Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
192601	Solve the System of Equations	-4x=4-y 2y=8x+8	$- 4 x = 4 - y$ $2 y = 8 x + 8$
192602	Multiply	(1/2x^3)(-2/3a^2x)(-3/5a^4m)	$(\frac{1}{2} x^{3}) (- \frac{2}{3} a^{2} x) (- \frac{3}{5} a^{4} m)$
192603	Solve the Absolute Value Inequality for x	\|2x+3\|>=19	$\| 2 x + 3 \| \geq 19$
192604	Graph	f(x)=1 if x<-2; 2x-3 if -2<=x<1; -x+5 if x>=1	$f (x) = {\begin{cases} 1 & x < - 2 \\ 2 x - 3 & - 2 \leq x < 1 \\ - x + 5 & x \geq 1 \end{cases}$
192605	Find All Complex Solutions	sin(theta)+cos(theta) = square root of 2	$\sin (θ) + \cos (θ) = \sqrt{2}$
192606	Find the Exact Value	pi/2+pi	$\frac{π}{2} + π$
192607	Write in Standard Form	i/(3-2i)+(2i)/(3+8i)	$\frac{i}{3 - 2 i} + \frac{2 i}{3 + 8 i}$
192608	Simplify	2^n+2^n	$2^{n} + 2^{n}$
192609	Simplify the Radical Expression	square root of 15y^3	$\sqrt{15 y^{3}}$
192610	Evaluate	( square root of -1)^2	${(\sqrt{- 1})}^{2}$
192611	Simplify	(4p^2+32p)/(p-2)*(p^2+p-6)/(2p^3+16p^2)	$\frac{4 p^{2} + 32 p}{p - 2} \cdot \frac{p^{2} + p - 6}{2 p^{3} + 16 p^{2}}$
192612	Evaluate	15sin(60)	$15 \sin (60)$
192613	Solve for n	4^n*4^(2n-9)=64	$4^{n} \cdot 4^{2 n - 9} = 64$
192614	Graph	f(x)=(x+5)(x-1)^2(x+1)	$f (x) = (x + 5) {(x - 1)}^{2} (x + 1)$
192615	Solve the Inequality for x	5x-6<=2+(3x-4)	$5 x - 6 \leq 2 + (3 x - 4)$
192616	Find the Perpendicular Line	(1,9) and perpendicular to 2x+7y=1	$(1, 9)$ and perpendicular to $2 x + 7 y = 1$
192617	Solve for z	-(3z+4)=6z-3(3z+2)	$- (3 z + 4) = 6 z - 3 (3 z + 2)$
192618	Evaluate	-8(-10)-71/-1	$- 8 \times (- 10) - 7 \times \frac{1}{- 1}$
192619	Solve the Inequality for x	(1/3)^(2x+1)> square root of 27/(3^(x-1))	${(\frac{1}{3})}^{2 x + 1} > \sqrt{\frac{27}{3^{x - 1}}}$
192620	Evaluate	-1/2+(-4)+(-2 2/3)	$- \frac{1}{2} + (- 4) + (- 2 \frac{2}{3})$
192621	Evaluate Using the Given Value	m+p÷5 ; use m=1 ; and p=5	$m + p \div 5$ ; use $m = 1$ ; and $p = 5$
192622	Find the x and y Intercepts	(-4x+17)/(3x)	$\frac{- 4 x + 17}{3 x}$
192623	Evaluate	3^(-1/2)x^(1/2)	$3^{- \frac{1}{2}} x^{\frac{1}{2}}$
192624	Simplify	x+x^2-xy^2-y^2	$x + x^{2} - x y^{2} - y^{2}$
192625	Solve for q	8/q+2=(q+4)/(q-1)	$\frac{8}{q} + 2 = \frac{q + 4}{q - 1}$
192626	Find the Parallel Line	Find the equation of the line through (7,2) which is parallel to the line y=-3x-2	Find the equation of the line through $(7, 2)$ which is parallel to the line $y = - 3 x - 2$
192627	Subtract	(8x^2-3x)-(5x-5-8x^2)	$(8 x^{2} - 3 x) - (5 x - 5 - 8 x^{2})$
192628	Simplify	6/(y-1)*(5-5y)/10	$\frac{6}{y - 1} \cdot \frac{5 - 5 y}{10}$
192629	Simplify	((-1/2)y^4)^3*(-16y^2)	${((- \frac{1}{2}) y^{4})}^{3} \cdot (- 16 y^{2})$
192630	Simplify	(2x^2-7x-15)/(x^2-25)*(x^2+x)/(2x^2+5x+3)	$\frac{2 x^{2} - 7 x - 15}{x^{2} - 25} \cdot \frac{x^{2} + x}{2 x^{2} + 5 x + 3}$
192631	Simplify	((2^157^12)/(7(2^2)^47^42))^3	${(\frac{2^{15} \cdot 7^{12}}{7 \cdot {(2^{2})}^{4} \cdot 7^{4} \cdot 2})}^{3}$
192632	Simplify	3/(2 square root of 6)	$\frac{3}{2 \sqrt{6}}$
192633	Evaluate	(-6x^2-x)-(-4x^2+10x-1)	$(- 6 x^{2} - x) - (- 4 x^{2} + 10 x - 1)$
192634	Solve Using the Quadratic Formula	24=x^2-4x+3	$24 = x^{2} - 4 x + 3$
192635	Find the End Behavior	f(x)=147x+686-84x^2+7x^3	$f (x) = 147 x + 686 - 84 x^{2} + 7 x^{3}$
192636	Solve for x	F=kx-kx_0	$F = k x - k x_{0}$
192637	Evaluate	27*((3^3)^-1)	$27 \cdot ({(3^{3})}^{- 1})$
192638	Solve for x	1/3e^(4x)=12	$\frac{1}{3} e^{4 x} = 12$
192639	Find the Holes in the Graph	f(x)=(2x)/(x^2-1)	$f (x) = \frac{2 x}{x^{2} - 1}$
192640	Solve for v	9v^2+25=-30v	$9 v^{2} + 25 = - 30 v$
192641	Solve the Inequality for x	9x-7i>9x-21u	$9 x - 7 i > 9 x - 21 u$
192642	Solve for k	2(2k-1)=4(k-2)	$2 (2 k - 1) = 4 (k - 2)$
192643	Find the Distance Between Two Points	(6,-9) and (1,3)	$(6, - 9)$ and $(1, 3)$
192644	Convert to Interval Notation	8y-3(y-2)>2y+4(2y+4)	$8 y - 3 (y - 2) > 2 y + 4 (2 y + 4)$
192645	Divide	((2x^2-9x-5)/(x^2-8x+15))÷((18x+9)/(x^2-9))	$\frac{2 x^{2} - 9 x - 5}{x^{2} - 8 x + 15} \div \frac{18 x + 9}{x^{2} - 9}$
192646	Find the Distance Between Two Points	(-6,0) and (-9,-4)	$(- 6, 0)$ and $(- 9, - 4)$
192647	Simplify	5 square root of 20x^4-3 square root of 45x^4	$5 \sqrt{20 x^{4}} - 3 \sqrt{45 x^{4}}$
192648	Solve for a	(x^4)^(1/3) cube root of x=x^a	${(x^{4})}^{\frac{1}{3}} \sqrt[3]{x} = x^{a}$
192649	Factor	f(x)=(x^2)/(x^2-4)	$f (x) = \frac{x^{2}}{x^{2} - 4}$
192650	Combine Like Terms	7/8x+9/10-2x-3/5	$\frac{7}{8} x + \frac{9}{10} - 2 x - \frac{3}{5}$
192651	Solve for x	56/(x^2-2x-15)-6/(x+3)=7/(x-5)	$\frac{56}{x^{2} - 2 x - 15} - \frac{6}{x + 3} = \frac{7}{x - 5}$
192652	Solve for t	-1t+14=-3t+10	$- 1 t + 14 = - 3 t + 10$
192653	Describe the Transformation	f(x-4)	$f (x - 4)$
192654	Find All Complex Solutions	(tan(theta)+1)(cos(theta)+1)=0	$(\tan (θ) + 1) (\cos (θ) + 1) = 0$
192655	Find the Exact Value	sin(45 degrees )^2+cos(60 degrees )^2	$\sin^{2} (45 °) + \cos^{2} (60 °)$
192656	Solve the Inequality for g	8(3g-2)<=12(2g+1)	$8 (3 g - 2) \leq 12 (2 g + 1)$
192657	Solve the System of Equations	y=5x+5 5y=25x	$y = 5 x + 5$ $5 y = 25 x$
192658	Solve for r	i/r=p	$\frac{i}{r} = p$
192659	Solve the Inequality for y	(3y-4)/0.2-8>12	$\frac{3 y - 4}{0.2} - 8 > 12$
192660	Describe the Transformation	h(x)=-3\|x\|-1	$h (x) = - 3 \| x \| - 1$
192661	Solve for x	log base 4 of x-4=- log base 4 of x-7+1	$\log_{4} (x - 4) = - \log_{4} (x - 7) + 1$
192662	Evaluate the Function	f(x)=(3x^2-5x+1)^3	$f (x) = {(3 x^{2} - 5 x + 1)}^{3}$
192663	Simplify	5/(2x)-(3x)/(x+1)	$\frac{5}{2 x} - \frac{3 x}{x + 1}$
192664	Graph	f(x)=(x^3-2x^2)/(x-2)	$f (x) = \frac{x^{3} - 2 x^{2}}{x - 2}$
192665	Graph	y=tan(x-(2pi)/3)	$y = \tan (x - \frac{2 π}{3})$
192666	Write in Standard Form	3+5d=4d^2	$3 + 5 d = 4 d^{2}$
192667	Simplify	(1/(4p)-3/p)/(1/(4p)+4/p)	$\frac{\frac{1}{4 p} - \frac{3}{p}}{\frac{1}{4 p} + \frac{4}{p}}$
192668	Graph Using a Table of Values	f(x)=-16/(x^2-2x-8)	$f (x) = \frac{- 16}{x^{2} - 2 x - 8}$
192669	Graph	g(x)=5x-7g(x^2+1)	$g (x) = 5 x - 7 g (x^{2} + 1)$
192670	Solve the Inequality for x	5/x<3	$\frac{5}{x} < 3$
192671	Simplify	( cube root of x^2)/( square root of x)	$\frac{\sqrt[3]{x^{2}}}{\sqrt{x}}$
192672	Determine if True	sin(x)^2+cos(x)^2=1	$\sin^{2} (x) + \cos^{2} (x) = 1$
192673	Write in Standard Form	(x)(x)=4	$(x) (x) = 4$
192674	Solve for x	1/(x-4)-4/(x^2-4x)=1	$\frac{1}{x - 4} - \frac{4}{x^{2} - 4 x} = 1$
192675	Graph Using a Table of Values	y=(2x+1)/x	$y = \frac{2 x + 1}{x}$
192676	Factor	2(x-2)(x+1)^2-3(x-2)^2(x+1)	$2 (x - 2) {(x + 1)}^{2} - 3 {(x - 2)}^{2} (x + 1)$
192677	Simplify	((4- square root of 5)(4+ square root of 5))/(2 square root of 11)	$\frac{(4 - \sqrt{5}) (4 + \sqrt{5})}{2 \sqrt{11}}$
192678	Simplify	4^4(5)+3(11)	$4^{4} (5) + 3 (11)$
192679	Factor	ax+ay+az	$a x + a y + a z$
192680	Solve for r	A=P(1+rt) for r	$A = P (1 + r t)$ for $r$
192681	Rationalize the Numerator	( square root of r+ square root of 2)/5	$\frac{\sqrt{r} + \sqrt{2}}{5}$
192682	Evaluate	(12(9)-2^5)/( cube root of 64)	$\frac{12 (9) - 2^{5}}{\sqrt[3]{64}}$
192683	Solve for a	(x^(1/3))^2 cube root of x=x^a	${(x^{\frac{1}{3}})}^{2} \sqrt[3]{x} = x^{a}$
192684	Solve for x	5x+2(1-x)=2(2x-1)	$5 x + 2 (1 - x) = 2 (2 x - 1)$
192685	Solve for θ	tan(2theta)=-1	$\tan (2 θ) = - 1$
192686	Find the Parallel Line	(-1,5) and parallel to x+2y=5	$(- 1, 5)$ and parallel to $x + 2 y = 5$
192687	Solve for g	-9g+9>-g-7	$- 9 g + 9 > - g - 7$
192688	Multiply	(3x^3-x^2)(-2x)	$(3 x^{3} - x^{2}) (- 2 x)$
192689	Solve for x	3-8x=8/5x	$3 - 8 x = \frac{8}{5} x$
192690	Solve for x	log base 2 of x-6+ log base 2 of 4x+7=3	$\log_{2} (x - 6) + \log_{2} (4 x + 7) = 3$
192691	Solve the Inequality for x	x+8<=3x+1	$x + 8 \leq 3 x + 1$
192692	Graph	f(x)=(x^2+4x-21)/(p(x))	$f (x) = \frac{x^{2} + 4 x - 21}{p (x)}$
192693	Solve the System of Inequalities	x+18>=8x+4 or 15x-15<=15x+5	$x + 18 \geq 8 x + 4$ or $15 x - 15 \leq 15 x + 5$
192694	Simplify	(3+2i)/(5-i)	$\frac{3 + 2 i}{5 - i}$
192695	Find the Domain and Range	(x+3)/(x^2-9)	$\frac{x + 3}{x^{2} - 9}$
192696	Solve for x	9+x/5-2=4.8	$9 + \frac{x}{5} - 2 = 4.8$
192697	Solve for x	-1=-3/2(3x+1)-3/2	$- 1 = - \frac{3}{2} (3 x + 1) - \frac{3}{2}$
192698	Simplify	(x^(-3/4)x^5)/(x^(1/4))	$\frac{x^{- \frac{3}{4}} x^{5}}{x^{\frac{1}{4}}}$
192699	Solve Using the Quadratic Formula	2x^2-7x+9=x+1	$2 x^{2} - 7 x + 9 = x + 1$
192700	Solve the Inequality for c	5/(2c-3)>1	$\frac{5}{2 c - 3} > 1$