Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
234001	Find the Points of Intersection	8x+4y=12 y=-2x+3	$8 x + 4 y = 12$ $y = - 2 x + 3$
234002	Solve Using the Quadratic Formula	1/2x^2-1/4=3/16x	$\frac{1}{2} x^{2} - \frac{1}{4} = \frac{3}{16} x$
234003	Identify the Sequence	5 , 15 , 45 ; dots	$5$ , $15$ , $45$ ; dots
234004	Solve for x	(3x)/7-1=6+x/2	$\frac{3 x}{7} - 1 = 6 + \frac{x}{2}$
234005	Simplify	(x^-2y^3)/(x^3z^-1)	$\frac{x^{- 2} y^{3}}{x^{3} z^{- 1}}$
234006	Solve for t	V=(2pir)/t	$V = \frac{2 π r}{t}$
234007	Evaluate	(x^6)/(x^-1*x^7)	$\frac{x^{6}}{x^{- 1} \cdot x^{7}}$
234008	Evaluate	-3x+9-2x=-12-5x	$- 3 x + 9 - 2 x = - 12 - 5 x$
234009	Find the Product	(xy^-6)^2	${(x y^{- 6})}^{2}$
234010	Factor	x^2+18=9x	$x^{2} + 18 = 9 x$
234011	Simplify	(3-x)/(1/x)	$\frac{3 - x}{\frac{1}{x}}$
234012	Solve for x	3x(x-2)-(x-6)=23(x-3)	$3 x (x - 2) - (x - 6) = 23 (x - 3)$
234013	Find the Roots (Zeros)	-3x(x+4)(3x+2)(x+9)^2	$- 3 x (x + 4) (3 x + 2) {(x + 9)}^{2}$
234014	Solve for x	24=4(6b-2x)	$24 = 4 (6 b - 2 x)$
234015	Evaluate	(4xy^2)^-3	${(4 x y^{2})}^{- 3}$
234016	Divide Using Long Polynomial Division	Use the long division method to find the result when 4x^3+7x^2+7x+3 is divided by 4x+3	Use the long division method to find the result when $4 x^{3} + 7 x^{2} + 7 x + 3$ is divided by $4 x + 3$
234017	Evaluate	5/(2y)+1/(6y)-4/(3y)	$\frac{5}{2 y} + \frac{1}{6 y} - \frac{4}{3 y}$
234018	Solve for x	Solve x^2=75	Solve $x^{2} = 75$
234019	Evaluate Using the Given Value	Evaluate x+5 if x=2	Evaluate $x + 5$ if $x = 2$
234020	Evaluate	csc(arctan(-5/12))	$\csc (\arctan (- \frac{5}{12}))$
234021	Simplify	(x-1)/(x^2-4)+2/(x-2)	$\frac{x - 1}{x^{2} - 4} + \frac{2}{x - 2}$
234022	Graph	Graph the line x=3	Graph the line $x = 3$
234023	Simplify the Radical Expression	cube root of -12* cube root of -18	$\sqrt[3]{- 12} \cdot \sqrt[3]{- 18}$
234024	Divide Using Long Polynomial Division	Use the long division method to find the result when 4x^3+16x^2+7x-20 is divided by 2x+5	Use the long division method to find the result when $4 x^{3} + 16 x^{2} + 7 x - 20$ is divided by $2 x + 5$
234025	Divide	3 3/41/8	$3 \frac{3}{4} \frac{1}{8}$
234026	Solve the System of Equations	3x+4y=-12 y=-3/2x	$3 x + 4 y = - 12$ $y = - \frac{3}{2} x$
234027	Graph	f(x)=10.5x if 0<=x<=2; 21+4(x-2) if x>2	$f (x) = {\begin{cases} 10.5 x & 0 \leq x \leq 2 \\ 21 + 4 (x - 2) & x > 2 \end{cases}$
234028	Solve the Rational Equation for x	fourth root of 3-8x^2=2x	$\sqrt[4]{3 - 8 x^{2}} = 2 x$
234029	Solve for w	19w-4w+23=8w-19	$19 w - 4 w + 23 = 8 w - 19$
234030	Subtract	(y^2)/(y^2+2y)-4/(y^2+2y)	$\frac{y^{2}}{y^{2} + 2 y} - \frac{4}{y^{2} + 2 y}$
234031	Simplify	1/((5x)^(-3/4))	$\frac{1}{{(5 x)}^{- \frac{3}{4}}}$
234032	Describe the Transformation	f(x)=-2^x , g(x)=5-2^x	$f (x) = - 2^{x}$ , $g (x) = 5 - 2^{x}$
234033	Solve the Inequality for x	sin(x)<1/2	$\sin (x) < \frac{1}{2}$
234034	Find the Degree, Leading Term, and Leading Coefficient	f(x)=1/2x^2+8-5x^3-19x	$f (x) = \frac{1}{2} x^{2} + 8 - 5 x^{3} - 19 x$
234035	Solve the System of Equations	x-2y=6 and 3x-6y=18	$x - 2 y = 6$ and $3 x - 6 y = 18$
234036	Write in Standard Form	(3x^2+2x-3)(x^2-x-1)	$(3 x^{2} + 2 x - 3) (x^{2} - x - 1)$
234037	Graph	3x+4y=-12 y=-3/2x	$3 x + 4 y = - 12$ $y = - \frac{3}{2} x$
234038	Multiply	square root of x-1* square root of x-1	$\sqrt{x - 1} \cdot \sqrt{x - 1}$
234039	Simplify	(2 square root of -3)/( square root of 2)	$\frac{2 \sqrt{- 3}}{\sqrt{2}}$
234040	Solve by Addition/Elimination	2/3x+3/4y=7/12 1/2x-2y=3	$\frac{2}{3} x + \frac{3}{4} y = \frac{7}{12}$ $\frac{1}{2} x - 2 y = 3$
234041	Solve for m	\|4m-4\|<36	$\| 4 m - 4 \| < 36$
234042	Graph	55>=5x+5>-25	$55 \geq 5 x + 5 > - 25$
234043	Find the Inverse	f(x)=8((x^(1/3))/9+4)	$f (x) = 8 (\frac{x^{\frac{1}{3}}}{9} + 4)$
234044	Solve the System of Equations	x-2y=2 y=-1/2x+5	$x - 2 y = 2$ $y = - \frac{1}{2} x + 5$
234045	Solve for p	e=4s+2p	$e = 4 s + 2 p$
234046	Solve for x	4x+8+27=6x	$4 x + 8 + 27 = 6 x$
234047	Find the Inverse	5^(x+4)=y	$5^{x + 4} = y$
234048	Simplify the Radical Expression	square root of 8+ square root of 2	$\sqrt{8} + \sqrt{2}$
234049	Solve the System of Equations	y=5/2x+9 y=1/2x+1	$y = \frac{5}{2} x + 9$ $y = \frac{1}{2} x + 1$
234050	Describe the Transformation	f(x)=- square root of 3x-5+5	$f (x) = - \sqrt{3 x - 5} + 5$
234051	Write in Exponential Form	fourth root of 3^6	$\sqrt[4]{3^{6}}$
234052	Simplify	(1+cos(2x))^2	${(1 + \cos (2 x))}^{2}$
234053	Simplify	(x^4)^-2(x^9)^(1/3)	${(x^{4})}^{- 2} {(x^{9})}^{\frac{1}{3}}$
234054	Simplify	3/5 square root of -100/9	$\frac{3}{5} \sqrt{- \frac{100}{9}}$
234055	Simplify	(4-2 square root of 3)	$(4 - 2 \sqrt{3})$
234056	Find the Inverse	f^-1(x)=1/(f(x))	$f^{- 1} (x) = \frac{1}{f (x)}$
234057	Solve for x	log base (x+1) of 8=3	$\log_{(x + 1)} (8) = 3$
234058	Find the Product	f(f^2+2f+25)	$f (f^{2} + 2 f + 25)$
234059	Solve for v	2/5*4^(5v)-8=4	$\frac{2}{5} \cdot 4^{5 v} - 8 = 4$
234060	Simplify	x/(2-x)+(3x+5)/(x^2-4)	$\frac{x}{2 - x} + \frac{3 x + 5}{x^{2} - 4}$
234061	Solve Using the Quadratic Formula	8x^3-1	$8 x^{3} - 1$
234062	Factor	x^(4/3)-10x^(2/3)+9=0	$x^{\frac{4}{3}} - 10 x^{\frac{2}{3}} + 9 = 0$
234063	Simplify	square root of x^2y^4z^8	$\sqrt{x^{2} y^{4} z^{8}}$
234064	Solve for x	9/(3x-15)=3/12	$\frac{9}{3 x - 15} = \frac{3}{12}$
234065	Evaluate	i^29i^27i^30	$i^{29} \cdot i^{27} \cdot i^{30}$
234066	Simplify	(5x+5)/(x-2)*(x^2-4x+4)/(x^2-1)	$\frac{5 x + 5}{x - 2} \cdot \frac{x^{2} - 4 x + 4}{x^{2} - 1}$
234067	Simplify	(8^2c^-1d^-6)/5	$\frac{8^{2} c^{- 1} d^{- 6}}{5}$
234068	Find the Holes in the Graph	(x-1)/(2x^2-22x+20)	$\frac{x - 1}{2 x^{2} - 22 x + 20}$
234069	Solve the Rational Equation for x	x^(4/3)=16	$x^{\frac{4}{3}} = 16$
234070	Multiply	x^2(10x^2+x)	$x^{2} (10 x^{2} + x)$
234071	Simplify	(x^(5/8))(x^(1/2))	$(x^{\frac{5}{8}}) (x^{\frac{1}{2}})$
234072	Simplify	(x^3+x^2y+xy^2)/((x^2)/y-(y^2)/x)	$\frac{x^{3} + x^{2} y + x y^{2}}{\frac{x^{2}}{y} - \frac{y^{2}}{x}}$
234073	Solve for x	2/(x^2-3x)=1/(x^2-3x)-1/(x-3)	$\frac{2}{x^{2} - 3 x} = \frac{1}{x^{2} - 3 x} - \frac{1}{x - 3}$
234074	Write in Standard Form	(2x^2-9x-9)(2x^2-x+1)	$(2 x^{2} - 9 x - 9) (2 x^{2} - x + 1)$
234075	Find the Degree, Leading Term, and Leading Coefficient	-y^3+3y-3y^2+2	$- y^{3} + 3 y - 3 y^{2} + 2$
234076	Solve by Factoring	3x^3+27x=3x(x^2+9)	$3 x^{3} + 27 x = 3 x (x^{2} + 9)$
234077	Graph	24+6y<=5x	$24 + 6 y \leq 5 x$
234078	Simplify	cube root of 27* cube root of 6	$\sqrt[3]{27} \cdot \sqrt[3]{6}$
234079	Solve for x	x+yi=(a+bi)^2	$x + y i = {(a + b i)}^{2}$
234080	Solve for b	N=b root of (1+2^b)/(1+2^(-b))	$N = \sqrt[b]{\frac{1 + 2^{b}}{1 + 2^{- b}}}$
234081	Simplify	(-2ab)^3(-a^2b)	${(- 2 a b)}^{3} (- a^{2} b)$
234082	Find the Inverse	10x^(1/3)-6	$10 x^{\frac{1}{3}} - 6$
234083	Find the Exact Value	csc(pi/2)-cos(pi/2)	$\csc (\frac{π}{2}) - \cos (\frac{π}{2})$
234084	Find the Roots (Zeros)	(x^2+1)(x^3+2x)(x^2-64)=0	$(x^{2} + 1) (x^{3} + 2 x) (x^{2} - 64) = 0$
234085	Simplify the Radical Expression	( square root of 27x^5)/( square root of 3x^3)	$\frac{\sqrt{27 x^{5}}}{\sqrt{3 x^{3}}}$
234086	Simplify	square root of 45x^2+9x^3+2x square root of 20+4x+ square root of 5x^2+x^3	$\sqrt{45 x^{2} + 9 x^{3}} + 2 x \sqrt{20 + 4 x} + \sqrt{5 x^{2} + x^{3}}$
234087	Simplify	(11y+13)/(3y-3)+(15y+17)/(4-4y)	$\frac{(11 y + 13)}{3 y - 3} + \frac{(15 y + 17)}{4 - 4 y}$
234088	Solve for x	-(-x+1)=x-1	$- (- x + 1) = x - 1$
234089	Solve by Addition/Elimination	-9x+y=10 10x-y=-9	$- 9 x + y = 10$ $10 x - y = - 9$
234090	Solve the Inequality for x	y>2x+3	$y > 2 x + 3$
234091	Solve for f	Solve the following equation: 3/5f=2 1/5	Solve the following equation: $\frac{3}{5} f = 2 \frac{1}{5}$
234092	Solve Using the Quadratic Formula	7-8z^2=6z+16	$7 - 8 z^{2} = 6 z + 16$
234093	Simplify	4k^2(6k^2+9kq-5q^2)	$4 k^{2} (6 k^{2} + 9 k q - 5 q^{2})$
234094	Write the Fraction in Simplest Form	(-2/5)^2	${(- \frac{2}{5})}^{2}$
234095	Divide Using Long Polynomial Division	(9x^2+3x^3-14)÷(x^2+x-3)	$(9 x^{2} + 3 x^{3} - 14) \div (x^{2} + x - 3)$
234096	Graph	(x-3)^2-2=x+1	${(x - 3)}^{2} - 2 = x + 1$
234097	Simplify	3x^-2y^4*4x^-2	$3 x^{- 2} y^{4} \cdot 4 x^{- 2}$
234098	Simplify the Radical Expression	1/(3- square root of 11)	$\frac{1}{3 - \sqrt{11}}$
234099	Find the Holes in the Graph	(2x^2-3x+1)/(2x+16)	$\frac{2 x^{2} - 3 x + 1}{2 x + 16}$
234100	Solve for x	-2/x=-5/(x-6)	$- \frac{2}{x} = - \frac{5}{x - 6}$