Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
218101	Evaluate the Function	f(x)=x^3+x^2-5x-6 at x=2	$f (x) = x^{3} + x^{2} - 5 x - 6$ at $x = 2$
218102	Simplify	square root of 2*5	$\sqrt{2 \cdot 5}$
218103	Solve for x	x^5-32=-64	$x^{5} - 32 = - 64$
218104	Divide Using Synthetic Division	(x^4-x^3+x^2-x+1)÷(x-1)	$(x^{4} - x^{3} + x^{2} - x + 1) \div (x - 1)$
218105	Find the Domain and Range	y=-3/2sin(x/3+pi/6)+2	$y = - \frac{3}{2} \sin (\frac{x}{3} + \frac{π}{6}) + 2$
218106	Factor	(5x-6)^2+x5(5x-6)5	${(5 x - 6)}^{2} + x \cdot 5 (5 x - 6) \cdot 5$
218107	Simplify	y^2+11y-6y+y^2	$y^{2} + 11 y - 6 y + y^{2}$
218108	Simplify	(-1/x)(1-x)/(1+x)x/(x^2-1)	$(- \frac{1}{x}) \cdot \frac{(1 - x)}{1 + x} \cdot \frac{x}{x^{2} - 1}$
218109	Factor	5(4x^2+3x-10)-(3x+2)(x+2)	$5 (4 x^{2} + 3 x - 10) - (3 x + 2) (x + 2)$
218110	Simplify	((2x^3)/(x+5))÷((x-5)/(3x-1))	$\frac{2 x^{3}}{x + 5} \div \frac{x - 5}{3 x - 1}$
218111	Evaluate	y=2(4)^-2	$y = 2 {(4)}^{- 2}$
218112	Graph	x^2\|x\|	$x^{2} \| x \|$
218113	Evaluate	(3x+2)-(x+4)	$(3 x + 2) - (x + 4)$
218114	Simplify	2/3y-2(4/3y+z)	$\frac{2}{3} y - 2 (\frac{4}{3} y + z)$
218115	Solve the Rational Equation for x	square root of 10x+15-4=x	$\sqrt{10 x + 15} - 4 = x$
218116	Simplify	(m^(-3/4)n^(-1/4))/((m^2n)^(1/2))	$\frac{m^{- \frac{3}{4}} n^{- \frac{1}{4}}}{{(m^{2} n)}^{\frac{1}{2}}}$
218117	Solve for x	(x+2)+(2y-1)i=-1+5i	$(x + 2) + (2 y - 1) i = - 1 + 5 i$
218118	Evaluate	-(2c^0)^3	$- {(2 c^{0})}^{3}$
218119	Simplify	( square root of 8- square root of 2)/( square root of 2)	$\frac{\sqrt{8} - \sqrt{2}}{\sqrt{2}}$
218120	Solve for w	9/4(w-1/9)=7/2	$\frac{9}{4} (w - \frac{1}{9}) = \frac{7}{2}$
218121	Simplify	(2 square root of 4-x^2)^2	${(2 \sqrt{4 - x^{2}})}^{2}$
218122	Find the Exact Value	(9^-3)/(9^12)	$\frac{9^{- 3}}{9^{12}}$
218123	Solve by Factoring	(2x-3)^2=25	${(2 x - 3)}^{2} = 25$
218124	Simplify	Simplify the expression (2x-6)/2	Simplify the expression $\frac{2 x - 6}{2}$
218125	Evaluate the Function	g(1-t)=3x^2-5x+1	$g (1 - t) = 3 x^{2} - 5 x + 1$
218126	Evaluate the Function	g(-3)=-2(-3)^3-3	$g (- 3) = - 2 {(- 3)}^{3} - 3$
218127	Graph	g(x)=-1 if x<-3; x^2-2 if -3<=x<=1; -1 if x>1	$g (x) = {\begin{cases} - 1 & x < - 3 \\ x^{2} - 2 & - 3 \leq x \leq 1 \\ - 1 & x > 1 \end{cases}$
218128	Multiply	y^2(y+5)(y-3)	$y^{2} (y + 5) (y - 3)$
218129	Simplify	((3x^3)/7)÷(4/(7x^2))	$\frac{3 x^{3}}{7} \div \frac{4}{7 x^{2}}$
218130	Simplify	(2x^3yz^0)^2	${(2 x^{3} y z^{0})}^{2}$
218131	Find All Complex Solutions	log of 5x=-1	$\log (5 x) = - 1$
218132	Simplify	((3m^-5n^2)/(4m^-2n^0))^2	${(\frac{3 m^{- 5} n^{2}}{4 m^{- 2} n^{0}})}^{2}$
218133	Solve the Inequality for x	(1/3)^x<(1/5)^x	${(\frac{1}{3})}^{x} < {(\frac{1}{5})}^{x}$
218134	Convert to a Decimal	3rev per s	$3$ revolutions per second
218135	Solve for x	x^( log of x)=10	$x^{\log (x)} = 10$
218136	Solve for x	x^3-3x^2-10x-x^2+3x+10=0	$x^{3} - 3 x^{2} - 10 x - x^{2} + 3 x + 10 = 0$
218137	Find the x and y Intercepts	f(x)=(3x^3+2x^2)/(x^2+x)	$f (x) = \frac{3 x^{3} + 2 x^{2}}{x^{2} + x}$
218138	Find the Degree, Leading Term, and Leading Coefficient	x^2-1/2	$x^{2} - \frac{1}{2}$
218139	Evaluate the Function	f(-1)=-x^2+x	$f (- 1) = - x^{2} + x$
218140	Solve for k	4/(k^2-8k+12)=k/(k-2)+1/(k-6)	$\frac{4}{k^{2} - 8 k + 12} = \frac{k}{k - 2} + \frac{1}{k - 6}$
218141	Combine Like Terms	-7+3(-4e-3)	$- 7 + 3 (- 4 e - 3)$
218142	Multiply	12y*(2/3xy^4)	$12 y \cdot (\frac{2}{3} x y^{4})$
218143	Solve the System of Equations	x^2+y^2=68 5y=-3x+34	$x^{2} + y^{2} = 68$ $5 y = - 3 x + 34$
218144	Find All Complex Solutions	cos(theta)*csc(theta)-2cos(theta)=0	$\cos (θ) \cdot \csc (θ) - 2 \cos (θ) = 0$
218145	Simplify	((3x^3)^2)^-2	${({(3 x^{3})}^{2})}^{- 2}$
218146	Solve for p	p/9=-9	$\frac{p}{9} = - 9$
218147	Simplify	(5/7)^-0.65	${(\frac{5}{7})}^{- 0.65}$
218148	Simplify	x^-2y^3*y^-2	$x^{- 2} y^{3} \cdot y^{- 2}$
218149	Factor	(mn)^4-n^2	${(m n)}^{4} - n^{2}$
218150	Rationalize the Denominator	(6- square root of 2)/(4-3 square root of 2)	$\frac{6 - \sqrt{2}}{4 - 3 \sqrt{2}}$
218151	Simplify	(2a^2b+2b^3)(3a^2b+3b+5b^3)	$(2 a^{2} b + 2 b^{3}) (3 a^{2} b + 3 b + 5 b^{3})$
218152	Evaluate	15/(a^2-1)=5/(2a-2)	$\frac{15}{a^{2} - 1} = \frac{5}{2 a - 2}$
218153	Find the Distance Between Two Points	(-9,-4) and (0,-7)	$(- 9, - 4)$ and $(0, - 7)$
218154	Solve for x	square root of 9x^2-11=5	$\sqrt{9 x^{2} - 11} = 5$
218155	Find the Exact Value	arccsc(sec((2pi)/3))	$arccsc (\sec (\frac{2 π}{3}))$
218156	Solve the System of Inequalities	0.4x-1<=0 2.3x>=4.6	$0.4 x - 1 \leq 0$ $2.3 x \geq 4.6$
218157	Find the Product	(-4x^4-3x^3)(-9x^2+x)	$(- 4 x^{4} - 3 x^{3}) (- 9 x^{2} + x)$
218158	Solve by Substitution	y=x+2 and 3x+3y=6	$y = x + 2$ and $3 x + 3 y = 6$
218159	Solve the System of Equations	y=-x+3 and 2x+2y=6	$y = - x + 3$ and $2 x + 2 y = 6$
218160	Multiply	(x-y)(x+y)(x^2-y^2)	$(x - y) (x + y) (x^{2} - y^{2})$
218161	Graph	D={x\|x<=-1}	$D = {x \| x \leq - 1}$
218162	Simplify	( fifth root of x^3 square root of x^5 cube root of x^2)/( cube root of x^2 fifth root of x^3 square root of x^7)	$\frac{\sqrt[5]{x^{3} \sqrt{x^{5} \sqrt[3]{x^{2}}}}}{\sqrt[3]{x^{2} \sqrt[5]{x^{3} \sqrt{x^{7}}}}}$
218163	Solve the Inequality for x	1/6<(2x-17)/12<=2/3	$\frac{1}{6} < \frac{2 x - 17}{12} \leq \frac{2}{3}$
218164	Divide Using Synthetic Division	Use synthetic division to find the result when x^3+6x^2+10x+25 is divided by x+5	Use synthetic division to find the result when $x^{3} + 6 x^{2} + 10 x + 25$ is divided by $x + 5$
218165	Simplify	-2/(x^2-1)+1/(x+1)-1/(x-1)	$\frac{- 2}{x^{2} - 1} + \frac{1}{x + 1} - \frac{1}{x - 1}$
218166	Find the Holes in the Graph	(x^2-16)/(2x^2-4x-16)	$\frac{x^{2} - 16}{2 x^{2} - 4 x - 16}$
218167	Simplify	(2x^-4)/(3xy)	$\frac{2 x^{- 4}}{3 x y}$
218168	Solve for b	b=( cube root of -25)^3	$b = {(\sqrt[3]{- 25})}^{3}$
218169	Simplify	-2-2(2+2(2-2))	$- 2 - 2 (2 + 2 (2 - 2))$
218170	Evaluate the Function	f(a)=a^4+3a^3-17a^2+2a-7 at a=3	$f (a) = a^{4} + 3 a^{3} - 17 a^{2} + 2 a - 7$ at $a = 3$
218171	Graph	x^2(x-1)	$x^{2} (x - 1)$
218172	Write in Standard Form	(x^2+x-3)(x^2-x+3)	$(x^{2} + x - 3) (x^{2} - x + 3)$
218173	Solve for x	6/x-9/7=(2x+9)/(7x)	$\frac{6}{x} - \frac{9}{7} = \frac{2 x + 9}{7 x}$
218174	Multiply	-1/5(-2 1/4)	$- \frac{1}{5} (- 2 \frac{1}{4})$
218175	Solve by Factoring	2cos(x)^2+cos(x)-1=0	$2 \cos^{2} (x) + \cos (x) - 1 = 0$
218176	Simplify	(-6k^2+7+4k^3)+(-9k^3+3k^4+1)	$(- 6 k^{2} + 7 + 4 k^{3}) + (- 9 k^{3} + 3 k^{4} + 1)$
218177	Solve for x	(x^2-x+4)^(3/2)-2=6	${(x^{2} - x + 4)}^{\frac{3}{2}} - 2 = 6$
218178	Solve the System of Inequalities	5-2x>31 and 7x+8>=-55	$5 - 2 x > 31$ and $7 x + 8 \geq - 55$
218179	Evaluate	x-6 = square root of x	$x - 6 = \sqrt{x}$
218180	Solve for y	x = square root of y-2	$x = \sqrt{y - 2}$
218181	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (1,3) and has a slope of 6 ?	What is the equation of the line that passes through the point $(1, 3)$ and has a slope of $6$ ?
218182	Simplify	3 square root of 2(2 square root of 30+4 square root of 120)	$3 \sqrt{2} (2 \sqrt{30} + 4 \sqrt{120})$
218183	Graph	\|y\|=x^2	$\| y \| = x^{2}$
218184	Simplify	((x-2)/(x+5)+(x-5)/(x+2))/((x-2)/(x+5)-(x-5)/(x+2))	$\frac{\frac{x - 2}{x + 5} + \frac{x - 5}{x + 2}}{\frac{x - 2}{x + 5} - \frac{x - 5}{x + 2}}$
218185	Solve for b	2bh=v for b	$2 b h = v$ for $b$
218186	Evaluate	(-7(2+8))/5+9(-2)	$\frac{- 7 (2 + 8)}{5} + 9 (- 2)$
218187	Write in Exponential Form	( square root of x^12)/( square root of x^5)	$\frac{\sqrt{x^{12}}}{\sqrt{x^{5}}}$
218188	Factor	(x+8)^(1/3)-(x+8)^(4/3)	${(x + 8)}^{\frac{1}{3}} - {(x + 8)}^{\frac{4}{3}}$
218189	Solve for x	4/(x+2)=7/x	$\frac{4}{x + 2} = \frac{7}{x}$
218190	Solve for x	0=x^3-3x^2+4x-12	$0 = x^{3} - 3 x^{2} + 4 x - 12$
218191	Simplify	(g^4-4g^2+11)+(-g^3+8g)	$(g^{4} - 4 g^{2} + 11) + (- g^{3} + 8 g)$
218192	Solve for x	cube root of 4x+8=0	$\sqrt[3]{4 x} + 8 = 0$
218193	Solve for x	5/2*x=1	$\frac{5}{2} \cdot x = 1$
218194	Solve the Inequality for x	(\|2x-3\|)/5>3	$\frac{\| 2 x - 3 \|}{5} > 3$
218195	Evaluate the Function	g(2+h)=x^3	$g (2 + h) = x^{3}$
218196	Simplify	-9(7a-1)-2a-5a^2+2	$- 9 (7 a - 1) - 2 a - 5 a^{2} + 2$
218197	Subtract	(x^2+17x)-(3x^2+5x)	$(x^{2} + 17 x) - (3 x^{2} + 5 x)$
218198	Evaluate	(-3x^-5)^3	${(- 3 x^{- 5})}^{3}$
218199	Expand Using Pascal's Triangle	(2p^3-3t)^4	${(2 p^{3} - 3 t)}^{4}$
218200	Solve by Factoring	5x^3=1080	$5 x^{3} = 1080$