See tutors' answers!

Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On


   
By Tutor
 | By Problem Number | 

Tutor:
New! Get regular updates about newly solved problems via algebra.com's RSS system.

Recent problems solved by 'Fombitz'

Fombitz answered: 13805 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989 , 6990..7019 , 7020..7049 , 7050..7079 , 7080..7109 , 7110..7139 , 7140..7169 , 7170..7199 , 7200..7229 , 7230..7259 , 7260..7289 , 7290..7319 , 7320..7349 , 7350..7379 , 7380..7409 , 7410..7439 , 7440..7469 , 7470..7499 , 7500..7529 , 7530..7559 , 7560..7589 , 7590..7619 , 7620..7649 , 7650..7679 , 7680..7709 , 7710..7739 , 7740..7769 , 7770..7799 , 7800..7829 , 7830..7859 , 7860..7889 , 7890..7919 , 7920..7949 , 7950..7979 , 7980..8009 , 8010..8039 , 8040..8069 , 8070..8099 , 8100..8129 , 8130..8159 , 8160..8189 , 8190..8219 , 8220..8249 , 8250..8279 , 8280..8309 , 8310..8339 , 8340..8369 , 8370..8399 , 8400..8429 , 8430..8459 , 8460..8489 , 8490..8519 , 8520..8549 , 8550..8579 , 8580..8609 , 8610..8639 , 8640..8669 , 8670..8699 , 8700..8729 , 8730..8759 , 8760..8789 , 8790..8819 , 8820..8849 , 8850..8879 , 8880..8909 , 8910..8939 , 8940..8969 , 8970..8999 , 9000..9029 , 9030..9059 , 9060..9089 , 9090..9119 , 9120..9149 , 9150..9179 , 9180..9209 , 9210..9239 , 9240..9269 , 9270..9299 , 9300..9329 , 9330..9359 , 9360..9389 , 9390..9419 , 9420..9449 , 9450..9479 , 9480..9509 , 9510..9539 , 9540..9569 , 9570..9599 , 9600..9629 , 9630..9659 , 9660..9689 , 9690..9719 , 9720..9749 , 9750..9779 , 9780..9809 , 9810..9839 , 9840..9869 , 9870..9899 , 9900..9929 , 9930..9959 , 9960..9989 , 9990..10019 , 10020..10049 , 10050..10079 , 10080..10109 , 10110..10139 , 10140..10169 , 10170..10199 , 10200..10229 , 10230..10259 , 10260..10289 , 10290..10319 , 10320..10349 , 10350..10379 , 10380..10409 , 10410..10439 , 10440..10469 , 10470..10499 , 10500..10529 , 10530..10559 , 10560..10589 , 10590..10619 , 10620..10649 , 10650..10679 , 10680..10709 , 10710..10739 , 10740..10769 , 10770..10799 , 10800..10829 , 10830..10859 , 10860..10889 , 10890..10919 , 10920..10949 , 10950..10979 , 10980..11009 , 11010..11039 , 11040..11069 , 11070..11099 , 11100..11129 , 11130..11159 , 11160..11189 , 11190..11219 , 11220..11249 , 11250..11279 , 11280..11309 , 11310..11339 , 11340..11369 , 11370..11399 , 11400..11429 , 11430..11459 , 11460..11489 , 11490..11519 , 11520..11549 , 11550..11579 , 11580..11609 , 11610..11639 , 11640..11669 , 11670..11699 , 11700..11729 , 11730..11759 , 11760..11789 , 11790..11819 , 11820..11849 , 11850..11879 , 11880..11909 , 11910..11939 , 11940..11969 , 11970..11999 , 12000..12029 , 12030..12059 , 12060..12089 , 12090..12119 , 12120..12149 , 12150..12179 , 12180..12209 , 12210..12239 , 12240..12269 , 12270..12299 , 12300..12329 , 12330..12359 , 12360..12389 , 12390..12419 , 12420..12449 , 12450..12479 , 12480..12509 , 12510..12539 , 12540..12569 , 12570..12599 , 12600..12629 , 12630..12659 , 12660..12689 , 12690..12719 , 12720..12749 , 12750..12779 , 12780..12809 , 12810..12839 , 12840..12869 , 12870..12899 , 12900..12929 , 12930..12959 , 12960..12989 , 12990..13019 , 13020..13049 , 13050..13079 , 13080..13109 , 13110..13139 , 13140..13169 , 13170..13199 , 13200..13229 , 13230..13259 , 13260..13289 , 13290..13319 , 13320..13349 , 13350..13379 , 13380..13409 , 13410..13439 , 13440..13469 , 13470..13499 , 13500..13529 , 13530..13559 , 13560..13589 , 13590..13619 , 13620..13649 , 13650..13679 , 13680..13709 , 13710..13739 , 13740..13769 , 13770..13799 , 13800..13829, >>Next

Graphs/322935: Find the slope and the y-intercept of the line
8X+4Y=12
1 solutions

Answer 231179 by Fombitz(13828) About Me  on 2010-07-16 11:18:40 (Show Source):
You can put this solution on YOUR website!
Put the equation in slope-intercept form, y=mx%2Bb
8x%2B4y=12
4y=-8x%2B12
y=-2x%2B3
Slope:m=-2
Interceptb=3
.
.
.


Systems-of-equations/322947: If 5a-b=9 and 3a+b=15, then a=b=?
1 solutions

Answer 231178 by Fombitz(13828) About Me  on 2010-07-16 11:16:18 (Show Source):
You can put this solution on YOUR website!
Add the two equations together to eliminate b.
5a-b%2B3a%2Bb=9%2B15
8a=24
highlight%28a=3%29
Then use either equation to solve for y.
9%2Bb=15
highlight%28b=6%29


Polynomials-and-rational-expressions/322941: Hello, ihow do i show my work for this problem 12r^10s^7/4r^2s
1 solutions

Answer 231177 by Fombitz(13828) About Me  on 2010-07-16 11:13:18 (Show Source):


Probability-and-statistics/322921: A box contains a total of 50 textbooks, of which 10 are biology books. If you select 2 at random, determine the probability that neither is a biology book.
1 solutions

Answer 231164 by Fombitz(13828) About Me  on 2010-07-16 08:48:16 (Show Source):
You can put this solution on YOUR website!

P(1st not biology)=40%2F50=4%2F5
P(2nd not biology)=39%2F49
P(2 books not biology)=%284%2F5%29%2839%2F49%29=156%2F245


Linear-equations/322924: Pls. help me understand how to do these math. Find the slope and the y-intercept.
1. y= 4x -9
2. y= -2x plus 3
3. -2x -8y =16
1 solutions

Answer 231163 by Fombitz(13828) About Me  on 2010-07-16 08:33:12 (Show Source):
You can put this solution on YOUR website!
The slope intercept form of a line is y=mx%2Bb where m is the slope and b is the intercept.
.
.
.
1. m=4, b=-9
2. You fill in the answer on this one.
3. Sometimes you have to move terms around to get it into slope-intercept form,
-2x-8y=16
-8y=2x%2B16
y=-%281%2F4%29x-2
Again, read off the slope and intercept.


Graphs/322925: graph ((y-2)2)/4-((x+3)2)/16=1
1 solutions

Answer 231162 by Fombitz(13828) About Me  on 2010-07-16 08:30:51 (Show Source):


real-numbers/322875: List in order from the least to the greatest.
2/3,-1/7,1/3,-2/7,-2/3,2/5,-1/3,-2/5,9/8
1 solutions

Answer 231138 by Fombitz(13828) About Me  on 2010-07-15 22:17:58 (Show Source):
You can put this solution on YOUR website!
Find a common denominator,
+3%2A7%2A5%2A8=840+
2%2F3=560%2F840+
-1%2F7=-120%2F840+
1%2F3=280%2F840+
-2%2F7=-240%2F840+
-2%2F3=-560%2F840+
2%2F5=336%2F840+
-1%2F3=-280%2F840
-2%2F5=-336%2F840+
9%2F8=945%2F840+
.
.
.
{-560, -336, -280, -240,-120,280,336,560,945}
{-2/3,-2/5,-1/3,-2/7,-1/7,1/3,2/5,2/3,9/8}


Functions/322839: determine the equation of the line described. put answer in slope-intercept form, if possible.
Through (-8,1), perpendicular to 5x+3y=-13
1 solutions

Answer 231137 by Fombitz(13828) About Me  on 2010-07-15 22:08:54 (Show Source):
You can put this solution on YOUR website!
5x%2B3y=-13
3y=-5x-13
y=-%285%2F3%29x-13%2F3
Perpendicular lines have slopes that are negative reciprocals,
m1%2Am2=-1
-%285%2F3%29%2Am2=-1
m2=3%2F5
.
.
.
y=mx%2Bb=%283%2F5%29x%2Bb
Use the point (-8,1) to solve for b.
1=%283%2F5%29%28-8%29%2Bb
b=5%2F5%2B24%2F5
b=29%2F5
.
.
highlight%28y=%283%2F5%29x%2B29%2F5%29
.
.
.


Polynomials-and-rational-expressions/322807: -2a^2/3a^2*20a/15a^3
1 solutions

Answer 231135 by Fombitz(13828) About Me  on 2010-07-15 22:03:07 (Show Source):


Expressions-with-variables/322781: 15^=x^+(x+3)^2
1 solutions

Answer 231134 by Fombitz(13828) About Me  on 2010-07-15 21:59:01 (Show Source):
You can put this solution on YOUR website!
I assume you mean like this,
15%5E2=x%5E2%2B%28x%2B3%29%5E2
225=x%5E2%2Bx%5E2%2B6x%2B9
2x%5E2%2B6x-216=0
x%5E2%2B3x-108=0
%28x%2B12%29%28x-9%29=0
Two solutions:
x%2B12=0
highlight%28x=-12%29
.
.
.
x-9=0
highlight%28x=9%29


Linear_Equations_And_Systems_Word_Problems/322824: A chemist has one solution that is 80% acid and a second solution that is 44% acid. She wants to combine the solutions to make a new solution that is 53% acid. If she needs to make 320 Milliliters of this new solution, how many milliliters of the two solutions should be mixed?
1 solutions

Answer 231133 by Fombitz(13828) About Me  on 2010-07-15 21:55:14 (Show Source):
You can put this solution on YOUR website!
Let A be the amount of 80% solution, B the amount of 44% solution.
1.A%2BB=320
.
.
.
80A%2B44B=53%28320%29
2.20A%2B11B=4240
From eq. 1,
A=320-B
20A=6400-20B
Substitute into eq. 2,
6400-20B%2B11B=4240
-9B=-2160
B=240
Then from eq. 1,
A%2B240=320
A=80
.
.
.
80 ml of 80% solution and 240 ml of 44% solution.


Quadratic_Equations/322680: factor if possible:
x^4 + 22x^2 + 121
1 solutions

Answer 231042 by Fombitz(13828) About Me  on 2010-07-15 16:05:16 (Show Source):


Quadratic_Equations/322749: The hypotenuse of a right triangle has a length of 13 cm. the sum of the lengths of the other two sides is 17. Find the unknown lengths.
1 solutions

Answer 231040 by Fombitz(13828) About Me  on 2010-07-15 16:04:22 (Show Source):
You can put this solution on YOUR website!
A%5E2%2BB%5E2=13%5E2
A%2BB=17
From eq. 2,
B=17-A
Substitute into eq. 1,
A%5E2%2B%2817-A%29%5E2=169
A%5E2%2B289-34A%2BA%5E2=169
2A%5E2-34A%2B120=0
A%5E2-17A%2B60=0
%28A-12%29%28A-5%29=0
Two solutions:
A=12
Then from eq. 2,
12%2BB=17
B=5
.
.
.
A-5=0
A=5
Then,
5%2BB=17
B=12
.
.
.
The other two sides are 5 and 12 cm long.


Quadratic_Equations/322709: x^+12=0 solve by any method factoring, extracting square roots, or completing square
1 solutions

Answer 231038 by Fombitz(13828) About Me  on 2010-07-15 16:01:10 (Show Source):


Human-and-algebraic-language/322719: Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours. How much time did each require?
1 solutions

Answer 231037 by Fombitz(13828) About Me  on 2010-07-15 15:59:59 (Show Source):
You can put this solution on YOUR website!
Convert to consistent units, minutes.
.
.
.
TL=TR%2B10
.
.
.
TL%2BTR=6%2860%29
Substituting form above,
TR%2B10%2BTR=360
2TR=350
TR=175
.
.
.
TL=TR%2B10
TL=185
Tom's time was 175 minutes, Linda's time was 185 minutes.


Probability-and-statistics/322703: A math test was given; a sample of the scores yielded the following results:
27, 21, 82, 79, 30, 58, 86, 6, 3, 59, 48, 86, 1, 61, 88, 21
Find the range, standard deviation, and variance for the sample scores
1 solutions

Answer 231034 by Fombitz(13828) About Me  on 2010-07-15 15:53:29 (Show Source):
You can put this solution on YOUR website!
Range:1-88
Mean:47.25
Standard Deviation: 30.8
Variance:1013.8


Polynomials-and-rational-expressions/322684: factor 2^16 - 1
1 solutions

Answer 231033 by Fombitz(13828) About Me  on 2010-07-15 15:47:12 (Show Source):
You can put this solution on YOUR website!
It's the difference of two squares.
%282%5E16+-+1+%29=%282%5E8-1%29%282%5E8%2B1%29
%282%5E16+-+1+%29=%282%5E4-1%29%282%5E4%2B1%29%282%5E8%2B1%29
%282%5E16+-+1+%29=%282%5E2-1%29%282%5E2%2B1%29%282%5E4%2B1%29%282%5E8%2B1%29
%282%5E16+-+1+%29=%282-1%29%282%2B1%29%282%5E2%2B1%29%282%5E4%2B1%29%282%5E8%2B1%29
%282%5E16+-+1+%29=%281%29%283%29%285%29%2817%29%28257%29
%282%5E16+-+1+%29=65535


Complex_Numbers/322760: is the actual equation the complex number?
example: 2-3i 1 solutions

Answer 231032 by Fombitz(13828) About Me  on 2010-07-15 15:39:45 (Show Source):
You can put this solution on YOUR website!
Yes, the whole expression (2-3i) is the complex number made up of the real part (2) and the imaginary part (-3i).


Sequences-and-series/322756: what two numbers whose product is -56 but whose sum is 10
1 solutions

Answer 231030 by Fombitz(13828) About Me  on 2010-07-15 15:33:28 (Show Source):
You can put this solution on YOUR website!
Let A and B be the numbers.
1.A%2BB=10
2.AB=-56
Useing eq. 1,
A=10-B
Substitute into eq. 2,
%2810-B%29B=-56
10B-B%5E2=-56
B%5E2-10B-56=0
%28B-14%29%28B%2B4%29=0
Two solutions:
B-14=0
B=14
Then from eq. 1,
A%2B14=10
A=-4
.
.
.
B%2B4=0
B=-4
Then from eq. 1,.
A-4=10
A=14
.
.
.
14 and -4 are the two numbers.


Radicals/322757: (square root of 7+square root of 10)Times(Square root of 7-square root of 10
1 solutions

Answer 231029 by Fombitz(13828) About Me  on 2010-07-15 15:30:36 (Show Source):
You can put this solution on YOUR website!
Use the FOIL method,

%28sqrt%287%29%2Bsqrt%2810%29%29%28sqrt%287%29-sqrt%2810%29%29=-3


Sequences-and-series/322742: 1/9 - 1/y² (y squared)
______________________(divided by)
1/3 + 1/y
1 solutions

Answer 231027 by Fombitz(13828) About Me  on 2010-07-15 15:27:44 (Show Source):


Expressions-with-variables/322753: how do i solve y=4x-8 and y=2x+10 using substitution?
1 solutions

Answer 231025 by Fombitz(13828) About Me  on 2010-07-15 15:08:52 (Show Source):
You can put this solution on YOUR website!
1.y=4x-8
2.y=2x%2B10
Substitute for y in eq. 1 using eq. 2,
2x%2B10=4x-8
2x=18
highlight%28x=9%29
Now use either equation to solve for y,
y=4%289%29-8
y=36-8
highlight%28y=28%29


Equations/322745: P=sigma*A*e*T^4 solve for T how would I simplify this having T by itself?
1 solutions

Answer 231020 by Fombitz(13828) About Me  on 2010-07-15 14:56:45 (Show Source):


Inverses/322748: 6t+18=18
1 solutions

Answer 231019 by Fombitz(13828) About Me  on 2010-07-15 14:55:25 (Show Source):
You can put this solution on YOUR website!
6t%2B18=18
6t=0 <--- Subtract 18 from both sides.
highlight%28t=0%29<--- Divide both sides by 6.


Complex_Numbers/322743: Please help me figure out how to find the complex zeros of the equation:
f(x)=4x^3+19x^2-61x+14
1 solutions

Answer 231018 by Fombitz(13828) About Me  on 2010-07-15 14:54:21 (Show Source):
You can put this solution on YOUR website!
Since there are three roots and complex roots come in pairs, at least one must be real.
+graph%28+300%2C+300%2C+-10%2C+5%2C+-500%2C+500%2C+4x%5E3%2B19x%5E2-61x%2B14%29
All three roots are real for this equation.
Looks like x=-7 and x=2 are roots.
Verify using the equation.
I'll do one, you verify the other.
4x%5E3%2B19x%5E2-61x%2B14=4%28-7%29%5E3%2B19%2849%29-61%28-7%29%2B14
4x%5E3%2B19x%5E2-61x%2B14=-1372%2B931%2B427%2B14
4x%5E3%2B19x%5E2-61x%2B14=0
.
.
.
Now that you have two factors.
%28x%2B7%29%28x-2%29=x%5E2%2B5x-14
You can use polynomial long division to find the remaining factor.
%284x%5E3%2B19x%5E2-61x%2B14%29%2F%28x%5E2%2B5x-14%29


Quadratic_Equations/322710: x^+85=18x solve by any method ( factoring, extracting square roots, or completing the square)
1 solutions

Answer 231016 by Fombitz(13828) About Me  on 2010-07-15 14:40:42 (Show Source):


Linear_Equations_And_Systems_Word_Problems/322718: Determine solution:
2x+3y+7z=13
3x+2y-5z=-22
5x+7y-3z=28
1 solutions

Answer 231015 by Fombitz(13828) About Me  on 2010-07-15 14:39:17 (Show Source):
You can put this solution on YOUR website!
I used matrix inversion to solve.


Quadratic_Equations/322707: Quadratic equation solve by completing the square x^+26x-84=0
1 solutions

Answer 231014 by Fombitz(13828) About Me  on 2010-07-15 14:36:42 (Show Source):


Linear-equations/322699: How do I find the equation for:
x intercept -3, y intercept 5?
1 solutions

Answer 231013 by Fombitz(13828) About Me  on 2010-07-15 14:34:17 (Show Source):
You can put this solution on YOUR website!
x%2FA%2By%2FB=1
When x=0, y=5,
x%2FA%2By%2FB=1
y%2FB=1
y=B=5
B=5
.
.
.
When y=0,x=-3
x%2FA%2By%2FB=1
x%2FA=1%7D%7D%0D%0A%7B%7B%7BA-3
.
.
.
x%2FA%2By%2FB=1
-x%2F3%2By%2F5=1
highlight%285x-3y=-15%29


Quadratic_Equations/322675: Factor, if possible
t^6 - 18t^3 + 81
1 solutions

Answer 231012 by Fombitz(13828) About Me  on 2010-07-15 14:30:08 (Show Source):
You can put this solution on YOUR website!
Substitute.
Let u=t%5E3, u%5E2=t%5E6
t%5E6+-+18t%5E3+%2B+81=u%5E2+-+18u+%2B+81
t%5E6+-+18t%5E3+%2B+81=%28u-9%29%5E2
t%5E6+-+18t%5E3+%2B+81=%28t%5E3-9%29%5E2


test/322731: What is the standard form of an equation of the line that passes through the point (-1, 5) and has a slope of 1/2?
1 solutions

Answer 231010 by Fombitz(13828) About Me  on 2010-07-15 14:25:02 (Show Source):
You can put this solution on YOUR website!
Use the point-slope form of a line, y-yp=m%28x-xp%29
y-5=%281%2F2%29%28x-%28-1%29%29
2y-10=x%2B1
-x%2B2y=11
highlight%28x-2y=-11%29