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# Recent problems solved by 'checkley71'

checkley71 answered: 8399 problems
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 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
 Polynomials-and-rational-expressions/64703: This question is from textbook algebra for college students Hello, Whats the vertex and intercepts for the quadratice function, and how do i sketch its graph: f(x) = x^2 - 6x Thank you.1 solutions Answer 46233 by checkley71(8403)   on 2006-12-25 10:40:56 (Show Source): You can put this solution on YOUR website!f(x)=x^2-6x (graph 300x200 pixels, x from -10 to 10, y from -10 to 10, of function x^2-6x) x^2-6x=0 x(x-6)=0 x=0 intercept x-6=0 x=6 intercept x=(0+6)/2 x=6/2 x=3 y=3^2-6*3 y=9-18 y=-9 vertex is (3,-9)
 Linear_Algebra/64665: This question is from textbook Finite Mathematics What is the Graphical Method?1 solutions Answer 46232 by checkley71(8403)   on 2006-12-25 10:10:59 (Show Source): You can put this solution on YOUR website!ASSUMING YOU HAVE AN EQUATION LIKE Y=5X+3 THIS IS THE EQUATION OF A LINE WHICH CAN BE EXPRESSED GRAPHICALLY THUS (graph 300x200 pixels, x from -5 to 5, y from -5 to 5, of function y+5x+3)
 Polynomials-and-rational-expressions/64644: This question is from textbook SIMPLIFY EACH EXPRESSION INVOLVING RATIONAL EXPONENTS (-64 ) -3/5 ____ 125 PLEASE HELP1 solutions Answer 46231 by checkley71(8403)   on 2006-12-25 10:01:21 (Show Source): You can put this solution on YOUR website!(-64)^-3/5 IS 1/FIFTHRT(-64^3)^5 OR 1/FIFTHRT(-8^5) OR 1/-8 (1/-8)/125 INVERT THE DENOMINATOR & MULTIPLY (1/-8)(1/125) -1/1000 ---------------------------------------------- MERRY CHRISTMAS
 expressions/64654: Evaluate the following expressions if a = -2 and b = 4. 2a^2-2b^2-4/3a+3b+11 solutions Answer 46230 by checkley71(8403)   on 2006-12-25 09:50:40 (Show Source): You can put this solution on YOUR website!2A^2-2B^2-4/3A+3B+1 2(-2)^2-2(4)^2-4/3(-2)+3*4+1 2*4-2*16+8/3+12+1 8-32+8/3+12+1 -11+8/3 (-33+8)/3 -25/3 ------------------------------------ MERRY CHRISTMAS
 Graphs/64761: Given a line containing the points (1,3), (2,4), (3,5) determine the slope-intercept form of the equation, give one additional point on this line and graph the function. What is the equation of line in slope-intercept form? Give one additional point in (x,y) form that would fall on this line: Graph the function: 1 solutions Answer 46229 by checkley71(8403)   on 2006-12-25 09:41:12 (Show Source): You can put this solution on YOUR website!FIRST FIND THE SLOPE (4-3)/(2-1) 1/1=1 SLOPE IS 1 NOW SUBSTITUTE ONE SET OF POINTS IN THE EQUATION Y=mX+b TO FIND THE Y INTERCEPT 3=1+b b=3-1 b=2 THUS WE HAVE THE LINE EQUATION AN ADDITIONAL POINT ON THIS LINE CAN BE FOUND BY SETTING Y=0 THUS 0=X+2 X=-2 OR THE OTHER POINT IS(-2,0) (graph 300x200 pixels,x from -6 to 6,y from -6 to 6, y+x+2) -------------------------------------------------------------------------- MERRY CHRISTMAS
 Radicals/64813: sqaure root of 2 - 3 over square root of 3 - 7 the other question is (4 sqaure root of 2 - square root of 6)(square root of 2 + 4 sqaure root of 6) and on the V section of the sqaure roots there is a 5 on the outside of V also (2m-5)2 power =491 solutions Answer 46227 by checkley71(8403)   on 2006-12-25 09:08:51 (Show Source): You can put this solution on YOUR website!SQRT(2-3)/SQRT(3-7) SQRT-1/SQRT-4 1i/2i ----------------------- DON'T UNDERSTAND THIS PROBLEM ------------------------------- (2M-5)^2=-49 4M^2-20M+25=-49 4M^2-20M+25+49=0 4M^2-20M+74 FORMULA =(20+-SQRT(400-1184))/8 =(20+-sqrt-784)/8 =(20+-28i)/8 =(20/8+-28i)/8 =2.5+-3.5i ------------------------------------------------ MERRY CHRISTMAS
 Polynomials-and-rational-expressions/64854: Divide: (y^3+3y^2-y+5)/(y-2)1 solutions Answer 46226 by checkley71(8403)   on 2006-12-25 08:36:19 (Show Source): You can put this solution on YOUR website!'''''''''Y^2+5Y+9 ''''_____________ Y-2)Y^3+3Y^2-Y+5 ''''Y^3-2Y^2 ''''------------ '''''''+5Y^2-Y '''''''+5Y^2-10Y ''''''''-------------- ''''''''''''+9Y+5 ''''''''''''+9Y-18 '''''''''''''------------ '''''''''''''''+23 _______________________________ MERRY CHRISTMAS
 Polynomials-and-rational-expressions/64879: 1.3x squared-12x 2.2w squared-8w-10 3.4x squared-251 solutions Answer 46225 by checkley71(8403)   on 2006-12-25 08:24:29 (Show Source): You can put this solution on YOUR website!3x^2-12x 3x(x-4) ____________________ 2w^2-8w-10 (2w+2)(w-5) ____________________ 4x^2-25 (2x-5)(2x+5) ____________________ MERRY CHRISTMAS
 Graphs/64741: 3x-y-6=01 solutions Answer 46210 by checkley71(8403)   on 2006-12-24 22:10:34 (Show Source): You can put this solution on YOUR website!IF THIS IS THE EQUATION OF A LINE THEN 3X-Y-6=0 -Y=-3X+6 Y=3X-6 THIS IS A LINE WITH A SLOPE OF 3 & A Y INTERCEPT OF (0,-6). TO FIND ANOTHER POINT ON THIS LINE SET Y=0 AND SOLVE FOR X THUS 0=3X-6 3X=6 X=6/3 X=2 OR (2,0) IN THE X INTERCEPT OF THIS LINE. ############################################################ MERRY CHRISTMAS
 Equations/65574: Solve and check the equation for X x - x+1 = 8 --- ----- ----- x-2 x x^2-2x I would first cross out the two x's Leaving the equation looking like: 0 x+1 = 8 ---- - ----- ----- x-2 0 x^2-2x To go from here I believe I would add x+1= 1x and subtract x-2 which equals -2x The equation would look like this: -2x - 1x = 8 ----- x^2-2x From here I am lost but I think I became lost a while ago1 solutions Answer 46209 by checkley71(8403)   on 2006-12-24 22:04:42 (Show Source): You can put this solution on YOUR website!X/(X-2)-(X+1)/X=8/(X^2-2X) COMBINE THE FRACTONS ON THE LEFT SIDE OF THE EQUATION & FACTORING THE DENOMINATOR OF THE RIGHT SIDE WE GET [(X^2)-(X+1)(X-2)]/X(X-2)=8/X(X-2) BECAUSE THE DENOMINATORS ARE EQUAL WE CAN SET THE NUMERATORS EQUAL THUS X^2-(X^2-X-2)=8 X^2-X^2+X+2=8 X=8-2 X=6 SOLUTION PROOF 6/(6-2)-(6+1)/6=8/(6^2-2*6) 6/4-7/6=8/(36-12) 6/4-7/6=8/24 6/4-7/6=1/3 (6*6-7*4)/24=1/3 (36-28)/24=1/3 8/24=1/3 1/3=1/3 ############################################### MERRY CHRISTMAS
 Equations/65575: Solve and check the equation for X 2 = 3 + 9 ----- ------- ----------- x+2 x+6 x^2+8x+12 I am confused on this probelm. They added way to many things in there for me to understand. Thank you for the help1 solutions Answer 46208 by checkley71(8403)   on 2006-12-24 21:51:54 (Show Source): You can put this solution on YOUR website!2/(X+2)=3/(X+6)+9/(X^2+8X+12) 2/(X+2)=3/(X+6)+9/(X+6)(X+2) 2/(X+2)=[3(X+2)+9]/(X+6)(X+2) CANCEL OUT THE (X+2) IN BOTH DENOMINATORS THUS 2=[3(X+2)+9]/X+6) NOW CROSS MULTIPLY 2(X+6)=3(X+2)+9 2X+12=3X+6+9 2X-3X=-12+15 -X=3 X=-3 PROOF 2/(-3+2)=3/(-3+6)+9/(9-24+12) 2/-1=3/3+9/-3 -2=1-3 -2=-2 ############################################## MERRY CHRISTMAS
 Equations/65576: Solve the equation for X 2/5 = x-2/20 To get this equation forst I must figure out what x is: 5-2=3 10-2=8 12-2=10 2/5 = x-2/20 2/5 = 10-2/20 Simplest form= 10/5=2 20/5=2 Leaving the eqation with x=12 Is this right:1 solutions Answer 46207 by checkley71(8403)   on 2006-12-24 21:34:25 (Show Source): You can put this solution on YOUR website!2/5=X-2/20 THE EASIEST WAY TO SOLVE THIS EQUATION IS TO CONVERT ALL NUMBERS TO DECIMAL . THUS 2/5=0.4 & 2/20=0.1 0.4=X-0.1 X=0.4+0.1 X=0.5 OR 1/2 PROOF 2/5=1/2-2/20 2/5=(10-2)/20 2/5=8/20 CROSS MULTIPLY 40=40 --------------------------------------------------- IF YOU MUST WORK IN FRATIONS THEN 2/5=X-2/20 X=2/5+2/20 FIND A COMMON DENOMINATOR (20) X=(8+2)/20 X=10/20 X=1/2 ########################################### MERRY CHRISTMAS
 Problems-with-consecutive-odd-even-integers/65577: If one-half of an interger is subtracted from three-fifths of the next consecutive interger, the difference is 3. What are the two intergers? I am lost on trying to figure out this problem, I can solve them without the fractions but with confuse me horribly. Thank you for the help1 solutions Answer 46206 by checkley71(8403)   on 2006-12-24 21:24:09 (Show Source): You can put this solution on YOUR website!(3/5)(X+1)-X/2)=3 (3X+3)/5-X/2=3 [(3X+3)*2-5X]/10=3 (6X+6-5X)/10=3 X+6=30 X=30-6 X=24 PROOF (3/5)(24+1)-24/2=3 3/5*25-12=3 75/5-12=3 15-12=3 3=3 ########################################### MERRY CHRISTMAS
 Travel_Word_Problems/65579: Ariana took 2h longer to drive 360mi on the first day of a trip than she took to drive 270mi on the second day. If her speed was the same on both days, what was the driving time each day? Thank you for helping me understand these problems:-)1 solutions Answer 46205 by checkley71(8403)   on 2006-12-24 21:18:21 (Show Source): You can put this solution on YOUR website!DISTANCE=RATE*TIME 360=R(T+2) 270=RT SOLVING FOR R IN THIS EQUATION WE GET R=270/T NOW SUBSTITUTING (270/T) FOR R IN THE FIRST EQUATION WE GET 360=(270/T)(T+2) 360=(270T+540)/T 360T=270T+540 360T-270T=540 90T=540 T=540/90 T=6 HOURS IS THE TIME FOR THE RETURN 270 MILE TRIP. 6+2=8 HOURS FOR THE FIRST TRIP WHICH TOOK 2 HOURS LONGER. THE RATE IS 270/6=45 MPH ########################################################### MERRY CHRISTMAS
 Travel_Word_Problems/65580: A plane flies 720mi agains a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the plane's speed in still air? Thank you so much1 solutions Answer 46204 by checkley71(8403)   on 2006-12-24 21:09:04 (Show Source): You can put this solution on YOUR website!720/(X+30)+720/(X-30)=10 [720(X-30)+720(X+30)]/(X+30)(X-30)=10 (720X-21600+720X+21600)/X^2-900=10 1440X/X^2-900=10 10X^2-9000=1440X 10X^2-1440X-9000=0 X^2-144X-900=0 (x-150)(x+6)=0 x-150=0 x=150 mph for the plane in still air. proof 720/180+720/120)=10 4+6=10 10=10 ################################################### MERRY CHRISTMAS
 Equations/65584: The combined resistance of two resistors r1 and r2 in a parallel circuit is given by the formula: Rt = 1 ------- 1 1 --- + --- R1 R2 Thank you for the help1 solutions Answer 46201 by checkley71(8403)   on 2006-12-24 20:54:38 (Show Source): You can put this solution on YOUR website!R=1/[(1/R1)+(1/R2)] SO IF THE TWO RESISTERS ARE 50 & 100 OHMS THEN R=1/[(1/50)+1/100)] R=1/[(2+1)/100] R=1/(3/100) R=1*(100/3) R=100/3 R=33 1/3 OHMS. ------------------------------------------ IF BOTH RESISTERS ARE 500 OHMS THEN R=1/[(1/500)+(1/500)] R=1/(2/500) R=1*500/2 R=500/2 R=250 OHMS. ################################################## MERRY CHRISTMAS
 logarithm/65586: This equation baffles me. 4^2x+1=2^3x+6 I need to solve this, can anyone help?1 solutions Answer 46197 by checkley71(8403)   on 2006-12-24 20:46:16 (Show Source): You can put this solution on YOUR website!IF you have (4^2)x+1=(2^3)x+6 then 16x+1=8x+6 16x-8x=6-1 8x=5 x=5/8 proof 16*5/8+1=8*5/8+6 80/8+1=40/8+6 10+1=5+6 11=11 ############################################ MERRY CHRISTMAS
 Equations/65582: Simplify the fraction: w+3 --- 4w ------- w-3 --- 2w This equation does not make sense to me, it is two fractions in one fraction. How do I figure this out? Thank you1 solutions Answer 46194 by checkley71(8403)   on 2006-12-24 20:40:35 (Show Source): You can put this solution on YOUR website![(w+3)/4w]/(w+3)/2w to divide a fraction by a fraction you need to invert the lower fraction and multiply the two fractions thus [(w+3)/4w] [(w+3)*2w]/[(w+3)*4w now you can cancel out the (w+3)and the 2w from the 4w leaving only 1/2w ############################################ MERRY CHRISTMAS
 Linear_Algebra/65068: how do you graph 4x>12 2y<61 solutions Answer 46192 by checkley71(8403)   on 2006-12-24 19:30:22 (Show Source): You can put this solution on YOUR website!(graph 300x200 pixels,x from -10 to 10, y from -10 to 15, of two functions 4x>20 and 2y<6)
 test/65572: thank you for all your help!!! in this problem: ((x-2)^2(x+7))/((x-2)(x+7)(x-8)), i had to simplify the fraction, which i came up with ((x-2))/((x+7)(x-8))....now its asking me to find the common factor and rewrite the expression......i thought the common factor was x+7....but i'm not sure how to rewrite the expression. this is what i came up with: x+7x*-8,7x*-8,7x*-56,....please help me solve this1 solutions Answer 46191 by checkley71(8403)   on 2006-12-24 19:21:31 (Show Source): You can put this solution on YOUR website!(x-2)^2(x+7)/(x-2)(x+7)(x-8) expanding the (x-2)^2 to (x-2)(x-2) we have (x-2)(x-2)(x+7)/(x-2)(x+7)(x+8) now factor out the (x-2) & the (x+7) we have left (x-2)/(x+8) ################################################################## MERRY CHRISTMAS
 Polynomials-and-rational-expressions/65117: solve by graphing 3y<-x+6 -y>-2x+4 there is a line under the < and > 1 solutions Answer 46190 by checkley71(8403)   on 2006-12-24 19:16:26 (Show Source): You can put this solution on YOUR website!(graph 300,200 pixels, x from-10 to 10,y from -10 to 10, of TWO functions 3y<=-x+6 and -y>=-2x+4)
 Equations/65569: 4y + 2y ---------- ---------- y^2 + 6y + 5 y^2 - 1 I am just so lost on how to understand these types of problems! I become frustrated because I always end up with the wrong answer. Is there any hope in understanding this type of problem? Thank you for the great help :-)1 solutions Answer 46189 by checkley71(8403)   on 2006-12-24 19:04:21 (Show Source): You can put this solution on YOUR website!4y/(y+5)(y+1)+2y/(y+1)(y-1) multiply the second fraction by (y+5) & multiply ther first fraction by (y-1) thus you now have a common denominator & can now add the numerators. [(2y)(y+5)+4y(y-1)]/(y+5)(y+1)(y-1) (2y^2+5y+4y^2-4y)/(y-5)(y+1)(y-1) 6y^2+y)/(y-5)(y+1)(y-1) factor out the y fron the numerator. y(6y+1)/(y+5)(y+1)(y-1) ######################################################### MERRY CHRISTMAS
 Square-cubic-other-roots/64691: This question is from textbook An Incremental Development please help to simplify : 3 * the square root of a^7x^2 * the square root of 8 * the square root of 81 solutions Answer 46150 by checkley71(8403)   on 2006-12-23 18:48:39 (Show Source): You can put this solution on YOUR website!3*SQRT(A^7X^2)*SQRT8*SQRT8 3*A^3XSQRTA*8 24A^3SQRTA ########################################################### MERRY CHRISTMAS
 Inequalities/65565: This question is from textbook Pre-Algebra Find the quotient. 12 3/4 divided by ( - 11/12 ) Thanks! Happy Holidays!1 solutions Answer 46149 by checkley71(8403)   on 2006-12-23 18:35:15 (Show Source): You can put this solution on YOUR website!12 3/4=51/4 (51/4)/-11/12 (51/4)*(-12/11) 51*-12/4*11 divide 12 by 4 we get 51*-3/11 -153/11 ############################################## MERRY CHRISTMAS
 Expressions-with-variables/65422: simplify: x^2-3x over 2x^2-3x-5 / 4x-12 over 4x^2-41 solutions Answer 46148 by checkley71(8403)   on 2006-12-23 15:35:02 (Show Source): You can put this solution on YOUR website!(X^2-3X)/(2X^2-3X-5)/(4X-12)/4X^2-4) X(X-3)/(2X-5)(X+1)/4(X-3)/(2X-2)(2X+2) NOW TO DIVIDE A FRACTION BY A FRACTION WE NEED TO INVERT THE LOWER FRACTION & THEN MULTIPLY THEM: THUS X(X-3)/2X-5)(X+1)*(2X-2)(2X+2)/4(X-3) NOW WE CAN CANCEL THE (X-3) FACTOR X/(2X-5)(X+1)*(2X-2)(2X+2/4 NOW WE EXPAND THE ALL THESE FATORS & GET X(2X-2)(2X+2/4(2X-5)(X+1) ############################################################### MERRY CHRISTMAS
 Exponents/64754: This question is from textbook Simplify each expression. Use only positive exponents. (-6m^2n^2)(3mn) 1 solutions Answer 46137 by checkley71(8403)   on 2006-12-23 11:21:15 (Show Source): You can put this solution on YOUR website!(-6M^2N^2)(3MN) -18M^3N^3
 Expressions-with-variables/64740: This question is from textbook Algebra 1 x=2y-7 y-3x=-9 2x+5y=12 x-6y=-11 x+y=6 3x-3y=13 1 solutions Answer 46136 by checkley71(8403)   on 2006-12-23 11:18:46 (Show Source): You can put this solution on YOUR website!X=2Y-7 NOW SUBSTITUTE (2Y-7) FOR X IN THE OTHER EQUATION WE GET Y-3(2Y-7)=-9 NOW SOLVE FOR Y Y-6Y+21=-9 Y-6Y=-9-21 -5Y=-30 Y=-30/-5 Y=6 SOLUTION NOW SUBSTITUTE 6 FOR Y IN EITHER EQUATION & SOLVE FOR X X=2*6-7 X=12-7 X=5 SOLUTION ------------------------------------------------------ X-6Y=-11 X=6Y-11 2(6Y-11)+5Y=12 12Y-22+5Y=12 17Y=12+22 17Y=34 Y=34/17 Y=2 SOLUTION NOW SUBSTITUTE 2 FOR Y & SOLVE FOR X X-6*2=-11 X-12=-11 X=-11+12 X=1 SOLUTION -------------------------------------------------------- X+Y=6 X=6-Y SUBSTITUTE (6-Y) FOR X & SOLVE FOR Y 3(6-Y)-3Y=13 18-3Y-3Y=13 -6Y=13-18 -6Y=-5 Y=5/6 SOLUTION NOW SOBSTITUTE (5/6) FOR Y & SOLVE FOR X X+(5/6)=6 X=+5/6=6 X=6-5/6 X=5 1/6 X=31/6 SOLUTION ------------------------------------------------- MERRY CHRISTMAS
 Signed-numbers/64736: using 7,26,46 and 15 how can i arrainge them to equal 160?1 solutions Answer 46135 by checkley71(8403)   on 2006-12-23 10:56:42 (Show Source): You can put this solution on YOUR website!(46-26)(15-7)=20*8=160
 Functions/65345: simplify (4a^3b^-3c^2)^3/(-2a^-2b^2c^-1)^41 solutions Answer 46134 by checkley71(8403)   on 2006-12-23 10:52:55 (Show Source): You can put this solution on YOUR website!(4A^3B^-3C^2)^3/(-2A^-2B^2C^-1)^4 CUBE THE NUMERATOR AND RAISE THE DENOMINATOR BY THE FOURTH POWER THUS: (64A^6B^1C^5)/(16A^2B^6C^3) NOW FACTOR OUT ALL TERMS 4A^4B^-5C^2 ########################################################## MERRY CHRISTMAS
 Equations/65426: 149x + [sqare root of]131 solutions Answer 46132 by checkley71(8403)   on 2006-12-23 10:43:53 (Show Source): You can put this solution on YOUR website!149X+SQRT13 IF THIS IS SET TO =O THEN 149X+3.60555=0 149X=-3.60555 X=-3.60555/149 X=-.024 ########################################################## MERRY CHRISTMAS