Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
237101	Graph	Where does the polynomial y=x^2-3x+2 cross the x-axis ?	Where does the polynomial $y = x^{2} - 3 x + 2$ cross the $x - a x i s$ ?
237102	Graph	f(x)=-2x-7 if x<-5; -(x+2)^2+6 if -5<=x<0; square root of x-1 if x>=0	$f (x) = {\begin{cases} - 2 x - 7 & x < - 5 \\ - {(x + 2)}^{2} + 6 & - 5 \leq x < 0 \\ \sqrt{x} - 1 & x \geq 0 \end{cases}$
237103	Solve for a	cube root of 128- cube root of 16=a cube root of b	$\sqrt[3]{128} - \sqrt[3]{16} = a \sqrt[3]{b}$
237104	Simplify	((3^5)/(3^3))^2	${(\frac{3^{5}}{3^{3}})}^{2}$
237105	Simplify	-3/(- square root of 9)	$- \frac{3}{- \sqrt{9}}$
237106	Find the Exact Value	91 , 321 , 972*0.007004	$91$ , $321$ , $972 \times 0.007004$
237107	Find the x and y Intercepts	y=(x^2+11x+18)/(2x+1)	$y = \frac{x^{2} + 11 x + 18}{2 x + 1}$
237108	Simplify	fourth root of 7+3 fourth root of 7-11 fourth root of 7	$\sqrt[4]{7} + 3 \sqrt[4]{7} - 11 \sqrt[4]{7}$
237109	Evaluate	(5 square root of 3+ square root of 15)*(3 square root of 5- square root of 15)	$(5 \sqrt{3} + \sqrt{15}) \cdot (3 \sqrt{5} - \sqrt{15})$
237110	Rationalize the Denominator	-1/(2+ square root of 3)	$- \frac{1}{2 + \sqrt{3}}$
237111	Simplify	2^-1+2^-1	$2^{- 1} + 2^{- 1}$
237112	Solve for x	2 cube root of x-10+4=0	$2 \sqrt[3]{x - 10} + 4 = 0$
237113	Simplify	square root of 320+ square root of 45+ cube root of 40	$\sqrt{320} + \sqrt{45} + \sqrt[3]{40}$
237114	Simplify	(1/(x^2)+1/x)/(1/(x^3))	$\frac{(\frac{1}{x^{2}} + \frac{1}{x})}{\frac{1}{x^{3}}}$
237115	Solve for x	9^(2x)*9^(1-3x)=27^(x+2)	$9^{2 x} \cdot 9^{1 - 3 x} = 27^{x + 2}$
237116	Solve for x	7/2=(3x+6)/x	$\frac{7}{2} = \frac{3 x + 6}{x}$
237117	Simplify	-1/(2+ square root of 3)	$- \frac{1}{2 + \sqrt{3}}$
237118	Solve for y	x=-2+2y	$x = - 2 + 2 y$
237119	Simplify	(2s^2p-5w^2)^2	${(2 s^{2} p - 5 w^{2})}^{2}$
237120	Find the Roots (Zeros)	x^3-4x^2+4x=0	$x^{3} - 4 x^{2} + 4 x = 0$
237121	Solve for x	2x-5(1-3x)=1-3(1-2x)	$2 x - 5 (1 - 3 x) = 1 - 3 (1 - 2 x)$
237122	Evaluate	3(p+(-3))+5p	$3 (p + (- 3)) + 5 p$
237123	Evaluate	7*((7+7)÷7)	$7 \times ((7 + 7) \div 7)$
237124	Evaluate	(2 square root of 6)^2-3( square root of 21)^2	${(2 \sqrt{6})}^{2} - 3 {(\sqrt{21})}^{2}$
237125	Graph	Graph the line x=8	Graph the line $x = 8$
237126	Combine Like Terms	25r^3+9s-2r^3+5s	$25 r^{3} + 9 s - 2 r^{3} + 5 s$
237127	Simplify	(5x-xy^2)-(4xy^2-2x)	$(5 x - x y^{2}) - (4 x y^{2} - 2 x)$
237128	Multiply	(x+2y)*(x^2-xy+3y)	$(x + 2 y) \cdot (x^{2} - x y + 3 y)$
237129	Determine if True	1+cot(x)^2=csc(x)^2	$1 + \cot^{2} (x) = \csc^{2} (x)$
237130	Simplify	(7v)/(7v^2+56v)(v-2)	$\frac{7 v}{7 v^{2} + 56 v} (v - 2)$
237131	Simplify	(a^4)^-5*a^13	${(a^{4})}^{- 5} \cdot a^{13}$
237132	Simplify	a^(1/4)b^-7c^0	$a^{\frac{1}{4}} b^{- 7} c^{0}$
237133	Divide	4 , 420÷170	$4$ , $420 \div 170$
237134	Write in Standard Form	(x^2+9x+18)-(x+6)	$(x^{2} + 9 x + 18) - (x + 6)$
237135	Simplify	(sec(x)tan(x))/(tan(x)^2+1)	$\frac{\sec (x) \tan (x)}{\tan^{2} (x) + 1}$
237136	Write the Fraction in Simplest Form	((-4x-12)/(x-7))÷((x^2-12x+36)/(2x-14))	$\frac{- 4 x - 12}{x - 7} \div \frac{x^{2} - 12 x + 36}{2 x - 14}$
237137	Evaluate	3(v-9w+1)	$3 (v - 9 w + 1)$
237138	Evaluate	(1+sin(theta))(1-sin(theta))=cos(theta)^2	$(1 + \sin (θ)) (1 - \sin (θ)) = \cos^{2} (θ)$
237139	Write Using Positive Exponents	x^7y^-5	$x^{7} y^{- 5}$
237140	Simplify	(3/(2x^2))/(10/(7x^2))	$\frac{\frac{3}{2 x^{2}}}{\frac{10}{7 x^{2}}}$
237141	Evaluate	8^6-64(8)^4+8^2-7*8-51	$8^{6} - 64 {(8)}^{4} + 8^{2} - 7 \cdot 8 - 51$
237142	Solve Using the Square Root Property	5(x-10)^2-33=-3	$5 {(x - 10)}^{2} - 33 = - 3$
237143	Solve for θ	cot(theta)=undefined	$\cot (θ) = u n d e f i n e d$
237144	Evaluate the Function	f(0)=0+2	$f (0) = 0 + 2$
237145	Convert to Interval Notation	-8<=(-3x+1)/4<=9	$- 8 \leq \frac{- 3 x + 1}{4} \leq 9$
237146	Multiply	a(a+3b)	$a (a + 3 b)$
237147	Solve for x	9x+4-x=4(2x+1)	$9 x + 4 - x = 4 (2 x + 1)$
237148	Simplify	-5/6(42x+18y)-(2y-x)	$- \frac{5}{6} (42 x + 18 y) - (2 y - x)$
237149	Simplify the Radical Expression	(3^4d^(-3/4))/(3^2d^(3/4))	$\frac{3^{4} d^{- \frac{3}{4}}}{3^{2} d^{\frac{3}{4}}}$
237150	Simplify	-((y^4)/4)^2	$- {(\frac{y^{4}}{4})}^{2}$
237151	Solve the Inequality for x	3/4>-(x-3)+2x	$\frac{3}{4} > - (x - 3) + 2 x$
237152	Simplify the Radical Expression	x square root of 63x^2+4 square root of 63x^4	$x \sqrt{63 x^{2}} + 4 \sqrt{63 x^{4}}$
237153	Simplify	(4x^5y^-3)(-3x^-3y^3)	$(4 x^{5} y^{- 3}) (- 3 x^{- 3} y^{3})$
237154	Simplify	-8/-6	$- \frac{8}{- 6}$
237155	Simplify the Radical Expression	square root of (5x)/(49y^4)	$\sqrt{\frac{5 x}{49 y^{4}}}$
237156	Find the Domain and Range	x^3-x^2+1	$x^{3} - x^{2} + 1$
237157	Solve for x	(x+4)/(2x)=12/16	$\frac{x + 4}{2 x} = \frac{12}{16}$
237158	Multiply	[[-3],[-1],[0]][[1,-1,-1,-1]]	$[\begin{array}{c} - 3 \\ - 1 \\ 0 \end{array}] [\begin{array}{c} 1 & - 1 & - 1 & - 1 \end{array}]$
237159	Subtract	9 square root of 5-2 square root of 5-4 square root of 3- square root of 3	$9 \sqrt{5} - 2 \sqrt{5} - 4 \sqrt{3} - \sqrt{3}$
237160	Simplify	((6^2-24)^2)÷((x/y)^-5)	${(6^{2} - 24)}^{2} \div {(\frac{x}{y})}^{- 5}$
237161	Solve for d	5 3/4=d-2 1/8	$5 \frac{3}{4} = d - 2 \frac{1}{8}$
237162	Simplify the Radical Expression	(1/(q^-8*q^2))^(1/8)	${(\frac{1}{q^{- 8} \cdot q^{2}})}^{\frac{1}{8}}$
237163	Solve the Absolute Value Inequality for x	\|3x-6\|=0	$\| 3 x - 6 \| = 0$
237164	Simplify	((7x^2)/3)/(5/(4x))	$\frac{\frac{7 x^{2}}{3}}{\frac{5}{4 x}}$
237165	Divide	( fourth root of x^2y^3)/( cube root of xy)	$\frac{\sqrt[4]{x^{2} y^{3}}}{\sqrt[3]{x y}}$
237166	Graph	csc(theta)>0 and cos(theta)<0	$\csc (θ) > 0$ and $\cos (θ) < 0$
237167	Write in Standard Form	4x+3x^2-5x^3+8x^4	$4 x + 3 x^{2} - 5 x^{3} + 8 x^{4}$
237168	Graph	-f(2(x-2))+1	$- f (2 (x - 2)) + 1$
237169	Find the LCD	(12x)/(x-1) and x/(x-6)	$\frac{12 x}{x - 1}$ and $\frac{x}{x - 6}$
237170	Simplify	3/4 cube root of 128+2/5 cube root of 250	$\frac{3}{4} \sqrt[3]{128} + \frac{2}{5} \sqrt[3]{250}$
237171	Simplify	(2t^2+13t+15)÷(t+6)	$(2 t^{2} + 13 t + 15) \div (t + 6)$
237172	Find All Complex Solutions	2cos(x)sin(x)-cos(x)=0	$2 \cos (x) \sin (x) - \cos (x) = 0$
237173	Evaluate	10+12/6+12	$10 + \frac{12}{6} + 12$
237174	Plot	y>x-5	$y > x - 5$
237175	Evaluate	square root of cube root of 81	$\sqrt{\sqrt[3]{81}}$
237176	Solve the Absolute Value Inequality for y	\|y\|=0	$\| y \| = 0$
237177	Find the x and y Intercepts	f(x)=x^2(x-5)(x^2+2)	$f (x) = x^{2} (x - 5) (x^{2} + 2)$
237178	Evaluate	1/3pir^2h	$\frac{1}{3} π r^{2} h$
237179	Write in Standard Form	(3m^2-4m+1)(2m^2+5m-9)	$(3 m^{2} - 4 m + 1) (2 m^{2} + 5 m - 9)$
237180	Solve the Inequality for x	x^4<9x^2	$x^{4} < 9 x^{2}$
237181	Graph	y=-1/2(x+5)+4	$y = - \frac{1}{2} (x + 5) + 4$
237182	Solve the System of Inequalities	x<5 and x>-5	$x < 5$ and $x > - 5$
237183	Write in Standard Form	-9i(3i-8)	$- 9 i (3 i - 8)$
237184	Factor	9x^2y^7-3x^4y^3-27y^8x	$9 x^{2} y^{7} - 3 x^{4} y^{3} - 27 y^{8} x$
237185	Simplify	(6r+2+8r^3)-(5r^3-11-8r^5)-(6r+9r^5)	$(6 r + 2 + 8 r^{3}) - (5 r^{3} - 11 - 8 r^{5}) - (6 r + 9 r^{5})$
237186	Graph	(y^3)/16-x^2=1	$\frac{y^{3}}{16} - x^{2} = 1$
237187	Simplify	((4t^2-16)/8)/((t-2)/6)	$\frac{\frac{4 t^{2} - 16}{8}}{\frac{t - 2}{6}}$
237188	Solve the Rational Equation for v	9/(v-3)-5/(v+1)=28/(v^2-2v-3)	$\frac{9}{v - 3} - \frac{5}{v + 1} = \frac{28}{v^{2} - 2 v - 3}$
237189	Evaluate	243/5-486/3+243	$\frac{243}{5} - \frac{486}{3} + 243$
237190	Find the Exact Value	csc(pi/2)^2	$\csc^{2} (\frac{π}{2})$
237191	Simplify	( fifth root of r^6)/( cube root of r^2)	$\frac{\sqrt[5]{r^{6}}}{\sqrt[3]{r^{2}}}$
237192	Find a,b,c	((x-2)^2)/9-((y-1)^2)/4=1	$\frac{{(x - 2)}^{2}}{9} - \frac{{(y - 1)}^{2}}{4} = 1$
237193	Graph	y<-x+2 y<3	$y < - x + 2$ $y < 3$
237194	Solve the Inequality for y	2x+3y<15	$2 x + 3 y < 15$
237195	Simplify	((x^2+x-20)/(4x^2-40x+96)*3/(25-x^2))÷((x+6)/(36-x^2))	$\frac{x^{2} + x - 20}{4 x^{2} - 40 x + 96} \cdot \frac{3}{25 - x^{2}} \div \frac{x + 6}{36 - x^{2}}$
237196	Solve for θ	2cos(theta)^2=2+sin(theta)	$2 \cos^{2} (θ) = 2 + \sin (θ)$
237197	Divide Using Long Polynomial Division	Use the long division method to find the result when 4x^3+14x^2+16x+5 is divided by 2x+1	Use the long division method to find the result when $4 x^{3} + 14 x^{2} + 16 x + 5$ is divided by $2 x + 1$
237198	Graph	y<-6/5x+6 y<3/4x+1	$y < - \frac{6}{5} x + 6$ $y < \frac{3}{4} x + 1$
237199	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (-8,3) and has a slope of -1/4 ?	What is the equation of the line that passes through the point $(- 8, 3)$ and has a slope of $- \frac{1}{4}$ ?
237200	Simplify the Radical Expression	-5 square root of x^3	$- 5 \sqrt{x^{3}}$