Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
180001	Graph	y=-x+2,x<=1; x+1,x>1	$y = {\begin{cases} - x + 2, x \leq 1 \\ x + 1, x > 1 \end{cases}$
180002	Graph Using a Table of Values	f(x)=-(1/2)^(-x)	$f (x) = - {(\frac{1}{2})}^{- x}$
180003	Solve for y	15-3yi=1/2x+2i	$15 - 3 y i = \frac{1}{2} x + 2 i$
180004	Simplify	(1/x)^2-1	${(\frac{1}{x})}^{2} - 1$
180005	Graph	y< square root of x+4	$y < \sqrt{x + 4}$
180006	Simplify	f(x) = square root of cube root of x^3* fourth root of x	$f (x) = \sqrt{\sqrt[3]{x^{3} \cdot \sqrt[4]{x}}}$
180007	Solve the Inequality for x	x^2<=8x-13	$x^{2} \leq 8 x - 13$
180008	Graph	f(x)=-5x if x<0; 5x if x>=0	$f (x) = {\begin{cases} - 5 x & x < 0 \\ 5 x & x \geq 0 \end{cases}$
180009	Graph	f(x)=x^4-3x^3+x-1	$f (x) = x^{4} - 3 x^{3} + x - 1$
180010	Simplify	-7/3	$\frac{- 7}{3}$
180011	Solve for x	(3x+6)/3=6	$\frac{3 x + 6}{3} = 6$
180012	Evaluate	4^x=32	$4^{x} = 32$
180013	Graph	(3,pi/6)	$(3, \frac{π}{6})$
180014	Find the Roots (Zeros)	f(x)=2x(x-3)(2-x)	$f (x) = 2 x (x - 3) (2 - x)$
180015	Solve the Absolute Value Inequality for v	\|v+5\|-6<-5	$\| v + 5 \| - 6 < - 5$
180016	Solve for x	12-7+4x=25	$12 - 7 + 4 x = 25$
180017	Evaluate	(y^3)^2	${(y^{3})}^{2}$
180018	Solve for x	2tx+n^3=4f	$2 t x + n^{3} = 4 f$
180019	Divide	(3x^2y^3-5a^2x^4)/(-3x^2)	$\frac{3 x^{2} y^{3} - 5 a^{2} x^{4}}{- 3 x^{2}}$
180020	Find the Holes in the Graph	f(x)=(3x^2+15x)/(x^2+7x+10)	$f (x) = \frac{3 x^{2} + 15 x}{x^{2} + 7 x + 10}$
180021	Find the x and y Intercepts	f(x)=x(5-x)(7-x)	$f (x) = x (5 - x) (7 - x)$
180022	Graph	Ax+By+C=0	$A x + B y + C = 0$
180023	Solve for a	(x^(2/3))^(3/2)=x^a	${(x^{\frac{2}{3}})}^{\frac{3}{2}} = x^{a}$
180024	Solve for x	(x+2)/(x+9)=8/x	$\frac{x + 2}{x + 9} = \frac{8}{x}$
180025	Simplify	6/(6^(1/4))	$\frac{6}{6^{\frac{1}{4}}}$
180026	Simplify	-4i*4i	$- 4 i \cdot 4 i$
180027	Solve for m	(a^3+27)=(a+3)(a^2+ma+9)	$(a^{3} + 27) = (a + 3) (a^{2} + m a + 9)$
180028	Simplify	(2x^5+y)^2	${(2 x^{5} + y)}^{2}$
180029	Solve for x	1349=8700(0.945)^(x-4)-551	$1349 = 8700 {(0.945)}^{x - 4} - 551$
180030	Simplify	(3x^2+y^3)^2	${(3 x^{2} + y^{3})}^{2}$
180031	Find the First Term	a_n=3n+4	$a_{n} = 3 n + 4$
180032	Evaluate	10--3	$10 - - 3$
180033	Describe the Transformation	g(x)=f(x)-1	$g (x) = f (x) - 1$
180034	Simplify	(6-7i)/(1-2i)	$\frac{6 - 7 i}{1 - 2 i}$
180035	Simplify	(x+1)/((x+1)^2+1)	$\frac{x + 1}{{(x + 1)}^{2} + 1}$
180036	Find the Holes in the Graph	f(x)=(2x+6)/(x^2+4x+3)	$f (x) = \frac{2 x + 6}{x^{2} + 4 x + 3}$
180037	Solve the Inequality for u	-3\|2-4u\|+5<-13	$- 3 \| 2 - 4 u \| + 5 < - 13$
180038	Combine Like Terms	-6(x+2)-2	$- 6 (x + 2) - 2$
180039	Factor by Grouping	a(x+1)+b(x+1)	$a (x + 1) + b (x + 1)$
180040	Evaluate	(-2+1)/2	$\frac{- 2 + 1}{2}$
180041	Solve for x	1/2(x+6)=1/2x-9	$\frac{1}{2} (x + 6) = \frac{1}{2} x - 9$
180042	Solve for x	x=x/a+b	$x = \frac{x}{a} + b$
180043	Simplify	2/( square root of 2)*( square root of 2)/( square root of 2)	$\frac{2}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$
180044	Solve for x	5\|x+3\|-4=8\|x+3\|-4	$5 \| x + 3 \| - 4 = 8 \| x + 3 \| - 4$
180045	Simplify	((8)(-7)(6))/((-4)(-2)(-3))	$\frac{(8) (- 7) (6)}{(- 4) (- 2) (- 3)}$
180046	Solve the Absolute Value Inequality for x	\|3x+4\|=x	$\| 3 x + 4 \| = x$
180047	Solve Using the Quadratic Formula	1/(x+1)-1/(x-1)=1	$\frac{1}{x + 1} - \frac{1}{x - 1} = 1$
180048	Find the Domain and Range	y=(x-5)/x	$y = \frac{x - 5}{x}$
180049	Solve for x	5(x-3)>=-2x	$5 (x - 3) \geq - 2 x$
180050	Solve Using the Quadratic Formula	0.20=(x^2)/(45-x)	$0.2 = \frac{x^{2}}{45 - x}$
180051	Simplify	(5x-10)/(x^2-36)*(4x+24)/(x^2+5x-14)	$\frac{5 x - 10}{x^{2} - 36} \cdot \frac{4 x + 24}{x^{2} + 5 x - 14}$
180052	Find the x and y Intercepts	y=2x^3+x^2-7x-6 ?	$y = 2 x^{3} + x^{2} - 7 x - 6$ ?
180053	Solve the Absolute Value Inequality for x	\|2x-1\|<3	$\| 2 x - 1 \| < 3$
180054	Solve for x	20+2(3x+10)=2x-3(3+x)	$20 + 2 (3 x + 10) = 2 x - 3 (3 + x)$
180055	Solve for x	8/x+15/(x^2)=-1	$\frac{8}{x} + \frac{15}{x^{2}} = - 1$
180056	Solve the System of Equations	y=-2x+4 7y=-14x+28	$y = - 2 x + 4$ $7 y = - 14 x + 28$
180057	Find the x and y Intercepts	y=-2x^4-2x^2-3x+6x^3+3/4	$y = - 2 x^{4} - 2 x^{2} - 3 x + 6 x^{3} + \frac{3}{4}$
180058	Find the x and y Intercepts	f(x)=-5+8x-2x^2	$f (x) = - 5 + 8 x - 2 x^{2}$
180059	Solve for x	-4/3(6-5/8x)=1/2(7/3x+18)	$- \frac{4}{3} (6 - \frac{5}{8} x) = \frac{1}{2} (\frac{7}{3} x + 18)$
180060	Simplify	1/(2 square root of 4)	$\frac{1}{2 \sqrt{4}}$
180061	Solve the System of Equations	y=2/3x+2 6x-4y=-10	$y = \frac{2}{3} x + 2$ $6 x - 4 y = - 10$
180062	Solve the Inequality for x	5x+2>3x+10	$5 x + 2 > 3 x + 10$
180063	Factor	(x^2-16)/(x-4)	$\frac{x^{2} - 16}{x - 4}$
180064	Find the Holes in the Graph	f(x)=(2x-14)/(x^2-5x+6)	$f (x) = \frac{2 x - 14}{x^{2} - 5 x + 6}$
180065	Solve the Absolute Value Inequality for x	\|2x-1\|+4=8	$\| 2 x - 1 \| + 4 = 8$
180066	Graph Using a Table of Values	f(x)=-x+2	$f (x) = - x + 2$
180067	Evaluate the Function	f(x)=1/3x for x=4	$f (x) = \frac{1}{3} x$ for $x = 4$
180068	Find the Function	f(x)=4-x	$f (x) = 4 - x$
180069	Factor	xy-2y	$x y - 2 y$
180070	Solve the System of Equations	y=6x y=4x	$y = 6 x$ $y = 4 x$
180071	Simplify	(2x^4+y)^2	${(2 x^{4} + y)}^{2}$
180072	Find the Product	(a+2b)^2	${(a + 2 b)}^{2}$
180073	Solve for x	151=235x-16x^2	$151 = 235 x - 16 x^{2}$
180074	Solve for t	-3/10t=1/2(1/5t-14)+1/10t	$- \frac{3}{10} t = \frac{1}{2} (\frac{1}{5} t - 14) + \frac{1}{10} t$
180075	Find g(f(x))	f(x)=x+4 g(x)=x+4	$f (x) = x + 4$ $g (x) = x + 4$
180076	Graph	g(x)=f(x+3)-2	$g (x) = f (x + 3) - 2$
180077	Simplify	(3n^2+14n)/(9n^2-64)+16/(9n^2-64)	$\frac{3 n^{2} + 14 n}{9 n^{2} - 64} + \frac{16}{9 n^{2} - 64}$
180078	Solve for y	x=3/5(y+z)	$x = \frac{3}{5} (y + z)$
180079	Solve the Absolute Value Inequality for x	-6\|8x-4\|=-72	$- 6 \| 8 x - 4 \| = - 72$
180080	Simplify	(3a+6)/(5a^2+7a-6)-5/(3a)	$\frac{3 a + 6}{5 a^{2} + 7 a - 6} - \frac{5}{3 a}$
180081	Solve for θ	3tan(theta)^3=tan(theta)	$3 \tan^{3} (θ) = \tan (θ)$
180082	Find the First Term	a_n=4(3)^(n-1)	$a_{n} = 4 {(3)}^{n - 1}$
180083	Write in Standard Form	(4a^3-3a-8)-(a-5)	$(4 a^{3} - 3 a - 8) - (a - 5)$
180084	Solve for θ	sec(theta)+ square root of 2=0	$\sec (θ) + \sqrt{2} = 0$
180085	Simplify	5/(x^2)-3/(6x^2+12x)	$\frac{5}{x^{2}} - \frac{3}{6 x^{2} + 12 x}$
180086	Find the Holes in the Graph	f(x)=(2x+8)/(x^2+6x+8)	$f (x) = \frac{2 x + 8}{x^{2} + 6 x + 8}$
180087	Simplify	( square root of x^3)	$(\sqrt{x^{3}})$
180088	Solve for x	square root of x^2-x-2=x-2	$\sqrt{x^{2} - x - 2} = x - 2$
180089	Solve the Inequality for x	x/(x-5)>0	$\frac{x}{x - 5} > 0$
180090	Write Using Positive Exponents	(36x^-4y^2z^0)/(5x^2y^-3z^-2)	$\frac{36 x^{- 4} y^{2} z^{0}}{5 x^{2} y^{- 3} z^{- 2}}$
180091	Solve the Inequality for p	20-2p>-2(p+2)+4p	$20 - 2 p > - 2 (p + 2) + 4 p$
180092	Evaluate	\|x\|=4	$\| x \| = 4$
180093	Solve the System of Equations	x-2y=11 x+5y=-17	$x - 2 y = 11$ $x + 5 y = - 17$
180094	Solve the Inequality for x	x^2-16x+55>0	$x^{2} - 16 x + 55 > 0$
180095	Solve for x	5x^2=-30x-65	$5 x^{2} = - 30 x - 65$
180096	Graph	x^2<=-4x	$x^{2} \leq - 4 x$
180097	Solve the Inequality for b	-4b-5>-25	$- 4 b - 5 > - 25$
180098	Simplify	(-15xz-4xy)+(20xy-9yz-16xz)	$(- 15 x z - 4 x y) + (20 x y - 9 y z - 16 x z)$
180099	Graph	y>-x+2 y<1/2x-4	$y > - x + 2$ $y < \frac{1}{2} x - 4$
180100	Evaluate the Function	f(0)=5	$f (0) = 5$