Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
228001	Solve the System of Inequalities	8x+15<=4x-5 and -7x+2<-6x+3	$8 x + 15 \leq 4 x - 5$ and $- 7 x + 2 < - 6 x + 3$
228002	Find the Exact Value	cos(150 degrees )^2	$\cos^{2} (150 °)$
228003	Find the Parallel Line	What is an equation of the line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6 ?	What is an equation of the line that passes through the point $(- 2, - 4)$ and is parallel to the line $5 x - 2 y = 6$ ?
228004	Find the LCM	10 and 5	$10$ and $5$
228005	Simplify	1/6(4/5)^-2	$\frac{1}{6} {(\frac{4}{5})}^{- 2}$
228006	Simplify the Radical Expression	square root of 25+10 square root of 5+5	$\sqrt{25 + 10 \sqrt{5} + 5}$
228007	Solve for b	y=2cos(b(x-2))-1	$y = 2 \cos (b (x - 2)) - 1$
228008	Solve for θ	sin(theta)-sin(2theta)=0	$\sin (θ) - \sin (2 θ) = 0$
228009	Solve for x	e^(4x-2)>=16	$e^{4 x - 2} \geq 16$
228010	Find the Degree, Leading Term, and Leading Coefficient	f(x)=-8x-5-x^4+8x^3	$f (x) = - 8 x - 5 - x^{4} + 8 x^{3}$
228011	Find the End Behavior	y=x^3-4x^2+3x-12	$y = x^{3} - 4 x^{2} + 3 x - 12$
228012	Find the Roots (Zeros)	y=(x-3)(x-1)(2x-1)	$y = (x - 3) (x - 1) (2 x - 1)$
228013	Simplify	2^-1(x/y)^0	$2^{- 1} {(\frac{x}{y})}^{0}$
228014	Solve the Rational Equation for x	(8x)/(x+1)-2=-8/(x+1)	$\frac{8 x}{x + 1} - 2 = - \frac{8}{x + 1}$
228015	Simplify	(40x^3y^9)/((2x^6y^-10)^-3)	$\frac{40 x^{3} y^{9}}{{(2 x^{6} y^{- 10})}^{- 3}}$
228016	Simplify	(a/b)/c	$\frac{(\frac{a}{b})}{c}$
228017	Find the Distance Between Two Points	(7,2) and (-1,-3)	$(7, 2)$ and $(- 1, - 3)$
228018	Evaluate Using the Given Value	1/2x^4-3/4x^2 for x=2	$\frac{1}{2} x^{4} - \frac{3}{4} x^{2}$ for $x = 2$
228019	Solve the Inequality for q	q-12>=-13	$q - 12 \geq - 13$
228020	Simplify	1/(1/x+1/(x+1))	$\frac{1}{\frac{1}{x} + \frac{1}{x + 1}}$
228021	Solve for x	3x=x^2-4	$3 x = x^{2} - 4$
228022	Solve for x	4=6/(2x-3)	$4 = \frac{6}{2 x - 3}$
228023	Multiply	cube root of x* cube root of x^2	$\sqrt[3]{x} \cdot \sqrt[3]{x^{2}}$
228024	Subtract	(x^2+2x-1)-(-x^3+2x-1)	$(x^{2} + 2 x - 1) - (- x^{3} + 2 x - 1)$
228025	Multiply	(x+3)(2x+1)(2x-3)	$(x + 3) (2 x + 1) (2 x - 3)$
228026	Multiply	(6x+48)/(x^2-9x)*(x^2-81)/(x^2+17x+72)	$\frac{6 x + 48}{x^{2} - 9 x} \cdot \frac{x^{2} - 81}{x^{2} + 17 x + 72}$
228027	Solve by Addition/Elimination	-3x+y=-9 12x-4y=24	$- 3 x + y = - 9$ $12 x - 4 y = 24$
228028	Solve for y	e^(y-1)-27=54	$e^{y - 1} - 27 = 54$
228029	Solve for y	y=-3cos(pi/2)	$y = - 3 \cos (\frac{π}{2})$
228030	Simplify	(3i+5)+(6+ square root of -25)	$(3 i + 5) + (6 + \sqrt{- 25})$
228031	Simplify	( fourth root of 8)( cube root of 2)	$(\sqrt[4]{8}) (\sqrt[3]{2})$
228032	Solve for x	1/(x-3)-2/(x+5)=(2x-1)/(x^2+2x-15)	$\frac{1}{x - 3} - \frac{2}{x + 5} = \frac{2 x - 1}{x^{2} + 2 x - 15}$
228033	Solve for k	g(x)=0.25^x+k	$g (x) = {0.25}^{x} + k$
228034	Describe the Transformation	y=3(x-4)^2	$y = 3 {(x - 4)}^{2}$
228035	Factor	P(x)=(x-1)(x^2-5x+6)	$P (x) = (x - 1) (x^{2} - 5 x + 6)$
228036	Simplify the Radical Expression	(26)(1/4)	$(26) (\frac{1}{4})$
228037	Write as a Single Logarithm	1/4 log base 3 of 2+1/4 log base 3 of x	$\frac{1}{4} \log_{3} (2) + \frac{1}{4} \log_{3} (x)$
228038	Divide	((3x+15)/(49x^2-4))÷((2x-7)/(7x-2))	$\frac{3 x + 15}{49 x^{2} - 4} \div \frac{2 x - 7}{7 x - 2}$
228039	Rationalize the Denominator	(5- square root of 2)/( square root of 2)	$\frac{5 - \sqrt{2}}{\sqrt{2}}$
228040	Simplify	(x+1)/(x^2)*x/(x^2-1)	$\frac{x + 1}{x^{2}} \cdot \frac{x}{x^{2} - 1}$
228041	Evaluate	1-2/3+1/5	$1 - \frac{2}{3} + \frac{1}{5}$
228042	Write in Standard Form	-3i*(-9+8i)	$- 3 i \cdot (- 9 + 8 i)$
228043	Find the Roots (Zeros)	2x+3/(x-1)=(3x)/(x-1)	$2 x + \frac{3}{x - 1} = \frac{3 x}{x - 1}$
228044	Simplify	8(12-9)^2-4*7	$8 {(12 - 9)}^{2} - 4 \cdot 7$
228045	Solve for x	4(x+2)-7=3x+1+x	$4 (x + 2) - 7 = 3 x + 1 + x$
228046	Find the Exact Value	sin(300)^2	$\sin^{2} (300)$
228047	Simplify the Radical Expression	square root of (a^4b^4)/(c^3)	$\sqrt{\frac{a^{4} b^{4}}{c^{3}}}$
228048	Simplify the Radical Expression	15 square root of 3+ square root of 5-2 square root of 3	$15 \sqrt{3} + \sqrt{5} - 2 \sqrt{3}$
228049	Solve for D	H=b/(D+d)	$H = \frac{b}{D + d}$
228050	Solve for θ	2sin(theta)-1=csc(theta)	$2 \sin (θ) - 1 = \csc (θ)$
228051	Find the x and y Intercepts	f(x)=-4x(x^2+1)(2x+1)^2(x+6)^2	$f (x) = - 4 x (x^{2} + 1) {(2 x + 1)}^{2} {(x + 6)}^{2}$
228052	Solve for q	(5q+1)^(1/4)+7=5	${(5 q + 1)}^{\frac{1}{4}} + 7 = 5$
228053	Simplify	4*3+(18x)÷9-12	$4 \cdot 3 + 18 x \div 9 - 12$
228054	Simplify	2 cube root of 2+ square root of 5-4 cube root of 2+2 square root of 5	$2 \sqrt[3]{2} + \sqrt{5} - 4 \sqrt[3]{2} + 2 \sqrt{5}$
228055	Simplify	(x+8)/(x+2)+1/((x+8)/(x+2))	$\frac{x + 8}{x + 2} + \frac{1}{\frac{x + 8}{x + 2}}$
228056	Simplify	(1+cot(x)^2)cos(x)^2	$(1 + \cot^{2} (x)) \cos^{2} (x)$
228057	Solve for x	(x^2-5)^2-3x^2+15=-2	${(x^{2} - 5)}^{2} - 3 x^{2} + 15 = - 2$
228058	Divide Using Synthetic Division	(2x^3+x-6)÷(x+2)	$(2 x^{3} + x - 6) \div (x + 2)$
228059	Multiply	cube root of 3 , cube root of 24	$\sqrt[3]{3}$ , $\sqrt[3]{24}$
228060	Divide	(x/y)÷(y/x)	$\frac{x}{y} \div \frac{y}{x}$
228061	Simplify	(csc(x)-sec(x))^2	${(\csc (x) - \sec (x))}^{2}$
228062	Simplify	(a^0b^-2)/(c^-3d)	$\frac{a^{0} b^{- 2}}{c^{- 3} d}$
228063	Simplify	x^2+2-3x^2+4x+6	$x^{2} + 2 - 3 x^{2} + 4 x + 6$
228064	Find the Quotient	(-2x^3+3x^2-1)/(x-1)	$\frac{- 2 x^{3} + 3 x^{2} - 1}{x - 1}$
228065	Describe the Transformation	f(x)=0.2(x-3)^4+2	$f (x) = 0.2 {(x - 3)}^{4} + 2$
228066	Graph	x+5<=5 or x+5>=6	$x + 5 \leq 5$ or $x + 5 \geq 6$
228067	Find the Domain and Range	y = square root of 1/2x+5	$y = \sqrt{\frac{1}{2} x} + 5$
228068	Simplify	b^3(3b^-1)^-2	$b^{3} {(3 b^{- 1})}^{- 2}$
228069	Solve the Inequality for x	(4x)/5+3>x+5	$\frac{4 x}{5} + 3 > x + 5$
228070	Solve the Rational Equation for x	square root of x-3-2=0	$\sqrt{x - 3} - 2 = 0$
228071	Simplify	((3c)/-2)^-1(d/4)^-2	${(\frac{3 c}{- 2})}^{- 1} {(\frac{d}{4})}^{- 2}$
228072	Solve for x	x=1/3(6+ log of 2.1)x^3	$x = \frac{1}{3} (6 + \log (2.1)) x^{3}$
228073	Solve the Inequality for z	-8-8z<=-3	$- 8 - 8 z \leq - 3$
228074	Evaluate	2/x+x/3	$\frac{2}{x} + \frac{x}{3}$
228075	Simplify	-5a-7b+a-5b-4-(-a)	$- 5 a - 7 b + a - 5 b - 4 - (- a)$
228076	Find All Complex Solutions	log base x of x+2=2	$\log_{x} (x + 2) = 2$
228077	Simplify	4-3/2(1/2x+3/2)	$4 - \frac{3}{2} (\frac{1}{2} x + \frac{3}{2})$
228078	Solve for x	sin(x/2)+cos(x)=0	$\sin (\frac{x}{2}) + \cos (x) = 0$
228079	Evaluate	25% of 100	$25 %$ of $100$
228080	Divide Using Long Polynomial Division	Use the long division method to find the result when 6x^3+5x^2+19x+6 is divided by 3x+1	Use the long division method to find the result when $6 x^{3} + 5 x^{2} + 19 x + 6$ is divided by $3 x + 1$
228081	Evaluate	5^(2x+1)<=125	$5^{2 x + 1} \leq 125$
228082	Find the x and y Intercepts	y=x^2-2 square root of 2x+2	$y = x^{2} - 2 \sqrt{2} x + 2$
228083	Simplify the Radical Expression	8 square root of 32x	$8 \sqrt{32 x}$
228084	Solve by Factoring	5x^2-3x+8=3x^2+8x-1	$5 x^{2} - 3 x + 8 = 3 x^{2} + 8 x - 1$
228085	Solve for x	5-(x-1)^(1/3)=8	$5 - {(x - 1)}^{\frac{1}{3}} = 8$
228086	Convert to Radical Form	x^(4/6)	$x^{\frac{4}{6}}$
228087	Solve for x	x^6+1=0	$x^{6} + 1 = 0$
228088	Simplify	-1/2*2/( square root of 3)	$- \frac{1}{2} \cdot \frac{2}{\sqrt{3}}$
228089	Solve the Inequality for a	13a>-26	$13 a > - 26$
228090	Simplify	square root of 11+8 square root of 7-2 square root of 7-6 square root of 11	$\sqrt{11} + 8 \sqrt{7} - 2 \sqrt{7} - 6 \sqrt{11}$
228091	Solve for x	-1/2\|x-5\|+3=2	$- \frac{1}{2} \| x - 5 \| + 3 = 2$
228092	Evaluate	( square root of x+2)^2	${(\sqrt{x} + 2)}^{2}$
228093	Divide	(3- fourth root of 5x^2)/( fourth root of 3x^3)	$\frac{3 - \sqrt[4]{5 x^{2}}}{\sqrt[4]{3 x^{3}}}$
228094	Solve the System of Equations	y=x^2+x-27 7=2x-y	$y = x^{2} + x - 27$ $7 = 2 x - y$
228095	Simplify	(2.71^3)^2(2.71)^-5	${({2.71}^{3})}^{2} {(2.71)}^{- 5}$
228096	Solve the Absolute Value Inequality for x	8+\|6-4x\|=17	$8 + \| 6 - 4 x \| = 17$
228097	Evaluate the Function	f(x)=(4x-28)/(6x-7) at x=7	$f (x) = \frac{4 x - 28}{6 x - 7}$ at $x = 7$
228098	Solve for x	3/x=21/6	$\frac{3}{x} = \frac{21}{6}$
228099	Simplify	((x^2+11x+18)/(x^2+x)*(1-x^2)/(x^2+8x-9))÷((x^2-4x-12)/(36-x^2))	$\frac{x^{2} + 11 x + 18}{x^{2} + x} \cdot \frac{1 - x^{2}}{x^{2} + 8 x - 9} \div \frac{x^{2} - 4 x - 12}{36 - x^{2}}$
228100	Evaluate	15% of 35	$15 %$ of $35$