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

decimal-numbers/299928: i need help on math
1 solutions

Answer 215327 by Fombitz(13828) About Me  on 2010-05-03 14:30:54 (Show Source):
You can put this solution on YOUR website!
Enter a question and someone may be able to help.


Miscellaneous_Word_Problems/299864: How do you solve:
The area of a rectangle varies jointly with its length and width. If both the length and width are tripled, by what factor is the area multiplied?
Thank you!
1 solutions

Answer 215326 by Fombitz(13828) About Me  on 2010-05-03 14:30:13 (Show Source):
You can put this solution on YOUR website!
+A1=L%2AW+
A2=%283L%2A3W%29=%283%2A3%29%28L%2AW%29=9%2AA1
The area increases 9 times as much.


Expressions-with-variables/299888: The product of two consecutive positive integers is 272. Find the integers
1 solutions

Answer 215314 by Fombitz(13828) About Me  on 2010-05-03 12:57:16 (Show Source):
You can put this solution on YOUR website!
N%28N%2B1%29=272
N%5E2%2BN-272=0
Look for integer factors close to sqrt%28272%29=16.49
16%2A17=272
%28N-16%29%28N%2B17%29=272
Since we only want positive solutions,
N-16=0
N=16
16 and 17 are the two consecutive positive integers whose product is 272.


Polynomials-and-rational-expressions/299880: a cable that is 55 ft. long is to be cut into two pieces whose legnths have a ratio of 4 to 7. find the lenght of the two pices.
1 solutions

Answer 215311 by Fombitz(13828) About Me  on 2010-05-03 12:48:59 (Show Source):
You can put this solution on YOUR website!
Let's call the two length A and B.
1.A%2BB=55
2.A%2FB=4%2F7
From eq. 2,
A%2FB=4%2F7
7A=4B
Substitute into eq. 1,
A%2BB=55
7A%2B7B=385
4B%2B7B=385
11B=385
highlight_green%28B=35%29
Then from eq. 1,
A%2B35=55
highlight_green%28A=20%29


Trigonometry-basics/298392: Find, to the nearest minute, the angle whose measure is 3.45 radians.
1 solutions

Answer 214676 by Fombitz(13828) About Me  on 2010-04-29 17:12:51 (Show Source):
You can put this solution on YOUR website!
360 degrees=2%2Api radians
3.45%2A%28360%2F%282%2Api%29%29=+196.67
1 degree=60 minutes
0.67 degree=40.2 minutes
196.67=196 degrees 40 minutes (to the nearest minute).


Probability-and-statistics/298414: A state has license plates with 3 letters and 3 numbers. if the letter x is never used, how many possible different plates could there be.
1 solutions

Answer 214675 by Fombitz(13828) About Me  on 2010-04-29 17:09:32 (Show Source):
You can put this solution on YOUR website!
Letters: A-Z without X would be 25 total
Numbers: 0-9 would be 10 total
3 letters, 3 numbers
N=25*25*25*10*10*10=15,625,000 different plates.


Average/298427: what is the average of 57 55 52
1 solutions

Answer 214673 by Fombitz(13828) About Me  on 2010-04-29 17:07:12 (Show Source):


Quadratic_Equations/298351: Find the value of x. If necessary, round to the nearest tenth.
Image Hosted by WoO Pics
1 solutions

Answer 214666 by Fombitz(13828) About Me  on 2010-04-29 16:05:42 (Show Source):
You can put this solution on YOUR website!
The area of a triangle is,
A=%281%2F2%29bh
in this case b=x and h=x.
%281%2F2%29x%2Ax=61
x%5E2=122
x=11.045
To the nearest tenth, x=11.0.


Linear-equations/298395: Why is it true that at x-intercept, the value of y is 0, and at y-intercept, the value of x is 0
1 solutions

Answer 214665 by Fombitz(13828) About Me  on 2010-04-29 16:03:54 (Show Source):
You can put this solution on YOUR website!
Because that's the definition of each of those intercepts.


real-numbers/298400: If a§b = 2a - 3b for all real numbers a and b, what is 2^(3§2)?
1 solutions

Answer 214664 by Fombitz(13828) About Me  on 2010-04-29 16:02:49 (Show Source):
You can put this solution on YOUR website!

a§b = 2a - 3b
3§2=2(3)-3(2)=6-6=0
2^(3§2)=2^(0)=1


Exponential-and-logarithmic-functions/298211: Is -7X10^11 in scientific notation? If not, please put in scientific notation.
1 solutions

Answer 214606 by Fombitz(13828) About Me  on 2010-04-29 08:45:39 (Show Source):
You can put this solution on YOUR website!
Yes, it's in scientific notation.
The coefficient, 7, is between 1 and 10, and the form is correct.


Equations/298177: I need to solve for all variables.
1)2x-x+5y+z=-3
2)3w+2x+2y-6z=-32
3)w+3x+3y-z=-47
4)5w-2x-3y+3z=49
1 solutions

Answer 214605 by Fombitz(13828) About Me  on 2010-04-29 08:43:18 (Show Source):
You can put this solution on YOUR website!
Check your equation 1. You have two instances of the variable x.


logarithm/298202: 5^(3t)=2
1 solutions

Answer 214604 by Fombitz(13828) About Me  on 2010-04-29 08:34:51 (Show Source):


Polynomials-and-rational-expressions/298154: f(x)=x^4-5x^3+5x^2+5x-6
f(2)
1 solutions

Answer 214603 by Fombitz(13828) About Me  on 2010-04-29 08:29:46 (Show Source):
You can put this solution on YOUR website!
Substitute every occurence of x with 2 in f(x) and simplify.
f%28x%29=x%5E4-5x%5E3%2B5x%5E2%2B5x-6
f%282%29=2%5E4-5%282%29%5E3%2B5%282%29%5E2%2B5%282%29-6
f%282%29=16-5%288%29%2B5%284%29%2B10-6
f%282%29=16-40%2B20%2B10-6
f%282%29=0


Linear-equations/298150: find the slope-intercept equation of the line that has given characteristics. slope 0 and y-intercept (0,6)
1 solutions

Answer 214601 by Fombitz(13828) About Me  on 2010-04-29 08:27:25 (Show Source):
You can put this solution on YOUR website!
Use the slope-intercept form of a line,
y=mx%2B6 where m is the slope, b is the intercept.
y=0%28x%29%2B6
y=6
+graph%28+300%2C+300%2C+-10%2C10%2C+-10%2C+10%2C+6%29+


Linear-systems/298223: the following system of equations is a dependent system.
x - 6y = 8
5x - 30y = 40

what is the correct way to write the solution?
a) no solution
b) x - 6y = 8
c) 0
d) all numbers

1 solutions

Answer 214599 by Fombitz(13828) About Me  on 2010-04-29 08:25:44 (Show Source):
You can put this solution on YOUR website!
b) Since the second equation is the first equation multiplied by 6 (hence dependent), every solution of the first equation will also solve the second equation, since they're the same equation.


Functions/298143: Let f represent the greatest integer function. For each item below, use a different notation to write an expression for f(x) and evaluate that expression.
f(5.9)
f(-2.9)
f(-4.8)
Can you point me in the right direction, please.
1 solutions

Answer 214598 by Fombitz(13828) About Me  on 2010-04-29 08:23:47 (Show Source):
You can put this solution on YOUR website!
Greatest integer function rounds down to the next integer.
If you look at a number line (which goes from negative to positive, left to right), you would choose the next integer to the left.
f%285.9%29=5
f%28-2.9%29=-3+
f%28-4.8%29=-5


Quadratic-relations-and-conic-sections/298218: Write an equation for an ellipse with center(-4,2) and a horizontal major axis?
(Thats all the information given in the book)
1 solutions

Answer 214596 by Fombitz(13828) About Me  on 2010-04-29 08:16:07 (Show Source):
You can put this solution on YOUR website!
The general equation for an ellipse centered at (h,k) is,
%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1
Substituting,
%28x%2B4%29%5E2%2Fa%5E2%2B%28y-2%29%5E2%2Fb%5E2=1
You are free to choose a and b.
The only other restriction is regarding the horizontal axis which means that
a%3Eb
.
.
.
So here's one example (of many) with a=2 and b=1,
%28x%2B4%29%5E2%2F4%2B%28y-2%29%5E2=1


Trigonometry-basics/297915: Find the exact value of the trigonometric function given that sin(u) = 12/13 and cos(v) = -4/5. (Both u and v are in Quadrant II.)
cos(v − u)
1 solutions

Answer 214466 by Fombitz(13828) About Me  on 2010-04-28 16:47:05 (Show Source):
You can put this solution on YOUR website!
cos%28v-u%29+=+cos%28v%29%2Acos%28u%29+%2B+sin%28x%29%2Asin%28y%29+
.
.
.
sin%28u%29+=+12%2F13
sin%5E2%28u%29%2Bcos%5E2%28u%29=1
%2812%2F13%29%5E2%2Bcos%5E2%28u%29=1
144%2F169%2Bcos%5E2%28u%29=169%2F169
cos%5E2%28u%29=%28169-144%29%2F169
cos%5E2%28u%29=25%2F169
cos%28u%29=0+%2B-+5%2F13
Quadrant II
cos%28u%29+=+-5%2F13
.
.
.
cos%28v%29=-4%2F5
sin%5E2%28v%29+%2Bcos%5E2%28v%29=1
sin%5E2%28v%29%2B%28-4%2F5%29%5E2=1
sin%5E2%28v%29%2B%2816%2F25%29=25%2F25
sin%5E2%28v%29=%2825-16%29%2F25
sin%5E2%28v%29=9%2F25
sin%28v%29=0+%2B-+3%2F5
Quadrant II
sin%28v%29=3%2F5
Now substitute directly,
cos%28v-u%29+=+cos%28v%29%2Acos%28u%29+%2B+sin%28v%29%2Asin%28u%29+
cos%28v-u%29+=+-%284%2F5%29%2A%28-%285%2F13%29%29+%2B+%283%2F5%29%2A%2812%2F13%29+
cos%28v-u%29+=+20%2F65%2B+36%2F65+
cos%28v-u%29+=+56%2F65+


Probability-and-statistics/297867: A bag contains 3 nickels, 4 dimes, and 5 quarters. If two coins are selected at random without replacing the first one selected, what is the probability that the two coins match?
1 solutions

Answer 214454 by Fombitz(13828) About Me  on 2010-04-28 16:29:15 (Show Source):
You can put this solution on YOUR website!
3 nickels
4 dimes
5 quarters
12 total coins
P(N)=3/12
P(D)=4/12
P(Q)=5/12
Once one coin is chosen then the total number of coins drops to 11 and the probability of each coin is adjusted.
P(N if nickel is chosen first)=2/11
P(D if dime is chosen first)=3/11
P(Q if quarter is chosen first)=4/11
Since each event is independent, multiply the probabilities.
P(nickel then nickel)=(3/12)(2/11)=1/22
P(dime then dime)=(4/12)(3/11)=1/11
P(quarter then quarter)=(5/12)(4/11)=5/33


Linear-equations/297887: write an equation of the line through the given points. (0,-6) (8,-16) Try to get back to me a.s.a.p! Thanks a lot!
1 solutions

Answer 214442 by Fombitz(13828) About Me  on 2010-04-28 16:19:30 (Show Source):
You can put this solution on YOUR website!
I hope this meets with your demanding schedule.
y-y1=%28%28y2-y1%29%2F%28x2-x1%29%29%28x-x1%29
Then you can solve either of these to get your answer.
y-%28-6%29=+%28%28-16-%28-6%29%29%2F%288-0%29%29%28x-0%29
y-%28-16%29=+%28%28-16-%28-6%29%29%2F%288-0%29%29+%28x-8%29


Geometry_proofs/297859: Hello,
I have 4 points given to me and I have to prove algebraically whether the figure is a kite. I can't just plot the points. How would I go about doing that?
1 solutions

Answer 214423 by Fombitz(13828) About Me  on 2010-04-28 16:05:25 (Show Source):
You can put this solution on YOUR website!
Given 4 points, divide them into two sets.
One set is the lengthwise component on the kite (line AB below).
The other set is the transverse (sideways) component of the kite (line CD).

Calculate the eqaution of the line using the slope and the point-slope form of a line for the length wise component.
y-ya=m1%28x-xa%29
m1=%28yb-ya%29%2F%28xb-xa%29
Then convert to slope-intercept form
y=m1%2Ax%2Bb1
Do the same for the transverse component to get its equation,
y=m2%2Ax%2Bb2
If it's a kite, the lines will be perpendicular and the relationship between the two slopes will be,
m1%2Am2=-1
If that's not the case, then stop there. It's not a kite.
.
.
.
If it is true then find the intersection point, I, between the two lines.
Solve the system of equations.
y=m1%2Ax%2Bb1
y=m2%2Ax%2Bb2
Since they both equal y, set them equal to each other.
m1%2Axi%2Bb1=m1%2Axi%2Bb2
Solve for x.
Then solve for y using either equation.
Now you have the point of intersection (xi,yi) of the two components of the kite.
If it's a kite, the distance from the intersection point (xi,yi) to the ends of the transverse components (C and D) must be identical.
Dci=Ddi
Dci%5E2=Ddi%5E2
%28xc-xi%29%5E2%2B%28yc-yi%29%5E2=%28xd-xi%29%5E2%2B%28yd-yi%29%5E2
If that's the case, then you've proven that the points form a kite.
If it's not true, then you don't have a kite.


Linear-systems/297817: Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent.
y = x + 4
3y - 5x = 6

1 solutions

Answer 214411 by Fombitz(13828) About Me  on 2010-04-28 15:43:37 (Show Source):
You can put this solution on YOUR website!
1.y+=+x+%2B+4
2.3y-5x+=+6
Substitute eq. 1 into eq. 2 directly and solve for x,
3%28x%2B4%29-5x=6
3x%2B12-5x=6
-2x=-6
highlight%28+x=3%29
Now use eq. 1 to solve for y.
y=x%2B4
y=3%2B4
highlight%28y=7%29
.
.
.
Graphical check of the solution.

Independent.


Linear-systems/297844: Solve and determine whether the equations are independent, inconsistent, or dependent:
x+3y=2
-x+y=1
1 solutions

Answer 214407 by Fombitz(13828) About Me  on 2010-04-28 14:52:22 (Show Source):
You can put this solution on YOUR website!
Add the equations together to solve for y
x%2B3y-x%2By=2%2B1
4y=3
highlight%28y=3%2F4%29
Now use either equation to solve for x,
-x%2By=1
x=y-1
x=3%2F4-1
highlight%28x=-1%2F4%29
Consistent and independent.


Linear-equations/297660: how to find the x and y intercepts of 25x+4y=9
1 solutions

Answer 214341 by Fombitz(13828) About Me  on 2010-04-28 10:48:32 (Show Source):
You can put this solution on YOUR website!
To find the x-intercept, set y=0 and solve for x.
25x%2B4y=9
25x%2B4%280%29=9
25x=9
x=9%2F25
(9/25,0)
.
.
.
To find the y-intercept, set x=0 and solve for y.
25x%2B4y=9
25%280%29%2B4y=9
4y=9
y=9%2F4
(0,9/4)


Quadratic-relations-and-conic-sections/297682: The axis of symmetry for the quadratic equation y = x2 + 4 lies on which axis?
1 solutions

Answer 214340 by Fombitz(13828) About Me  on 2010-04-28 10:46:10 (Show Source):
You can put this solution on YOUR website!
y+=+x%5E2+%2B+4
or in vertex form
y=%28x-0%29%5E2%2B4
The vertex lies on the axis of symmetry or x=0 which would be the y-axis.
+graph%28+300%2C300%2C+-5%2C+5%2C+-5%2C+15%2C++x%5E2%2B4%29+


Polynomials-and-rational-expressions/297650: Evaluate P(-1/2) if P(x) = 2x^4 + x^3 + 12
1 solutions

Answer 214339 by Fombitz(13828) About Me  on 2010-04-28 10:34:21 (Show Source):
You can put this solution on YOUR website!
Substitute -%281%2F2%29 for all occurences of x and simplify
P%28x%29+=+2x%5E4+%2B+x%5E3+%2B+12
P%28-1%2F2%29=2%28-1%2F2%29%5E4%2B%28-1%2F2%29%5E3%2B12
P%28-1%2F2%29=2%281%2F16%29-%281%2F8%29%2B12
P%28-1%2F2%29=%281%2F8%29-%281%2F8%29%2B12
P%28-1%2F2%29=12


Linear-systems/297620: x-y=2
5x+3y=18




1 solutions

Answer 214336 by Fombitz(13828) About Me  on 2010-04-28 10:31:29 (Show Source):
You can put this solution on YOUR website!
Solve graphically.


Linear-systems/297604: solve each system by graphing.
3x+2y=-6
x+3y=-2
1 solutions

Answer 214335 by Fombitz(13828) About Me  on 2010-04-28 10:29:44 (Show Source):


test/297603: Could any one pls help to solve this -How do you solve an equation like x3 + 2x2 – 88x + 200 = 0
1 solutions

Answer 214333 by Fombitz(13828) About Me  on 2010-04-28 10:28:24 (Show Source):
You can put this solution on YOUR website!
First step is to graph it.
graph%28300%2C300%2C-15%2C15%2C-100%2C100%2Cx%5E3%2B2%2Ax%5E2-88x%2B200%29
Yikes, unfortunately this equation does not have simple (integer or rational)
roots. I suggest using www.1728.com/cubic.htm which has a cubic equation solver. From that site,
x=6.687,x=-11.327,x=2.640 are roots for this equation.


Quadratic_Equations/297684: I understand how to use the quadratic formula when i'm asked to solve an problem that's straight forward like: x^2+8x+15=0, i can figure out that the answer is {-2/3,4}. I cant understand how to solve the following problem using the quadratic formula:
z^2/1=z/5+6/5
I'm not sure if it's because it involves fractions and i just get really nervous but i'm not sure how to go about solving this problem...
1 solutions

Answer 214330 by Fombitz(13828) About Me  on 2010-04-28 10:14:39 (Show Source):
You can put this solution on YOUR website!
z%5E2%2F1=z%2F5%2B6%2F5+
z%5E2-z%2F5-6%2F5=0
You can multiply by the LCD to get rid of the fractions, in this case by 5.
5z%5E2-z-6=0
Then a=5, b=-1, c=-6.
z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
z+=+%281+%2B-+sqrt%28+1-4%2A5%2A%28-6%29+%29%29%2F%282%2A5%29+
z+=+%281+%2B-+sqrt%28+121+%29%29%2F%2810%29+
z+=+%281+%2B-+11%29%2F%2810%29+
.
.
.
Or you can just move forward with the fractions.
z%5E2%2F1=z%2F5%2B6%2F5
z%5E2-z%2F5-6%2F5=0
a=1, b=-1%2F5, c=-6%2F5.
z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
z+=+%281%2F5+%2B-+sqrt%28+1%2F25-4%2A1%2A%28-6%2F5%29+%29%29%2F2+
z+=+%281%2F5+%2B-+sqrt%28+1%2F25%2B24%2F5%29+%29%2F2+
z+=+%281%2F5+%2B-+sqrt%28+1%2F25%2B120%2F25%29+%29%2F2+
z+=+%281%2F5+%2B-+sqrt%28+121%2F25%29+%29%2F2+
z+=+%281%2F5+%2B-+11%2F5%29+%2F2+
z+=+%281%2F5%29%281+%2B-+11%29%2F2+
z+=+%281+%2B-+11%29%2F10+
You'll get to the same place.
.
.
.
z=-10%2F10=highlight%28-1%29 and z=12%2F10=highlight%286%2F5%29
.
.
.
+graph%28+300%2C+300%2C+-3%2C+3%2C+-3%2C3%2C+x%5E2-x%2F5-6%2F5%29+