Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
188701	Graph	2x+3y<=12 3x-5y<=15	$2 x + 3 y \leq 12$ $3 x - 5 y \leq 15$
188702	Solve the System of Equations	1/3x-1/2y=-12 2x-1/5y=4/5	$\frac{1}{3} x - \frac{1}{2} y = - 12$ $2 x - \frac{1}{5} y = \frac{4}{5}$
188703	Solve for u	30u-25=9u^2	$30 u - 25 = 9 u^{2}$
188704	Solve for x	-x-1=6(-6x-3)	$- x - 1 = 6 (- 6 x - 3)$
188705	Solve for z	-8=-z/2+22	$- 8 = - \frac{z}{2} + 22$
188706	Solve the Inequality for x	2x-1/2>=7x+7/6	$2 x - \frac{1}{2} \geq 7 x + \frac{7}{6}$
188707	Evaluate	1/3(5)^3	$\frac{1}{3} {(5)}^{3}$
188708	Solve for x	1=7x^2+6x	$1 = 7 x^{2} + 6 x$
188709	Simplify	square root of 14*10 square root of 12	$\sqrt{14} \cdot 10 \sqrt{12}$
188710	Find the Roots (Zeros)	(x-2)^4(x+1)(x+4)=0	${(x - 2)}^{4} (x + 1) (x + 4) = 0$
188711	Multiply	2 square root of x*2 square root of x	$2 \sqrt{x} \cdot 2 \sqrt{x}$
188712	Solve for x	3-x+4/7=5	$3 - x + \frac{4}{7} = 5$
188713	Evaluate	1/3(-5)^2-4	$\frac{1}{3} {(- 5)}^{2} - 4$
188714	Solve for x	square root of -3-4x- square root of -2-2x=1	$\sqrt{- 3 - 4 x} - \sqrt{- 2 - 2 x} = 1$
188715	Graph	h(x)=f(x)+g(x)	$h (x) = f (x) + g (x)$
188716	Solve the Inequality for b	b+12/7>=1/3	$b + \frac{12}{7} \geq \frac{1}{3}$
188717	Find f(g(x))	f(x)=2x-5 and g(x)=x^2-2	$f (x) = 2 x - 5$ and $g (x) = x^{2} - 2$
188718	Simplify	(3y)/(2 square root of 3xy^3-5x^3)	$\frac{3 y}{2 \sqrt{3 x y^{3}} - 5 x^{3}}$
188719	Evaluate	-2*(16÷((8-4)^2))^2	$- 2 \cdot {(16 \div {(8 - 4)}^{2})}^{2}$
188720	Find the Domain and Range	f(x)=(2+x)/(x^2-7x)	$f (x) = \frac{2 + x}{x^{2} - 7 x}$
188721	Subtract	(2x-3)/(4x^2+5x+1)-(x-4)/(4x^2+5x+1)	$\frac{2 x - 3}{4 x^{2} + 5 x + 1} - \frac{x - 4}{4 x^{2} + 5 x + 1}$
188722	Evaluate	sin(theta)=1	$\sin (θ) = 1$
188723	Evaluate	20cos(60)	$20 \cos (60)$
188724	Simplify	1/2(x-1)	$\frac{1}{2} (x - 1)$
188725	Solve for m	10m-p=-n ; for m	$10 m - p = - n$ ; for $m$
188726	Simplify	((3x)/(2x+5))÷((2x)/(x+5))	$\frac{3 x}{2 x + 5} \div \frac{2 x}{x + 5}$
188727	Write in Standard Form	( square root of -72)^2	${(\sqrt{- 72})}^{2}$
188728	Find the Zeros Using Descartes' Rule of Signs	g(x)=2x^4+4x^3+6x^2+8x+9	$g (x) = 2 x^{4} + 4 x^{3} + 6 x^{2} + 8 x + 9$
188729	Combine Like Terms	(7+x)(7-x)	$(7 + x) (7 - x)$
188730	Simplify	(-0.2b^6)^3*5b	${(- 0.2 b^{6})}^{3} \cdot 5 b$
188731	Solve for x	4^2=2(2+x)	$4^{2} = 2 (2 + x)$
188732	Evaluate	((-4^3)/(-2^3))^2	${(\frac{- 4^{3}}{- 2^{3}})}^{2}$
188733	Solve for x	-1/2-7(x-2)=5(-4x-3)+5/2	$- \frac{1}{2} - 7 (x - 2) = 5 (- 4 x - 3) + \frac{5}{2}$
188734	Divide	(7+3i)/(7-3i)	$\frac{7 + 3 i}{7 - 3 i}$
188735	Find the GCF	5c^4d-15cd^3-3cd	$5 c^{4} d - 15 c d^{3} - 3 c d$
188736	Find the Distance Between Two Points	(-7,-5) and (-3,4)	$(- 7, - 5)$ and $(- 3, 4)$
188737	Rationalize the Denominator	square root of x/6	$\sqrt{\frac{x}{6}}$
188738	Solve for b	1/2bh=a	$\frac{1}{2} b h = a$
188739	Find the Domain and Range	y=4x-x^2	$y = 4 x - x^{2}$
188740	Solve for x	(e(x+c))/b=2	$\frac{e (x + c)}{b} = 2$
188741	Graph	(y+2)=4(x+1)^2	$(y + 2) = 4 {(x + 1)}^{2}$
188742	Divide	-45x^4+36x^3-15x^2-3x+16 by 5x-4	$- 45 x^{4} + 36 x^{3} - 15 x^{2} - 3 x + 16$ by $5 x - 4$
188743	Graph	3x+9<0	$3 x + 9 < 0$
188744	Find the Holes in the Graph	(-x-3)/(4x+12)	$\frac{- x - 3}{4 x + 12}$
188745	Solve for θ	sec(theta)=(2 square root of 3)/3	$\sec (θ) = \frac{2 \sqrt{3}}{3}$
188746	Find the Axis of Symmetry	y^2=8(x-5)	$y^{2} = 8 (x - 5)$
188747	Simplify	(-2xy^2)^5((x^7)/(8y^3))	${(- 2 x y^{2})}^{5} (\frac{x^{7}}{8 y^{3}})$
188748	Solve for v	\|-2v-4\|<8	$\| - 2 v - 4 \| < 8$
188749	Write in Standard Form	x^2-1	$x^{2} - 1$
188750	Simplify	(8^(1/4))(8^(1/4))(8^(1/4))*(8^(1/4))	$(8^{\frac{1}{4}}) \cdot (8^{\frac{1}{4}}) \cdot (8^{\frac{1}{4}}) \cdot (8^{\frac{1}{4}})$
188751	Solve the Inequality for h	4h<8	$4 h < 8$
188752	Graph	f(x)=2^x and g(x)=2^(-x)	$f (x) = 2^{x}$ and $g (x) = 2^{- x}$
188753	Factor by Grouping	20ax-5bx-2by+8ay	$20 a x - 5 b x - 2 b y + 8 a y$
188754	Solve for x	\|1/3x+4\|=3	$\| \frac{1}{3} x + 4 \| = 3$
188755	Simplify	(z^2-196)/(1372+98z-14z^2)	$\frac{z^{2} - 196}{1372 + 98 z - 14 z^{2}}$
188756	Solve the System of Inequalities	-7<-(2x)/5-3<5	$- 7 < - \frac{2 x}{5} - 3 < 5$
188757	Solve for x	2\|x\|=3	$2 \| x \| = 3$
188758	Factor	x^3+1/(x^3)	$x^{3} + \frac{1}{x^{3}}$
188759	Find the Distance Between Two Points	(3,6) and (1,9)	$(3, 6)$ and $(1, 9)$
188760	Graph	f(x)=x+5 if x<-2; 4 if x>1	$f (x) = {\begin{cases} x + 5 & x < - 2 \\ 4 & x > 1 \end{cases}$
188761	Find the Inverse	f(x)=-4/(5x)	$f (x) = - \frac{4}{5 x}$
188762	Evaluate	(2a^3b^4)^4	${(2 a^{3} b^{4})}^{4}$
188763	Find the Distance Between Two Points	(-9,-2) and (-3,6)	$(- 9, - 2)$ and $(- 3, 6)$
188764	Convert to Polar	y=- square root of 3x	$y = - \sqrt{3} x$
188765	Write the Fraction in Simplest Form	(x^2-4)/(x+2)+(x-3)/(x+2)	$\frac{x^{2} - 4}{x + 2} + \frac{x - 3}{x + 2}$
188766	Solve for a	(x^2)/( cube root of x)=x^a	$\frac{x^{2}}{\sqrt[3]{x}} = x^{a}$
188767	Factor	16x^3y^2z-8x^2y^3z^2	$16 x^{3} y^{2} z - 8 x^{2} y^{3} z^{2}$
188768	Solve for a	( square root of x^3)/((x^(1/5))^6)=x^a	$\frac{\sqrt{x^{3}}}{{(x^{\frac{1}{5}})}^{6}} = x^{a}$
188769	Factor	(8x^3+1)	$(8 x^{3} + 1)$
188770	Rationalize the Denominator	1/( cube root of 4+ square root of 2)	$\frac{1}{\sqrt[3]{4} + \sqrt{2}}$
188771	Solve for x	log base x+3 of 10x+9=2	$\log_{x + 3} (10 x + 9) = 2$
188772	Solve for y	y^2=x^2-1	$y^{2} = x^{2} - 1$
188773	Simplify	fifth root of (160m^6)/(n^7)	$\sqrt[5]{\frac{160 m^{6}}{n^{7}}}$
188774	Solve for x	e^2=x+1	$e^{2} = x + 1$
188775	Simplify	(3xy)(4x^2y^3)	$(3 x y) (4 x^{2} y^{3})$
188776	Solve for x	5/3x+1/3x=13 1/3+8/3x	$\frac{5}{3} x + \frac{1}{3} x = 13 \frac{1}{3} + \frac{8}{3} x$
188777	Find the Excluded Values	((x^2+9x+18)/(x^2+6x+8))÷((x^2-3x-18)/(x^2+2x-8))	$\frac{x^{2} + 9 x + 18}{x^{2} + 6 x + 8} \div \frac{x^{2} - 3 x - 18}{x^{2} + 2 x - 8}$
188778	Solve the Inequality for x	x^2-5x<=0	$x^{2} - 5 x \leq 0$
188779	Solve for x	4^(3x+2)=(x-5)*8^(2x)	$4^{3 x + 2} = (x - 5) \cdot 8^{2 x}$
188780	Simplify	4/x-(2x-1)/5	$\frac{4}{x} - \frac{2 x - 1}{5}$
188781	Solve the Inequality for w	\|6w+2\|-6>8	$\| 6 w + 2 \| - 6 > 8$
188782	Graph	y=5-e^x	$y = 5 - e^{x}$
188783	Solve for x	1/7x^2+1/21x-1=0	$\frac{1}{7} x^{2} + \frac{1}{21} x - 1 = 0$
188784	Solve for x	\|6x\|+3<=0	$\| 6 x \| + 3 \leq 0$
188785	Solve the System of Equations	y=5x y=9x+4	$y = 5 x$ $y = 9 x + 4$
188786	Factor	2/6x^2y^2+4/9x^3yz+8/15xyw	$\frac{2}{6} x^{2} y^{2} + \frac{4}{9} x^{3} y z + \frac{8}{15} x y w$
188787	Simplify	6/( square root of 5- square root of 2)	$\frac{6}{\sqrt{5} - \sqrt{2}}$
188788	Solve the System of Equations	x+4y=7 8y=14-2x	$x + 4 y = 7$ $8 y = 14 - 2 x$
188789	Simplify	(-7n^2)/(-14n^2-35n)	$\frac{- 7 n^{2}}{- 14 n^{2} - 35 n}$
188790	Evaluate	8(10-6q)+3(-7q-2)	$8 (10 - 6 q) + 3 (- 7 q - 2)$
188791	Solve for h	h-(-2)>=10	$h - (- 2) \geq 10$
188792	Graph	1/3x-1/6y=-2/3	$\frac{1}{3} x - \frac{1}{6} y = - \frac{2}{3}$
188793	Simplify	((x+8)/(x^2-6x-7))/((x^2+16x+64)/(x+1))	$\frac{\frac{x + 8}{x^{2} - 6 x - 7}}{\frac{x^{2} + 16 x + 64}{x + 1}}$
188794	Simplify	(6x^3y)/(y^2)*(x^2y^4)/(3xy)	$\frac{6 x^{3} y}{y^{2}} \cdot \frac{x^{2} y^{4}}{3 x y}$
188795	Simplify	((2-2^2)^3)/2	$\frac{{(2 - 2^{2})}^{3}}{2}$
188796	Simplify	(1/(2x)+2/(3x))/((x-1)/(x-3))	$\frac{\frac{1}{2 x} + \frac{2}{3 x}}{\frac{x - 1}{x - 3}}$
188797	Factor	36x-13x^3+x^5	$36 x - 13 x^{3} + x^{5}$
188798	Solve for a	2a+3=1/2(6+4a)	$2 a + 3 = \frac{1}{2} (6 + 4 a)$
188799	Find g(f(x))	f(x)=5x-1 and g(x)=4x^2-3	$f (x) = 5 x - 1$ and $g (x) = 4 x^{2} - 3$
188800	Simplify	((pg^3)^(1/2))/((pg)^(-1/2))	$\frac{{(p g^{3})}^{\frac{1}{2}}}{{(p g)}^{- \frac{1}{2}}}$