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 Linear-systems/391551: I'm trying to help my niece with her homework and I can't remember at all how to solve this problem. She's trying to solve this linear equation or system. She says she's supposed to get the answer by using the 3y? 2x-3y=-7 (negative 7) 3x+y=-5 (negative 5) I have the answer for her but would really like to know how to solve this and to show her the correct way. Thank you!1 solutions Answer 277890 by ankor@dixie-net.com(15639)   on 2011-01-07 08:14:00 (Show Source): You can put this solution on YOUR website!2x - 3y = -7 3x + y = -5 They probably want you to use elimination, by multiplying the 2nd equation by 3 and adding the two equations, you will eliminate y and easily can find x : 2x - 3y = -7 9x + 3y = -15 (multiplied by 3) ---------------- 11x + 0 = -22 Divide both sides by 11, and you have x = -2 : You can now find y by substituting -2 for x in the 2nd equation 3(-2) + y = -5 -6 + y = -5 Add 6 to both sides y = -5 + 6 y = +1 : Check your solutions by substitution in the 1st equation 2x - 3y = -7 2(-2) - 3(1) = -7 -4 - 3 = -7; confirms our solutions of x = -2, y = 1
 Graphs/391526: I need help understanding and graphing the equation to find the y-intercept y+x=-71 solutions Answer 277887 by ankor@dixie-net.com(15639)   on 2011-01-07 08:04:42 (Show Source): You can put this solution on YOUR website!I need help understanding and graphing the equation to find the y-intercept y+x=-7 You need to put the equation into the slope/intercept form (y = mx + b) where m is the slope and b is the y intercept (occurs when x=0) y + x = -7 subtract x from both sides and you have y = -x - 7, slope in this case m=-1 : Choose at least two values for x, and find y Let x = -3 y = -(-3) - 7 y = 3 - 7; minus a minus is a plus y = -4 plot the ordered pair, x=-3, y=-4 and Let x = +2 y = -2 - 7 y = -9 plot the ordered pair, x=2; y=-9 : Join these two points with a straight line the graph should look like this You can see the y intercept = -7, when x = 0
 Circles/391542: I have a geometry problem and i get lost in the steps. I have to find b in the volume of a cone. The equation is V=1/3(3.14)(r squared) h. Can you please help. r=2b squared h=24 Can you show me the steps? 1 solutions Answer 277823 by ankor@dixie-net.com(15639)   on 2011-01-06 22:10:29 (Show Source): You can put this solution on YOUR website!find b in the volume of a cone. The equation is V=1/3(3.14)(r squared) h. Can you please help. r=2b squared h=24 Multiply both sides by 3 Replace r with 2b^2 and h with 24 : Divide both sides by b^4 = Reduce fraction b^4 = Find the 4th root of both sides b =
 test/391523: Tina's circular glass table in her tv room has a area of 169Pi square inches. She wants to put a protective rubber border around the edge of the table for her child. How much meterial in inches does she need to buy1 solutions Answer 277818 by ankor@dixie-net.com(15639)   on 2011-01-06 21:49:10 (Show Source): You can put this solution on YOUR website!Tina's circular glass table in her tv room has a area of 169Pi square inches. She wants to put a protective rubber border around the edge of the table for her child. How much material in inches does she need to buy. : Use the Area equation [] to find the radius = Divide both sides by pi r^2 = 169 r = r = 13 inches is the radius : Find the circumference [} C = C = 81.68 inches, she should buy at least 82 inches (If it's sold by the foot, get 7 ft}
 Length-and-distance/391496: I need help please. Thanks a bunch in advance. Imagine you are traveling to chicago, and you pass a mile marker that says you have 191 miles to go. How long will it take you to get to chicago if your average speed for the rest of the trip is 66 mi/h?1 solutions Answer 277814 by ankor@dixie-net.com(15639)   on 2011-01-06 21:39:13 (Show Source): You can put this solution on YOUR website!you are traveling to chicago, and you pass a mile marker that says you have 191 miles to go. How long will it take you to get to chicago if your average speed for the rest of the trip is 66 mi/h? : Assume you know that: Time = dist/speed Therefore: T = T = 2.894 hrs which is 2 + .894(60) = 2 hrs 53.6 minutes : : Check this by finding the distance, dist = speed * time d = 2.894 * 66 d = 191.0 mi; confirms our solution
 Circles/391141: The diameter of circle C is 18 units long. Find the length of an arc that has a measure of 100 to the nearest tenth1 solutions Answer 277746 by ankor@dixie-net.com(15639)   on 2011-01-06 17:07:08 (Show Source): You can put this solution on YOUR website!The diameter of circle C is 18 units long. Find the length of an arc that has a measure of 100 to the nearest tenth : * = 15.7 units
 Equations/391435: solve for x. 4x(x-8)-5x(x-7)=-41 solutions Answer 277742 by ankor@dixie-net.com(15639)   on 2011-01-06 17:01:27 (Show Source): You can put this solution on YOUR website!solve for x. 4x(x-8)-5x(x-7)=-4 : 4x^2 - 32x - 5x^2 + 35x + 4 = 0 Combine like terms 4x^2 - 5x^2 - 32x + 35x + 4 = 0 -1x^2 + 3x + 4 = 0 Multiply by -1 x^2 - 3x - 4 = 0 Factors to (x+1)(x-4) = 0 Two solutions x = -1 x = 4 : You can check the solutions in the original equation.
 Quadratic_Equations/391413: The Square of a positive number is 12 more than 4 times the number. Find the number. 1 solutions Answer 277737 by ankor@dixie-net.com(15639)   on 2011-01-06 16:48:56 (Show Source): You can put this solution on YOUR website!The Square of a positive number is 12 more than 4 times the number. Find the number. : x^2 = 4x + 12 x^2 - 4x - 12 = 0, our old friend the quadratic equation Factors to (x-6)(x+2) = 0 Positive solution x = 6 : : check: 6^2 = 4(6) + 12
 Percentage-and-ratio-word-problems/391073: The denominator of a fraction exceeds twice the numerator by 10. The value of the fraction is 5/12. Find the fraction.1 solutions Answer 277542 by ankor@dixie-net.com(15639)   on 2011-01-05 21:51:35 (Show Source): You can put this solution on YOUR website!The denominator of a fraction exceeds twice the numerator by 10. The value of the fraction is 5/12. Find the fraction. : Let x = the numerator then (2x+10) = the denominator therefore: = Cross multiply 12x = 5(2x+10) 12x = 10x + 50 12x - 10x = 50 2x = 50 x = 25; the numerator : 2(25) + 10 = 60 is the denominator : reduces to
 Miscellaneous_Word_Problems/391206: \$9.50 for 3 sodas and 2 milkshakes. \$10.50 for 2 sodas and 3 milkshakes. How much does each drink cost? I need help figuring out the equations. I came up with x=soda y=milkshake 3x + 2y = 9.50 and 2x +3y = 10.50 But I can't make it work. Thank you so much!!!!!1 solutions Answer 277516 by ankor@dixie-net.com(15639)   on 2011-01-05 21:31:07 (Show Source): You can put this solution on YOUR website!See if we can make it work : 3x + 2y = 9.50 2x + 3y = 10.50 : We can use elimination here. Multiply the 1st equation by 3, the 2nd equation by 2 9x + 6y = 28.50 4x + 6y = 21.00 -------------------subtracting will eliminate y, find x 5x = 7.50 x = x = \$1.50 for each soda : Find y using the 1st equation 3(1.50) + 2y = 9.50 4.50 + 2y = 9.50 2y = 9.50 - 4.50 2y = 5.00 y = \$2.50 for each milksh : : Check solutions in the 2nd equation 2(1.50) + 3(2.50) = 10.50 3 + 7.50 = 10.50
 expressions/391144: I have a problem with algebra word problems. Please help with this one: at the beach 4 children working separately made 8 sandcastles in an hour.at this rate, hhow many sandcastles can 12 children make in 1/2 an hour. 1 solutions Answer 277500 by ankor@dixie-net.com(15639)   on 2011-01-05 21:08:24 (Show Source): You can put this solution on YOUR website!at the beach 4 children working separately made 8 sandcastles in an hour. : Find the rate of castle building in child-hrs (one child working 1 hr) 4 child-hrs made 8 castles = 2 castles per child-hr : at this rate, how many sandcastles can 12 children make in 1/2 an hour. .5*12*2 = 12 castles in 1/2 hr by 12 children
 Probability-and-statistics/391174: Just looking for the formula to solve the following question: 36 students took a test that required a passing grade of 70. The mean of those who passed was 78. The mean of those who failed was 60. The total mean was 71. How many students failed. I figured that 36 x 71 gives me the total number of points (2556). I know that 78 times some number less than 36 PLUS 60 times the rest of the 36 left over = 2556. I just can't figure out how to put this into a formula I can solve.1 solutions Answer 277486 by ankor@dixie-net.com(15639)   on 2011-01-05 20:17:14 (Show Source): You can put this solution on YOUR website!36 students took a test that required a passing grade of 70. The mean of those who passed was 78. The mean of those who failed was 60. The total mean was 71. How many students failed. : Let x = those that failed then (36-x) = those that passed : = 71
 Age_Word_Problems/390899: Amy is 5 years younger than Josh. She is twice Sam's age. Josh's age is less than 16. Sam is older than 4. How old is Sam?1 solutions Answer 277476 by ankor@dixie-net.com(15639)   on 2011-01-05 19:59:21 (Show Source): You can put this solution on YOUR website!Amy is 5 years younger than Josh. a = j-5 She is twice Sam's age. a = 2s : we can write this as 2s = j-5 s = Josh's age is less than 16. Sam is older than 4. How old is Sam? The only integer solution would be: j=15, s=5 ; Sam is 5
 Rectangles/390894: an architect is allowed no more then 15 square meters to add a small bedroom to a house. Because of the rooms design in relationship to the existing structure, the width of it's rectangle floor must be 7 meters less than two times the length. Find the precise length and width of the rectangular floor of maximum area that the architect is permitted. ~thanx 1 solutions Answer 277472 by ankor@dixie-net.com(15639)   on 2011-01-05 19:48:53 (Show Source): You can put this solution on YOUR website!an architect is allowed no more then 15 square meters to add a small bedroom to a house. Because of the rooms design in relationship to the existing structure, the width of it's rectangle floor must be 7 meters less than two times the length. Find the precise length and width of the rectangular floor of maximum area that the architect is permitted. : Let x = the required length then (2x-7) = the required width : The area: x(2x-7) = 15 2x^2 - 7x - 15 = 0 You can solve this using the quadratic formula, but this will factor (2x + 3)(x-5) = 0 The positive solution x = 5 m is the length then 2(5)-7 = 3 m is the width
 Expressions-with-variables/390882: find two positive numbers so that twice their sum equals their product and one number is 9 times the other number1 solutions Answer 277455 by ankor@dixie-net.com(15639)   on 2011-01-05 19:33:20 (Show Source): You can put this solution on YOUR website!: find two positive numbers so that twice their sum equals their product and one number is 9 times the other number : Let x = one number then 9x = the other number : 2(9x + x) = x * 9x 2(10x) = 9x^2 20x = 9x^2 divide both sides by x 20 = 9x x = is one number 9* = 20 is the other number : : See if this is true in the original statement: "two positive numbers that twice their sum equals their product" 2( + 20) = * 20 2( + ) = 2() =
 Mixture_Word_Problems/390868: A 50 ml solution of acid in water contains 25% acid. How much water would you add in order to make a 10% acid solution?1 solutions Answer 277449 by ankor@dixie-net.com(15639)   on 2011-01-05 19:21:55 (Show Source): You can put this solution on YOUR website!A 50 ml solution of acid in water contains 25% acid. How much water would you add in order to make a 10% acid solution? : Let x = amt of water to be added : Write an amt of alcohol equation .25(50) = .10(x+50) 12.5 = .10x + 5 12.5 - 5 = .1x 7.5 = .1x x = x = 75 ml of water required : : See if that's true .25(50) = .10(75+50) 12.5 = .1(125)
 Rational-functions/390846: what is 5 pounds : 10 ounces. as a fraction in simplest form?1 solutions Answer 277436 by ankor@dixie-net.com(15639)   on 2011-01-05 18:58:36 (Show Source): You can put this solution on YOUR website!what is 5 pounds : 10 ounces. as a fraction in simplest form? : How about: 5 lb reduce fraction 5 lb
 Trigonometry-basics/390901: There are two lamp posts (A and B) both 9.6m tall. When a man 1.6m tall stand X meters in front of lamp post A, his shadow casted by lampost B just touches the base of lampost A. The man then walks towards lamp post B for 12m and his shadow, casted by lamp post A, just touches the base of Lamp post B. What is the length of the man's shadow (show all working out)?1 solutions Answer 277429 by ankor@dixie-net.com(15639)   on 2011-01-05 18:47:22 (Show Source): You can put this solution on YOUR website!There are two lamp posts (A and B) both 9.6m tall. When a man 1.6m tall stand X meters in front of lamp post A, his shadow casted by lampost B just touches the base of lampost A. The man then walks towards lamp post B for 12m and his shadow, casted by lamp post A, just touches the base of Lamp post B. What is the length of the man's shadow. : We can use the rule of similar right triangles here The sides of the large triangle formed by the light pole (9.6) and the dist between the poles, (2x+12) : The sides of the small triangle formed by the man (1.6) and the dist from him to the light pole, x : A ratio equation = Cross multiply 9.6x = 1.6(2x+12) 9.6x = 3.2x + 19.2 9.6x - 3.2x = 19.2 6.4x = 19.2 x = x = 3 meters is the guys shadow
 Age_Word_Problems/390890: In 15 years, Maya will be twice as old as David is now. In 15 years, David will be as old as Maya will be 10 years from now. How old are Maya and David now?1 solutions Answer 277273 by ankor@dixie-net.com(15639)   on 2011-01-05 09:45:07 (Show Source): You can put this solution on YOUR website!let m = M's age now Let d = D's age now : write an equation for each statement: : "In 15 years, Maya will be twice as old as David is now. m + 15 = 2d or m = 2d - 15; (we can use this form for substitution) : "In 15 years, David will be as old as Maya will be 10 years from now. d + 15 = m + 10 d = m + 10 - 15 d = m - 5 Substitute (2d-15) for m (from the 1st statement) d = (2d - 15) - 5 d = 2d - 20 d - 2d = -20 -d = -20 d = 20 yrs old now find m m = 2d - 15 m = 2(20) - 15 m = 25 yrs old now : : Check solutions in the statement: "In 15 years, David will be as old as Maya will be 10 years from now." 15 + 20 = 25 + 10
 Pythagorean-theorem/390934: The side of a right triangle are 8,15 and 17 units. If each side is doubled, how many square units will be the area of the new triangle.1 solutions Answer 277272 by ankor@dixie-net.com(15639)   on 2011-01-05 09:27:37 (Show Source): You can put this solution on YOUR website!The side of a right triangle are 8,15 and 17 units. If each side is doubled, how many square units will be the area of the new triangle. : We don't care about the hypotenuse (17) : Area of original triangle .5 * 8 * 15 = 60 Area of side doubled triangle .5 * 16 * 30 = 240 : It will add: 240 - 60 = 180 sq units
 Miscellaneous_Word_Problems/390944: Can someone help me do this problem step by step so I can understand it. I am confused. Thank you so much. A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement? Thank you so much I just do not understand.1 solutions Answer 277270 by ankor@dixie-net.com(15639)   on 2011-01-05 09:19:31 (Show Source): You can put this solution on YOUR website!A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement? : Let x = the width of the enlargement then x = the height of the enlargement : The area is height * width, therefore x*x = 192 which is x^2 = 192 multiply both sides by 3 to get rid of the denominator 4x^2 = 192 * 3 4x^2 = 576 Divide both sides by 4 and you have x^2 = 144 x = x = 12 is width then * 12 = 16 is the height : : We can confirm this by finding the area with these values 12 * 16 = 192 : Not that hard, right?
 test/390729: The line passing through (x,4) and (4,-5) is perpendicular to a line with a slope of -7/3. What is the value of x?1 solutions Answer 277171 by ankor@dixie-net.com(15639)   on 2011-01-04 21:27:04 (Show Source): You can put this solution on YOUR website!The line passing through (x,4) and (4,-5) is perpendicular to a line with a slope of -7/3. What is the value of x? ; Find the slope of the line perpendicular to slope of -7/3 using: m1*m2 = -1 Let m1 = -7/3, find m2 *m2 = -1 m2 = *-1 m2 = : Use the slope formula = m2 Using the given values = : = Cross multiply 3(4-x) = -9*7 12 - 3x = -63 -3x = -63 - 12 -3x = -75 x = x = +25 : : Check this by finding the slope using x=25 = =
 Travel_Word_Problems/390724: Please help me solve the following word problem: At 7:00 a.m. a plane left Houston for Detroit, 1750 miles away, flying at 400 mph. At 8:30 a.m. a plane left Detroit for Houston at 500 mph. At what time did they pass each other? Thanks, Alison1 solutions Answer 277097 by ankor@dixie-net.com(15639)   on 2011-01-04 18:50:30 (Show Source): You can put this solution on YOUR website!At 7:00 a.m. a plane left Houston for Detroit, 1750 miles away, flying at 400 mph. At 8:30 a.m. a plane left Detroit for Houston at 500 mph. At what time did they pass each other? : Let t = travel time of the Detroit plane then (t+1.5) = travel time of the Houston plane : When they meet, their travel distances will total 1750 mi Write a distance equation; dist = speed/time : 400(t+1.5) + 500t = 1750 400t + 600 + 500t = 1750 400t + 500t = 1750 - 600 900t = 1150 t = t = 1.278 hrs which is: 1 + .278(60) ~ 1:17 (1 hr 17 min) : 8:30 + 1:17 = 9:47 am; the time they meet : Check solution, find the distance of each 400 * (1.278 + 1.5) = 1111.2 mi 500 * 1.278 = 639 mi ---------------------- total miles: 1750.2 mi close enough
 Numbers_Word_Problems/390544: multiples of 7 is 7N, 7(N+1), 7(N+2), and so on, where N is some unspecified integer. Find three consecutive multiples of 7 such that the product of -3 and the sum of the first and third is 21 less than 5 times the opposite of the second1 solutions Answer 277017 by ankor@dixie-net.com(15639)   on 2011-01-04 15:19:58 (Show Source): You can put this solution on YOUR website!multiples of 7 is 7N, 7(N+1), 7(N+2), and so on, where N is some unspecified integer. Find three consecutive multiples of 7 such that the product of -3 and the sum of the first and third is 21 less than 5 times the opposite of the second : Let the three integers be: 7n, 7(n+1), 7(n+2) : -3(7n + 7(n+2)) = 5(-7(n+1) - 21 : -3(7n + 7n + 14)) = 5(-7(n+1) - 21 : -3(14n + 14)) = 5(-7(n+1) - 21 : -42m - 42 = 5(-7n - 7) - 21 : -42n - 42 = -35n - 35 - 21 : -42n - 42 = -35n - 56 Get rid of all those negatives, multiply by -1 42n + 42 = 35n + 56 : 42n - 35n = 56 - 42 : 7n = 14 : n = 2 : The three integers 14, 21, 28 : : See if that checks out in the statement; "the product of -3 and the sum of the first and third is 21 less than 5 times the opposite of the second" -3(14+28) = 5(-21) - 21 -3(42) = -105 - 21 -126 = - 126; confirms our solution of n=2
 Linear-equations/390354: How can i solve -4x+y=5 and 11x-9y=5 by multiplying first? 1 solutions Answer 276989 by ankor@dixie-net.com(15639)   on 2011-01-04 13:25:27 (Show Source): You can put this solution on YOUR website!How can i solve -4x+y=5 and 11x-9y=5 by multiplying first? : Assume you mean to solve using elimination, -4x + y = 5 11x - 9y = 5 : Multiply the 1st equation by 9 -36x + 9y = 45 11x - 9y = 5 ------------------adding will eliminate y, find x -25x + 0 = 50 x = x = -2 : Find y using the 1st equation -4(-2) + y = 5 8 + y = 5 y = 5 - 8 y = -3 : : Check solution in the 2nd equation 11(-2) - 9(-3) = 5 -22 + 25 = 5; confirms our solution x=-2, y=-3
 Travel_Word_Problems/390348: The word problem is: Boats A and B leave the same point at the same time at right angles. B travels 7 km/h slower than A. After 4 hours they are 68 km apart. Find the speed of each boat. That is exactly how it is written in the book and I can't figure it out. Can you please help me? If so thank you.1 solutions Answer 276865 by ankor@dixie-net.com(15639)   on 2011-01-03 22:04:32 (Show Source): You can put this solution on YOUR website!Boats A and B leave the same point at the same time at right angles. B travels 7 km/h slower than A. After 4 hours they are 68 km apart. Find the speed of each boat. : Let x = boat A's speed then (x-7) = boat B's speed : Dist = speed times time A's dist: 4x B's dist: 4(x-7) = (4x-28) : (4x)^2 + (4x-28)^2 = 68^2 16x^2 + 16x^2 - 224x + 784 = 4624 32x^2 - 224x - 3840 = 0 Simplify, divide by 32 x^2 - 7x - 120 = 0 Factors to (x-15(x+9) positive solution x = 15 is boat A's speed you can find boat b's speed