Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
5401	Solve Using an Augmented Matrix	x+2y=9 , -x+2y=1	$x + 2 y = 9$ , $- x + 2 y = 1$
5402	Solve Using an Augmented Matrix	x+2y-7z=-2 , -2x-5y+2z=1 , 3x+5y+4z=-9	$x + 2 y - 7 z = - 2$ , $- 2 x - 5 y + 2 z = 1$ , $3 x + 5 y + 4 z = - 9$
5403	Solve Using an Augmented Matrix	x+2y-w=-4 , 3x+6z+9w=60 , x+2y-z=4 , 3x-y+z+w=8	$x + 2 y - w = - 4$ , $3 x + 6 z + 9 w = 60$ , $x + 2 y - z = 4$ , $3 x - y + z + w = 8$
5404	Solve Using an Augmented Matrix	-x+2y-z=0 , -x-y+2z=0 , 2x-z=6	$- x + 2 y - z = 0$ , $- x - y + 2 z = 0$ , $2 x - z = 6$
5405	Solve Using an Augmented Matrix	x+3y+4z=10 , -3x+7y+42=2	$x + 3 y + 4 z = 10$ , $- 3 x + 7 y + 42 = 2$
5406	Solve Using an Augmented Matrix	-x+3y+z=20 , x-y+5z=10 , -5x-4y+4z=-17	$- x + 3 y + z = 20$ , $x - y + 5 z = 10$ , $- 5 x - 4 y + 4 z = - 17$
5407	Solve Using an Augmented Matrix	-x+3y=11 , 3x-9y=-30	$- x + 3 y = 11$ , $3 x - 9 y = - 30$
5408	Solve Using an Augmented Matrix	x+3y=2 , y=-2	$x + 3 y = 2$ , $y = - 2$
5409	Solve Using an Augmented Matrix	x+3y=9 , 3x-y=7	$x + 3 y = 9$ , $3 x - y = 7$
5410	Solve Using an Augmented Matrix	-x+4y+4z=5 , x-y+5z=7 , -2x-6y-3z=16	$- x + 4 y + 4 z = 5$ , $x - y + 5 z = 7$ , $- 2 x - 6 y - 3 z = 16$
5411	Solve Using an Augmented Matrix	x+5y=10 , 3x+15y=30	$x + 5 y = 10$ , $3 x + 15 y = 30$
5412	Solve Using an Augmented Matrix	x+5y=14 , -x-4y-z=-12 , 3y=9	$x + 5 y = 14$ , $- x - 4 y - z = - 12$ , $3 y = 9$
5413	Solve Using an Augmented Matrix	x+5y-5z=-23 , y-2z=-3	$x + 5 y - 5 z = - 23$ , $y - 2 z = - 3$
5414	Solve Using an Augmented Matrix	x+6y=-26 , 7x+8y=-12	$x + 6 y = - 26$ , $7 x + 8 y = - 12$
5415	Solve Using an Augmented Matrix	x+7y=2 , 5x+2y=15	$x + 7 y = 2$ , $5 x + 2 y = 15$
5416	Solve Using an Augmented Matrix	x+7y=25 , -7x+5y=-13	$x + 7 y = 25$ , $- 7 x + 5 y = - 13$
5417	Solve Using an Augmented Matrix	x+y+3z=-5 , -2x-4y+14z=16 , x+z=-2	$x + y + 3 z = - 5$ , $- 2 x - 4 y + 14 z = 16$ , $x + z = - 2$
5418	Solve Using an Augmented Matrix	x+y+z+w=-1 , 3x+3y-3z-3w=9 , 2x-3y+3z+w=-16 , x-y+5z+2w=-16	$x + y + z + w = - 1$ , $3 x + 3 y - 3 z - 3 w = 9$ , $2 x - 3 y + 3 z + w = - 16$ , $x - y + 5 z + 2 w = - 16$
5419	Solve Using an Augmented Matrix	x+y+z=102 , 2x+3y+4z=303 , 11x+17y+23z=1517	$x + y + z = 102$ , $2 x + 3 y + 4 z = 303$ , $11 x + 17 y + 23 z = 1517$
5420	Solve Using an Augmented Matrix	x+y+z=1230 , 120x+150y+180z=32400 , 180x+80y+80z=34200 , 5x+6y+4z=800	$x + y + z = 1230$ , $120 x + 150 y + 180 z = 32400$ , $180 x + 80 y + 80 z = 34200$ , $5 x + 6 y + 4 z = 800$
5421	Solve Using an Augmented Matrix	x+y+z=22 , x+y/10+z/6=5 , x/2+y/15+z/8=77/24	$x + y + z = 22$ , $x + \frac{y}{10} + \frac{z}{6} = 5$ , $\frac{x}{2} + \frac{y}{15} + \frac{z}{8} = \frac{77}{24}$
5422	Solve Using an Augmented Matrix	x+y+z=3 , 2x+z=0 , 3x-y-z=1	$x + y + z = 3$ , $2 x + z = 0$ , $3 x - y - z = 1$
5423	Solve Using an Augmented Matrix	x+y+z=-3 , 2x-y+3z=-15 , 3x+y-4z=-15	$x + y + z = - 3$ , $2 x - y + 3 z = - 15$ , $3 x + y - 4 z = - 15$
5424	Find g(f(x))	f(x)=-x+5 , g(x)=2x-1	$f (x) = - x + 5$ , $g (x) = 2 x - 1$
5425	Find g(h(x))	g(x)=3/x , h(x)=4/(x+2)	$g (x) = \frac{3}{x}$ , $h (x) = \frac{4}{x + 2}$
5426	Find g(h(x))	g(x)=x^2(4-x) , h(x)=7x-1	$g (x) = x^{2} (4 - x)$ , $h (x) = 7 x - 1$
5427	Find P(d(x))	P(x)=x^4-12x^2-67 , d(x)=x+4	$P (x) = x^{4} - 12 x^{2} - 67$ , $d (x) = x + 4$
5428	Find r(s(x))	r(x)=3x-5 , s(x)=x+2	$r (x) = 3 x - 5$ , $s (x) = x + 2$
5429	Find S(D(p))	S(p)=9p+12 , D(p)=280-9p	$S (p) = 9 p + 12$ , $D (p) = 280 - 9 p$
5430	Find s(t(x))	s(x)=4x-3 , t(x)=x-1	$s (x) = 4 x - 3$ , $t (x) = x - 1$
5431	Find s(t(x))	s(x)=x-5 , t(x)=2x+2	$s (x) = x - 5$ , $t (x) = 2 x + 2$
5432	Add	[[1,2,5],[3,4,-7],[1,0,-1]]-[[-1,-2,-6],[-3,-4,0],[1,3,2]]	$[\begin{array}{c} 1 & 2 & 5 \\ 3 & 4 & - 7 \\ 1 & 0 & - 1 \end{array}] - [\begin{array}{c} - 1 & - 2 & - 6 \\ - 3 & - 4 & 0 \\ 1 & 3 & 2 \end{array}]$
5433	Add	[[1,0.0420,0.0420,0.0420],[0.0351,1,0.0351,0.0351],[0.0330,0.0330,1,0.0330],[0.0233,0.0233,0.0233,1]]^-1[[79400],[67800],[63600],[46400]]	${[\begin{array}{c} 1 & 0.042 & 0.042 & 0.042 \\ 0.0351 & 1 & 0.0351 & 0.0351 \\ 0.033 & 0.033 & 1 & 0.033 \\ 0.0233 & 0.0233 & 0.0233 & 1 \end{array}]}^{- 1} [\begin{array}{c} 79400 \\ 67800 \\ 63600 \\ 46400 \end{array}]$
5434	Add	[[1,7,-7,-1],[4,1,1,6],[4,-1,1,-1],[1,-1,-4,6]]^-1[[30],[6],[4],[13]]	${[\begin{array}{c} 1 & 7 & - 7 & - 1 \\ 4 & 1 & 1 & 6 \\ 4 & - 1 & 1 & - 1 \\ 1 & - 1 & - 4 & 6 \end{array}]}^{- 1} [\begin{array}{c} 30 \\ 6 \\ 4 \\ 13 \end{array}]$
5435	Add	3[[5,0],[-1,3],[4,7]]+2[[4,10],[-2,-3],[6,9]]	$3 \cdot [\begin{array}{c} 5 & 0 \\ - 1 & 3 \\ 4 & 7 \end{array}] + 2 \cdot [\begin{array}{c} 4 & 10 \\ - 2 & - 3 \\ 6 & 9 \end{array}]$
5436	Add	[[0.1,0.03],[0.07,0.6]][[5],[10]]	$[\begin{array}{c} 0.1 & 0.03 \\ 0.07 & 0.6 \end{array}] [\begin{array}{c} 5 \\ 10 \end{array}]$
5437	Add	[[1,0,0.5,0.5],[0,1,0.5,5.5]]	$[\begin{array}{c} 1 & 0 & 0.5 & 0.5 \\ 0 & 1 & 0.5 & 5.5 \end{array}]$
5438	Add	[[1,-3,2],[4,1,-5],[0,-3,2]]+[[5,3,4],[-1,8,2]]	$[\begin{array}{c} 1 & - 3 & 2 \\ 4 & 1 & - 5 \\ 0 & - 3 & 2 \end{array}] + [\begin{array}{c} 5 & 3 & 4 \\ - 1 & 8 & 2 \end{array}]$
5439	Add	[[1,-4,9,0],[3,2,-5,6]]+[[3,12,-11],[7,2,8]]	$[\begin{array}{c} 1 & - 4 & 9 & 0 \\ 3 & 2 & - 5 & 6 \end{array}] + [\begin{array}{c} 3 & 12 & - 11 \\ 7 & 2 & 8 \end{array}]$
5440	Add	[[14,12],[14,6]][[-12,12],[24,-28]]	$[\begin{array}{c} 14 & 12 \\ 14 & 6 \end{array}] [\begin{array}{c} - 12 & 12 \\ 24 & - 28 \end{array}]$
5441	Add	[[2,1,-1],[3,0,2]]+[[1,-2,3],[4,0,1],[-1,1,2]]	$[\begin{array}{c} 2 & 1 & - 1 \\ 3 & 0 & 2 \end{array}] + [\begin{array}{c} 1 & - 2 & 3 \\ 4 & 0 & 1 \\ - 1 & 1 & 2 \end{array}]$
5442	Find f(g(x))	f(x)=3x-5 , g(x)=2x+1	$f (x) = 3 x - 5$ , $g (x) = 2 x + 1$
5443	Find f(g(x))	f(x)=4x+4 , g(x)=5x^2+5x	$f (x) = 4 x + 4$ , $g (x) = 5 x^{2} + 5 x$
5444	Find f(g(x))	f(x)=4x-1 , g(x)=x^2+1	$f (x) = 4 x - 1$ , $g (x) = x^{2} + 1$
5445	Find f(g(x))	f(x)=5x-3 , g(x)=3x^2-3x	$f (x) = 5 x - 3$ , $g (x) = 3 x^{2} - 3 x$
5446	Find f(h(x))	f(x)=2/(1-5x) , h(x)=1/x	$f (x) = \frac{2}{1 - 5 x}$ , $h (x) = \frac{1}{x}$
5447	Find f(h(x))	f(x)=2x+2 , h(x)=2x	$f (x) = 2 x + 2$ , $h (x) = 2 x$
5448	Find f(h(x))	f(x)=x+1 , h(x)=x^2+2x+1	$f (x) = x + 1$ , $h (x) = x^{2} + 2 x + 1$
5449	Find f(h(x))	f(x)=x-1 , h(x)=2	$f (x) = x - 1$ , $h (x) = 2$
5450	Find f(h(x))	h(x) = square root of x-4+4 , f(x) = square root of x	$h (x) = \sqrt{x - 4} + 4$ , $f (x) = \sqrt{x}$
5451	Solve for x	(11x+22)x(-11x-33)<0	$(11 x + 22) x (- 11 x - 33) < 0$
5452	Find g(f(x))	f(x) = square root of x , g(x)=-5x-8	$f (x) = \sqrt{x}$ , $g (x) = - 5 x - 8$
5453	Find g(f(x))	f(x)=x^2-4 , g(x)=x^2+2x	$f (x) = x^{2} - 4$ , $g (x) = x^{2} + 2 x$
5454	Add	[[-2,-8],[-11,5]]+3[[5,3,-11],[44,0,5],[-3,2,8]]	$[\begin{array}{c} - 2 & - 8 \\ - 11 & 5 \end{array}] + 3 [\begin{array}{c} 5 & 3 & - 11 \\ 44 & 0 & 5 \\ - 3 & 2 & 8 \end{array}]$
5455	Solve Using an Augmented Matrix	3x+2y=1 , -9x-6y=-3	$3 x + 2 y = 1$ , $- 9 x - 6 y = - 3$
5456	Solve Using an Augmented Matrix	-3x+2y=10 , -4x+3y=2	$- 3 x + 2 y = 10$ , $- 4 x + 3 y = 2$
5457	Solve Using an Augmented Matrix	-3x+2y=13 , 5x+2y=5	$- 3 x + 2 y = 13$ , $5 x + 2 y = 5$
5458	Solve Using an Augmented Matrix	w+x+3y+z=2 , 7w+7x+21y+7z=14 , 4w+4x+12y+4z=8 , 5w+5x+15y+5z=10	$w + x + 3 y + z = 2$ , $7 w + 7 x + 21 y + 7 z = 14$ , $4 w + 4 x + 12 y + 4 z = 8$ , $5 w + 5 x + 15 y + 5 z = 10$
5459	Solve Using an Augmented Matrix	x1+2x2+8x3=2 , x1+x2+4x3=1	$x \cdot 1 + 2 x \cdot 2 + 8 x \cdot 3 = 2$ , $x \cdot 1 + x \cdot 2 + 4 x \cdot 3 = 1$
5460	Solve Using an Augmented Matrix	x1+2x2=21 , -3x1-7x2=-71	$x \cdot 1 + 2 x \cdot 2 = 21$ , $- 3 x \cdot 1 - 7 x \cdot 2 = - 71$
5461	Solve Using an Augmented Matrix	x1+9x2=67 , 4x1-x2=9	$x \cdot 1 + 9 x \cdot 2 = 67$ , $4 x \cdot 1 - x \cdot 2 = 9$
5462	Solve Using an Augmented Matrix	x1-2x2=k1 , x1-x2=k2	$x \cdot 1 - 2 x \cdot 2 = k \cdot 1$ , $x \cdot 1 - x \cdot 2 = k \cdot 2$
5463	Solve Using an Augmented Matrix	x-2y+z=-3 , 2x-y-2z=2 , x+3y-3z=5	$x - 2 y + z = - 3$ , $2 x - y - 2 z = 2$ , $x + 3 y - 3 z = 5$
5464	Solve Using an Augmented Matrix	x-2y=0 , x+y+z=320 , 25000x+80000y+70000z=16000000	$x - 2 y = 0$ , $x + y + z = 320$ , $25000 x + 80000 y + 70000 z = 16000000$
5465	Solve Using an Augmented Matrix	x-2y=10 , -2x+4y=-18 , 3x-6y=28	$x - 2 y = 10$ , $- 2 x + 4 y = - 18$ , $3 x - 6 y = 28$
5466	Solve Using an Augmented Matrix	-x-2y=13 , 3x+6y=-39	$- x - 2 y = 13$ , $3 x + 6 y = - 39$
5467	Solve Using an Augmented Matrix	x-2y=3 , 8x-16y=24 , 4x-8y=12	$x - 2 y = 3$ , $8 x - 16 y = 24$ , $4 x - 8 y = 12$
5468	Solve Using an Augmented Matrix	x-2y=-5 , 3x-2y=-3 , 2x+y=3	$x - 2 y = - 5$ , $3 x - 2 y = - 3$ , $2 x + y = 3$
5469	Solve Using an Augmented Matrix	x-2y=8 , 3x+4y=4	$x - 2 y = 8$ , $3 x + 4 y = 4$
5470	Solve Using an Augmented Matrix	-x-3y=12 , 2x+6y=-24	$- x - 3 y = 12$ , $2 x + 6 y = - 24$
5471	Solve Using a Matrix by Row Operations	5x-y-6z=2 , 9x+y-z=5 , 9x+y-5z=7	$5 x - y - 6 z = 2$ , $9 x + y - z = 5$ , $9 x + y - 5 z = 7$
5472	Solve Using a Matrix by Row Operations	5x-y-z=0 , x+y+z=6	$5 x - y - z = 0$ , $x + y + z = 6$
5473	Solve Using a Matrix by Row Operations	6x+4y=8 , 9x+6y=12	$6 x + 4 y = 8$ , $9 x + 6 y = 12$
5474	Solve Using a Matrix by Row Operations	6x-2y=10 , -3x+y=5	$6 x - 2 y = 10$ , $- 3 x + y = 5$
5475	Solve Using a Matrix by Row Operations	6x-2y=32 , 5x-7y=-8	$6 x - 2 y = 32$ , $5 x - 7 y = - 8$
5476	Solve Using a Matrix by Row Operations	6x-3y+5z=11 , 12x-6y+10z=25 , 18x-9y+15z=35	$6 x - 3 y + 5 z = 11$ , $12 x - 6 y + 10 z = 25$ , $18 x - 9 y + 15 z = 35$
5477	Solve Using a Matrix by Row Operations	6x-5y+6z=-15 , -6x+5y-6z=15 , 12x-10y+12z=-30	$6 x - 5 y + 6 z = - 15$ , $- 6 x + 5 y - 6 z = 15$ , $12 x - 10 y + 12 z = - 30$
5478	Solve Using a Matrix by Row Operations	6x-5y=-3 , 8x-y=13	$6 x - 5 y = - 3$ , $8 x - y = 13$
5479	Solve Using a Matrix by Row Operations	6x-5Y=30 , 12x-10y=6	$6 x - 5 Y = 30$ , $12 x - 10 y = 6$
5480	Solve Using a Matrix by Row Operations	6x-y+7x=8 , -7y+7z=14 , 7x+7y+5z=8	$6 x - y + 7 x = 8$ , $- 7 y + 7 z = 14$ , $7 x + 7 y + 5 z = 8$
5481	Solve Using a Matrix by Row Operations	7x+3y+5z=-13 , 3x+y+2z=17	$7 x + 3 y + 5 z = - 13$ , $3 x + y + 2 z = 17$
5482	Solve Using a Matrix by Row Operations	7x+3y+5z=16 , 3x+y+2z=20	$7 x + 3 y + 5 z = 16$ , $3 x + y + 2 z = 20$
5483	Solve Using a Matrix by Row Operations	7x+5y-z=0 , 9x-y+2z=1 , 16x+4y+z=1	$7 x + 5 y - z = 0$ , $9 x - y + 2 z = 1$ , $16 x + 4 y + z = 1$
5484	Solve Using a Matrix by Row Operations	7x-3x+3z=5 , 7x+2y-z=12 , 35x-10y+11z=32	$7 x - 3 x + 3 z = 5$ , $7 x + 2 y - z = 12$ , $35 x - 10 y + 11 z = 32$
5485	Solve Using a Matrix by Row Operations	7x-3y+2z=-9 , 5x-2y+9z=4 , 9y-5z=-5	$7 x - 3 y + 2 z = - 9$ , $5 x - 2 y + 9 z = 4$ , $9 y - 5 z = - 5$
5486	Solve Using a Matrix by Row Operations	7x-3y+3z=5 , 7x+2y-z=12 , 35x-10y+11z=32	$7 x - 3 y + 3 z = 5$ , $7 x + 2 y - z = 12$ , $35 x - 10 y + 11 z = 32$
5487	Solve Using a Matrix by Row Operations	7x-3y+3z=6 , 7x+4y-3z=11 , 28x-5y+6z=29	$7 x - 3 y + 3 z = 6$ , $7 x + 4 y - 3 z = 11$ , $28 x - 5 y + 6 z = 29$
5488	Solve Using a Matrix by Row Operations	7x-6y=-1 , -14x+12y=2	$7 x - 6 y = - 1$ , $- 14 x + 12 y = 2$
5489	Solve Using a Matrix by Row Operations	7x-y-6z=8 , 2x+y-z=5 , 5x+y-4z=9	$7 x - y - 6 z = 8$ , $2 x + y - z = 5$ , $5 x + y - 4 z = 9$
5490	Solve Using a Matrix by Row Operations	8x+5y+u=7 , x+6y+v=9 , -32x-2y+m=0	$8 x + 5 y + u = 7$ , $x + 6 y + v = 9$ , $- 32 x - 2 y + m = 0$
5491	Solve Using a Matrix by Row Operations	8x+7y=-34 , 16+14y=-36	$8 x + 7 y = - 34$ , $16 + 14 y = - 36$
5492	Solve Using a Matrix by Row Operations	8x-7y=-5 , -16x+14y=10	$8 x - 7 y = - 5$ , $- 16 x + 14 y = 10$
5493	Solve Using a Matrix by Row Operations	9x+3y=15 , 2x+4y=10 , x+3y=6	$9 x + 3 y = 15$ , $2 x + 4 y = 10$ , $x + 3 y = 6$
5494	Solve Using a Matrix by Row Operations	9x+5y=7 , -7x-4y=0	$9 x + 5 y = 7$ , $- 7 x - 4 y = 0$
5495	Solve Using a Matrix by Row Operations	9x-6Y+2Z=-3 , 5x-y+2=5 , y-4z=-2	$9 x - 6 Y + 2 Z = - 3$ , $5 x - y + 2 = 5$ , $y - 4 z = - 2$
5496	Solve Using a Matrix by Row Operations	c=15x+600 , r=30x	$c = 15 x + 600$ , $r = 30 x$
5497	Solve Using a Matrix by Row Operations	m=3 , b=7	$m = 3$ , $b = 7$
5498	Solve Using a Matrix by Row Operations	n=22 , p=0.05 , q=0.095	$n = 22$ , $p = 0.05$ , $q = 0.095$
5499	Solve Using a Matrix by Row Operations	n=6 , p=0.24	$n = 6$ , $p = 0.24$
5500	Solve Using a Matrix by Row Operations	x1+4x2=14 , -2x1+5x2=11	$x \cdot 1 + 4 x \cdot 2 = 14$ , $- 2 x \cdot 1 + 5 x \cdot 2 = 11$