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Quadratic_Equations/149896: This question is from textbook A rectangular garden has dimensions of 18 ft by 13 ft. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet? 1 solutions Answer 110026 by checkley77(12569)   on 2008-07-27 16:11:52 (Show Source): You can put this solution on YOUR website! 18*13=234 ft^2 for the garden. 234+516=750 is the area for the garden plus the path. (18+2x)(13+2x)=750 234+36x+26x+4x^2=750 4x^2+62x+234-750=0 4x^2+62x-516=0 2(2x^2+31x-258)=0 2(2x+43)(x-6)=0 x-6=0 x=6 for the width of the path. proof: (18+2*6)(13+2*6)+750 (18+12)(13+12)=750 30*25=750 750=750

Percentage-and-ratio-word-problems/149677: Lucy has invested some money invested at 18% and three times as much invested at 12%. her total annual income from the 2 investment is 85,000 pesos. how much was invested at each rate? 1 solutions Answer 109881 by checkley77(12569)   on 2008-07-25 18:17:01 (Show Source): You can put this solution on YOUR website! .18x+.12*3x=85,000 .18x+.36x=85,000 .54x=85,000 x=85,000/.54 x=157,407.40 invested @ 18% 3*157,407.40=472,222.20 invested @ 12% proof: .18*157,407.40+.12*472,222.20=85,000 28,333.33+56,666.67=85,000 85,000=85,000

Polynomials-and-rational-expressions/149683: This question is from textbook Elementary and Intermediate Algebra Bear population. To estimate the size of the bear population on the Keweenaw Peninsula, conservationists. Captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population? 1 solutions Answer 109880 by checkley77(12569)   on 2008-07-25 18:09:37 (Show Source): You can put this solution on YOUR website! 2/100=50/x 2x=5,000 x=5,000/2 x=2,500 is the estimated number of bears.

Money_Word_Problems/149685: Walt made an extra $9000.00 lst year from his part time job. He invested part of the money at 9% and the rest at 8%. He made a total of $770.00 in interest. How much was invested at 8%? 1 solutions Answer 109879 by checkley77(12569)   on 2008-07-25 18:07:13 (Show Source): You can put this solution on YOUR website! .09x+.08(9,000-x)=770 .o9x+720-.08x=770 .01x=770-720 .01x=50 x=50/.01 x=5,000 invested @ 9% 9,000-5,000=4,000 invested @ 8% proof: .09*5000+.08*4000=770 450+320=770 770=770

Radicals/149710: simplify: 5√9a³b³ + 4a√36ab³ - 2b√81a³b 1 solutions Answer 109877 by checkley77(12569)   on 2008-07-25 17:58:06 (Show Source): You can put this solution on YOUR website! 5√9a³b³ + 4a√36ab³ - 2b√81a³b 5*3absqrtab+4*6absqrtab-2*9absqrtab 15ab+24ab-18ab(sqrtab) 21ab(sqrtab)

Linear-equations/149731: 7x+2y=0 1 solutions Answer 109873 by checkley77(12569)   on 2008-07-25 17:51:12 (Show Source): You can put this solution on YOUR website! 7x+2y=0 IF THIS IS A LINE EQUATION THEN: 2Y=-7X+0 Y=-7X/2 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = -7x/2).

Money_Word_Problems/149770: Please help with this problem:Becoming a millionaire: How much would you have to invest now at 6.5% interest compounded semi-annually to have a million dollars in 40 years? 1 solutions Answer 109871 by checkley77(12569)   on 2008-07-25 17:46:36 (Show Source): You can put this solution on YOUR website! 1,000,000=x(1+.065/2)^40*2 1,000,000=x(1.0325)^80 1,000,000=12.9183x x=1,000,000/12.9183 x=$77,409.57 would be the initial investment.

percentage/149611: Principle Rate Time $400 14% 1yr Please find the simple interest and simplify 1 solutions Answer 109792 by checkley77(12569)   on 2008-07-24 17:23:12 (Show Source): You can put this solution on YOUR website! 400(.14)^1 400*.14=$56.00 is the interest.

sets-and-operations/149452: how do you find three consecutive numbers who's product is 15, 600? 1 solutions Answer 109649 by checkley77(12569)   on 2008-07-23 17:49:25 (Show Source): You can put this solution on YOUR website! LET X-1, X & X+1 BE THE THREE NUMBERS. (X-1)X(X+1)=15,600 A SIMPLE TEST CAN DETERMINE THE VALUE OF THE MIDDLE NUMBER. X^3-X=15,600 X^3=15,600+X NOW FIND THE CUBE ROOT OF 15,600: CUBERT15,600=24.98 NOW ADD THE MEXT WHOLE NUMBER ABOVE 24.98 (25) TO 15,600+25=15,625. NOW FIND THE CUBERT15,625 CUBERT15,625=25 WHICH IS THE MIDDLE NUMBER. 24,25,26 ARE THE 3 NUMBERS. PROOF: 24*25*26=15,600 15,600=15,600

Quadratic_Equations/149427: In a right triangle, one of the legs is 2 feet longer than the shorter leg. The hypotenuse is 10 feet. Find the lenghths of the missing 2 sides of the triangle. 1 solutions Answer 109642 by checkley77(12569)   on 2008-07-23 17:17:18 (Show Source): You can put this solution on YOUR website! X^2+(X+2)^2=10^2 X^2+X^2+4X+4=100 2X^2+4X+4-100=0 2X^2+4X-96=0 2(X^2+2X-48)=0 2(X+8)(X-6)=0 X-6=0 X=6 FEET FOR THE SHORTER SIDE. 6+2=8 FEET FOR THE LONGER SIDE. PROOF: 6^2+8^2=10^2 36+64=100 100=100

Rectangles/149450: This question is from textbook page 397 THE PERIMETER OF A RECTANGLE IS 96. THE LENGTH OF THE RECTANGLE IS SIX LESS THAN TWICE THE WIDTH. FIND THE DIMENSIONS OF THE RECTANGLE. 1 solutions Answer 109640 by checkley77(12569)   on 2008-07-23 17:11:39 (Show Source): You can put this solution on YOUR website! P=2L+2W 96=2(2W-6)+2W 96=4W-12+2W 96=4W-12 4W=96+12 4W=108 W=108/4 W=18 FOR THE WIDTH. 2*18-6=36-6=30 FOR THE LENGTH. PROOF: 96=2*30+2*18 96=60+36 96=96

Graphs/149231: if p & q are positve single digit numbers find all possible solutions of 3p-4q=4 1 solutions Answer 109530 by checkley77(12569)   on 2008-07-22 19:40:02 (Show Source): You can put this solution on YOUR website! 3p-4q=4 3*4-4*2=4 (P=4,Q=2) 12-8=4 3*8-4*5=4 (P=8,Q=4) 24-20=4

Graphs/149232: if p & q are positve single digit numbers find all possible solutions of 3p-4q=4 1 solutions Answer 109529 by checkley77(12569)   on 2008-07-22 19:38:40 (Show Source): You can put this solution on YOUR website! 3p-4q=4 3*4-4*2=4 (P=4,Q=2) 12-8=4 3*8-4*5=4 (P=8,Q=4) 24-20=4

Graphs/149239: 2x=y+1 2x-y=5 solve by graphing 1 solutions Answer 109528 by checkley77(12569)   on 2008-07-22 19:32:40 (Show Source): You can put this solution on YOUR website! 2x=y+1 Y=2X-1 (RED LINE) 2x-y=5 Y=2X-5 (GREEN LINE) (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 2x -1 and 2x -5). THSE PARALLEL LINES INDICATE THAT THERE IS NO S0LUTION TO THESE 2 EQUATIONS.

Quadratic_Equations/149278: A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet? 1 solutions Answer 109526 by checkley77(12569)   on 2008-07-22 19:16:50 (Show Source): You can put this solution on YOUR website! 18*13=234 FT^2 FOR THE GARDEN. 234+516=750 FOR THE TOTAL AREA WITH THE PATH. (18+2X)(13+2X)=750 234+26X+36X+4X^2=750 4X^2+62X+234-750=0 4X^2+62X-516=0 2(2X^2+31X-258)=0 2(2X-12)(X+21.5)=0 2X-12=0 2X=12 X=6 FT. IS THE ANSWER FOR THE WIDTH OF THE PATH. PROOF: (18+2*6)(13+2*6)=750 (18+12)(13+12)=750 30*25=750 750=750

Finance/149274: Find the value of $950 invested at 4.5% with interest compounded monthly for 5 years 1 solutions Answer 109524 by checkley77(12569)   on 2008-07-22 19:03:12 (Show Source): You can put this solution on YOUR website! P(1+.045/12)^5*12 950(1.0037)^60 950*1.248=$1,185.66 AMOUNT OF THE INVESTNMENT AFTER 5 YEARS.

Linear_Equations_And_Systems_Word_Problems/149284: Find the slope of the line that contains the points (2.346, –0.215) and (4.492, –3.322). Round to the nearest thousandth. Match your result to the correct answer below. A) –0.517 B) 0.517 C) –1.448 D) 1.448 1 solutions Answer 109521 by checkley77(12569)   on 2008-07-22 18:55:47 (Show Source): You can put this solution on YOUR website! (2.346, –0.215) and (4.492, –3.322) SLOPE=(-3.322+.215)/(4.495-2.346) SLOPE=-3.107/2.149 SLOPE=-1.446 ANSWER. C) IS THE ANSWER.

Quadratic_Equations/149282: Please, I need help with the next step, something is not right. .05(113 – 2y) + 8 + .10(2y) = $10.45 1 solutions Answer 109520 by checkley77(12569)   on 2008-07-22 18:49:31 (Show Source): You can put this solution on YOUR website! .05(113 – 2y) + 8 + .10(2y) = $10.45 5.65-.1Y+8+.2Y=$10.45 .1Y=10.45-5.65-8 .1Y=-3.2 Y=-3.2/.1 Y=-32 ANSWER. PROOF: .05(113-2*-32)+8+.1(2*-32)=10.45 .05(113+64)+8+.1*-64=10.65 .05*177+8-6.4=10.65 8.85+8-6.4=10.65 10.45=10.45

Linear-systems/149287: Write the slope-intercept equation of the line l that goes through (12, 3) and has a slopeof 1/3 . 1 solutions Answer 109517 by checkley77(12569)   on 2008-07-22 18:36:46 (Show Source): You can put this solution on YOUR website! slope=1/3 through (12,3) Y=mX+b WHERE m=SLOPE & b=Y INTERCEPT. 3=12*1/3+b 3=4+b b=3-4 b=-1 THE Y INTERCEPT. THUS THE EQUATION IS: Y=X/3-1

Linear-systems/149113: Find the solution by substitution: 3x-2y=-5 x=y-2 1 solutions Answer 109398 by checkley77(12569)   on 2008-07-21 19:39:34 (Show Source): You can put this solution on YOUR website! 3x-2y=-5 x=y-2 3(Y-2)-2Y=-5 3Y-6-2Y=-5 Y=6-5 Y=1 ANSWER. X=1-2 X=-1 ANSWER. PROOF: 3*-1-2*1=-5 -3-2=-5 -5=-5

Coordinate-system/149141: find the y-intercept of 6x-y=-12 1 solutions Answer 109397 by checkley77(12569)   on 2008-07-21 19:33:09 (Show Source): You can put this solution on YOUR website! Y=mX+b IS THE STANDARD LINE EQUATION WHERE m=SLOPE & b=Y INTERCEPT. 6x-y=-12 -Y=-6X-12 Y=6X+12 THUS THE Y INTERCEPT (b)=12

Expressions-with-variables/149122: Solve each question by the by the addition method 1) 3x+2y=3 4x-3y=-13 2)3x-y=5 -6x+2y=1 1 solutions Answer 109396 by checkley77(12569)   on 2008-07-21 19:30:05 (Show Source): You can put this solution on YOUR website! 1) 3x+2y=3 MULTIPLY THIS EQUATION BY 3 4x-3y=-13 MULTIPLY THIS EQUATION BY 2 & THEN ADD THEM. 9X+6Y=9 8X-6Y=-26 -------------------------------- 17X=-17 X=-17/17 X=-1 ANSWER. 3*-1+2Y=3 -3+2Y=3 2Y=3+3 2Y=6 Y=6/2 Y=3 ANSWER. ----------------------------------------------------------------------- 2)3x-y=5 MULTIPLY BY 2 & ADD. -6x+2y=1 6X-2Y=10 ---------------------------------- 0+0=11 THERE ARE NO SOLUTIONS FOR THESE 2 EQUATIONS. THESE EQUATIONS REPRESENT PARALLEL LINES IN GEOMETRY.

Quadratic_Equations/149125: Problem: Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what are it's dimensions? 1 solutions Answer 109394 by checkley77(12569)   on 2008-07-21 19:19:55 (Show Source): You can put this solution on YOUR website! area=L*W 75=3W*W 75=3W^2 W^2=75/3 W^2=25 W=SQRT25 W=5 WIDTH OF THE GARDEN. 3*5=15 FOR THE LENGTH OF THE GARDEN. PROOF: 75=15*5 75=75

Miscellaneous_Word_Problems/149130: To determine the number of deer in a game preserve,a man catches 715 deer, tags them and lets them loose,later, 312 of them are caught, 156 of them are tagged. How many of them are in the preserve? 1 solutions Answer 109393 by checkley77(12569)   on 2008-07-21 19:16:34 (Show Source): You can put this solution on YOUR website! 156/312=715/x 156x=312*715 156x=223,080 x=223,050/156 x=1,430 is the estimated number of deer in the preserve.

Numbers_Word_Problems/148935: Find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 4 times the third. 1 solutions Answer 109275 by checkley77(12569)   on 2008-07-20 19:00:13 (Show Source): You can put this solution on YOUR website! LET X BE THE FIRST NTEGER, (X+1) BE THE SECOND & 9X+2) BE THE THIRD. X(X+2)-(X+1)=4(X+2)+1 X^2+2X-X-1=4X+8+1 X^2+2X-X-4X-1-8-1=0 X^2-3X-10=0 (X-5)(X+2)=0 X-5=0 X=5 ANSWER FOR THE FIRST INTEGER. 5+1=6 THE SECOND. 5+2=7 THE THIRD. PROOF: 5*7-6=4*7+1 35-6=28+1 29=29

Linear-systems/148936: y = 3x + 2 2x + y = - 8 1 solutions Answer 109272 by checkley77(12569)   on 2008-07-20 18:53:27 (Show Source): You can put this solution on YOUR website! y=3x+2 (RED LINE) 2x+y=-8 Y=-2X-8 (GREEN LINE) (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 3x +2 and -2x -8). solution (-2,-4)

Problems-with-consecutive-odd-even-integers/148937: Jon has a 26-ft ladder leaning against his house.If the bottom of the ladder is 10 ft. from the base of the house, how high does the ladder reach. 1 solutions Answer 109269 by checkley77(12569)   on 2008-07-20 18:49:40 (Show Source): You can put this solution on YOUR website! X^2+10^2=26^2 X^2+100=676 X^2=676-100 X^2=576 X=SQRT576 X=24 FT. IS THE HEIGHT OF THE TOP OF THE LADDER.

Expressions-with-variables/148939: x=y+6 y=-2-x My daughter is trying to solve this equation by substitution. I am useless in attempting to help her. We would greatly appreciate you explaining the answer. 1 solutions Answer 109268 by checkley77(12569)   on 2008-07-20 18:46:51 (Show Source): You can put this solution on YOUR website! x=y+6 NOW SUBSTITUTE (Y+6) FOR X IN THE OTHER EQUATION. y=-2-x Y=-2-(Y+6) Y=-2-Y-6 Y+Y=-8 2Y=-8 Y=-8/2 Y=-4 ANSWER. X=-4+6 X=2 ANSWER. PROOF: -4=-2-2 -4=-4

Linear_Equations_And_Systems_Word_Problems/148931: Please help me put the word problem below in linear equations. Thank you so much in advance. Please help me. How do I go about this with the question? An express and local train leave gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train. 1 solutions Answer 109266 by checkley77(12569)   on 2008-07-20 18:43:39 (Show Source): You can put this solution on YOUR website! LET THE TIME OF THE LOCAL TRAIN=50/X LET THE TIME OF THE EXPRESS=50/2X 50/X=50/2X+1 50/X-50/2X=+1 (2*50-50)/2X=+1 (100-50)/2X=+1 50/2X=+1 2X=50 X=50/2 X=25 MPH FOR THE LOCAL 25*2=50 MPH FOR THE EXPRESS. PROOF: 50/25=50/50+1 2=1+1 2=2

Linear_Equations_And_Systems_Word_Problems/148933: Walt made an extra $9000 last year from a part-time job. he invested part of the money at 9% and the rest at 8%. he made a total of $770 in interest. How much was invested at 8%? 1 solutions Answer 109263 by checkley77(12569)   on 2008-07-20 18:26:17 (Show Source): You can put this solution on YOUR website! .09X+.08(9000-X)=770 .09X+720-.08X=770 .01X=770-720 .01X=50 X=50/.01 X=5,000 INVESTED @ 9% 9,000-5,000=4,000 INVESTED @ 8%. PROOF: .09*5000+.08*4000=770 450+320=770 770=770

Linear_Equations_And_Systems_Word_Problems/148934: Hi, I have to translate the following into a quadratic equation and solve it. Please help. The length of a rectangular garden is three times its width: if the area of the garden is 75 square meters, what are its dimensions? 1 solutions Answer 109262 by checkley77(12569)   on 2008-07-20 18:20:40 (Show Source): You can put this solution on YOUR website! the formula is: L*W=75 GIVEN L=3W THEN 3W*W=75 3W^2=75 W^2=25 W=SQRT25 W=5 METERS. L=3*5 L=15 METERS. PROOF: 15*5=75 75=75