Mathway | Popular Problems

Popular Problems

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Rank	Topic	Problem	Formatted Problem
90001	Determine the Possible Number of Real Roots	6x^3-7x^2+2x+8	$6 x^{3} - 7 x^{2} + 2 x + 8$
90002	Solve by Addition/Elimination	3+2x-y=0 , -3-7y=10x	$3 + 2 x - y = 0$ , $- 3 - 7 y = 10 x$
90003	Solve by Addition/Elimination	4x^2-2y^2=-4 , 3x^2+5y^2=23	$4 x^{2} - 2 y^{2} = - 4$ , $3 x^{2} + 5 y^{2} = 23$
90004	Determine the Possible Number of Real Roots	7x^5-33x^4-4x^2+3x+52	$7 x^{5} - 33 x^{4} - 4 x^{2} + 3 x + 52$
90005	Solve for y	-18-5y>=52	$- 18 - 5 y \geq 52$
90006	Determine the Possible Number of Real Roots	x^3-10x^2-13x+22	$x^{3} - 10 x^{2} - 13 x + 22$
90007	Solve by Addition/Elimination	2x+3y=2 , 4x+6y=4	$2 x + 3 y = 2$ , $4 x + 6 y = 4$
90008	Solve by Addition/Elimination	2x^2-4y^2=-8 , 5x^2+3y^2=32	$2 x^{2} - 4 y^{2} = - 8$ , $5 x^{2} + 3 y^{2} = 32$
90009	Solve by Addition/Elimination	2x^2-3y^2=-19 , 3x^2+2y^2=30	$2 x^{2} - 3 y^{2} = - 19$ , $3 x^{2} + 2 y^{2} = 30$
90010	Determine the Possible Number of Real Roots	x^4+2x^3-3x^2-4x+20	$x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 20$
90011	Solve by Addition/Elimination	2x-2y=-8 , x+2y=-1	$2 x - 2 y = - 8$ , $x + 2 y = - 1$
90012	Determine the Possible Number of Real Roots	x^4+5x^3+5x^2-5x-6	$x^{4} + 5 x^{3} + 5 x^{2} - 5 x - 6$
90013	Solve by Addition/Elimination	5x+6y=1 , 10x+12y=2	$5 x + 6 y = 1$ , $10 x + 12 y = 2$
90014	Determine the Possible Number of Real Roots	x^4-7x^3+3x^2+63x-108	$x^{4} - 7 x^{3} + 3 x^{2} + 63 x - 108$
90015	Solve by Addition/Elimination	8x-6y=-20 , -16x+7y=30	$8 x - 6 y = - 20$ , $- 16 x + 7 y = 30$
90016	Find the Maximum/Minimum Value	f(x)=8x^2-8x	$f (x) = 8 x^{2} - 8 x$
90017	Find the Maximum/Minimum Value	h(t)=48t-16t^2	$h (t) = 48 t - 16 t^{2}$
90018	Find the Distance Between Two Points	(1,0) , (4,4)	$(1, 0)$ , $(4, 4)$
90019	Find the Concavity	natural log of x^2+9	$\ln (x^{2} + 9)$
90020	Find the Distance Between Two Points	(-4,-4) , (4,4)	$(- 4, - 4) (4, 4)$
90021	Find the Concavity	natural log of x^4+27	$\ln (x^{4} + 27)$
90022	Find the Distance Between Two Points	(4,1) , (9,1)	$(4, 1)$ , $(9, 1)$
90023	Find the Concavity	x^4-2x^3	$x^{4} - 2 x^{3}$
90024	Solve by Substitution	x^2+y^2=25 , y=2x-5	$x^{2} + y^{2} = 25$ , $y = 2 x - 5$
90025	Solve Using the Quadratic Formula	x^2+10x+12=36	$x^{2} + 10 x + 12 = 36$
90026	Find the Average Rate of Change	g(x)=4-x^2 , a=-1 , b=5	$g (x) = 4 - x^{2}$ , $a = - 1$ , $b = 5$
90027	Find the Average Rate of Change	y=3x+4 , (2,3)	$y = 3 x + 4$ , $(2, 3)$
90028	Find the Average Rate of Change	y=3x-5 , (0,1) , (3,-9)	$y = 3 x - 5$ , $(0, 1)$ , $(3, - 9)$
90029	Find the Average Rate of Change	y=9-56x , (0,0) , (-1,-3)	$y = 9 - 56 x$ , $(0, 0)$ , $(- 1, - 3)$
90030	Find the Maximum/Minimum Value	f(x)=-2x^2+4x-9	$f (x) = - 2 x^{2} + 4 x - 9$
90031	Find the Average Rate of Change	y-2=3x , (0,3) , (-3,0)	$y - 2 = 3 x$ , $(0, 3)$ , $(- 3, 0)$
90032	Find the Maximum/Minimum Value	f(x)=3x^2-30x+77	$f (x) = 3 x^{2} - 30 x + 77$
90033	Find the Average Rate of Change	y-2=3x , (1.1,2) , (2.3,5)	$y - 2 = 3 x$ , $(1.1, 2)$ , $(2.3, 5)$
90034	Evaluate	(5+4i)/(6+8i)	$\frac{5 + 4 i}{6 + 8 i}$
90035	Find the Degree	d(x)=x+pi	$d (x) = x + π$
90036	Find the Vertex	r(x)=4x^2+8x+9	$r (x) = 4 x^{2} + 8 x + 9$
90037	Find the Degree	f(x)=2/3-1/2x	$f (x) = \frac{2}{3} - \frac{1}{2} x$
90038	Find the Vertex	p(x)=x^2-8x+7	$p (x) = x^{2} - 8 x + 7$
90039	Find the Degree	f(x)=(-2+1)^2(x-3)^2(x+1)	$f (x) = {(- 2 + 1)}^{2} {(x - 3)}^{2} (x + 1)$
90040	Find the Vertex	f(x)=-3x^2	$f (x) = - 3 x^{2}$
90041	Find the Vertex	f(x)=-3x^2-12x+3	$f (x) = - 3 x^{2} - 12 x + 3$
90042	Find the Degree	f(x)=(7-x^4)/9	$f (x) = \frac{7 - x^{4}}{9}$
90043	Find the Degree	f(x)=(x^2-4)/(x^2)	$f (x) = \frac{x^{2} - 4}{x^{2}}$
90044	Find the Vertex	f(x)=4x^2-8x+2	$f (x) = 4 x^{2} - 8 x + 2$
90045	Find the Degree	f(x)=(x^2-4)/(x^6)	$f (x) = \frac{x^{2} - 4}{x^{6}}$
90046	Graph	y+3=-2/3*(x-4)	$y + 3 = - \frac{2}{3} \cdot (x - 4)$
90047	Find the Degree	f(x)=(x^5-9)/(x^2)	$f (x) = \frac{x^{5} - 9}{x^{2}}$
90048	Find the Degree	f(x)=(x+4)(x-1)^7	$f (x) = (x + 4) {(x - 1)}^{7}$
90049	Find the Vertex	d(t)=-16t^2+32t+56	$d (t) = - 16 t^{2} + 32 t + 56$
90050	Solve for x	(x-8)(x-8)=0	$(x - 8) (x - 8) = 0$
90051	Simplify	square root of 7y^6z	$\sqrt{7 y^{6} z}$
90052	Find the Degree	f(x) = square root of x( square root of x-6)	$f (x) = \sqrt{x} (\sqrt{x} - 6)$
90053	Find the Vertex	f(x)=-x^2+4x-1	$f (x) = - x^{2} + 4 x - 1$
90054	Find the Vertex	f(x)=x^2+4x+9	$f (x) = x^{2} + 4 x + 9$
90055	Simplify	square root of -8x	$\sqrt{- 8 x}$
90056	Find the Degree	f(x)=2x(x-2)^2(x+1)^2	$f (x) = 2 x {(x - 2)}^{2} {(x + 1)}^{2}$
90057	Find the Center and Radius	x^2+y^2+16x+6y+9=0	$x^{2} + y^{2} + 16 x + 6 y + 9 = 0$
90058	Find the Vertex	f(x)=x^2+10x+26	$f (x) = x^{2} + 10 x + 26$
90059	Find the Degree	f(x)=2x+x^4	$f (x) = 2 x + x^{4}$
90060	Find the Vertex	f(x)=x^2+10x+27	$f (x) = x^{2} + 10 x + 27$
90061	Find the Degree	f(x)=3x+7x^4	$f (x) = 3 x + 7 x^{4}$
90062	Find the Vertex	f(x)=x^2-10x+16	$f (x) = x^{2} - 10 x + 16$
90063	Find the Degree	f(x)=3x+x^3	$f (x) = 3 x + x^{3}$
90064	Solve by Factoring	square root of 12-5x=5x	$\sqrt{12 - 5 x} = 5 x$
90065	Find the Vertex	f(x)=x^2+8x+14	$f (x) = x^{2} + 8 x + 14$
90066	Find the Degree	f(x)=-5x^4-9x^3-5	$f (x) = - 5 x^{4} - 9 x^{3} - 5$
90067	Find the Vertex	f(x)=x^2+8x+21	$f (x) = x^{2} + 8 x + 21$
90068	Find the Degree	f(x)=5x+x^4	$f (x) = 5 x + x^{4}$
90069	Divide	(2x^3-3x^2+4x-7)/(x^2+3)	$\frac{2 x^{3} - 3 x^{2} + 4 x - 7}{x^{2} + 3}$
90070	Find the Degree	f(x)=-8+3x	$f (x) = - 8 + 3 x$
90071	Factor	25a^2-100	$25 a^{2} - 100$
90072	Find the Vertex	f(x)=x^2-2x-6	$f (x) = x^{2} - 2 x - 6$
90073	Find the Vertex	f(x)=x^2-3x+2	$f (x) = x^{2} - 3 x + 2$
90074	Find the Degree	f(x)=-x^2(x+9)^3(x^2-1)	$f (x) = - x^{2} {(x + 9)}^{3} (x^{2} - 1)$
90075	Find the Degree	f(x)=x^3(x-2)(x+1)^3	$f (x) = x^{3} (x - 2) {(x + 1)}^{3}$
90076	Solve Using the Quadratic Formula	4x^2-225=0	$4 x^{2} - 225 = 0$
90077	Find the Degree	g(x)=(6-x^6)/5	$g (x) = \frac{6 - x^{6}}{5}$
90078	Find the Degree	g(x)=(x-5)^2+2x^3	$g (x) = {(x - 5)}^{2} + 2 x^{3}$
90079	Find the Degree	g(x)=2(x-1)^2(x^2+2)	$g (x) = 2 {(x - 1)}^{2} (x^{2} + 2)$
90080	Find the Vertex	f(x)=x^2-7	$f (x) = x^{2} - 7$
90081	Find the Degree	g(x)=2(x-1)^2(x^2+3)	$g (x) = 2 {(x - 1)}^{2} (x^{2} + 3)$
90082	Find the Vertex	f(x)=2x^2+8x+2	$f (x) = 2 x^{2} + 8 x + 2$
90083	Find the Degree	G(x)=2(x-1)^2(x^2+5)	$G (x) = 2 {(x - 1)}^{2} (x^{2} + 5)$
90084	Find the Vertex	f(x)=-2x^2+8x-10	$f (x) = - 2 x^{2} + 8 x - 10$
90085	Find the Degree	g(x)=-6x-4	$g (x) = - 6 x - 4$
90086	Find the Vertex	f(x)=2x^2-3x+4	$f (x) = 2 x^{2} - 3 x + 4$
90087	Find the Range	(x+1)^2+(y-2)^2=16	${(x + 1)}^{2} + {(y - 2)}^{2} = 16$
90088	Find the Vertex	f(x)=2x^2-3x+5	$f (x) = 2 x^{2} - 3 x + 5$
90089	Find the Range	(x+1)^2+(y-2)^2=36	${(x + 1)}^{2} + {(y - 2)}^{2} = 36$
90090	Find the Vertex	f(x)=2x^2-4x-1	$f (x) = 2 x^{2} - 4 x - 1$
90091	Find the Vertex	x^2	$x^{2}$
90092	Find the Vertex	x^2+2x-24	$x^{2} + 2 x - 24$
90093	Find the Range	(x+3)^2+(y+5)^2=25	${(x + 3)}^{2} + {(y + 5)}^{2} = 25$
90094	Find the Range	(x+3)^2+(y-4)^2=36	${(x + 3)}^{2} + {(y - 4)}^{2} = 36$
90095	Find the Range	(x+3)^2+(y-6)^2=9	${(x + 3)}^{2} + {(y - 6)}^{2} = 9$
90096	Find the Roots (Zeros)	f(x)=-3	$f (x) = - 3$
90097	Find the Range	(x+4)^2+(y-2)^2=16	${(x + 4)}^{2} + {(y - 2)}^{2} = 16$
90098	Find the Properties	P(x)=-750x^2+15000x	$P (x) = - 750 x^{2} + 15000 x$
90099	Find the Range	(x+4)^2+(y-3)^2=9	${(x + 4)}^{2} + {(y - 3)}^{2} = 9$
90100	Find the Range	(x+4)^2+(y-5)^2=25	${(x + 4)}^{2} + {(y - 5)}^{2} = 25$