Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
21301	Solve the Function Operation	Given that f(x)=x^2-4x-21 and g(x)=x+3 ; find (f-g)(x) and express the result in standard form.	Given that $f (x) = x^{2} - 4 x - 21$ and $g (x) = x + 3$ ; find $(f - g) (x)$ and express the result in standard form.
21302	Solve by Graphing	-x+y=1 x-y=1	$- x + y = 1$ $x - y = 1$
21303	Solve the System of Equations	y=-2x^2-4x-1 y=2x+4	$y = - 2 x^{2} - 4 x - 1$ $y = 2 x + 4$
21304	Find the Degree, Leading Term, and Leading Coefficient	1/10x+9	$\frac{1}{10} x + 9$
21305	Factor	24x^2y^2+18xy^4-2xy^3	$24 x^{2} y^{2} + 18 x y^{4} - 2 x y^{3}$
21306	Solve for y	x=( square root of 58+y)/1.98	$x = \frac{\sqrt{58 + y}}{1.98}$
21307	Solve the Inequality for x	-3x^2+39<=-9x+9	$- 3 x^{2} + 39 \leq - 9 x + 9$
21308	Solve for x	-2+(2x+7)/x=7/2	$- 2 + \frac{2 x + 7}{x} = \frac{7}{2}$
21309	Find the Derivative - d/dh	V=1/3pir^2h	$V = \frac{1}{3} π r^{2} h$
21310	Multiply	7/9*(-9/8)	$\frac{7}{9} \cdot (- \frac{9}{8})$
21311	Graph	5x-9y>=8 7x-4y<10	$5 x - 9 y \geq 8$ $7 x - 4 y < 10$
21312	Evaluate	cos(pi/4+pi/3)	$\cos (\frac{π}{4} + \frac{π}{3})$
21313	Solve for d	fourth root of 27-2d = fourth root of d-3	$\sqrt[4]{27 - 2 d} = \sqrt[4]{d - 3}$
21314	Simplify	(2 square root of 5x)/( square root of 7y^2)	$\frac{2 \sqrt{5 x}}{\sqrt{7 y^{2}}}$
21315	Find the Roots (Zeros)	9x^4-16=0	$9 x^{4} - 16 = 0$
21316	Solve for x	3/4x+3/2x=9/4	$\frac{3}{4} x + \frac{3}{2} x = \frac{9}{4}$
21317	Evaluate the Summation	sum from i=1 to 7 of 840/i	$\sum_{i = 1}^{7} \frac{840}{i}$
21318	Find the Antiderivative	(sin(x))/(cos(x)^5)	$\frac{\sin (x)}{\cos^{5} (x)}$
21319	Evaluate	(5(7)+5^2)/5	$\frac{5 (7) + 5^{2}}{5}$
21320	Solve for x	( square root of x-27)^3=64	${(\sqrt{x - 27})}^{3} = 64$
21321	Simplify	(2/3x^5y^-5)*(1/3x^2y^2)	$(\frac{2}{3} x^{5} y^{- 5}) \cdot (\frac{1}{3} x^{2} y^{2})$
21322	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (-3,1) and has a slope of 2/3 ?	What is the equation of the line that passes through the point $(- 3, 1)$ and has a slope of $\frac{2}{3}$ ?
21323	Divide	(10 cube root of z)/(2z^2)	$\frac{10 \sqrt[3]{z}}{2 z^{2}}$
21324	Find the Holes in the Graph	f(x)=(2x^2-8x-24)/(x^2-36)	$f (x) = \frac{2 x^{2} - 8 x - 24}{x^{2} - 36}$
21325	Simplify	(2-2x+x^2)(x+5)	$(2 - 2 x + x^{2}) (x + 5)$
21326	Simplify the Radical Expression	(y^(5/4))/(y^(1/4))	$\frac{y^{\frac{5}{4}}}{y^{\frac{1}{4}}}$
21327	Simplify	4x^2(x-2)(x+2)	$4 x^{2} (x - 2) (x + 2)$
21328	Find the Slope	(5,14) and (1,6)	$(5, 14)$ and $(1, 6)$
21329	Write in Standard Form	-3x-4x^2-5x^5+6x^3	$- 3 x - 4 x^{2} - 5 x^{5} + 6 x^{3}$
21330	Add	-2/3+1/6	$- \frac{2}{3} + \frac{1}{6}$
21331	Simplify	-9+(-1/3y)+6-4/3y	$- 9 + (- \frac{1}{3} y) + 6 - \frac{4}{3} y$
21332	Evaluate	2(2)^-1	$2 {(2)}^{- 1}$
21333	Factor by Grouping	4xy+12x^2	$4 x y + 12 x^{2}$
21334	Simplify the Radical Expression	(4 square root of 7+3)(6 square root of 7-1)	$(4 \sqrt{7} + 3) (6 \sqrt{7} - 1)$
21335	Evaluate the Limit	limit as x approaches 4 of 3x(x+5)	$lim_{x \to 4} 3 x (x + 5)$
21336	Simplify	((2-3i)/(1+i))*((3+2i)/(3i))	$(\frac{2 - 3 i}{1 + i}) \cdot (\frac{3 + 2 i}{3 i})$
21337	Evaluate	((-2)^2-4)/((-2)+2)	$\frac{{(- 2)}^{2} - 4}{(- 2) + 2}$
21338	Write with Rational (Fractional) Exponents	fourth root of 7^5* fourth root of 7	$\sqrt[4]{7^{5}} \cdot \sqrt[4]{7}$
21339	Evaluate	5^x+1=106	$5^{x} + 1 = 106$
21340	Simplify	16 square root of x+ square root of x-12 square root of y-2 square root of y	$16 \sqrt{x} + \sqrt{x} - 12 \sqrt{y} - 2 \sqrt{y}$
21341	Simplify	Simplify 5 fifth root of 2x^3y^4*3 fifth root of 16x^2y	Simplify $5 \sqrt[5]{2 x^{3} y^{4}} \cdot 3 \sqrt[5]{16 x^{2} y}$
21342	Solve for x	-2x^2+x+1=0	$- 2 x^{2} + x + 1 = 0$
21343	Divide Using Long Polynomial Division	(3x^3-11x^2y+11xy^2-2y^3)÷(x-2y)	$(3 x^{3} - 11 x^{2} y + 11 x y^{2} - 2 y^{3}) \div (x - 2 y)$
21344	Simplify	x*1/(x^2)	$x \cdot \frac{1}{x^{2}}$
21345	Solve for x	(x^2-36)/(x-6)<=0	$\frac{x^{2} - 36}{x - 6} \leq 0$
21346	Simplify	( cube root of -5)/(40^(1/3))	$\frac{\sqrt[3]{- 5}}{40^{\frac{1}{3}}}$
21347	Simplify	-10a^2+6a^3+3a-6a^3-4a+8a^2	$- 10 a^{2} + 6 a^{3} + 3 a - 6 a^{3} - 4 a + 8 a^{2}$
21348	Write in Standard Form	(4x^5+x^3-7x^2+2)(3x-1)	$(4 x^{5} + x^{3} - 7 x^{2} + 2) (3 x - 1)$
21349	Solve for r	3 square root of r = square root of 8r+16	$3 \sqrt{r} = \sqrt{8 r + 16}$
21350	Evaluate	45% of 40	$45 %$ of $40$
21351	Find Amplitude, Period, and Phase Shift	y=sin((4x)/3+pi)	$y = \sin (\frac{4 x}{3} + π)$
21352	Graph	-4k-3<-7 or 1-k>=6	$- 4 k - 3 < - 7$ or $1 - k \geq 6$
21353	Find the Domain	square root of 4x^2-12x+9	$\sqrt{4 x^{2} - 12 x + 9}$
21354	Multiply	-14/37*10/140	$- \frac{14}{37} \cdot \frac{10}{140}$
21355	Solve the Function Operation	f(x)=-(x-1)^2-3 if x<3; -4 if x=3; -3 if x>3 Find f(8)	$f (x) = {\begin{cases} - {(x - 1)}^{2} - 3 & x < 3 \\ - 4 & x = 3 \\ - 3 & x > 3 \end{cases}$ Find $f (8)$
21356	Find the Domain and Range	g(x)=3(1/(x+1))-2	$g (x) = 3 (\frac{1}{x + 1}) - 2$
21357	Solve for v	15v-2v+29=5v-27	$15 v - 2 v + 29 = 5 v - 27$
21358	Simplify	cube root of (640a^3b^8)/(5ab^4)	$\sqrt[3]{\frac{640 a^{3} b^{8}}{5 a b^{4}}}$
21359	Combine Like Terms	1/3x+3/4+2/3x-1/4-2/3x	$\frac{1}{3} x + \frac{3}{4} + \frac{2}{3} x - \frac{1}{4} - \frac{2}{3} x$
21360	Solve the Inequality for x	3(x+4)>2x+x+7	$3 (x + 4) > 2 x + x + 7$
21361	Find the Center and Radius	(x+2)^2-(y+2)^2=4^2	${(x + 2)}^{2} - {(y + 2)}^{2} = 4^{2}$
21362	Solve for θ	(2sin(theta)+1)/(sin(theta)-1)=0	$\frac{2 \sin (θ) + 1}{\sin (θ) - 1} = 0$
21363	Evaluate	((8-2)(3+2)-1)3	$((8 - 2) \times (3 + 2) - 1) \times 3$
21364	Solve for r	(5,9) , (r,-3) , m=-4	$(5, 9)$ , $(r, - 3)$ , $m = - 4$
21365	Simplify	3x-1+3x-1+3x-1+3x-1	$3 x - 1 + 3 x - 1 + 3 x - 1 + 3 x - 1$
21366	Evaluate	(sin((3pi)/2)-5cos((13pi)/4))/(tan((25pi)/4))	$\frac{\sin (\frac{3 π}{2}) - 5 \cos (\frac{13 π}{4})}{\tan (\frac{25 π}{4})}$
21367	Graph	S(t)=1/2 square root of x-3+1	$S (t) = \frac{1}{2} \sqrt{x - 3} + 1$
21368	Simplify the Radical Expression	square root of 6*4 square root of 6	$\sqrt{6} \cdot 4 \sqrt{6}$
21369	Convert to Rectangular	x=4cos(theta) y=3sin(theta)	$x = 4 \cos (θ)$ $y = 3 \sin (θ)$
21370	Evaluate	4pi*135/360	$4 π \cdot \frac{135}{360}$
21371	Solve for n	4(5n-1)^(1/3)-1=0	$4 {(5 n - 1)}^{\frac{1}{3}} - 1 = 0$
21372	Find the Inverse	f(x)=1/2(x-1)^3+3	$f (x) = \frac{1}{2} {(x - 1)}^{3} + 3$
21373	Solve for u	square root of u=-10	$\sqrt{u} = - 10$
21374	Evaluate	((x^(2/5)*x^(4/5))/(x^(2/5)))^(1/2)	${(\frac{x^{\frac{2}{5}} \cdot x^{\frac{4}{5}}}{x^{\frac{2}{5}}})}^{\frac{1}{2}}$
21375	Solve for x	x/(x-1)+4/(x+1)=2/((x-1)(x+1))	$\frac{x}{x - 1} + \frac{4}{x + 1} = \frac{2}{(x - 1) (x + 1)}$
21376	Find the x and y Intercepts	f(x)=x^2(x^2-2)(x+1)(x^2+9)	$f (x) = x^{2} (x^{2} - 2) (x + 1) (x^{2} + 9)$
21377	Simplify the Radical Expression	square root of 16x^2*x^(2/3)+ cube root of 8x^5	$\sqrt{16 x^{2}} \cdot x^{\frac{2}{3}} + \sqrt[3]{8 x^{5}}$
21378	Multiply	x*(x+1)	$x \cdot (x + 1)$
21379	Expand Using Sum/Difference Formulas	x(x+2)	$x (x + 2)$
21380	Solve for x	-2cos(x)=-2	$- 2 \cos (x) = - 2$
21381	Write in Standard Form	-2x^2+x+5x^3+4x+2x^2	$- 2 x^{2} + x + 5 x^{3} + 4 x + 2 x^{2}$
21382	Evaluate	-2^3*(-2)^0	$- 2^{3} \cdot {(- 2)}^{0}$
21383	Solve the Inequality for x	3(2x+7)>6(x-5)	$3 (2 x + 7) > 6 (x - 5)$
21384	Find the Exact Value	(10^-15)/(3.9*10^-7)	$\frac{10^{- 15}}{3.9 \cdot 10^{- 7}}$
21385	Simplify	(a^2)/((a^3)/(a^5))	$\frac{a^{2}}{\frac{a^{3}}{a^{5}}}$
21386	Simplify	-2x-10-10x^2+3	$- 2 x - 10 - 10 x^{2} + 3$
21387	Find the Domain	(m-n)/(mn)*(2mn)/(mn-m^2)	$\frac{m - n}{m n} \cdot \frac{2 m n}{m n - m^{2}}$
21388	Write in Standard Form	h(x)=-x^3+2x^2-15x^7	$h (x) = - x^{3} + 2 x^{2} - 15 x^{7}$
21389	Solve the Inequality for x	-1/2<=(8-3x)/5<=1/4	$- \frac{1}{2} \leq \frac{8 - 3 x}{5} \leq \frac{1}{4}$
21390	Solve the Inequality for x	(4\|x-9\|)/3>8	$\frac{4 \| x - 9 \|}{3} > 8$
21391	Graph	x+y<=4 2x-y>=3	$x + y \leq 4$ $2 x - y \geq 3$
21392	Evaluate the Integral	integral of (5t^8-2t^4+t+3) with respect to x	$\int (5 t^{8} - 2 t^{4} + t + 3) d x$
21393	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (-4,-7) and has a slope of 5/2 ?	What is the equation of the line that passes through the point $(- 4, - 7)$ and has a slope of $\frac{5}{2}$ ?
21394	Simplify	((r^3)^4)/((r^3)^8)	$\frac{{(r^{3})}^{4}}{{(r^{3})}^{8}}$
21395	Solve for n	-3(7n+3)<6n	$- 3 (7 n + 3) < 6 n$
21396	Find the Domain	e^(x^2)	$e^{x^{2}}$
21397	Solve the Function Operation	2^(5x)=32 , 768	$2^{5 x} = 32$ , $768$
21398	Evaluate	(x^a)/(x^b)	$\frac{x^{a}}{x^{b}}$
21399	Solve the Inequality for x	3+ square root of 3x+12<=9	$3 + \sqrt{3 x + 12} \leq 9$
21400	Solve for h	T=2rpih+2pir^2 ; for h	$T = 2 r π h + 2 π r^{2}$ ; for $h$