^{2} - 20 x^{2} + 60 y + 160 x - 255 = 0$
41428	Write in Standard Form	-x^2+y^2-18x-14y-132=0	$- x^{2} + y^{2} - 18 x - 14 y - 132 = 0$
41429	Write in Standard Form	y^2+x+10y+26=0	$y^{2} + x + 10 y + 26 = 0$
41430	Write in Standard Form	x=20y^2-120y+60	$x = 20 y^{2} - 120 y + 60$
41431	Write in Standard Form	y^2-4y=4x	$y^{2} - 4 y = 4 x$
41432	Find the Domain and Range	f(x)=7	$f (x) = 7$
41433	Find the Asymptotes	f(x)=(x^2+x-6)/(x^3-1)	$f (x) = \frac{x^{2} + x - 6}{x^{3} - 1}$
41434	Find the x and y Intercepts	3x^2+3y^2-24x+6y-24=0	$3 x^{2} + 3 y^{2} - 24 x + 6 y - 24 = 0$
41435	Find the Inverse	5x-1	$5 x - 1$
41436	Convert to Interval Notation	(3x+5)/(x^2+2x-35)>=0	$\frac{3 x + 5}{x^{2} + 2 x - 35} \geq 0$
41437	Convert to Interval Notation	(x-1)/(x-3)<0	$\frac{x - 1}{x - 3} < 0$
41438	Find the Vertex	y^2-2x-10y+21=0	$y^{2} - 2 x - 10 y + 21 = 0$
41439	Find the Vertex	x^2+4x+6y-2=0	$x^{2} + 4 x + 6 y - 2 = 0$
41440	Find the Vertex	x^2+6x-2y+5=0	$x^{2} + 6 x - 2 y + 5 = 0$
41441	Find the Vertex	x^2-12y=0	$x^{2} - 12 y = 0$
41442	Find the Vertex	(y+2)^2=4(x-1)	${(y + 2)}^{2} = 4 (x - 1)$
41443	Find the Difference Quotient	f(x)=3x-6	$f (x) = 3 x - 6$
41444	Identify the Conic	y^2=3x	$y^{2} = 3 x$
41445	Find the Roots (Zeros)	f(x)=x^3+7x^2+7x-15	$f (x) = x^{3} + 7 x^{2} + 7 x - 15$
41446	Find the Perpendicular Line	y=3x-21 , (-7,0)	$y = 3 x - 21$ , $(- 7, 0)$
41447	Find the Roots (Zeros)	2x^4-5x^3-20x^2+115x-52	$2 x^{4} - 5 x^{3} - 20 x^{2} + 115 x - 52$
41448	Solve for p	(3p+12)/(p^2-7p+10)-3/(2p-4)=1/(p-2)	$\frac{3 p + 12}{p^{2} - 7 p + 10} - \frac{3}{2 p - 4} = \frac{1}{p - 2}$
41449	Find Three Ordered Pair Solutions	f(x)=3x-5	$f (x) = 3 x - 5$
41450	Find the Vertex	f(x)=x^2-2x+3	$f (x) = x^{2} - 2 x + 3$
41451	Find the Center and Radius	x^2+y^2-2x+8y-47=0	$x^{2} + y^{2} - 2 x + 8 y - 47 = 0$
41452	Find the Center and Radius	x^2+y^2+2x+8y-64=0	$x^{2} + y^{2} + 2 x + 8 y - 64 = 0$
41453	Find the Center and Radius	9x^2+9y^2+36x+72y=0	$9 x^{2} + 9 y^{2} + 36 x + 72 y = 0$
41454	Find the Center and Radius	9x^2+9y^2+36x-72y=0	$9 x^{2} + 9 y^{2} + 36 x - 72 y = 0$
41455	Find the Center and Radius	4x^2+4y^2-24x+48y=0	$4 x^{2} + 4 y^{2} - 24 x + 48 y = 0$
41456	Split Using Partial Fraction Decomposition	11/(x(1-x))	$\frac{11}{x (1 - x)}$
41457	Find All Complex Solutions	cos(theta)=-( square root of 3)/2	$\cos (θ) = - \frac{\sqrt{3}}{2}$
41458	Find the Tangent Given the Point	(2/9,( square root of 77)/9)	$(\frac{2}{9}, \frac{\sqrt{77}}{9})$
41459	Find the Value Using the Unit Circle	-(7pi)/6	$- \frac{7 π}{6}$
41460	Identify the Sequence	97 , 48 1/2 , 24 1/4 , 12 1/8	$97$ , $48 \frac{1}{2}$ , $24 \frac{1}{4}$ , $12 \frac{1}{8}$
41461	Find the Domain and Range	y=(x-3)^2-5	$y = {(x - 3)}^{2} - 5$
41462	Convert to a Simplified Fraction	square root of 15	$\sqrt{15}$
41463	Convert from Degrees to Radians	arctan(-( square root of 3)/3)	$\arctan (- \frac{\sqrt{3}}{3})$
41464	Convert from Degrees to Radians	119 degrees	$119 °$
41465	Find the Inverse	5x-6	$5 x - 6$
41466	Expand Using De Moivre's Theorem	(cos((3pi)/5)+isin((3pi)/5))^3	${(\cos (\frac{3 π}{5}) + i \sin (\frac{3 π}{5}))}^{3}$
41467	Find the Domain and Range	f(x)=3x-9	$f (x) = 3 x - 9$
41468	Write in Standard Form	y^2+2y+x^2-24x=14	$y^{2} + 2 y + x^{2} - 24 x = 14$
41469	Write in Standard Form	x^2-9y^2+2x-54y-80=0	$x^{2} - 9 y^{2} + 2 x - 54 y - 80 = 0$
41470	Find the Domain and Range	r(x)=e^(x-2)+2	$r (x) = e^{x - 2} + 2$
41471	Write in Standard Form	x^2+5y^2-8x-30y-39=0	$x^{2} + 5 y^{2} - 8 x - 30 y - 39 = 0$
41472	Write in Standard Form	x^2+y^2+10x-6y+30=0	$x^{2} + y^{2} + 10 x - 6 y + 30 = 0$
41473	Write in Standard Form	x^2+y^2-16=0	$x^{2} + y^{2} - 16 = 0$
41474	Write in Standard Form	-9x^2+y^2-72x-153=0	$- 9 x^{2} + y^{2} - 72 x - 153 = 0$
41475	Write in Standard Form	9x^2-4y^2-36x+8y-4=0	$9 x^{2} - 4 y^{2} - 36 x + 8 y - 4 = 0$
41476	Write in Standard Form	9x^2-18x+4y^2+8y=23	$9 x^{2} - 18 x + 4 y^{2} + 8 y = 23$
41477	Write in Standard Form	9x^2-4y^2-90x+32y-163=0	$9 x^{2} - 4 y^{2} - 90 x + 32 y - 163 = 0$
41478	Write in Standard Form	9x^2+25y^2-54x+150y+81=0	$9 x^{2} + 25 y^{2} - 54 x + 150 y + 81 = 0$
41479	Write in Standard Form	16x^2+25y^2-96x+50y-231=0	$16 x^{2} + 25 y^{2} - 96 x + 50 y - 231 = 0$
41480	Write in Standard Form	31x^2+10 square root of 3xy+21y^2-144=0	$31 x^{2} + 10 \sqrt{3 x y} + 21 y^{2} - 144 = 0$
41481	Write in Standard Form	4x^2+16y^2-48x+160y+480=0	$4 x^{2} + 16 y^{2} - 48 x + 160 y + 480 = 0$
41482	Write in Standard Form	4x^2+4y^2-20x-32y+81=0	$4 x^{2} + 4 y^{2} - 20 x - 32 y + 81 = 0$
41483	Write in Standard Form	4x^2+9y^2-8x-36y+4=0	$4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0$
41484	Write in Standard Form	4x^2-3y^2+8x+16=0	$4 x^{2} - 3 y^{2} + 8 x + 16 = 0$
41485	Find the x and y Intercepts	4x^2+4y^2-24x+8y-60=0	$4 x^{2} + 4 y^{2} - 24 x + 8 y - 60 = 0$
41486	Find the Asymptotes	r(x)=(4x-4)/(x+2)	$r (x) = \frac{4 x - 4}{x + 2}$
41487	Convert to Interval Notation	6^x<3^x	$6^{x} < 3^{x}$
41488	Convert to Interval Notation	(x^2+9x-22)/(x+4)>=0	$\frac{x^{2} + 9 x - 22}{x + 4} \geq 0$
41489	Factor over the Complex Numbers	-8i	$- 8 i$
41490	Verify the Identity	cos(theta)^4-sin(theta)^4=1-2sin(theta)^2	$\cos^{4} (θ) - \sin^{4} (θ) = 1 - 2 \sin^{2} (θ)$
41491	Convert to Trigonometric Form	( square root of 3+i)^6	${(\sqrt{3} + i)}^{6}$
41492	Find the Asymptotes	(2x^3+24x^2+35x-175)/(x^2+14x+45)	$\frac{2 x^{3} + 24 x^{2} + 35 x - 175}{x^{2} + 14 x + 45}$
41493	Convert to Logarithmic Form	Q^P=t	$Q^{P} = t$
41494	Find the Vertex	x^2+14x-2y+47=0	$x^{2} + 14 x - 2 y + 47 = 0$
41495	Find the Vertex	x^2+10x-2y+13=0	$x^{2} + 10 x - 2 y + 13 = 0$
41496	Find the Vertex	2y^2-15x-4y-28=0	$2 y^{2} - 15 x - 4 y - 28 = 0$
41497	Find the Vertex	x^2=40y	$x^{2} = 40 y$
41498	Find the Sum of the Infinite Geometric Series	1 , 1/6 , 1/36 , 1/216	$1$ , $\frac{1}{6}$ , $\frac{1}{36}$ , $\frac{1}{216}$
41499	Find the Domain	f(x) = square root of 1-x	$f (x) = \sqrt{1 - x}$
41500	Solve for t	t^(1/2)+3t^(1/4)+2=0	$t^{\frac{1}{2}} + 3 t^{\frac{1}{4}} + 2 = 0$