Questions on Algebra: Linear Algebra (NOT Linear Equations) answered by real tutors!

Tutors Answer Your Questions about Linear Algebra (FREE)

Question 28550: A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Identify 2 points that satisfy the inequalities.
Click here to see answer by stanbon(57967)

Question 28699: The relationship between the air temperatur t (in degrees Fahrenheit) and the altitude h ( in feet above sea level) is approcimately linear. At 1000 ft, the temperature is 60*. At 5000ft the temperature is 42*. Express t in therms of h. Use proper or improper fractions or exact decimals only no decimal approcimations.
Click here to see answer by josmiceli(9817)

Question 28706: use factoring to solve the following equations:
9x^2-16=0
i tried (3x-4)(3x-4) but this is wrong. then I thought about using the square root property, but the instructions say factoring.
Click here to see answer by longjonsilver(2297)

Question 28622: 5(y-2)-10=55

Click here to see answer by emmychan(11)

Question 28841: i need help with graphing linear equations
x+y=7
-x+y=6
-x+5y=5
y=-2x+7
Click here to see answer by elima(1433)

Question 28969: use completing the square to find the vertex of the quadratic function
y=-2x^2+16x+4
This is what i tried
y=-2(x^2-8x)+ 4
Y= -2(x-4)^2 +16-16+4
Y=-2(x-4)^2-12
vertex= (-4,-12) the answer is supposed to be vertex= (4,36)
Thanks for the help in advance
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29122: Solve the system.
x + 2y = –15
–2x + 4y = 6

Click here to see answer by sdmmadam@yahoo.com(530)

Question 29229: can someone show me how to solve by addition method...
2x=2-y
3x+y=-1
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29242: 0 = 5(x^3) + 10 + 10(x^2)
solve for x? or factor?
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29241: 0 = 5(x^3) + 10 + 10(x^2)
solve for x? or factor?

Click here to see answer by sdmmadam@yahoo.com(530)

Question 29326: a-6/12=a-2/12
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29238: Let V be the plane 6x1 + 4x2 - 2x3 = 0 in R^3 and let x= (6 -2 4)
a) find the orthogonal decomposition of x with respect to V
b) find the point in V which is closest to x
Click here to see answer by venugopalramana(3286)

Question 29300: 0 = 5(x^3) + 10 + 10(x^2)
solve for x? or factor?
Click here to see answer by longjonsilver(2297)

Question 29236: how do i prove W^(perpendicular sign) is a subspace of R^n
Click here to see answer by venugopalramana(3286)

Question 29237: how do i prove W^(perpendicular sign) is a subspace of R^n
Click here to see answer by venugopalramana(3286)

Question 29411: What is the equation of the line with a slope of -5/2 that goes through the point (-4,-1)?
Click here to see answer by stanbon(57967)

Question 29316: x+y+z=-7
2x+5y+2z=-26
-x+9y-3z=-21
what are the variables?
Click here to see answer by elima(1433)

Question 29774: Solve for x to four decimal places: e^2x =3
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29816: If f(x) =x^3 and g (x) = -6+3x, find g(f(x)).
Click here to see answer by Earlsdon(6294)

Question 29815: Write the equation 4^3=64 in logarithmic form
Click here to see answer by Cintchr(481)

Question 29820: Evaluate: log[3]243
PlEaSe HeLp
Click here to see answer by Cintchr(481)

Question 29822: Write an exponential form: t=log[99^s]
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29814: Let f(x) = 9-x^2, g(x) = 3-x. Find (f+g) (x).
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29817: I am stummped!
let f(x)=9-x^2, g(x)=3-x. Find (f-g) (x).
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29813: Given f(x) = x^3 and g(x) = 3+6x^2, find (g o f) (x).

Click here to see answer by sdmmadam@yahoo.com(530)

Question 29824: Write as single logarithm: 2log[b]^x-7log[b]y
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29839: I have to solve this proof but dont understand it all.
Here it is: Let v and w be independent column vectors in R^3, and let A be an invertible 3X3 matrix.Prove that the vectors Av and Aw are independent.
Click here to see answer by khwang(438)

Question 29823: Express in terms of logarithms of x, y, and z:
log [a] 7xy^5/ [z]^4
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29818: Find the equation of the inverse of f(x) = 7x+3/8
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29819: Solve 1/4 =8^5x-4

Click here to see answer by shyamsundhar(3)

Question 29872: Solve: log[8](3x+2)=4
Thanks
Click here to see answer by jb007mi6(53)

Question 29873: Question:
Given log[10]3=S and log[10]11=T, find log[10]33
Here are the possible answers:
S+T
ST
10^st
10^s+t
Click here to see answer by jb007mi6(53)

Question 29868: Given f(x) =x^3 and g (x) = 3+6x^2, find (g o f) (x).
Here are the possible answers:
a. none of these
b. 3+6x^2/x^3
c. 3+6x^6
d. 3+6x^2
Thanks for helping
Click here to see answer by jb007mi6(53)

Question 29869: Let f(x)=9-x^2, g(x)=3-x. Find (f+g) (x).
Here are my four choices:
(1) -x^2-x+12
(2) 3+x
(3) -x^2+x+6
(4) x^3=3x^2-9x+27
Thanks!
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29871: Express in terms of logarithms of x, y, and z: log[a] 7xy^5/ z^4
Possible answers:
(1) 35+log[a]xy-4loga^z
(2) log[a]7+log[a]x+5log[a]y-4log[a]z
(3)log[a]7+log[a]x+5log[a]y/ 4log[a]z
(4) 7+log[a]x+5log[a]y-4log[a]z
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29870: Question: Solve 1/4=8^5x-4
POssible Four Answers:
(1) 2/15
(2) 2/3
(3) 2/5
(4) 14/15
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29867: Determine the domain of the function h(x) = 3x/ x(x^2-81).
Thanks!
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29821: Determine the domain of the function h(x)= 3x/x(x^2-81)
Click here to see answer by sdmmadam@yahoo.com(530)

Question 29879: Find all real solutions of the following equation:log[4]x+log [4] (x+12) = 3
Here are the possible solutions:
(1) x=12
(2) x=4
(3) x= 16,12
(d) none of these

Click here to see answer by Cintchr(481)

Question 29494: Let a be a fixed vector in R^3, and define W to be the subset of R^3 given by
W={x: a^Tx=0}. Provce that W is a subspace of R^3.
Click here to see answer by khwang(438)

Question 29491: If U and V are subsets of Rn,then the set U+V is defined by
U+V={ x:x=u+v, u in U and v in V}.
Prove that if U and V are subspaces of Rn, then U+V is a subspace of Rn.
Click here to see answer by khwang(438)

Question 29866: QUestion: The number of bacteris present in a culture after t minutes is given as B=10e^ky. If thre are 7212 bacteria present after 11 minutes, find k.
The possible answers are:
72.39
0.658
6.581
0.598
Thanks for your help
Click here to see answer by ikdeep(226)

Question 29926: Given f(x)=x^3 and g(x) = 3+6x^2, find (g o f) (x)
Answers to choose from:
(a) 3+6x^2/x^3
(b) 3+6x^2/x^3
(c) 3+6x^6
(d) 3+6x^2
Please help!
Click here to see answer by sdmmadam@yahoo.com(530)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510