Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
184101	Describe the Transformation	y=1/4\|x\|	$y = \frac{1}{4} \| x \|$
184102	Find the Exact Value	square root of 2/3- square root of 3/2	$\sqrt{\frac{2}{3}} - \sqrt{\frac{3}{2}}$
184103	Find f(g(x))	f(x)=1/(8x+3) g(x)=12-5x	$f (x) = \frac{1}{8 x + 3}$ $g (x) = 12 - 5 x$
184104	Solve the Inequality for x	-x^2+4x+12>0	$- x^{2} + 4 x + 12 > 0$
184105	Graph	x-4y>=-8 3x+y<=6	$x - 4 y \geq - 8$ $3 x + y \leq 6$
184106	Find the Holes in the Graph	f(x)=(x+4)/(-2x-6)	$f (x) = \frac{x + 4}{- 2 x - 6}$
184107	Evaluate	5(-2k-3)+2k	$5 (- 2 k - 3) + 2 k$
184108	Simplify	(5x^2-40x-45)/(15x^2-195x+540)*(x^2-14x+40)/(x^3-9x^2-10x)	$\frac{5 x^{2} - 40 x - 45}{15 x^{2} - 195 x + 540} \cdot \frac{x^{2} - 14 x + 40}{x^{3} - 9 x^{2} - 10 x}$
184109	Find the Holes in the Graph	f(x)=(-x^2-2x+3)/(x^2+5x+6)	$f (x) = \frac{- x^{2} - 2 x + 3}{x^{2} + 5 x + 6}$
184110	Solve for x	(2x-1)^2=0	${(2 x - 1)}^{2} = 0$
184111	Solve for v	-4/3(12v-18)+32=-8(7+2v)	$- \frac{4}{3} (12 v - 18) + 32 = - 8 (7 + 2 v)$
184112	Solve for b	y=mx+b for b	$y = m x + b$ for $b$
184113	Simplify	( square root of 6)/( square root of 3- square root of 5)	$\frac{\sqrt{6}}{\sqrt{3} - \sqrt{5}}$
184114	Find g(f(x))	f(x)=6x+1 , g(x) = square root of x	$f (x) = 6 x + 1$ , $g (x) = \sqrt{x}$
184115	Evaluate	6(11-3)=4(7+5)	$6 (11 - 3) = 4 (7 + 5)$
184116	Expand the Logarithmic Expression	log of (x^4)/( cube root of yz^2)	$\log (\frac{x^{4}}{\sqrt[3]{y} z^{2}})$
184117	Find f(g(x))	f(x)=4/x g(x)=4/x	$f (x) = \frac{4}{x}$ $g (x) = \frac{4}{x}$
184118	Write Using Negative Exponents	5/(x^2)	$\frac{5}{x^{2}}$
184119	Find the x and y Intercepts	f(x)=-2-6x-8x^3+8x^2	$f (x) = - 2 - 6 x - 8 x^{3} + 8 x^{2}$
184120	Solve for θ	sin(theta)^2-cos(theta)^2=0	$\sin^{2} (θ) - \cos^{2} (θ) = 0$
184121	Simplify	(t+2)/(3t-9)+(3-2t)/(5t-15)	$\frac{t + 2}{3 t - 9} + \frac{3 - 2 t}{5 t - 15}$
184122	Simplify	(1/(x^2)-1/(3x))/(9/x-x)	$\frac{\frac{1}{x^{2}} - \frac{1}{3 x}}{\frac{9}{x} - x}$
184123	Rationalize the Denominator	square root of 1/3	$\sqrt{\frac{1}{3}}$
184124	Graph	y=(x-2)/(x^2-4)	$y = \frac{x - 2}{x^{2} - 4}$
184125	Divide	2/(5/2)	$\frac{2}{\frac{5}{2}}$
184126	Solve for k	(1/27)/(3^(2k))=27	$\frac{\frac{1}{27}}{3^{2 k}} = 27$
184127	Solve for G	d=5/6(F+G)	$d = \frac{5}{6} (F + G)$
184128	Solve the Inequality for A	A=1/2h(a+b)	$A = \frac{1}{2} h (a + b)$
184129	Find the Exact Value	square root of 16/25	$\sqrt{\frac{16}{25}}$
184130	Simplify	(6x^3)/(15x^4-60x^3)	$\frac{6 x^{3}}{15 x^{4} - 60 x^{3}}$
184131	Graph	(x-4)	$(x - 4)$
184132	Graph	f(x)=x(x+1)	$f (x) = x (x + 1)$
184133	Solve for x	1/(x-9)+4=9/(x^2-9x)	$\frac{1}{x - 9} + 4 = \frac{9}{x^{2} - 9 x}$
184134	Rationalize the Denominator	3/( cube root of 3)	$\frac{3}{\sqrt[3]{3}}$
184135	Graph	f(x)=3sin(pi/2x)	$f (x) = 3 \sin (\frac{π}{2} x)$
184136	Solve for x	x+4=5x+2	$x + 4 = 5 x + 2$
184137	Factor	x^2-a^2+2xy+y^2+2ab-b^2	$x^{2} - a^{2} + 2 x y + y^{2} + 2 a b - b^{2}$
184138	Simplify	2 cube root of 5+3 cube root of 5-3 cube root of 5	$2 \sqrt[3]{5} + 3 \sqrt[3]{5} - 3 \sqrt[3]{5}$
184139	Find the x and y Intercepts	f(x)=(2x-18)/(25x^2-81)	$f (x) = \frac{2 x - 18}{25 x^{2} - 81}$
184140	Solve for x	x^2+x+1/4=0	$x^{2} + x + \frac{1}{4} = 0$
184141	Solve for x	-4/(x-2)+6/x=-(2x)/(x-2)	$- \frac{4}{x - 2} + \frac{6}{x} = - \frac{2 x}{x - 2}$
184142	Graph	f(x)=x^2-4 if x<=2; 3x-6 if x>2	$f (x) = {\begin{cases} x^{2} - 4 & x \leq 2 \\ 3 x - 6 & x > 2 \end{cases}$
184143	Find the Roots (Zeros)	y=3(x+4)(x+1)(x-3)	$y = 3 (x + 4) (x + 1) (x - 3)$
184144	Simplify	((-6a^5b)^2)/(12a^7b)-8a^3b	$\frac{{(- 6 a^{5} b)}^{2}}{12 a^{7} b} - 8 a^{3} b$
184145	Solve for x	1/4x=12-x	$\frac{1}{4} x = 12 - x$
184146	Solve for x	2/3(1+x)=a	$\frac{2}{3} (1 + x) = a$
184147	Find g(f(x))	f(x)=x^2+4x-1 g(x)=2x-7	$f (x) = x^{2} + 4 x - 1$ $g (x) = 2 x - 7$
184148	Graph	y-3=-2/3(x+6) ?	$y - 3 = - \frac{2}{3} (x + 6)$ ?
184149	Find the x and y Intercepts	f(x)=3 cube root of -2x+1	$f (x) = 3 \sqrt[3]{- 2 x} + 1$
184150	Evaluate	1/3*3^(7-1)	$\frac{1}{3} \cdot 3^{7 - 1}$
184151	Find the Holes in the Graph	f(x)=(x^2-8x+15)/(x^2-64)	$f (x) = \frac{x^{2} - 8 x + 15}{x^{2} - 64}$
184152	Simplify	(1-x/5)/((x-8)/15+1/x)	$\frac{1 - \frac{x}{5}}{\frac{x - 8}{15} + \frac{1}{x}}$
184153	Solve for x	tan(x)^2=sec(x)-1	$\tan^{2} (x) = \sec (x) - 1$
184154	Graph	3<=x-8	$3 \leq x - 8$
184155	Simplify	(-3x^2+x+5)-(4x^2-2x)	$(- 3 x^{2} + x + 5) - (4 x^{2} - 2 x)$
184156	Simplify	(z+2)^-3(z+2)^-1	${(z + 2)}^{- 3} {(z + 2)}^{- 1}$
184157	Write in Exponential Form	n root of x^(3n)	$\sqrt[n]{x^{3 n}}$
184158	Solve for a	x^2 cube root of x^4=x^a	$x^{2} \sqrt[3]{x^{4}} = x^{a}$
184159	Find the x and y Intercepts	f(x)=6x+2x^3-4x^2-4	$f (x) = 6 x + 2 x^{3} - 4 x^{2} - 4$
184160	Convert to Interval Notation	x<=-9 or x>=4	$x \leq - 9$ or $x \geq 4$
184161	Solve for h	h+1/3=5/3	$h + \frac{1}{3} = \frac{5}{3}$
184162	Evaluate	2-53-(5-7)-(2)3^2	$2 - 5 \cdot 3 - (5 - 7) - (2) \cdot 3^{2}$
184163	Find the Exact Value	7+(5-9)^2+3(16÷8)	$7 + {(5 - 9)}^{2} + 3 (16 \div 8)$
184164	Find All Complex Solutions	x^(2/3)-2x^(1/3)-3=0	$x^{\frac{2}{3}} - 2 x^{\frac{1}{3}} - 3 = 0$
184165	Solve Using the Quadratic Formula	f(x)=4x^2-9	$f (x) = 4 x^{2} - 9$
184166	Evaluate	e^x=0	$e^{x} = 0$
184167	Write in Standard Form	y=-11/3x-2 5/6	$y = - \frac{11}{3} x - 2 \frac{5}{6}$
184168	Simplify	1/(x^2)-4/(3x^2+15x)	$\frac{1}{x^{2}} - \frac{4}{3 x^{2} + 15 x}$
184169	Factor	x^5+x^3+x^2+1	$x^{5} + x^{3} + x^{2} + 1$
184170	Solve for x	x^4=64	$x^{4} = 64$
184171	Solve for x	4^(5x-13)=1/(8x)	$4^{5 x - 13} = \frac{1}{8 x}$
184172	Find the Distance Between Two Points	(0,0) and (-3,4)	$(0, 0)$ and $(- 3, 4)$
184173	Solve for x	y-y_1=m(x-x_1) for x	$y - y_{1} = m (x - x_{1})$ for $x$
184174	Solve for u	u^2+(4u)/5=5	$u^{2} + \frac{4 u}{5} = 5$
184175	Simplify	2/(2(3x-5)+3)	$\frac{2}{2 (3 x - 5) + 3}$
184176	Solve the Inequality for z	15>-5+z	$15 > - 5 + z$
184177	Factor	a(n+2)+(n+2)	$a (n + 2) + (n + 2)$
184178	Find the Roots (Zeros)	f(x)=2(x+1)(x-3)(x-1)^2	$f (x) = 2 (x + 1) (x - 3) {(x - 1)}^{2}$
184179	Solve for c	-9(c+7)=-13c+7	$- 9 (c + 7) = - 13 c + 7$
184180	Simplify	1/2+-7/2i	$\frac{1}{2} + \frac{- 7}{2} i$
184181	Find the Exact Value	6!	$6!$
184182	Solve for x	2xy-xz=4	$2 x y - x z = 4$
184183	Simplify	3(1)^2	$3 {(1)}^{2}$
184184	Solve for y	(y+3)/t=t^2	$\frac{y + 3}{t} = t^{2}$
184185	Simplify	(5/6)/(3/4)	$\frac{\frac{5}{6}}{\frac{3}{4}}$
184186	Multiply	5/154/143/13	$\frac{5}{15} \cdot \frac{4}{14} \cdot \frac{3}{13}$
184187	Find the Function	f(x)=x^2+6x	$f (x) = x^{2} + 6 x$
184188	Graph	y^2=-3x-2	$y^{2} = - 3 x - 2$
184189	Solve for y	y=(y(y^3)^2)/(y^3)	$y = \frac{y {(y^{3})}^{2}}{y^{3}}$
184190	Graph	f(x)=-3/2\|x\|+5 if x<=4; -2x+3 if x>4	$f (x) = {\begin{cases} - \frac{3}{2} \| x \| + 5 & x \leq 4 \\ - 2 x + 3 & x > 4 \end{cases}$
184191	Identify the Sequence	1 , 2 , 4 , 8 , 16 , 32	$1$ , $2$ , $4$ , $8$ , $16$ , $32$
184192	Convert to Interval Notation	{x\|-1<=x}	${x \| - 1 \leq x}$
184193	Simplify	a^2+1-3a+2a^2+2a	$a^{2} + 1 - 3 a + 2 a^{2} + 2 a$
184194	Simplify	(x^2+8x-20)/(x^4+7x^3-18x^2)*(4x^4+8x^3-252x^2)/(6x+60)	$\frac{x^{2} + 8 x - 20}{x^{4} + 7 x^{3} - 18 x^{2}} \cdot \frac{4 x^{4} + 8 x^{3} - 252 x^{2}}{6 x + 60}$
184195	Simplify	((x-2)/3-1/x)/(x/3-(x^2)/9)	$\frac{\frac{x - 2}{3} - \frac{1}{x}}{\frac{x}{3} - \frac{x^{2}}{9}}$
184196	Solve for x	2/5x+1/2=7/6	$\frac{2}{5} x + \frac{1}{2} = \frac{7}{6}$
184197	Find the Exact Value	-2^-2	$- 2^{- 2}$
184198	Solve for x	x^2=36^2	$x^{2} = 36^{2}$
184199	Find g(f(x))	f(x)=2x^2-7x+6 g(x)=4x+10	$f (x) = 2 x^{2} - 7 x + 6$ $g (x) = 4 x + 10$
184200	Find the Function	h(t)=-t^2+t+1	$h (t) = - t^{2} + t + 1$