Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
9901	Solve the Matrix Equation	[[1/7,2/7],[3/7,-1/7]][[1,2],[3,1]][[x],[y]]=[[1/7,2/7],[3/7,-1/7]][[-1],[4]]	$[\begin{array}{c} \frac{1}{7} & \frac{2}{7} \\ \frac{3}{7} & \frac{- 1}{7} \end{array}] [\begin{array}{c} 1 & 2 \\ 3 & 1 \end{array}] [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} \frac{1}{7} & \frac{2}{7} \\ \frac{3}{7} & - \frac{1}{7} \end{array}] [\begin{array}{c} - 1 \\ 4 \end{array}]$
9902	Solve the Matrix Equation	[[0,2,1],[3,0,1],[1,1,1]][[x],[y],[z]]=[[4],[3],[6]]	$[\begin{array}{c} 0 & 2 & 1 \\ 3 & 0 & 1 \\ 1 & 1 & 1 \end{array}] [\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} 4 \\ 3 \\ 6 \end{array}]$
9903	Solve the Matrix Equation	[[1,0,2],[0,1,2],[0,0,0]]*[[x],[y],[z]]=[[6],[5],[1]]	$[\begin{array}{c} 1 & 0 & 2 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}] \cdot [\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} 6 \\ 5 \\ 1 \end{array}]$
9904	Solve the Matrix Equation	[[1,1],[1,2]][[x],[y]]=[[60],[81]]	$[\begin{array}{c} 1 & 1 \\ 1 & 2 \end{array}] [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 60 \\ 81 \end{array}]$
9905	Solve the Matrix Equation	[[-1,-1],[2,3]][[x1],[x2]]=[[16],[-40]]	$[\begin{array}{c} - 1 & - 1 \\ 2 & 3 \end{array}] [\begin{array}{c} x \cdot 1 \\ x \cdot 2 \end{array}] = [\begin{array}{c} 16 \\ - 40 \end{array}]$
9906	Solve the Matrix Equation	[[1,2,7],[4,5,6],[7,8,9]][[x],[y],[z]]=[[12],[11],[17]]	$[\begin{array}{c} 1 & 2 & 7 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}] [\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} 12 \\ 11 \\ 17 \end{array}]$
9907	Solve the Matrix Equation	[[1,2],[3,4],[x,-1]]-3[[y-1,2],[1,2],[4,2z,1]]=2[[-4,-4],[0,-1],[4,4]]	$[\begin{array}{c} 1 & 2 \\ 3 & 4 \\ x & - 1 \end{array}] - 3 [\begin{array}{c} y - 1 & 2 \\ 1 & 2 \\ 4 & 2 z & 1 \end{array}] = 2 [\begin{array}{c} - 4 & - 4 \\ 0 & - 1 \\ 4 & 4 \end{array}]$
9908	Solve the Matrix Equation	[[1,-3],[2,-2]][[a,b],[c,d]]=[[-1,4],[2,8]]	$[\begin{array}{c} 1 & - 3 \\ 2 & - 2 \end{array}] [\begin{array}{c} a & b \\ c & d \end{array}] = [\begin{array}{c} - 1 & 4 \\ 2 & 8 \end{array}]$
9909	Solve the Matrix Equation	[[1,x],[y,-2],[2,z]]=[[1,2],[5,-2],[-3,4]]	$[\begin{array}{c} 1 & x \\ y & - 2 \\ 2 & z \end{array}] = [\begin{array}{c} 1 & 2 \\ 5 & - 2 \\ - 3 & 4 \end{array}]$
9910	Solve the Matrix Equation	[[15,-27,-28],[45,25,10],[41,-19,22]][[x],[y],[z]]=[[-13],[-11],[24]]	$[\begin{array}{c} 15 & - 27 & - 28 \\ 45 & 25 & 10 \\ 41 & - 19 & 22 \end{array}] [\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} - 13 \\ - 11 \\ 24 \end{array}]$
9911	Solve the Matrix Equation	[[15,8],[4x,0]]-[[2,5],[x,3y+6]]=[[13,3],[12,4y+8]]	$[\begin{array}{c} 15 & 8 \\ 4 x & 0 \end{array}] - [\begin{array}{c} 2 & 5 \\ x & 3 y + 6 \end{array}] = [\begin{array}{c} 13 & 3 \\ 12 & 4 y + 8 \end{array}]$
9912	Solve the Matrix Equation	[[2,-1,0],[-1,2,-1],[0,-1,3]][[a],[b],[b]]=[[-12],[6],[12]]	$[\begin{array}{c} 2 & - 1 & 0 \\ - 1 & 2 & - 1 \\ 0 & - 1 & 3 \end{array}] [\begin{array}{c} a \\ b \\ b \end{array}] = [\begin{array}{c} - 12 \\ 6 \\ 12 \end{array}]$
9913	Solve the Matrix Equation	[[2,3],[-1,2]][[-4],[1]]=x	$[\begin{array}{c} 2 & 3 \\ - 1 & 2 \end{array}] [\begin{array}{c} - 4 \\ 1 \end{array}] = x$
9914	Solve the Matrix Equation	[[2,-3],[1,-2]][[a,b],[c,d]]=[[-7,3],[-5,1]]	$[\begin{array}{c} 2 & - 3 \\ 1 & - 2 \end{array}] [\begin{array}{c} a & b \\ c & d \end{array}] = [\begin{array}{c} - 7 & 3 \\ - 5 & 1 \end{array}]$
9915	Solve the Matrix Equation	[[2,-3],[3,-1]]*[[a,b],[c,d]]=[[-6,-4],[5,8]]	$[\begin{array}{c} 2 & - 3 \\ 3 & - 1 \end{array}] \cdot [\begin{array}{c} a & b \\ c & d \end{array}] = [\begin{array}{c} - 6 & - 4 \\ 5 & 8 \end{array}]$
9916	Solve the Matrix Equation	[[2,3],[-4,4]][[x1],[x2]]=[[5],[20]]	$[\begin{array}{c} 2 & 3 \\ - 4 & 4 \end{array}] [\begin{array}{c} x \cdot 1 \\ x \cdot 2 \end{array}] = [\begin{array}{c} 5 \\ 20 \end{array}]$
9917	Solve the Matrix Equation	[[2,4],[-6,-4],[x,4]]+[[4,10],[-4,-2],[-5,y]]=[[6,6],[-10,-6],[-4,2]]	$[\begin{array}{c} 2 & 4 \\ - 6 & - 4 \\ x & 4 \end{array}] + [\begin{array}{c} 4 & 10 \\ - 4 & - 2 \\ - 5 & y \end{array}] = [\begin{array}{c} 6 & 6 \\ - 10 & - 6 \\ - 4 & 2 \end{array}]$
9918	Solve the Matrix Equation	[[2,4x],[3z,w]]=[[2x,y],[z+6,-8]]	$[\begin{array}{c} 2 & 4 x \\ 3 z & w \end{array}] = [\begin{array}{c} 2 x & y \\ z + 6 & - 8 \end{array}]$
9919	Solve the Matrix Equation	[[2,-7],[1,7]]+x=[[1,4],[7,5]]	$[\begin{array}{c} 2 & - 7 \\ 1 & 7 \end{array}] + x = [\begin{array}{c} 1 & 4 \\ 7 & 5 \end{array}]$
9920	Solve the Matrix Equation	[[2x,4y-3],[z,5w]]=[[10,10],[7,15]]	$[\begin{array}{c} 2 x & 4 y - 3 \\ z & 5 w \end{array}] = [\begin{array}{c} 10 & 10 \\ 7 & 15 \end{array}]$
9921	Determine if Injective (One to One)	f(x)=2x-8	$f (x) = 2 x - 8$
9922	Determine if Injective (One to One)	f(x)=-3x^2+5	$f (x) = - 3 x^{2} + 5$
9923	Determine if Injective (One to One)	f(x)=4.2x+31	$f (x) = 4.2 x + 31$
9924	Determine if Injective (One to One)	f(x)=4x^3-5x^2-2x	$f (x) = 4 x^{3} - 5 x^{2} - 2 x$
9925	Determine if Injective (One to One)	f(x)=-5x+3	$f (x) = - 5 x + 3$
9926	Determine if Injective (One to One)	f(x)=5x-6	$f (x) = 5 x - 6$
9927	Determine if Injective (One to One)	f(x)=x^3+3x	$f (x) = x^{3} + 3 x$
9928	Determine if Injective (One to One)	f(x)=x+5	$f (x) = x + 5$
9929	Determine if Injective (One to One)	g(x)=(2x)/(x^2+x-6)	$g (x) = \frac{2 x}{x^{2} + x - 6}$
9930	Determine if Injective (One to One)	g(x)=3 square root of x	$g (x) = 3 \sqrt{x}$
9931	Determine if Injective (One to One)	x=60x+50y	$x = 60 x + 50 y$
9932	Determine if Injective (One to One)	y=100/(-x)	$y = \frac{100}{- x}$
9933	Determine if Injective (One to One)	y=2x^2-12x+16	$y = 2 x^{2} - 12 x + 16$
9934	Determine if Surjective (Onto)	f(x)=x^2+3x	$f (x) = x^{2} + 3 x$
9935	Determine if Surjective (Onto)	f(x)=x^2-5	$f (x) = x^{2} - 5$
9936	Determine if Surjective (Onto)	f(x)=x+1	$f (x) = x + 1$
9937	Find the Constant of Variation	x^2+y^2+2x-2y-14=0	$x^{2} + y^{2} + 2 x - 2 y - 14 = 0$
9938	Find the Constant of Variation	2x-3y=-2	$2 x - 3 y = - 2$
9939	Find the Constant of Variation	3x+2y=21	$3 x + 2 y = 21$
9940	Find the Constant of Variation	4y^2+x^2=144	$4 y^{2} + x^{2} = 144$
9941	Find the Constant of Variation	4x-2y=8	$4 x - 2 y = 8$
9942	Find the Constant of Variation	9x-8y=9	$9 x - 8 y = 9$
9943	Find the Angle Between the Vectors	(0,154000) , (10,87000)	$(0, 154000)$ , $(10, 87000)$
9944	Find the Angle Between the Vectors	(6,0) , (0,-8)	$(6, 0)$ , $(0, - 8)$
9945	Find the Angle Between the Vectors	(9,8) , (9,3)	$(9, 8)$ , $(9, 3)$
9946	Find the Angle Between the Vectors	u=(5,-4) , v=(2,1)	$u = (5, - 4)$ , $v = (2, 1)$
9947	Find the Quadrant of the Angle	100/2	$\frac{100}{2}$
9948	Find the Quadrant of the Angle	-2/3	$- \frac{2}{3}$
9949	Find the Quadrant of the Angle	27^(-2/3)	$27^{- \frac{2}{3}}$
9950	Find the Quadrant of the Angle	0.21875	$0.21875$
9951	Find the Quadrant of the Angle	0.4313	$0.4313$
9952	Find the Quadrant of the Angle	-2.300	$- 2.3$
9953	Find the Quadrant of the Angle	-2i	$- 2 i$
9954	Find the Quadrant of the Angle	-54	$- 54$
9955	Determine if Injective (One to One)	\|x+1\|=6	$\| x + 1 \| = 6$
9956	Determine if Injective (One to One)	x^2+3y^2=3	$x^{2} + 3 y^{2} = 3$
9957	Determine if Injective (One to One)	f(x)=(2x^3+x)/(x^3-1)	$f (x) = \frac{2 x^{3} + x}{x^{3} - 1}$
9958	Determine if Injective (One to One)	f(x)=2x+3	$f (x) = 2 x + 3$
9959	Determine if Injective (One to One)	f(x)=(x+1)^2	$f (x) = {(x + 1)}^{2}$
9960	Determine if Injective (One to One)	f(x)=1/(x^2)	$f (x) = \frac{1}{x^{2}}$
9961	Determine if Injective (One to One)	f(x)=(3x-5)/(7x+2)	$f (x) = \frac{3 x - 5}{7 x + 2}$
9962	Determine if Injective (One to One)	f(x)=(8x^2+7x-10)/(2x+3)	$f (x) = \frac{8 x^{2} + 7 x - 10}{2 x + 3}$
9963	Determine if Injective (One to One)	f(x)=x/2-3	$f (x) = \frac{x}{2} - 3$
9964	Determine if Injective (One to One)	f(x)=-x^2+6x-4	$f (x) = - x^{2} + 6 x - 4$
9965	Determine if Injective (One to One)	f(x)=x^3	$f (x) = x^{3}$
9966	Determine if Injective (One to One)	f(x)=x^3+x	$f (x) = x^{3} + x$
9967	Determine if Injective (One to One)	f(x)=x^5+1	$f (x) = x^{5} + 1$
9968	Determine if Injective (One to One)	f(x)=2(x-3)^2+1	$f (x) = 2 {(x - 3)}^{2} + 1$
9969	Find the Equation Using Two Points	f(10)=0 , f(20)=10	$f (10) = 0$ , $f (20) = 10$
9970	Find the Equation Using Two Points	f(3)=7 , g(4)=2	$f (3) = 7$ , $g (4) = 2$
9971	Find the Equation Using Two Points	g(2)=5 , f(5)=11	$g (2) = 5$ , $f (5) = 11$
9972	Find the Equation Using Two Points	h(100)=2 , g(200)=20	$h (100) = 2$ , $g (200) = 20$
9973	Find the Sum of the Functions	C(x)=27000+55x+0.2x^2 , R(x)=445x-0.8x^2	$C (x) = 27000 + 55 x + 0.2 x^{2}$ , $R (x) = 445 x - 0.8 x^{2}$
9974	Find the Sum of the Functions	f(x)=\|2x+1\| , g(x)=\|x-4\|	$f (x) = \| 2 x + 1 \|$ , $g (x) = \| x - 4 \|$
9975	Find the Sum of the Functions	f(x)=2x-1 , g(x)=3x-2	$f (x) = 2 x - 1$ , $g (x) = 3 x - 2$
9976	Find the Sum of the Functions	f(x)=3x , g(x)=4x+2	$f (x) = 3 x$ , $g (x) = 4 x + 2$
9977	Find the Sum of the Functions	f(x)=x-5 , g(x)=3x+6	$f (x) = x - 5$ , $g (x) = 3 x + 6$
9978	Find the Sum of the Functions	R(x)=81.50 , C(x)=63x+1850	$R (x) = 81.5$ , $C (x) = 63 x + 1850$
9979	Find the Sum of the Functions	C(x)=13x+68 , R(x)=30x	$C (x) = 13 x + 68$ , $R (x) = 30 x$
9980	Find the Sum of the Functions	f(x)=3x+5 , g(x)=7x+8	$f (x) = 3 x + 5$ , $g (x) = 7 x + 8$
9981	Find the Sum of the Functions	f(x)=x+3 , g(x)=-6+10	$f (x) = x + 3$ , $g (x) = - 6 + 10$
9982	Find the Difference of the Two Functions	f(x)=x^2+1 , g(x)=1-x^2	$f (x) = x^{2} + 1$ , $g (x) = 1 - x^{2}$
9983	Find the Difference of the Two Functions	S(p)=9p+12 , D(p)=280-9p	$S (p) = 9 p + 12$ , $D (p) = 280 - 9 p$
9984	Find the Product	f(x)=2-2x , g(x)=-9x+2	$f (x) = 2 - 2 x$ , $g (x) = - 9 x + 2$
9985	Find the Product	R(x)=-x^2+8x , C(x)=3x+4	$R (x) = - x^{2} + 8 x$ , $C (x) = 3 x + 4$
9986	Find the Product	r(x)=400x , c(x)=x^2-100x+3000	$r (x) = 400 x$ , $c (x) = x^{2} - 100 x + 3000$
9987	Find the Product	r(x)=8x-0.001x^2 , c(x)=5x	$r (x) = 8 x - 0.001 x^{2}$ , $c (x) = 5 x$
9988	Find the Product	s(x)=x-6 , t(x)=4x+1	$s (x) = x - 6$ , $t (x) = 4 x + 1$
9989	Find the Product	f(x)=x^3-4 , g(x)=(x+2)/3	$f (x) = x^{3} - 4$ , $g (x) = \frac{x + 2}{3}$
9990	Find the Product	f(x)=x+3 , g(x)=-6+10	$f (x) = x + 3$ , $g (x) = - 6 + 10$
9991	Find the Product	g(x)=x^2 , f(x)=1/(4-x)	$g (x) = x^{2}$ , $f (x) = \frac{1}{4 - x}$
9992	Find the Quotient of the Two Functions	f(x)=(x-1)/(x+2) , g(x)=(x-1)/x	$f (x) = \frac{x - 1}{x + 2}$ , $g (x) = \frac{x - 1}{x}$
9993	Find the Quotient of the Two Functions	f(x)=x^2+1 , g(x)=1-x^2	$f (x) = x^{2} + 1$ , $g (x) = 1 - x^{2}$
9994	Find the Quotient of the Two Functions	f(x)=9x-1 , g(x)=7-4x	$f (x) = 9 x - 1$ , $g (x) = 7 - 4 x$
9995	Find the Quotient of the Two Functions	P(x)=x^4-6x^2-30 , d(x)=x+3	$P (x) = x^{4} - 6 x^{2} - 30$ , $d (x) = x + 3$
9996	Find the Domain of the Sum of the Functions	c(x)=110+6.1x , R(x)=3x-0.04x^2	$c (x) = 110 + 6.1 x$ , $R (x) = 3 x - 0.04 x^{2}$
9997	Find the Domain of the Sum of the Functions	f(x)=\|2x+1\| , g(x)=\|x-4\|	$f (x) = \| 2 x + 1 \|$ , $g (x) = \| x - 4 \|$
9998	Find the Domain of the Sum of the Functions	f(x)=\|x+2\| , g(x)=-x^2	$f (x) = \| x + 2 \|$ , $g (x) = - x^{2}$
9999	Find the Domain of the Sum of the Functions	f(x)=(7x)/(x-8) , g(x)=6/(8-x)	$f (x) = \frac{7 x}{x - 8}$ , $g (x) = \frac{6}{8 - x}$
10000	Find the Domain of the Sum of the Functions	f(x)=x/(x-7) , g(x)=-1/x	$f (x) = \frac{x}{x - 7}$ , $g (x) = - \frac{1}{x}$