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Algebra

Rank	Topic	Problem	Formatted Problem
238301	Solve the System of Equations	y=x^2 2y+6=2(x+3)	$y = x^{2}$ $2 y + 6 = 2 (x + 3)$
238302	Solve for x	5(3-2x)>=10	$5 (3 - 2 x) \geq 10$
238303	Simplify	( cube root of 9)÷( square root of 3)	$\sqrt[3]{9} \div \sqrt{3}$
238304	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (2,-2) and has a slope of -1/2 ?	What is the equation of the line that passes through the point $(2, - 2)$ and has a slope of $- \frac{1}{2}$ ?
238305	Evaluate	80/(cos(60))	$\frac{80}{\cos (60)}$
238306	Solve for x	xy^2+x^2y-6x-3=0	$x y^{2} + x^{2} y - 6 x - 3 = 0$
238307	Find All Complex Solutions	x-3 = square root of 19-3x	$x - 3 = \sqrt{19 - 3 x}$
238308	Evaluate	87e^(0.3x)=5918	$87 e^{0.3 x} = 5918$
238309	Solve the System of Equations	x=1 2x+y=4	$x = 1$ $2 x + y = 4$
238310	Factor	a^2-xy-ax+ay	$a^{2} - x y - a x + a y$
238311	Factor by Grouping	9xz^3+18yz^2+24z^2	$9 x z^{3} + 18 y z^{2} + 24 z^{2}$
238312	Solve for x	-1/2x^2+5x=8	$- \frac{1}{2} x^{2} + 5 x = 8$
238313	Evaluate	1/2( log base 2 of 4+ log base 2 of 16)- log base 2 of 2	$\frac{1}{2} (\log_{2} (4) + \log_{2} (16)) - \log_{2} (2)$
238314	Solve the System of Equations	y=-2x+7 and y=5x-7	$y = - 2 x + 7$ and $y = 5 x - 7$
238315	Simplify	(-5/7)(-21/10)	$(- \frac{5}{7}) (- \frac{21}{10})$
238316	Graph	y=x\|x\|+\|x\|-5x	$y = x \| x \| + \| x \| - 5 x$
238317	Graph	x^2-18x+81<=0	$x^{2} - 18 x + 81 \leq 0$
238318	Graph	f(x)=x^3 g(x)=x^3-4	$f (x) = x^{3}$ $g (x) = x^{3} - 4$
238319	Graph	y=-4sec(pix)+2	$y = - 4 \sec (π x) + 2$
238320	Find the Inverse	f(x)=2x^2-8x+1 , x>=2	$f (x) = 2 x^{2} - 8 x + 1$ , $x \geq 2$
238321	Divide Using Long Polynomial Division	(2b^3-6b^2+8b)÷(2b^2+b+1)	$(2 b^{3} - 6 b^{2} + 8 b) \div (2 b^{2} + b + 1)$
238322	Write in Exponential Form	sixth root of 3^5* sixth root of 3^5	$\sqrt[6]{3^{5}} \cdot \sqrt[6]{3^{5}}$
238323	Solve for x	3.5=(4+2x)/(0.5-x)	$3.5 = \frac{4 + 2 x}{0.5 - x}$
238324	Solve for x	\|x-2\|>=-4	$\| x - 2 \| \geq - 4$
238325	Simplify	( square root of 12- square root of 8)/( square root of 8- square root of 3)	$\frac{\sqrt{12} - \sqrt{8}}{\sqrt{8} - \sqrt{3}}$
238326	Solve for y	(x+y)/9=M	$\frac{x + y}{9} = M$
238327	Write in Standard Form	8y^3-3xy^2-x^2y+2x^3	$8 y^{3} - 3 x y^{2} - x^{2} y + 2 x^{3}$
238328	Convert to Radical Form	7^(1/5)*49^(7/5)	$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$
238329	Factor	25(4x-3)^2-9(2x+1)^2	$25 {(4 x - 3)}^{2} - 9 {(2 x + 1)}^{2}$
238330	Graph	table[[x,y],[1,3],[2,6],[3,9]]	$\begin{array}{c} x & y \\ 1 & 3 \\ 2 & 6 \\ 3 & 9 \end{array}$
238331	Solve the System of Equations	2x^2+3y^2=19 2x^2+y^2=9	$2 x^{2} + 3 y^{2} = 19$ $2 x^{2} + y^{2} = 9$
238332	Evaluate	(-( square root of 2)/2)(( square root of 3)/2)	$(- \frac{\sqrt{2}}{2}) (\frac{\sqrt{3}}{2})$
238333	Solve for x	6x-12+2x=3+8x-15	$6 x - 12 + 2 x = 3 + 8 x - 15$
238334	Simplify	limit as x approaches negative infinity of x/(2x-3)	$lim_{x \to - \infty} \frac{x}{2 x - 3}$
238335	Simplify	((6u+72)/(2u+24))÷((u^2+21u+108)/(u^2+20u+96))	$\frac{6 u + 72}{2 u + 24} \div \frac{u^{2} + 21 u + 108}{u^{2} + 20 u + 96}$
238336	Solve for m	44=-8+m^3	$44 = - 8 + m^{3}$
238337	Solve the Inequality for r	15<3r	$15 < 3 r$
238338	Solve the Inequality for y	(4-y)/5-5y>=0	$\frac{(4 - y)}{5} - 5 y \geq 0$
238339	Graph	-2x^3+3x^2-x-3	$- 2 x^{3} + 3 x^{2} - x - 3$
238340	Multiply	3 square root of 6 and 5 square root of 12	$3 \sqrt{6}$ and $5 \sqrt{12}$
238341	Solve the Inequality for x	-3/4(4x+12)<=-(2x+8)	$- \frac{3}{4} (4 x + 12) \leq - (2 x + 8)$
238342	Solve for d	(1/2)^2*4^(3d)=1	${(\frac{1}{2})}^{2} \cdot 4^{3 d} = 1$
238343	Solve the Inequality for x	-5/3x<=-5	$- \frac{5}{3} x \leq - 5$
238344	Simplify	-5/2*(2x+5)/x	$- \frac{5}{2} \cdot \frac{2 x + 5}{x}$
238345	Convert to a Decimal	What is -3 1/3 written as a decimal?	What is $- 3 \frac{1}{3}$ written as a decimal?
238346	Simplify	(uv)/(4vu^4)	$\frac{u v}{4 v u^{4}}$
238347	Evaluate	8*(1/2)^2	$8 \cdot {(\frac{1}{2})}^{2}$
238348	Evaluate	(-xy)^2*(2x^9y^5)^4	${(- x y)}^{2} \cdot {(2 x^{9} y^{5})}^{4}$
238349	Graph	x/5=y/3	$\frac{x}{5} = \frac{y}{3}$
238350	Solve the System of Inequalities	3x+y<=9 y>=4	$3 x + y \leq 9$ $y \geq 4$
238351	Identify the Sequence	-32 , 10 2/3 , -3 5/9 , 1 5/27	$- 32$ , $10 \frac{2}{3}$ , $- 3 \frac{5}{9}$ , $1 \frac{5}{27}$
238352	Solve the Inequality for n	0.6n>=12-0.4n	$0.6 n \geq 12 - 0.4 n$
238353	Simplify	(8a^-6b^-4)/(a^-2b^-3)	$\frac{8 a^{- 6} b^{- 4}}{a^{- 2} b^{- 3}}$
238354	Evaluate	(a+b-c)(a+b+c)	$(a + b - c) (a + b + c)$
238355	Simplify the Radical Expression	(b3/7)(b4/7)	$(b \frac{3}{7}) (b \frac{4}{7})$
238356	Solve for x	cube root of 5x^2+8x-4- cube root of 9x=0	$\sqrt[3]{5 x^{2} + 8 x - 4} - \sqrt[3]{9 x} = 0$
238357	Evaluate	(-6+- square root of 6^2-42-8)/(2(2))	$\frac{- 6 + - \sqrt{6^{2} - 4 \cdot 2 \cdot - 8}}{2 (2)}$
238358	Find the Domain and Range	y=sin(x-pi)	$y = \sin (x - π)$
238359	Find All Complex Solutions	1/(x-1)+1/(x+2)=5/4	$\frac{1}{x - 1} + \frac{1}{x + 2} = \frac{5}{4}$
238360	Find the Degree, Leading Term, and Leading Coefficient	p(x)=(x-2)(x+1)(x+3)	$p (x) = (x - 2) (x + 1) (x + 3)$
238361	Find the Intersection	y<=-x-2 y>=-5x+2	$y \leq - x - 2$ $y \geq - 5 x + 2$
238362	Write in Standard Form	(4x^2+3x+7)(-2x^2+x+2)	$(4 x^{2} + 3 x + 7) (- 2 x^{2} + x + 2)$
238363	Write in y=mx+b Form	(1,1) , (8,-3/4)	$(1, 1)$ , $(8, - \frac{3}{4})$
238364	Graph	2f(x)=-5	$2 f (x) = - 5$
238365	Solve the System of Inequalities	5x-9y>=8 7x-4y<10	$5 x - 9 y \geq 8$ $7 x - 4 y < 10$
238366	Simplify	(2x^2(x+7))/(3x(x+7))	$\frac{2 x^{2} (x + 7)}{3 x (x + 7)}$
238367	Solve the Inequality for y	-3x+2y>5y+9	$- 3 x + 2 y > 5 y + 9$
238368	Solve the Rational Equation for x	3-1/(x+1)=x/(x+1)	$3 - \frac{1}{x + 1} = \frac{x}{x + 1}$
238369	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (6,-8) and has a slope of -2/3 ?	What is the equation of the line that passes through the point $(6, - 8)$ and has a slope of $- \frac{2}{3}$ ?
238370	Write in Exponential Form	( fifth root of 3)^5	${(\sqrt[5]{3})}^{5}$
238371	Simplify	((x^8y^5)/(x^9y^3))^-6	${(\frac{x^{8} y^{5}}{x^{9} y^{3}})}^{- 6}$
238372	Write the Fraction in Simplest Form	(tan(pi/2-x)csc(x))/(csc(x)^2)	$\frac{\tan (\frac{π}{2} - x) \csc (x)}{\csc^{2} (x)}$
238373	Simplify	(x^2)^-2+x^4x^5	${(x^{2})}^{- 2} + x^{4} x^{5}$
238374	Solve for b	y=-1/2x+b	$y = - \frac{1}{2} x + b$
238375	Solve for x	199927=7x^4	$199927 = 7 x^{4}$
238376	Simplify	6y^2-3y^3+6x^2+2y^3+y^3-3y^2+3y^2	$6 y^{2} - 3 y^{3} + 6 x^{2} + 2 y^{3} + y^{3} - 3 y^{2} + 3 y^{2}$
238377	Write the Fraction in Simplest Form	limit as x approaches 2 of (2-x)/( square root of x+2-2)	$lim_{x \to 2} \frac{2 - x}{\sqrt{x + 2} - 2}$
238378	Solve for x	log base 256 of x<1/4	$\log_{256} (x) < \frac{1}{4}$
238379	Simplify	(6x^3)/(7y^3)(14x)/(15y^2)(25y^4)/(x^3)	$\frac{6 x^{3}}{7 y^{3}} \cdot \frac{14 x}{15 y^{2}} \cdot \frac{25 y^{4}}{x^{3}}$
238380	Solve for y	(y-0)^2=9-9((x+3)^2)/16	${(y - 0)}^{2} = 9 - 9 \frac{{(x + 3)}^{2}}{16}$
238381	Multiply	315/3	$3 \cdot 1 \cdot \frac{5}{3}$
238382	Solve for b	a=1/4b	$a = \frac{1}{4} b$
238383	Evaluate	square root of 3 4/9*7 8/31	$\sqrt{3 \frac{4}{9} \cdot 7 \frac{8}{31}}$
238384	Solve the Inequality for x	5 square root of x-1>10	$5 \sqrt{x - 1} > 10$
238385	Solve for x	4x^5-40x^3+36x=0	$4 x^{5} - 40 x^{3} + 36 x = 0$
238386	Simplify the Radical Expression	( fifth root of 3)^5	${(\sqrt[5]{3})}^{5}$
238387	Expand Using the Binomial Theorem	(1/2x^3y^2-4y)^9	${(\frac{1}{2} x^{3} y^{2} - 4 y)}^{9}$
238388	Simplify	7/(8n)*2n	$\frac{7}{8 n} \cdot 2 n$
238389	Combine Like Terms	-3+7x^2-4x-5+3x^2-2x	$- 3 + 7 x^{2} - 4 x - 5 + 3 x^{2} - 2 x$
238390	Find the Domain and Range	f(x,y)=4	$f (x, y) = 4$
238391	Simplify	(-3/5)/(4/5)	$\frac{- \frac{3}{5}}{\frac{4}{5}}$
238392	Divide	(6/5)÷(-12/25)	$\frac{6}{5} \div (- \frac{12}{25})$
238393	Evaluate	(x^2y^-4y^-8)/(x^3)	$\frac{x^{2} y^{- 4} y^{- 8}}{x^{3}}$
238394	Graph	x/(x+4)>=2	$\frac{x}{x + 4} \geq 2$
238395	Solve for y	(5+y)/(y-3)=14/10	$\frac{5 + y}{y - 3} = \frac{14}{10}$
238396	Find the LCM	21 and 6	$21$ and $6$
238397	Rationalize the Denominator	(2 square root of 5x)/( square root of 7y^2)	$\frac{2 \sqrt{5 x}}{\sqrt{7 y^{2}}}$
238398	Solve for t	t^2-8t+16=0	$t^{2} - 8 t + 16 = 0$
238399	Evaluate	67/(tan(42))	$\frac{67}{\tan (42)}$
238400	Multiply	(3y-4)(5y+2)(2y-1)	$(3 y - 4) (5 y + 2) (2 y - 1)$