Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
192501	Graph	f(x)=0 if x<-3; -2x if -3<=x<0; x^2 if x>=0	$f (x) = {\begin{cases} 0 & x < - 3 \\ - 2 x & - 3 \leq x < 0 \\ x^{2} & x \geq 0 \end{cases}$
192502	Find the End Behavior	f(x)=544x^2-112x^3+8x^4+768-1088x	$f (x) = 544 x^{2} - 112 x^{3} + 8 x^{4} + 768 - 1088 x$
192503	Evaluate	pi/4-(3pi)/4	$\frac{π}{4} - \frac{3 π}{4}$
192504	Solve for x	7+(4x)/9=x/2	$7 + \frac{4 x}{9} = \frac{x}{2}$
192505	Solve the System of Equations	x+y=0 3x-2y=10	$x + y = 0$ $3 x - 2 y = 10$
192506	Evaluate	(654)/(321)	$\frac{6 \cdot 5 \cdot 4}{3 \cdot 2 \cdot 1}$
192507	Solve for θ	4cos(theta)^2-4cos(theta)+1=0	$4 \cos^{2} (θ) - 4 \cos (θ) + 1 = 0$
192508	Find the Domain and Range	y=-1/5sin(5x)	$y = - \frac{1}{5} \sin (5 x)$
192509	Evaluate	log base w of ((x^2-6)^4)/( cube root of x^2+8)	$\log_{w} (\frac{{(x^{2} - 6)}^{4}}{\sqrt[3]{x^{2} + 8}})$
192510	Find the LCM	15 and 20	$15$ and $20$
192511	Solve for a	-2/3a+10=2/3a-6	$- \frac{2}{3} a + 10 = \frac{2}{3} a - 6$
192512	Simplify	( square root of 5+ square root of 180)( square root of 8- square root of 2)	$(\sqrt{5} + \sqrt{180}) (\sqrt{8} - \sqrt{2})$
192513	Solve for x	square root of 8x=x	$\sqrt{8 x} = x$
192514	Solve the System of Inequalities	-15x+4<=109 ; OR , -6x+70>-2	$- 15 x + 4 \leq 109$ ; OR , $- 6 x + 70 > - 2$
192515	Solve the System of Inequalities	-3y>9 or 2y-6>2	$- 3 y > 9$ or $2 y - 6 > 2$
192516	Simplify	9/(x^2-8x-9)-2/(x^2-81)	$\frac{9}{x^{2} - 8 x - 9} - \frac{2}{x^{2} - 81}$
192517	Simplify	(((4x^3y^4)^3)/((8xy^2)^2))^2	${(\frac{{(4 x^{3} y^{4})}^{3}}{{(8 x y^{2})}^{2}})}^{2}$
192518	Solve the System of Equations	3x-y=3 -3x+y=3	$3 x - y = 3$ $- 3 x + y = 3$
192519	Find All Complex Solutions	(cot(theta)-1)(sin(theta)+1)=0	$(\cot (θ) - 1) (\sin (θ) + 1) = 0$
192520	Solve for a	(x^(1/6))^5 fourth root of x^3=x^a	${(x^{\frac{1}{6}})}^{5} \sqrt[4]{x^{3}} = x^{a}$
192521	Solve for x	2x+4/5(5x-5/4)=-2x-(-4x+10)	$2 x + \frac{4}{5} (5 x - \frac{5}{4}) = - 2 x - (- 4 x + 10)$
192522	Solve for a	ab=-3a+1	$a b = - 3 a + 1$
192523	Solve for s	2s=6t+8w	$2 s = 6 t + 8 w$
192524	Solve for x	4.6x-7=4x-(-x+1)+5.3	$4.6 x - 7 = 4 x - (- x + 1) + 5.3$
192525	Determine if Perpendicular	x-2y=18 2x+y=6	$x - 2 y = 18$ $2 x + y = 6$
192526	Write the Fraction in Simplest Form	arccos(cos((4pi)/5))	$\arccos (\cos (\frac{4 π}{5}))$
192527	Factor	4a^2b^2-25m^2n^2	$4 a^{2} b^{2} - 25 m^{2} n^{2}$
192528	Simplify	3/8+1/8+2/3-1/2	$\frac{3}{8} + \frac{1}{8} + \frac{2}{3} - \frac{1}{2}$
192529	Solve the System of Equations	y=-4x 8x-y=6	$y = - 4 x$ $8 x - y = 6$
192530	Graph	f(x)=1/2(x-2)^4	$f (x) = \frac{1}{2} {(x - 2)}^{4}$
192531	Solve the Inequality for x	-(2x-3)<=4-(2x+4)	$- (2 x - 3) \leq 4 - (2 x + 4)$
192532	Evaluate	log base 3 of x=-2	$\log_{3} (x) = - 2$
192533	Solve the Rational Equation for x	5/(x-3)>3/(x+1)	$\frac{5}{x - 3} > \frac{3}{x + 1}$
192534	Find the End Behavior	f(x)=42x^5-231x^4-966x^3-7840+2772x^2+3192x+7x^6	$f (x) = 42 x^{5} - 231 x^{4} - 966 x^{3} - 7840 + 2772 x^{2} + 3192 x + 7 x^{6}$
192535	Solve for x	-2x(7x+8)(49x^2-100)=0	$- 2 x (7 x + 8) (49 x^{2} - 100) = 0$
192536	Simplify	(-7/(x+7)-2/(x+6))/(-6/(x+7))	$\frac{- \frac{7}{x + 7} - \frac{2}{x + 6}}{- \frac{6}{x + 7}}$
192537	Graph	5x+2y>3 y<x	$5 x + 2 y > 3$ $y < x$
192538	Solve for z	2/(z+1)-1/(z-1)=-2/(z^2-1)	$\frac{2}{z + 1} - \frac{1}{z - 1} = \frac{- 2}{z^{2} - 1}$
192539	Solve for x	5^(2x)<125^(x-5)	$5^{2 x} < 125^{x - 5}$
192540	Graph	(f+g)(1)	$(f + g) (1)$
192541	Graph	f(x)=sin((2x)/3)	$f (x) = \sin (\frac{2 x}{3})$
192542	Solve for x	(x^2-4)/(x-2)=2	$\frac{x^{2} - 4}{x - 2} = 2$
192543	Write in Standard Form	(x-5)^2=2x+3	${(x - 5)}^{2} = 2 x + 3$
192544	Find the Product	cube root of 5* square root of 2	$\sqrt[3]{5} \cdot \sqrt{2}$
192545	Solve for θ	2cos(theta)^2+sin(theta)=1	$2 \cos^{2} (θ) + \sin (θ) = 1$
192546	Convert to Radical Form	(x-1)^(1/2)	${(x - 1)}^{\frac{1}{2}}$
192547	Evaluate the Function	f(x)=3x+2 when x=0	$f (x) = 3 x + 2$ when $x = 0$
192548	Solve the Inequality for n	2n-3>=5n-6	$2 n - 3 \geq 5 n - 6$
192549	Find the Product	(2m+n)^3	${(2 m + n)}^{3}$
192550	Evaluate	-2^(-(-1))	$- 2^{- (- 1)}$
192551	Evaluate	5/(2(x-4)^2-6)	$\frac{5}{2 {(x - 4)}^{2} - 6}$
192552	Divide	9x^2-18x-7÷(3x+1)	$9 x^{2} - 18 x - 7 \div (3 x + 1)$
192553	Solve for x	3/(1-x)+1/(1+x)=28/(1-x^2)	$\frac{3}{1 - x} + \frac{1}{1 + x} = \frac{28}{1 - x^{2}}$
192554	Graph	h(x)=f(x)+2	$h (x) = f (x) + 2$
192555	Solve for r	20r^2+11r-3=0	$20 r^{2} + 11 r - 3 = 0$
192556	Factor by Grouping	9x^2-16y^2	$9 x^{2} - 16 y^{2}$
192557	Find the Domain and Range	F(x)=10/( square root of 1-x)	$F (x) = \frac{10}{\sqrt{1 - x}}$
192558	Combine Like Terms	4(-5z+2)+(-6)	$4 (- 5 z + 2) + (- 6)$
192559	Find the Product	(x^10+10y^12)^2	${(x^{10} + 10 y^{12})}^{2}$
192560	Write in Standard Form	-3x+17x^4+2x^2	$- 3 x + 17 x^{4} + 2 x^{2}$
192561	Solve for h	y=a cube root of x-h+k	$y = a \sqrt[3]{x - h} + k$
192562	Evaluate	2 permute 3	${}_{2}P_{3}$
192563	Simplify	(x+2/3)^2	${(x + \frac{2}{3})}^{2}$
192564	Simplify	(-3y)(-5x^2y^3)^3	$(- 3 y) {(- 5 x^{2} y^{3})}^{3}$
192565	Simplify	-2/( square root of 2)	$\frac{- 2}{\sqrt{2}}$
192566	Describe the Transformation	y=4x^2-5	$y = 4 x^{2} - 5$
192567	Solve for x	2x^2=x	$2 x^{2} = x$
192568	Find the Distance Between Two Points	(-6,5) and (3,-7)	$(- 6, 5)$ and $(3, - 7)$
192569	Evaluate	log base a of MN	$\log_{a} (M N)$
192570	Find the Holes in the Graph	(5x+5)/(-x^2-2x-1)	$\frac{5 x + 5}{- x^{2} - 2 x - 1}$
192571	Graph	y-x^2	$y - x^{2}$
192572	Find the Distance Between Two Points	(4,4) and (8,-3)	$(4, 4)$ and $(8, - 3)$
192573	Simplify	(10^2*7^5)^5	${(10^{2} \cdot 7^{5})}^{5}$
192574	Convert to Interval Notation	-3<=x	$- 3 \leq x$
192575	Write in Standard Form	(2x-3)(4x-5)=-6	$(2 x - 3) (4 x - 5) = - 6$
192576	Solve for w	4w^2+4w+1=75	$4 w^{2} + 4 w + 1 = 75$
192577	Write the Fraction in Simplest Form	cube root of 8x^2y^6	$\sqrt[3]{8 x^{2} y^{6}}$
192578	Solve for x	-7x+8/5(-5/4x-2)=3x	$- 7 x + \frac{8}{5} (- \frac{5}{4} x - 2) = 3 x$
192579	Simplify	3- square root of 49+(2(3+4^2))÷(1/2)	$3 - \sqrt{49} + 2 (3 + 4^{2}) \div \frac{1}{2}$
192580	Solve for y	10(1-2y)=-5(2y-1)	$10 (1 - 2 y) = - 5 (2 y - 1)$
192581	Simplify	(6x)/(6y)	$\frac{6 x}{6 y}$
192582	Evaluate Using the Given Value	4(x-3)+5x-x^2 for x=2	$4 (x - 3) + 5 x - x^{2}$ for $x = 2$
192583	Find the Function	f(x) = square root of x+6	$f (x) = \sqrt{x + 6}$
192584	Simplify	((3x+4)/(xy))/((x^2+5)/(xy))	$\frac{\frac{3 x + 4}{x y}}{\frac{x^{2} + 5}{x y}}$
192585	Solve the Absolute Value Inequality for x	\|x^2+x-1\|=1	$\| x^{2} + x - 1 \| = 1$
192586	Solve the System of Equations	-4x=4-y 2y=8x+8	$- 4 x = 4 - y$ $2 y = 8 x + 8$
192587	Multiply	(1/2x^3)(-2/3a^2x)(-3/5a^4m)	$(\frac{1}{2} x^{3}) (- \frac{2}{3} a^{2} x) (- \frac{3}{5} a^{4} m)$
192588	Solve the Absolute Value Inequality for x	\|2x+3\|>=19	$\| 2 x + 3 \| \geq 19$
192589	Graph	f(x)=1 if x<-2; 2x-3 if -2<=x<1; -x+5 if x>=1	$f (x) = {\begin{cases} 1 & x < - 2 \\ 2 x - 3 & - 2 \leq x < 1 \\ - x + 5 & x \geq 1 \end{cases}$
192590	Find All Complex Solutions	sin(theta)+cos(theta) = square root of 2	$\sin (θ) + \cos (θ) = \sqrt{2}$
192591	Find the Exact Value	pi/2+pi	$\frac{π}{2} + π$
192592	Write in Standard Form	i/(3-2i)+(2i)/(3+8i)	$\frac{i}{3 - 2 i} + \frac{2 i}{3 + 8 i}$
192593	Simplify	2^n+2^n	$2^{n} + 2^{n}$
192594	Simplify the Radical Expression	square root of 15y^3	$\sqrt{15 y^{3}}$
192595	Evaluate	( square root of -1)^2	${(\sqrt{- 1})}^{2}$
192596	Simplify	(4p^2+32p)/(p-2)*(p^2+p-6)/(2p^3+16p^2)	$\frac{4 p^{2} + 32 p}{p - 2} \cdot \frac{p^{2} + p - 6}{2 p^{3} + 16 p^{2}}$
192597	Evaluate	15sin(60)	$15 \sin (60)$
192598	Solve for n	4^n*4^(2n-9)=64	$4^{n} \cdot 4^{2 n - 9} = 64$
192599	Graph	f(x)=(x+5)(x-1)^2(x+1)	$f (x) = (x + 5) {(x - 1)}^{2} (x + 1)$
192600	Solve the Inequality for x	5x-6<=2+(3x-4)	$5 x - 6 \leq 2 + (3 x - 4)$