# See tutors' answers!

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

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'checkley71'

checkley71 answered: 8399 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, >>Next

 Geometry_proofs/65764: Hi, I've been having some trouble with this proof that was assigned for homework. THANKS!! Prove: triangleABC = triangleDEC Given: 1. <1 = <6 BC = EC1 solutions Answer 46493 by checkley71(8403)   on 2006-12-29 18:31:15 (Show Source): You can put this solution on YOUR website!WE HAVE <1=<6 THEREFORE <3=<4 OPPOSITE ANGLES OF INTERSECTING LINES ARE EQUAL. & BC=EC NOW WE HAVE TWO ANGLES AND THE INCLUDED SIDE EQUAL THEREFORE TYHE TRIANGLES ARE EQUAL.
 Geometry_proofs/65768: Hello, I really can't figure this proof out, I've been trying for hours now and I just can't get it. Maybe you can help? Prove: triangleTSW = triangleQPW Given: TQ bisects SP SP bisects TQ1 solutions Answer 46492 by checkley71(8403)   on 2006-12-29 18:23:21 (Show Source): You can put this solution on YOUR website!TQ BISECTS SP THEN SW=WP SP BISECTS TQ THEN TW=TQ BECAUSE THESE LINES BISECT THE OPPOSITE ANGLES ARE EQUAL THUS NOW WE HAVE TWO EQUAL SIDES AND THE INTERNAL ANGLE EQUAL THEN THE TRIANGLES ARE EQUAL.
 Rate-of-work-word-problems/65774: A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path? 1 solutions Answer 46491 by checkley71(8403)   on 2006-12-29 18:16:11 (Show Source): You can put this solution on YOUR website!(30-2x)(20-2x)=400 600-40x-60x+4x^2=400 4x^2-100x=-600+400 4x^2-100x=-200 4x^2-100x+200=0 x^2-25x+50=0 using the quadratic equation for x we get x=(-b+-sqrt[b^2-4ac])/2a x=(25+-sqrt625-4*1*50])/2*1 x=(25+-sqrt[625-200])/2 x=(25+-sqrt425)/2 x=(25+-20.6155)/2 x=(25+20.6155)/2 x=45.6155/2 x=22.8 not a solution because it is longer than the garden. x=(25-20.6155)/2 x=4.3845/2 x=2.19 feet for the path
 Numbers_Word_Problems/65771: Find two consecutive positive intergers such that the sum of their square is 85. Thank you for the help1 solutions Answer 46490 by checkley71(8403)   on 2006-12-29 18:01:11 (Show Source): You can put this solution on YOUR website!X^2+(X+1)^2=85 X^2+X^2+2X+1=85 2X^2+2X+1-85=0 2X^2+2X-84=0 X^2+X-42=0 (X+7)(X-6)=0 X=7=0 X=-7 X-6=0 X=6 SOLUTION FOR THE FIRST INTERGER 6=1=7 FOR THE SECOND INTERGER PROOF 6^6+7*7=84 36+49=85 85=85 ################################################ happy new year
 Rectangles/65775: The length of a rectangle is 1cm longer than its width. If the diaganol of rectangle is 4cm, what are the dimensions (length and width) of the rectangle? Thank you1 solutions Answer 46489 by checkley71(8403)   on 2006-12-29 17:41:33 (Show Source): You can put this solution on YOUR website!using the pathagorian theorum a^2+b^2=c^2 a=x, b=(x+1), c=4 x^2+(x+1)^2=4^2 x^2+x^2+2x+1=16 2x^2+2x-15=0 using the quadratic equation x=(-b+-sqrt[b^2-4ac])/2a x=(-2+-sqrt[2^2-4*2*-15])/2*2 x=(-2+-sqrt[4+120])/4 x=(-2+-sqrt124)/4 x=(-2+-11.1355)/4 x=(-2+11.1355)/4 x=9.1355/4 x=2.2839 cm for the width. length is 2.2839+1=3.2839 proof 2.2839^2+3.2839^2=4^2 5.216+10.784=16 16=16 ######################################### HAPPY NEW YEAR.
 Graphs/65765: This question is from textbook Beginning Algebra Graph the following equation, using the intercept method. 2x + 3y = 6 I am a bit confusded on how to graph these since there are two variables. If I worked the problem right I came up with 1. 2x + 3y = 5 6-5 = 1 This is as far as I got. 1 solutions Answer 46488 by checkley71(8403)   on 2006-12-29 17:18:57 (Show Source): You can put this solution on YOUR website!TRO PUT THESE EQUATIONS IN THE LINE FORM WE HAVE: 2X+3Y=6 3Y=-2X+6 Y=-2X/3+6/3 Y=-2X/3+2 THUS THIS LINE HAS A SLOPE OF -2/3 & A Y INTERCEPT OF 2 ----------------------------------------------------------------------- 2X+3Y=5 3Y=-2X=5 Y=-2X/3+5/3 THUS THIS LINE ALSO HAS A SLOPE OF -2/3 & A Y INTERCEPT OF 5/3 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions -2/3X+2 and -2/3X+5/3). (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions x^2 and x^2/10-x).
 Equations/65704: Solve for X: 2(x-5)^2=3 I know the first step I believe is to multiply the 2 towards the x and the 5: 2*x = 2x 2*5 = 10 (2x - 10)^2 = 3 The next step is to figure out what X is correct? 2(x) - 10^2 = 3 Gosh I am lost on this step, could someone please give me a hand, thank you1 solutions Answer 46424 by checkley71(8403)   on 2006-12-27 22:43:14 (Show Source): You can put this solution on YOUR website!FIRST YOU MUST RESOLVE THE ITEMS WITHIN THE ( ) (X-5)^2=X^2-10X+25 NOW MULTIPLY THIS BY 2 2(X^2-10X+25)=2X^2-20X+50 NOW SET THIS =3 2X^2-20X+50=3 NOW SUBTRACT 3 FROM BOTH SIDES 2X^2-20X+50-3=0 2X^2-20X+47=0 THIS EQUATION DOESN'T FACTOR NORMALLY THUS WE NEED THE QUADRATIC EQUATION TO FIND THE X VALUES THUS X=(-B+-SQRT[B^2-4AC])/2A X=(20+-SQRT[400-4*2*47])/2*2 X=(20+-SQRT[400-376])/4 X=(20+-SQRT[24])/4 X=(20+-4.899)/4 X=(20+4.899)/4 X=6.22 SOLUTION X=(20-4.899)/4 X=15.101/4 X=3.77 SOLUTION
 Inequalities/65694: This question is from textbook Pre-Algebra Find the quotient. 8 7/10 divided by 33/50 Thanks! Please work fast! Happy Holidays!~!~!~!~!~!~!~!~!~!1 solutions Answer 46423 by checkley71(8403)   on 2006-12-27 22:32:08 (Show Source): You can put this solution on YOUR website!8.7/.66 13.181818 ______________________ OR (87/10)/(33/50) NOW INVERT THE DENOMINATOR & MULTIPLY (87/10)(50/33) 87*5/33 435/33 145/11
 Inequalities/65717: This question is from textbook Pre-Algebra Evalute the expression. 5/8 + 5/12 divided by 10/21 Thanks! Please work fast! Don't forget to post it! Happy Holidays!~!~!~!~!1 solutions Answer 46422 by checkley71(8403)   on 2006-12-27 22:28:02 (Show Source): You can put this solution on YOUR website!(5/8+5/12)/(10/21) [(5*12+5*8)/96]/(10/21) [(60+40)/96]/(10/21) (100/96)/(10/21) INVERT THE DENOMINATOR & MULTIPLY (100/96)(21/10) (10*21)/96 210/96 35/16
 Quadratic_Equations/65718: This question is from textbook An Incremental Development please help to solve (4x - 3 / 7) = (5 + x-2 / 3) thank you1 solutions Answer 46421 by checkley71(8403)   on 2006-12-27 22:20:41 (Show Source): You can put this solution on YOUR website!4X-3/7=5+X-2/3 4X-X=5-2/3+3/7 3X=(105-14+9)/21 3X=100/21 X=(100/21)/3 X=(100/21)(1/3) X=100/63
 Equations/65705: Solve for X x^2 + 4x + 4 = 7 (factor the left hand side) 4x + 4 = 8x x^2 + 8x = 7 I have 2 X's and this confuses me since I can not factor them to come up with it to = 7, can someone please explain, thank you1 solutions Answer 46420 by checkley71(8403)   on 2006-12-27 22:14:26 (Show Source): You can put this solution on YOUR website!X^2+4X+4=7 X^2+4X+4-7=0 X^2+4X-3=0 THIS QUADRATIC DOES NOT FACTOR NORMALLY THUS WE NEED TO USE THE QUADRATIC FORMULA TO FIND THE VALUES OF X THUS X=(-B+-SQRT[B^2-4AC])/2A X=(-4+-SQRT[4*4-4*1*-3])/2*1 X=(-4+-SQRT[16+12])/2 X=(-4SQRT[28])/2 X=(-4+-5.29)/2 X=(-4+5.29)/2 X=1.29/2 X=.645 SOLUTION X=(-4-5.29)/2 X=-9.29/2 X=-4.645 SOLUTION
 Quadratic_Equations/65719: This question is from textbook An Incremental Development Please help to solve : 4 = 3x^2 + x by using the quadratic formula1 solutions Answer 46418 by checkley71(8403)   on 2006-12-27 22:05:10 (Show Source): You can put this solution on YOUR website!4=3X^2+X 3X^2+X-4=0 X=(-B+-SQRT[B^2-4AC])/2A X=(-1+-SQRT[1^2-4*3*-4])/2*3 X=(-1+-SQRT[1+48])/6 X=(-1+-SQRT[49])/6 X=(-1+-7)/6 X=-1/6+-7/6 X=.1666+7/6 X=-.1666+1.1666 X=1 SOLUTION X=-.1666-1.16666 X=-1.33333 SOLUTION
 Square-cubic-other-roots/65723: This question is from textbook An Incremental Development simplify (5 times the square root of 16 - 3)(2 times the square root of 10 + 2)1 solutions Answer 46416 by checkley71(8403)   on 2006-12-27 21:54:02 (Show Source): You can put this solution on YOUR website!(5*SQRT16-3)(2*SQRT10+2) I ASSUME BECAUSE THERE ARE NO () AROUND THE 16 & 10 THAT THIS IS THE PROBLEM? (5*4-3)(2*3.16+2) (20-3)(6.32+2) 17*8.32 141.44 ___________________________________________ HOWEVER IF THERE SHOULD BE () AROUND THE (16-3) & THE (10+2) THEN (5SQRT13)(2SQRT12) (5*3.61)(2*3.46) 18.05+6.92 24.97
 Radicals/65683: Use the properties for radicals to simplify the espression. Assume all variables represent positive real numbers. sqrt 5/3 This is not a real number correct? Or do I need to divide them like a regular fraction to get: 1 sqrt2/3?1 solutions Answer 46380 by checkley71(8403)   on 2006-12-27 16:11:03 (Show Source): You can put this solution on YOUR website!SQRT(5/3) SQRT(1.66667) 1.291
 Inequalities/65671: This question is from textbook Pre-Algebra Find the quotient. 30 divided by ( - 4 1/8 ) Thanks! Please work fast! Happy Holidays!~!~!~!~!~!~!~!~!~!1 solutions Answer 46379 by checkley71(8403)   on 2006-12-27 16:08:12 (Show Source): You can put this solution on YOUR website!30/(-4 1/8) 30/(-33/8) 30*-8/33 -240/33 -7 9/33
 Radicals/65686: Multiply then simplify the radical expression: sqrt13 * sqrt5 = 13 * 5 = sqrt65? I believe this is how I would perform this operation. Thanks for the help.1 solutions Answer 46377 by checkley71(8403)   on 2006-12-27 16:02:38 (Show Source): You can put this solution on YOUR website!SQRT13*SQRT5 3.60555*2.23607 8.6225 ALSO SQRT13*SQRT5=SQRT13*5=SQRT65=8.06225
 Radicals/65685: Simplify by co,bining like terms: sqrt 63 - 2sqrt28 + 5sqrt7 I sure thope this makes sense to someone else more than it does to me. I can not see any like terms involved in this process. Thank you for the help.1 solutions Answer 46374 by checkley71(8403)   on 2006-12-27 15:55:34 (Show Source): You can put this solution on YOUR website!SQRT63-2SQRT28+5SQRT7 SQRT9*7-SQRT4*7+5SQRT7 3SQRT7-2SQRT7+5SQRT7 (3-2+5)SQRT7 6SQRT7
 Radicals/65678: This question is from textbook Beginning algebra Problem 24: 3 sqrt -8/27 I believe this is not a real number, is this correct? If it is I would say it is -2/3 From here I am lost, hope you can help me:-)1 solutions Answer 46370 by checkley71(8403)   on 2006-12-27 15:47:13 (Show Source): You can put this solution on YOUR website!3SQRT-8/27 IF THIS IS 3 TIMES THE SQRT -8/27 3SQRT-(2*2*2)/(3*3*3) 3*2/3SQRT-2/3 6/3SQRT-2/3 2SQRT-2/3 ________________________________ IF THIS IS THE CUBERT-8/27 THEN CUBERT(-2*-2*-2)/(3*3*3) -2/3
 Inequalities/65670: This question is from textbook Pre-Algebra Find the quotient. - 18/35 divided by( - 2 4/5 ) Thanks! Please work fast! Happy Holidays!~!~!~!~!~!~!~!~!~!~!1 solutions Answer 46362 by checkley71(8403)   on 2006-12-27 14:35:29 (Show Source): You can put this solution on YOUR website!(-18/35)/(-2 4/5) (-18/35)/(-14/5) NOW INVERT THE DENOMINATOR AND MULTIPLY THE TWO FRACTIONS THUS (-18/35)(-5/14) (18*5)/(35*14) 90/490 9/49 ______________________________________________ HAPPY NEW YEAR
 Systems-of-equations/65641: Hi! Could someone please help me solve this problem and all exponents should be positive. (3x4y^3-5y) - (2x+3y^3-5y)1 solutions Answer 46349 by checkley71(8403)   on 2006-12-27 10:23:27 (Show Source): You can put this solution on YOUR website!3X4Y^3-5Y-2X-3Y^3+5Y 3X4Y^3-2X-3Y^3 (THE -5Y & THE +5Y CANCEL OUT). _____________________________________________________ HAPPY HEW YEAR
 Graphs/65643: DOes this mean that i have to show 3different graphs separate or all in one graph. which the equations that i would graph from this would be: 3x-6 x = 1 y=3 Solve each of the following systems of linear inequalities graphically. 3x – y LESS THAN OR EQUAL TO 6 x GREATER THAN OR EQUAL TO 1 y LESS THAN OR EQUAL TO 3 1 solutions Answer 46348 by checkley71(8403)   on 2006-12-27 10:20:23 (Show Source): You can put this solution on YOUR website! (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, function 3X-6). (graph 300x200 pixels, x from -6 to 5, y from -5 to 5, function X-1). (graph 300x200 pixels, x from -6 to 5, y from -5 to 5, function Y-3). _________________________________________________________ HAPPY NEW YEAR
 Graphs/65646: Graph each of the following inequalities. 4x + y > 4 Graph each of the following inequalities. 3x – 4y < 12 1 solutions Answer 46347 by checkley71(8403)   on 2006-12-27 10:11:15 (Show Source): You can put this solution on YOUR website! (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, function 4x-y-4). (graph 300x200 pixels, x from -6 to 5, y from -12 to 10, function y+4x-4). ________________________________________________________________ THIS IS AN UP DATE. ________________________________________________________________ HAPPY NEW YEAR
 Miscellaneous_Word_Problems/65659: why are variables useful in algebra? What makes the use of variables difficult to understand? Create one statement in english representing an algebraic relationship.1 solutions Answer 46345 by checkley71(8403)   on 2006-12-27 09:54:38 (Show Source): You can put this solution on YOUR website!SIMPLE PROBLEM: A DOZEN EQQS COST \$1.20. WHAT IS THE PRICE OF EACH (1) EGG. ALGEBRAIC REPRESENTATION OF THIS PROBLEM, QUESTION IS 12E=\$1.20 OR 12 EGGS = \$1.20 NOW YOU NEED TO DIVIDE 12 EGGS BY 12 TO GET 1 EGG WHICH SAYS YOU NEED TO ALSO DIVIDE THE \$1.20 BY 12 TO MAINTAIN A BALANCED EQUATION. 12E/12=\$1.20/12 1E=\$.10 OR ONE EGG EQUALS \$ .10 ------------------------------------------------------------- HAPPY NEW YEAR.
 Linear-equations/65648: Simplify each of the followingby combining like terms. #36 x^2y + xy - y + 10x^2y - 2y + xy1 solutions Answer 46331 by checkley71(8403)   on 2006-12-26 19:45:45 (Show Source): You can put this solution on YOUR website!x^2y+xy-y+10x^2y-2y+xy (x^2y+10x^2y)+(xy+xy)-y-2y 11x^2y+2xy-3y
 Exponential-and-logarithmic-functions/64634: A volcano that is currently about one-half mile below the surface of the pacific ocean near the big island of Hawaii will eventually become a new Hawaiian island, Loihi. The volcan will break the surface of the ocean in about 50000 years. On average, how many inches does the volcano rise in a year. State your answer in per year.1 solutions Answer 46322 by checkley71(8403)   on 2006-12-26 12:45:10 (Show Source): You can put this solution on YOUR website!(.5*5280*12)/50000 31680/50000 .6336 inches per year is the estimated growth of this volcano.
 Square-cubic-other-roots/65604: This question is from textbook An Incremental Development help to simplify 2.3 times the square root of 3621 solutions Answer 46262 by checkley71(8403)   on 2006-12-25 22:31:30 (Show Source): You can put this solution on YOUR website!2.3*SQRT362 TRIED FACTORING 362 TO GET SOME OF IT OUT OF THE RADICAL. NO LUCK SO WHAT YOU HAVE IS 2.3*19.026297 43.760483 _________________________________________________ MERRY CHRISTMAS
 Inequalities/65620: This question is from textbook Pre-Algebra Find the quotient. -24 4/9 divided by 8/15 Thanks! Please work fast! Happy Holidays!~!~!~!~!~!~!~!~!1 solutions Answer 46259 by checkley71(8403)   on 2006-12-25 22:05:20 (Show Source): You can put this solution on YOUR website!(-24 4/9)/(8/15) [((-24*9)+4)/9]/(8/15) [((-216+4))/9]/(8/15) (-220/9)/(8/15 now invert the denominator and multiply the two fractions thus (-220/9)(15/8) NOW MULTIPLY NUMERATORS & DENOMINATORS THUS (-220*15)/(9*8) 3300/72 45 5/8 ##################################### MERRY CHRISTMAS
 Polynomials-and-rational-expressions/65587: This question is from textbook Algebra for college students Hello, How do I find the vertex and intercept, and sketch its graph: g(x) = x^2 + 2x - 24 Thank you so much!1 solutions Answer 46243 by checkley71(8403)   on 2006-12-25 16:35:56 (Show Source): You can put this solution on YOUR website!x^2+2x-24 (x-4)(x+6) x-4=0 x=4 one intercept on the x axis x+6=0 x=-6 another x intercept coordinates of vertex x=(4-6)/2 x=-2/2 x=-1 y=-1*-1+2*-1-24 y=1-2-24 y=1-26 y=-25 then the vertex is (-1,-25) (graph 300x200 pixels, x from -10 to 10, y from -30 to 10, of functions x^2+x-24). ##################################################################### MERRY CHRISTMAS
 expressions/64934: I need to simplify these but can't figure it out. I'm awful at math. Thanks for any help. a. y^3 (10x^2 + 3y-1) (5x^3 - 3xy - y) b. (a^2 + 2b)(5a^3 - 3b^-3/2 - 1)/b^-2 1 solutions Answer 46239 by checkley71(8403)   on 2006-12-25 11:48:28 (Show Source): You can put this solution on YOUR website!Y^3(10X^2+3Y-1)(5X^3-3XY-Y) FIRST WE MULTIPLY BOTH TERMS ( )( ) BY Y^3 THUS (10X^2Y^3+3Y^4-Y^3)(5X^3Y^3-3XY^4-Y^4) NOW MULTIPLY THESE TWO TERMS THUS (5X^3Y^3-3XY^4-Y^4) --------------------------------------- 50X^5Y^6+15X^3Y^7-5X^3Y^6 *********-30X^3Y^7-9XY^8+3XY^7 ******************-10X^2Y^7-3Y^8+Y^7 ------------------------------------------------------- 50X^5Y^6-15X^3Y^7-5X^3Y^6-9XY^8+3XY^7-10X^2Y^7-3Y^8+Y^7 ############################################################### MERRY CHRISTMAS
 Graphs/64969: Solve the system of inequalities by graphing. y>x 2x+y 2. graph:5x+3y greater than or equal to 15 x is less than or equal to y x is less than or equal to 4 3. find the max. and min. values and where they occur for z=4x+7y subject to the constraints: x+y is greater than or equal to 2 3x-4y is less than or equal to 6 6y is less than or equal to x+12 1 solutions Answer 46238 by checkley71(8403)   on 2006-12-25 11:15:24 (Show Source): You can put this solution on YOUR website!Y>X & 2X+Y<-3 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y>x and 2x+y<-3). ______________________________________________________________________ 5x+3y>=15 & x<=y & x<=4 (graph 300x200 pixels, x from -6 to 5, y from -30 to 30, of THREE functions 5x+3y>=15, x<=y, x<=4). _______________________________________________________________________ 4x+7y, x+y>=2, 3x-4y<=6, 6y<=x+12 (graph 300x200 pixels, x from -20 to 20, y from -10 to 10, of FOUR functions 4x+7y, x+y>=2, 3x-4y<=6, 6y<=x+12). ____________________________________________________________________________ MERRY CHRISTMAS
 Polynomials-and-rational-expressions/64705: This question is from textbook algebra for college students Hello, How do i fint the vertex and intercepts, and sketch its graph: g(x) = x^2 - 4x - 12 Thank you!1 solutions Answer 46235 by checkley71(8403)   on 2006-12-25 10:52:50 (Show Source): You can put this solution on YOUR website!x^2-4x-12 (x-6)(x+2) x-6=0 x=6 x intercept x+2=0 x=-2 x intercept x=6-2/2=4/2=2 y=2^2-2*4-12 y=4-8-12 y=-16 thus the vertex is(2,-16) (graph 300x200 pixels, x from -15 to 15, y from -20 to 15, of function x^2-4x-12). #################################################################### MERRY CHRISTMAS