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# Recent problems solved by 'checkley71'

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 Quadratic_Equations/132848: Sam is a guest on the TV show Math Jeopardy, and has just chosen the \$300 question in the category "Quadratic Equations." The answer is "The solutions are x=3 and x=-2." What question could Sam ask that would win the \$300? Is there more than one possible correct question? Explain.1 solutions Answer 97202 by checkley71(8403)   on 2008-03-20 17:31:39 (Show Source): You can put this solution on YOUR website!ONE QUESTION WOULD BE: WHAT IS THE VALUE OF X IN THE EQUATION X^2-X-6=0 SOLUTION: (X-3)(X+2)=0 X-3=0 X=3 ANSWER. X+2=0 X=-2 ANSWER.
 Quadratic_Equations/132849: Robin is mowing a rectangular field that measures 24 yards by 32 yards, by pushing the mower around and around the outside of the plot. This creates a widening border that surrounds the unmowed grass in the center. During a brief rest, Robin wonders whether the job is half done yet. How wide is the uniform mowed border when Robin is half done?1 solutions Answer 97200 by checkley71(8403)   on 2008-03-20 17:26:06 (Show Source): You can put this solution on YOUR website!24*32=768 FT^2 IS THE TOTAL LAWN AREA. (24-2X)(32-2X)=768/2 768-64X-48X+4X^2=384 4X^2-112X+768-384=0 4X^2-112X+384=0 4(X^2-28X+96)=0 4(X-24)(X-4)=0 X-4=0 X=4 ANSWER FOR THE WIDTH OF THE MOWED AREA. (24-8)(32-8)=384 16*24=384 384=384
 Linear_Equations_And_Systems_Word_Problems/132872: Please help! I cannot figure out how to set this problem up. I have to include the cost function as well. Thank you! Here it is: An appliance repair service charges \$50 to come out for a service call which is applied toward the first 30 minutes of service should a repair be needed. If a repair is needed, the charge of \$37 per 30 minutes (after the initial half hour included in the service call charge) for labor and the cost of parts. Write a cost function to determine the amount a customer needing a repair that takes 1.5 hours and requires a \$103 part.1 solutions Answer 97199 by checkley71(8403)   on 2008-03-20 17:11:57 (Show Source): You can put this solution on YOUR website!50+(2*37)+103=50+74+103=\$227 FOR THE TOTAL SERVICE BILL.
 Quadratic_Equations/132877: In 1990, Michael's college tuition was \$1500. In 1995, tuition at the same college cost \$3200. Assuming that an exponential model applies, how much will tuition cost in 2009?? I think the answer is \$6837 ????????1 solutions Answer 97198 by checkley71(8403)   on 2008-03-20 17:06:41 (Show Source): You can put this solution on YOUR website!(1905-1990)/(3,000-1500) 5/1500=(2009-1990)/X-1500) 5/1500=19/(X-1500) 5(X-1500)=19*1500 5X-7500=28500 5X=28500+7500 5X=36000 X=36000/5 X=\$7200 IS THE PROJECTED TUITION IN 2009 PROOF: 5/1500=19/(7200-1500) 5/1500=19/5700 19*1500=5*5700 28500=28500
 Polynomials-and-rational-expressions/132898: Can someone show me hoe to sovle foe C? 1 solutions Answer 97195 by checkley71(8403)   on 2008-03-20 16:57:28 (Show Source): You can put this solution on YOUR website!IF YOU SET THIS ITEM=0 THEN: B-6C=0 -6C=-B C=-B/-6 C=B/6
 Quadratic_Equations/132899: A group of people want to share equally the cost of a \$200,000 airplane. They want to find 5 more people to join their club so that the cost per person decreases by \$2000. How many people are currently in the club?1 solutions Answer 97194 by checkley71(8403)   on 2008-03-20 16:54:29 (Show Source): You can put this solution on YOUR website!200,000/X=200,000/(X+5)+2000 200,000/X-200,000/(X+5)=2,000 COMBINE THE X FRACTIONS USING A COMMON DENOMINATOR. [200,000(X+5)-200,000X)/X(X+5)=2,000 (200,000X+1,000,000-200,000X)/(X^2+5X)=2,000 NOW CROSS MULTIPLY 2,000(X^2+5X)=1,000,000 2,000(X^2+5X)-1,000,000=0 2,000(X^2+5X-500)=0 2,000(X+25)(X-20)=0 X-20=0 X=20 IS THE NUMBER OF ORIGINAL CLUB MEMBERS. PROOF: 200,000/20=200,000/25+2,000 10,000=8,000+2,000 10,000=10,000
 Linear_Equations_And_Systems_Word_Problems/132933: The creekside Theater is putting on a play.The hanson Family bought 5 adult ticketsand 2 child tickets for 129.00. The Rivera family bought 2 adult tickets and 6 cgild Tickets for 107.50. Write a system of equations to represent the situation. Then solve the system.How much Does a Adult ticket cost and how much does a child ticket cost.1 solutions Answer 97187 by checkley71(8403)   on 2008-03-20 16:17:10 (Show Source): You can put this solution on YOUR website!5A+2C=129 2A+6C=107.50 NOW MULTIPLY THE FIRST EQUATION BY -3 & ADD THEM. -15A-6C=-387 -------------------------------- -13A=-279.5 A=-279.5/-13 A=\$21.50 COST OF THE ADULT TICKET. 5*21.5+2C=129 107.5+2C=129 2C=129-107.5 2C=21.5 C=21.5/2 C=\$10.75 COST OF THE CHILDREN'S TICKET. PROOF: 2*21.50+6*10.75=107.5 43+64.5=107.50 107.50=107.50
 Equations/132937: Please help me solve this formula for the specified variable: 1/a+1/b=c for b1 solutions Answer 97178 by checkley71(8403)   on 2008-03-20 15:58:32 (Show Source): You can put this solution on YOUR website!1/A+1/B=C SUBTRACT 1/A FROM BOTH SIDES. 1/B=C-1/A CROSS MULTIPLY. B(C-1/A)=1 DIVIDE BY (C-1/A) B=1/(C-1/A) ANSWER.
 Miscellaneous_Word_Problems/132945: A basketball player completed 42.5% of his field goals in the most recent season. He made 281 field goals. How many did he attempt? (type an integer or a decimal. round to the nearest integer as needed) Please help. i know i keep coming up with the wrong answer. I got 6.7 lol1 solutions Answer 97176 by checkley71(8403)   on 2008-03-20 15:55:20 (Show Source): You can put this solution on YOUR website!281/.425=661 SHOTS ATTEMPTED.
 Travel_Word_Problems/132949: A cyclist traveled at a rate of 24mph to visit a nearby town. The cyclist averaged 18mph on the return trip. If the round trip took 4.9 hours find the distance to the nearby town.1 solutions Answer 97174 by checkley71(8403)   on 2008-03-20 15:51:32 (Show Source): You can put this solution on YOUR website!D/24+D/18=4.9 (18D+24D)/24*18=4.9 42D/432=4.9 42D=432*4.9 42D=2116.8 D=2116.8/42 D=50.4 MILES IS THE DISTANCE TO THE NEARBY TOWN. PROOF: 50.4/24+50.4/18=4.9 2.1+2.8=4.9 4.9=4.9
 Travel_Word_Problems/132950: This question is from textbook Applied College Algebra A ballet performance brought in \$61,800 on the sale of 3000 tickets. If the tickets sold for \$14 and \$25, how many of each type of tickets were sold?1 solutions Answer 97171 by checkley71(8403)   on 2008-03-20 15:46:36 (Show Source): You can put this solution on YOUR website!14X+25(3000-X)=61,800 14X+75,000-25X=61,800 -11X=61,800-75,000 -11X=-13,200 X=-13,200/-11 X=1,200 TICKETS FOR \$14 WERE SOLD. 3,000-1,200=1,800 TICKETS FOR \$25 WERE SOLD. PROOF: 14*1,200+25*1,800=61,800 16,800+45,000=61,800 61,800=61,800
 Equations/132958: 1/2N + 11 = 2N please show me the correct steps1 solutions Answer 97169 by checkley71(8403)   on 2008-03-20 15:40:45 (Show Source): You can put this solution on YOUR website!n/2+11=2n n/2-2n=-11 -n/2=-11 -n=-22 -n=-22/-1 n=22 answer. proof: 22/2+=11=2*22 11+11=22 22=22
 Equations/132959: Which best describes the effect on the graph of f(x)=4x+8 if the y-intercept is changed to-3?1 solutions Answer 97168 by checkley71(8403)   on 2008-03-20 15:37:30 (Show Source): You can put this solution on YOUR website!f(x)=4x+8 this line has a slope (m) of 3 & a y intercept (b) of 8 f(x)=4x-3 this line is a parallel line with slope of 4 & a y intercept (b) of -3.
 Quadratic_Equations/132828: Some students planned for a get-together. The budget for food was \$500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by \$5. How many students attended the get-together? 1 solutions Answer 97068 by checkley71(8403)   on 2008-03-19 18:36:20 (Show Source): You can put this solution on YOUR website!500/X=500/(X-5)-5 500/X-500/(X-5)=-5 (500(X-5)+X)/X(X-5)=-5 (500X-2500-500X)/(X^2+5X)=-5 CROSS MULTIPLY. -5(X^2+5X)=-2500 -5X^2+25X+2500=0 -5(X^2-5X-500=0 -5(X-25)(X+20)=0 X-25=0 X=25 NUMBER OF STUDENTS ORIGINALLY PLANNED TO ATTEND. PROOF: 500/25=500/(25-5)-5 20=(500/20)-5 25=25-5 20=20
 Quadratic_Equations/132831: Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream1 solutions Answer 97063 by checkley71(8403)   on 2008-03-19 18:23:32 (Show Source): You can put this solution on YOUR website!12/(9-X)+12/(9+X)=3 [12(9+X)+12(9-X)]/(9+X)(9-X)=3 [108(12X+108-12X]/(81-X^2)=3 216/(81-X^2)=3 NOW CROSS MULTIPLY 3(81-X^2)=216 243-3X^2-216=0 -3X^2+27=0 -3(X^2-9)=0 -3(X+3)(X-3)=0 X-3=0 X=3 KMH IS THE SPEED OF THE CURRENT. PROOF: 12/(9-3)+12/(9+3)=3 12/6+12/12=3 2+1=3 3=3
 Complex_Numbers/132732: please help me i do not understand ((3y+15)/y) / ((y+5)/y)1 solutions Answer 97061 by checkley71(8403)   on 2008-03-19 18:07:28 (Show Source): You can put this solution on YOUR website![(3Y+15)/Y]/(Y+5)/Y NOW INVERT THE DIVISOR AND MULTIPLY THE FRACTIONS: [(3Y+15)/Y]
 Proportions/132743: Can you please help me solve for x 500/(x+5)+5=500/x1 solutions Answer 97059 by checkley71(8403)   on 2008-03-19 18:02:57 (Show Source): You can put this solution on YOUR website!500/(X+5)+5=500/X 500/(X+5)-500/X=-5 [500*X-500(X+5)]/X(X+5)=-5 (500X-500X-2500)/(X^2+5X)=-5 CROSS MULTIPLY -5(X^2+5X)=-2500 -5X^2-25X+2500=0 -5(X^2+5X-500)=0 -5(X+25)(X-20)=0 X+25=0 X=-25 ANSWER. X-20=0 X=20 ANSWER.
 Quadratic_Equations/132748: A motor boat travels 300km downstream and returns 300km upstream in a total of 12 hours. The speed of the current is 6km/h. Write the equation that could be used to determine the speed of the motorboat in still water? I think it is (300/x )+(300/x+6)=12 Can someone please confirm this for me ????1 solutions Answer 97055 by checkley71(8403)   on 2008-03-19 17:53:42 (Show Source): You can put this solution on YOUR website!300/(X-6)+300/(X+6)=12 THE FIRST FRACTION IS THE SPEED UP STREAM AGAINST THE TIDE & THE SECOND FRACTION IS THE SPEED WITH THE CURRENT. [300(X+6)+300(X-6)]/(X+6)(X-6)=12 (300X+1800+300X-1800)/(X^2-36)=12 600X/(X^2-36)=12 NOW CROSS MULTIPLY. 12(X^2-36)=600X 12X^2-432-600X=0 12X^2-600X-432=0 12(X^2-50X-36)=0 USING THE QUADRATIC EQUATUION: WE GET: X=(50+-SQRT[-50^2-4*1*-36])/2*1 X=(5)=-SQRT[2500+144])/2 X=(50+-SQRT2644)/2 X=(50+-51.42)/2 X=(50+51.42)/2 X=101.42/2 X=50.71 ANSWER FOR THE SPEED OF THE MOTOR BOAT. PROOF: 300/(50.71+6)+300/(50.71-6)=12 300/56.71+300/44.71=12 5.29+6.71=12 12=12
 Square-cubic-other-roots/132754: How do you solve a question like: 4 (square-root-of) 3 + 6 (square-root-of) 2 - 5 (square-root-of) 4 I add it and I just don't understand it. It was on my placement test. Not homework. I just want to know how to solve it1 solutions Answer 97048 by checkley71(8403)   on 2008-03-19 17:31:11 (Show Source): You can put this solution on YOUR website!4SQRT3+6SQRT2-5SQRT4 4SQRT3+6SQRT2-5*2 4SQRT3+6SQRT2-10 ANSWER. SQRT WITH DIFFERENT VALUES (3 & 2) CANNOT BE COMBINED.
 Linear-equations/132758: express the following equation in the form Y= mx+b a. 2y= 6x+81 solutions Answer 97047 by checkley71(8403)   on 2008-03-19 17:27:02 (Show Source): You can put this solution on YOUR website!2y=6x+8 y=6x/2+8/2 Y=3X+4 ANSWER. m=3 & b=4.
 Miscellaneous_Word_Problems/132790: A stamp collection consists of 5, 13, and 18 cent stamps. The number of 13 cent stamps is one less than twice the number of 5 cent stamps. The number of 18 cent stamps is five more than the number of 13 cent stamps. The total value of all the stamps is \$2.60. Find the number of 13 cent stamps.1 solutions Answer 97044 by checkley71(8403)   on 2008-03-19 17:24:08 (Show Source): You can put this solution on YOUR website!X=NUMBER OF .05 STAMPS 2X-1=NUMBER OF .13 STAMPS (2X-1)+5=NUMBER OF .18 STAMPS .05X+.13(2X-1)+.18[(2X-1)+5]=2.60 .05X+.26X-.13+.36X+.18(2X+4)=2.60 .05X+.26X-.13+.36X+.18X+.72=2.60 .67X=2.60+.13-.72 .67X=201 X=2.01/.67 X=3 IS THE NUMBEER OF 5 CENT STAMPS 2*3-1=6-1=5 IS THE NUMBER OF 13 CENT STAMPS. 5+5=10 IS THE NUMBER OF 18 CENT STAMPS PROOF: .05*3+.13*5+.18*10=2.60 .15+.65+1.80=2.60 2.60=2.60
 Signed-numbers/132791: Given f(x)=2x^2-3x+5, Find f(1).1 solutions Answer 97042 by checkley71(8403)   on 2008-03-19 17:07:36 (Show Source): You can put this solution on YOUR website!F(X)=2X^2-3X+5 F(1)=2*1^2-3*1+5 F(1)=2*1-3*1+5 F(1)=2-3+5 F(1)=4 ANSWER.
 Reduction-of-unit-multipliers/132802: 3L=?mL1 solutions Answer 97040 by checkley71(8403)   on 2008-03-19 17:04:51 (Show Source): You can put this solution on YOUR website!3L=.003ml
 Quadratic_Equations/132804: Factor 7p + 5x = Help me factor this please. Not good at all with these problems.1 solutions Answer 97039 by checkley71(8403)   on 2008-03-19 17:00:21 (Show Source): You can put this solution on YOUR website!7P+5X NO FACTORING POSSIBLE HERE BECAUSE YOU HAVE 2 UNKNOWN FACTORS AND NO COMMON FACTORS WITHIN THE INTEGERS.
 Quadratic_Equations/132801: 9x-8=5x Help me please.1 solutions Answer 97038 by checkley71(8403)   on 2008-03-19 16:57:43 (Show Source): You can put this solution on YOUR website!9X-8=5X 9X-5X=8 4X=8 X=8/4 X=2 ANSWER. PROOF: 9*2-8=5*2 18-8=10 10=10
 Square-cubic-other-roots/132778: solve: square 4x-13=11 solutions Answer 97037 by checkley71(8403)   on 2008-03-19 16:53:16 (Show Source): You can put this solution on YOUR website!4X-13=1 4X=1+13 4X=14 X=14/4 X=7/2 OR 3.5 ANSWER.
 Finance/132798: Jane has \$10 000 to invest. She invested part of it in a term deposit that pays 4% per year and the rest of her money was invested in bonds paying 5% per year. If Jane earned \$440 in interest for one year, how much money did she invest at each rate?1 solutions Answer 97035 by checkley71(8403)   on 2008-03-19 16:47:12 (Show Source): You can put this solution on YOUR website!.05X+.04(10,000-X)=440 .05X+400-.04X=440 .01X=440-400 .01X=40 X=40/.01 X=4,000 AMOUNT INVESTED @ 5%. 10,000-4,000=6,000 AMOUNT INVESTED @ 4%. PROOF: .05*4,000+.04*6000=440 200+240=440 440=440
 Quadratic_Equations/132621: A square lawn is surrounded by a walk one metre wide. If the area of the walk is equal to half the area of the lawn,what are the dimensions of the lawn???1 solutions Answer 96990 by checkley71(8403)   on 2008-03-18 21:22:57 (Show Source): You can put this solution on YOUR website!LET X BE THE LAWN SIDE MEASUREMENT. X^2=THE LAWN AREA. (X+2)^2-X^2=X^2/2 TOTAL AREA [(X+2)^2] MINUS THE LAWN AREA [X^2] = 1/2 THE LAWN AREA [X^2/2]. X^2+4X+4-X^2=X^2/2 4X+4=X^2/2 X^2=2(4X+4) X^2=8X+8 X^2-8X-8=0 USING THE QUADRATIC EQUATION: WE GET: X=(8+-SQRT[-8^2-4*1*-8])/2*1 X=(8+-SQRT64+32])/2 X=(8+-SQRT96)/2 X=(8+-9.7979)/2 X=(8+9.7979)/2 X=17.7979/2 X=8.899 METERS FOR THE DIMENSION OF THE SQUARE. PROOF: (8.899+2)^2-8.899^2=8.899^2/2 10.899^2-79.192=79.192/2 118.788-79.192=39.596 39.596=39.596
 Quadratic_Equations/132623: In 1990,Joshua's university tuition was \$1500. In 1995, tuition at the same university cost \$3200. Assuming that an exponential model applies, how much will tuition cost in 2009?1 solutions Answer 96987 by checkley71(8403)   on 2008-03-18 21:04:30 (Show Source): You can put this solution on YOUR website!(1995-1990)/(3200-1500)=(2009-1990)/(X-1500) 5/1700=19/(X-1500 5(X-1500)=19*1700 5X-7500=32300 5X=32300+7500 5X=39800 X=39800/5 X=\$7,960 IS THE PROJECTED TUITION FOR 2009.
 percentage/132663: An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. a student purchases a flute for \$306. I need to find the original price,but i don't know where to start, please help me thanks. 1 solutions Answer 96985 by checkley71(8403)   on 2008-03-18 20:57:07 (Show Source): You can put this solution on YOUR website!(.9*.85)X=306 .765X=306 X=306/.765 X=400 WAS THE ORIGINAL PRICE. PROOF 400(1-.10)(1-.15)=306 400*.9*.85=306 400*.765=306 306=306
 Proportions/132665: Solve Proportions: 9/-15 = -27/P My question is: If just the demonitor or just the numerator is a negative number does this make the entire fraction negative? Thank you for your help, Brooke1 solutions Answer 96983 by checkley71(8403)   on 2008-03-18 20:53:10 (Show Source): You can put this solution on YOUR website!9/-15=-9/15=-(9/15) -9/15=-27/P NOW CROSS MULTIPLY. -9P=15*-27 -9P=-405 P=-405/-9 P=45 ANSWER.