Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
218001	Solve for b	6^(b-7)=36	$6^{b - 7} = 36$
218002	Simplify	(x^2-9)/(6x^2+x-1)(2x^2+5x+2)/(x^2+4x+3)(x^2-x-2)/(x^2-3x)	$\frac{x^{2} - 9}{6 x^{2} + x - 1} \cdot \frac{2 x^{2} + 5 x + 2}{x^{2} + 4 x + 3} \cdot \frac{x^{2} - x - 2}{x^{2} - 3 x}$
218003	Solve the Rational Equation for x	x-3 = square root of 30-2x	$x - 3 = \sqrt{30 - 2 x}$
218004	Solve for x	(1/3x-11)^(1/2)=5	${(\frac{1}{3} x - 11)}^{\frac{1}{2}} = 5$
218005	Multiply	-6(3i)(-2i)	$- 6 (3 i) (- 2 i)$
218006	Simplify	(21d^18e^5)/(7d^11e^3)	$\frac{21 d^{18} e^{5}}{7 d^{11} e^{3}}$
218007	Divide Using Long Polynomial Division	(7n^4-68n^3+46n^2-7n-18)÷(n-9)	$(7 n^{4} - 68 n^{3} + 46 n^{2} - 7 n - 18) \div (n - 9)$
218008	Simplify the Radical Expression	(3^-8*7^3)^-2	${(3^{- 8} \cdot 7^{3})}^{- 2}$
218009	Simplify	simplify: (9^4)/(9^24)	simplify: $\frac{9^{4}}{9^{24}}$
218010	Graph	x+y<=4 and x>=3	$x + y \leq 4$ and $x \geq 3$
218011	Evaluate	(-(q^4)/5)^-3	${(- \frac{q^{4}}{5})}^{- 3}$
218012	Solve for B	cot(theta)=A/B	$\cot (θ) = \frac{A}{B}$
218013	Solve for y	square root of 6y+5 = square root of 2y+10	$\sqrt{6 y + 5} = \sqrt{2 y + 10}$
218014	Graph	y=-x if x<2; x-6 if x>=2	$y = {\begin{cases} - x & x < 2 \\ x - 6 & x \geq 2 \end{cases}$
218015	Solve for x	3x-11+4x-7+44=180	$3 x - 11 + 4 x - 7 + 44 = 180$
218016	Solve for d	t = square root of d/16	$t = \sqrt{\frac{d}{16}}$
218017	Convert to Interval Notation	x<-9 or x>-6	$x < - 9$ or $x > - 6$
218018	Multiply	(8x+64)/(x-4)*(x^2-49)/(x^2+x-56)	$\frac{8 x + 64}{x - 4} \cdot \frac{x^{2} - 49}{x^{2} + x - 56}$
218019	Graph	table[[x,y],[-1,-4],[0,-3],[1,-2]]	$\begin{array}{c} x & y \\ - 1 & - 4 \\ 0 & - 3 \\ 1 & - 2 \end{array}$
218020	Simplify	((6^4)/(3^2))^3	${(\frac{6^{4}}{3^{2}})}^{3}$
218021	Divide Using Synthetic Division	Use synthetic division to find the result when 4x^3+3x^2-10x-9 is divided by x+1	Use synthetic division to find the result when $4 x^{3} + 3 x^{2} - 10 x - 9$ is divided by $x + 1$
218022	Solve for x	4(3-x)+6x=x+12-3x	$4 (3 - x) + 6 x = x + 12 - 3 x$
218023	Write the Fraction in Simplest Form	limit as x approaches 0 of (e^(2x)-1)/(e^x-1)	$lim_{x \to 0} \frac{e^{2 x} - 1}{e^{x} - 1}$
218024	Find the Roots (Zeros)	y=x^2-2 square root of 2x+2	$y = x^{2} - 2 \sqrt{2} x + 2$
218025	Factor	6a^(2x)-24b^2	$6 a^{2 x} - 24 b^{2}$
218026	Evaluate	((3m^-2n)^-3)/(6mn^-2)	$\frac{{(3 m^{- 2} n)}^{- 3}}{6 m n^{- 2}}$
218027	Find the Product	2m^2*2m^3	$2 m^{2} \cdot 2 m^{3}$
218028	Solve the Inequality for x	3(x-5)+x<13	$3 (x - 5) + x < 13$
218029	Rationalize the Denominator	-1/( cube root of 2m^2n)	$- \frac{1}{\sqrt[3]{2 m^{2} n}}$
218030	Solve for x	4x^2-8x+4=1	$4 x^{2} - 8 x + 4 = 1$
218031	Simplify	(cot(x)^2)/(1+cot(x)^2)	$\frac{\cot^{2} (x)}{1 + \cot^{2} (x)}$
218032	Find the Product	-2/3n^2(-9n^2+3n+6)	$- \frac{2}{3} n^{2} (- 9 n^{2} + 3 n + 6)$
218033	Simplify the Radical Expression	((2^4)/(3^4))^(1/8)	${(\frac{2^{4}}{3^{4}})}^{\frac{1}{8}}$
218034	Simplify the Radical Expression	((3q^(5/2)r^(1/4))/(6^(1/2)))^2	${(\frac{3 q^{\frac{5}{2}} r^{\frac{1}{4}}}{6^{\frac{1}{2}}})}^{2}$
218035	Find the Domain and Range	y=4+ square root of x+6	$y = 4 + \sqrt{x + 6}$
218036	Simplify	(3 square root of 20)/( square root of 45)	$\frac{3 \sqrt{20}}{\sqrt{45}}$
218037	Solve for c	c^3+27=0	$c^{3} + 27 = 0$
218038	Simplify	2y*3x^-1y^4	$2 y \cdot 3 x^{- 1} y^{4}$
218039	Find the Midpoint	What is the midpoint of the points (2,4) and (-5,5) ?	What is the midpoint of the points $(2, 4)$ and $(- 5, 5)$ ?
218040	Factor	5ax-2ay-3bz+2by+3az-5bx	$5 a x - 2 a y - 3 b z + 2 b y + 3 a z - 5 b x$
218041	Graph	P(x)=x^4-3x^2+x-8	$P (x) = x^{4} - 3 x^{2} + x - 8$
218042	Solve for x	log base 9 of x+6+ log base 9 of x+4=1/2	$\log_{9} (x + 6) + \log_{9} (x + 4) = \frac{1}{2}$
218043	Factor	xz(x+z)+xy(x-y)-yz(y+z)	$x z (x + z) + x y (x - y) - y z (y + z)$
218044	Solve for h	h^2+7h+10=0	$h^{2} + 7 h + 10 = 0$
218045	Simplify	e^x*6e^(3x-1)	$e^{x} \cdot 6 e^{3 x - 1}$
218046	Simplify	10/( square root of 3x^5)	$\frac{10}{\sqrt{3 x^{5}}}$
218047	Evaluate	1/3*5/6-2/9	$\frac{1}{3} \cdot \frac{5}{6} - \frac{2}{9}$
218048	Solve for b	10+5b^2=200	$10 + 5 b^{2} = 200$
218049	Solve the Inequality for x	(x-\|5x+2\|)/(2x+\|5x+2\|)>x	$\frac{x - \| 5 x + 2 \|}{2 x + \| 5 x + 2 \|} > x$
218050	Solve for x	x^2+2x-8<=0	$x^{2} + 2 x - 8 \leq 0$
218051	Simplify	( square root of 15)/(2 square root of 4)	$\frac{\sqrt{15}}{2 \sqrt{4}}$
218052	Simplify	-36114/9	$- 36 \cdot 11 \cdot \frac{4}{9}$
218053	Solve for x	2/5=x/3+1/3	$\frac{2}{5} = \frac{x}{3} + \frac{1}{3}$
218054	Convert to Radical Form	(64n^12)^(-1/6)	${(64 n^{12})}^{- \frac{1}{6}}$
218055	Solve the System of Inequalities	k-3<-7 or k+5>=8	$k - 3 < - 7$ or $k + 5 \geq 8$
218056	Simplify	-z^3 square root of 16z^3+3 square root of 36z^7	$- z^{3} \sqrt{16 z^{3}} + 3 \sqrt{36 z^{7}}$
218057	Simplify	(x^2)/(2 square root of x)	$\frac{x^{2}}{2 \sqrt{x}}$
218058	Simplify	-1/3 square root of -90	$- \frac{1}{3} \sqrt{- 90}$
218059	Divide Using Synthetic Division	Use synthetic division to find the result when 4x^4+9x^3-3x^2+2x+10 is divided by x+1	Use synthetic division to find the result when $4 x^{4} + 9 x^{3} - 3 x^{2} + 2 x + 10$ is divided by $x + 1$
218060	Simplify the Radical Expression	20x^6 cube root of -1/1000x^36	$20 x^{6} \sqrt[3]{\frac{- 1}{1000} x^{36}}$
218061	Simplify the Radical Expression	fourth root of (3a^2)/(8b^7)	$\sqrt[4]{\frac{3 a^{2}}{8 b^{7}}}$
218062	Simplify	(3a^-1b^-4)/(3ab)	$\frac{3 a^{- 1} b^{- 4}}{3 a b}$
218063	Find the Roots (Zeros)	f(x)=x^4-4x^3+2x^2+x+4	$f (x) = x^{4} - 4 x^{3} + 2 x^{2} + x + 4$
218064	Solve the Rational Equation for x	8/(3x-2)=2/(x-1)	$\frac{8}{3 x - 2} = \frac{2}{x - 1}$
218065	Graph	f(x)=-x(x+2)(x-2)(x+1)	$f (x) = - x (x + 2) (x - 2) (x + 1)$
218066	Solve for x	105=(x-2)(x)(x+2)	$105 = (x - 2) (x) (x + 2)$
218067	Graph the Intersection (and)	y<=-3x+1 y>=-1/4x+6	$y \leq - 3 x + 1$ $y \geq - \frac{1}{4} x + 6$
218068	Solve for x	3^x+3^(1+x)=36	$3^{x} + 3^{1 + x} = 36$
218069	Solve for x	12/(7-x)=x	$\frac{12}{7 - x} = x$
218070	Solve for x	(-3cos(x)-5sin(x))^2-16sin(x)^2=(18+15 square root of 3)/2	${(- 3 \cos (x) - 5 \sin (x))}^{2} - 16 \sin^{2} (x) = \frac{18 + 15 \sqrt{3}}{2}$
218071	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (8,-8) and has a slope of -1/4 ?	What is the equation of the line that passes through the point $(8, - 8)$ and has a slope of $- \frac{1}{4}$ ?
218072	Simplify	csc(theta)^2+cot(theta)^2-1	$\csc^{2} (θ) + \cot^{2} (θ) - 1$
218073	Simplify the Radical Expression	(b^-2)/(b^4)	$\frac{b^{- 2}}{b^{4}}$
218074	Simplify	(12x^3y^5)1/2	$(12 x^{3} y^{5}) \frac{1}{2}$
218075	Multiply	-4(rs^2)(-5r^4s)	$- 4 (r s^{2}) (- 5 r^{4} s)$
218076	Factor	(3x^2-12)/(8x^2-18x+4)	$\frac{3 x^{2} - 12}{8 x^{2} - 18 x + 4}$
218077	Find the Domain and Range	f(x)=5-3(x-1)	$f (x) = 5 - 3 (x - 1)$
218078	Solve for x	x2/3=4	$x \frac{2}{3} = 4$
218079	Solve by Completing the Square	x^2+bx+c=0	$x^{2} + b x + c = 0$
218080	Write in Exponential Form	2 square root of x^2	$2 \sqrt{x^{2}}$
218081	Evaluate	x^2+(y-2)^2=4	$x^{2} + {(y - 2)}^{2} = 4$
218082	Simplify	1/( square root of -5)	$\frac{1}{\sqrt{- 5}}$
218083	Solve for x	7 1/4x+x-2 11/12x+1 2/3x=5 3/5	$7 \frac{1}{4} x + x - 2 \frac{11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$
218084	Solve by Substitution	x-2y=3 and 4x-8y=12	$x - 2 y = 3$ and $4 x - 8 y = 12$
218085	Solve for m	(2m-1)/19=m/10	$\frac{2 m - 1}{19} = \frac{m}{10}$
218086	Simplify	(-4^-2y)^2	${(- 4^{- 2} y)}^{2}$
218087	Simplify	square root of -2x^2	$\sqrt{- 2 x^{2}}$
218088	Solve for x	a=(4x)/t-p	$a = \frac{4 x}{t} - p$
218089	Solve for x	0=x^3+x^2-9x-9	$0 = x^{3} + x^{2} - 9 x - 9$
218090	Write the Fraction in Simplest Form	((4x^-2j^3)^-3)/(3x^6j^-4)	$\frac{{(4 x^{- 2} j^{3})}^{- 3}}{3 x^{6} j^{- 4}}$
218091	Write in Standard Form	-2x+3=4y	$- 2 x + 3 = 4 y$
218092	Simplify	cube root of fourth root of y^11	$\sqrt[3]{\sqrt[4]{y^{11}}}$
218093	Subtract	(m^2+n^2)-(4m^2+7n^2)	$(m^{2} + n^{2}) - (4 m^{2} + 7 n^{2})$
218094	Solve for x	square root of 8-x=2x+d	$\sqrt{8 - x} = 2 x + d$
218095	Evaluate	sin(theta)(csc(theta)-sin(theta))	$\sin (θ) (\csc (θ) - \sin (θ))$
218096	Simplify	1/(cos(x))-(sin(x))/(cos(x))	$\frac{1}{\cos (x)} - \frac{\sin (x)}{\cos (x)}$
218097	Solve the Inequality for k	\|k-4\|>3	$\| k - 4 \| > 3$
218098	Find the Excluded Values	1-5/(x-2)=-20/(x^2-4)	$1 - \frac{5}{x - 2} = - \frac{20}{x^{2} - 4}$
218099	Divide	( cube root of 6)/( fourth root of 6)	$\frac{\sqrt[3]{6}}{\sqrt[4]{6}}$
218100	Find All Complex Solutions	z^4=-1	$z^{4} = - 1$