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 Linear-equations/580486: solve this equation using the elimination method: y=-18/19x-416/19 y= -17/19x-414/191 solutions Answer 371263 by mananth(12270)   on 2012-02-29 22:10:06 (Show Source): You can put this solution on YOUR website!y=-18/19x-416/19 y= -17/19x-414/19 equate the two equations
 Mixture_Word_Problems/580475: How much of a pure 100% acid must be added to 2 liters of a 10% acid solution in order to produce a 20% solution? How much 20% solution will there be?1 solutions Answer 371256 by mananth(12270)   on 2012-02-29 21:59:29 (Show Source): You can put this solution on YOUR website!------------ percent ---------------- Amount Acid type I 10 ---------------- 2 liters Pure acid 100 ---------------- x liters Total 20 ---------------- 2 + x liters 10*2+100x=20(2 +x) 20+100 x=40+20 x 100x-20 x =-20+ 40 80 x = 20 / 80 x = 0.25 of liters Pure acid 0.25 of liters Acid type I m.ananth@hotmail.ca
 Linear-equations/580378: write an equation of a vertical line through (4,3). write an equation of the line parallel to the line 8x - 2y = 7 passing through (2,-1). find all values of x for which (x,6) is on the graph of f (x) = x2 + 3x -41 solutions Answer 371227 by mananth(12270)   on 2012-02-29 20:24:55 (Show Source): You can put this solution on YOUR website!write an equation of a vertical line through (4,3). x=4 write an equation of the line parallel to the line 8x - 2y = 7 passing through (2,-1). 8 x -2 y = 7 Find the slope of this line make y the subject -2 y = -8 x + 7 Divide by -2 y = 4 x -3 1/2 Compare this equation with y=mx+b slope m = 4 The slope of a line parallel to the above line will be the same The slope of the required line will be 4 m= 4 ,point ( 2 , -1 ) Find b by plugging the values of m & the point in y=mx+b -1 = 8 + b b= 9 m= 4 Plug value of the slope and b in y = mx +b The required equation isy = 4 x + 9 find all values of x for which (x,6) is on the graph of f (x) = x2 + 3x -4 6=x^2+3x-5 x^2+3x-10=0 (x+5)(x-2)=0 x=-5 & 2
 Linear-systems/580387: 5y=7x+22 x=-6y+171 solutions Answer 371225 by mananth(12270)   on 2012-02-29 20:18:53 (Show Source): You can put this solution on YOUR website!5y=7x+22 x=-6y+17 Re write the equations -7 x + 5 y = 22 .............1 1 x + 6 y = 17 .............2 Eliminate y multiply (1)by -6 Multiply (2) by 5 42 x -30 y = -132 5 x + 30 y = 85 Add the two equations 47 x = -47 / 47 x = -1 plug value of x in (1) -7 x + 5 y = 22 7 + 5 y = 22 5 y = 22 -7 5 y = 15 y = 3
 Numbers_Word_Problems/580381: The sum of the digits in a two-digit number is 7. The new number obtained when the digits are reversed is 27 less than the original number. Find the original number1 solutions Answer 371221 by mananth(12270)   on 2012-02-29 20:12:47 (Show Source): You can put this solution on YOUR website!let the two digit number be xy x in the ten's place & y in units place x+y=7........................(1) 10y+x= 10x+y-27 9y-9x=27 /9 y-x=3........................(2) Add (1) & (2) 2y= 7+3 2y=10 y=5 x+y =7 y=5 so x= 2 The number is 25
 percentage/580373: William has scored a total of 235 points on the first three math tests taken in his mathematics class. If his mathematics tests are always worth 100 points, how many points must he earn on his next test in order to have an average of 80%? a.) 80 b.) 85 c.) 90 d.) 95 Thank you in advance! Btw, if you can, could you please also show step by step examples on how to solve and do slopes on charts?1 solutions Answer 371217 by mananth(12270)   on 2012-02-29 20:02:33 (Show Source): You can put this solution on YOUR website!assume he has to get x points to get an average of 80 His total points will be 235+x Number of tests will be 4 (235+x)/4 = 80 multiply by 4 235+x= 4*80 235+x= 320 x=320-235 x= 85 he has to get 85 points to average 80
 Linear-systems/580339: I need help with solving 3x+y=-8 and -2x-y=6 by substitution.1 solutions Answer 371210 by mananth(12270)   on 2012-02-29 19:26:27 (Show Source): You can put this solution on YOUR website!3x+1y= -8 .............1 y=-8-3x -2x-y= 6 Substitute y in (2) -2x-1(-8-3x)=6 -2x+8+3x=6 -2x+3x= -2 x=-2 / 1 x=-2 Plug the value of x in (1) 3x+y=-8 3*-2+y =-8 -6 + y = -8 1 y = -2 / 1 y= -2 m.ananth@hotmail.ca
 Linear-systems/580321: An airplane flew for 6 hours with a 22-km/h tail wind. the return flight against the same wind took 8 hours. find the speed of the plane in stil air. how do i set up this equation?1 solutions Answer 371207 by mananth(12270)   on 2012-02-29 19:20:11 (Show Source): You can put this solution on YOUR website!let the distance be y speed of plane in still air be x withwind speed = x+22 against wind speed = x-22 time with wind = 6 hours time against wind = 8 hours distance = speed & time (x+22)6 =Y (x-22)*8 y (x+22)*6 = (x-22)*8 6x+132=8x-176 8x-6x=132+176 2x=308 /2 x= 154 Speed of plane in still air = 154 mph
 test/580326: y= -3x y= x-8 Solving linear equations using the substitution method1 solutions Answer 371202 by mananth(12270)   on 2012-02-29 19:09:01 (Show Source): You can put this solution on YOUR website!y= -3x y= x-8 substitute y in the second equation -3x=x-8 add -x to both sides -4x=-8 /-4 x=2 plug x =2 in y=-3x y=-3*2 y=-6
 Surface-area/579969: What is an equation for the surface area of a cylinder whose height is equal to its diameter as a function on its volume? HELP!1 solutions Answer 371112 by mananth(12270)   on 2012-02-29 09:49:04 (Show Source): You can put this solution on YOUR website!Volume V = pi * r^2 * h h=2r V= pi * r^2*(2r)^2 V= pi*4r^4
 Linear-equations/579968: What is an equation of a line perpendicular to y=2x-7?1 solutions Answer 371111 by mananth(12270)   on 2012-02-29 09:46:13 (Show Source): You can put this solution on YOUR website!A perpendicular to this line can pass through this line at any point. unless we know the co-ordinates of that point we cannot find the equation in general the perpendicular will be y = -1/2 x + something because the slope is negative reciprocal of the given line
 Linear_Equations_And_Systems_Word_Problems/579946: Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 35 pounds of feed worth \$0.36 per pound by mixing one kind worth \$0.18 per pound with another worth \$0.53 per pound. How many pounds of the cheaper kind should they use in the mix? 1 solutions Answer 371110 by mananth(12270)   on 2012-02-29 09:37:26 (Show Source): You can put this solution on YOUR website!\$ ---------------- quantity Type I 0.18 ---------------- x pounds Type II 0.53 ------ 35 - x pounds Mixture 0.36 ---------------- 35 0.18x+0.53(35-x)=0.36*35 0.18x+0.53(35-x )=12.6 0.18x+ 18.55-0.53x=12.6 0.18x-0.53x=12.6--18.55 -0.35 x = -5.95 / -0.35 x=17 pounds\$ 0.18 Type I 18 pounds\$ 0.53 Type II m.ananth@hotmail.ca
 Linear-systems/579932: When using the addition method, I don't understand how to solve this problem: 4x+5/2y=11 3x-4/3y= -11 I did what my textbook suggested and tried to eliminate fractions, but ended up with something even more difficult: 24x+15y=11 18x-8y= -11 Please help I'm not sure what I should do! Christina1 solutions Answer 371103 by mananth(12270)   on 2012-02-29 09:00:30 (Show Source): You can put this solution on YOUR website!(4x+5)/2y=11 multipluy by 2y 4x+5 = 22y 4x-22y=-5.....................(1) (3x-4)/3y= -11 multiply by 3y 3x-4 = -33y 3x+33y=4.......................(2) 4 x -22 y = -5 .............1 3 x + 33 y = 4 .............2 Eliminate y multiply (1)by 3 Multiply (2) by 2 12 x -66 y = -15 6 x + 66 y = 8 Add the two equations 18 x = -7 / 18 x = - 7/18 plug value of x in (1) 4 x -22 y = -5 -14/9 -22 y = -5 -22 y = -5 -14/ 9 -22 y = -59/ 9 y = 14/47
 Linear_Algebra/579949: what is the slope of (7,0) and (0,-5)1 solutions Answer 371101 by mananth(12270)   on 2012-02-29 08:41:36 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 7 0 0 -5 slope m = (y2-y1)/(x2-x1) ( 7 - 0 )/( 0 - -5 ) ( -5 / -7 ) m= 5/7
 Linear-systems/579893: y-x=3x 2(x+y)=14-y 3a+6b=-15 a=-2b-5 pls. solve by substitution1 solutions Answer 371091 by mananth(12270)   on 2012-02-29 01:39:20 (Show Source): You can put this solution on YOUR website!y-x=3x add x to both sides y= 4x 2(x+y)=14-y substitute y 2(x+4x)=14+3x 10x=14+3x add -3x to both sides 7x=14 /7 x=2 when x =2 y = 4x = 4*2=8 (2,8)
 Triangles/579900: assume x is an acute angle in a right triangle sin x= 3/4; cos x how do i solve this? 1 solutions Answer 371090 by mananth(12270)   on 2012-02-29 01:35:35 (Show Source): You can put this solution on YOUR website!Sin x = 3/4 sin x = opposite side / hypotenuse=3/4 opposite side = 3 hypotenuse = 4 so adjacent side = sqrt(4^2-3^2) by hypotenuse theorem = Cos x = adjacent side / hypotenuse Cos x =
 Geometry_Word_Problems/579894: 1. From a second - story window directly across the street, the angle of elevation of the top of an office building is 57 degrees and 20 minutes and the angle of depression of the base is 18 degrees and 10 minutes. If the buildings are 38 m. apart, what is the height of the building ? 2. Mr. Reyes wanted to know the height of the tree. What he did was form a point A on the ground and observed that the angle of elevation of the top of the tree was 30 degrees. He then moved 50 ft. away from A. In his second position at B, the angle of elevation of the top of the tree was 22 degrees. Find the height of the tree.1 solutions Answer 371087 by mananth(12270)   on 2012-02-29 01:30:32 (Show Source): You can put this solution on YOUR website!angle of elevation = 57 deg 27 mins distance from the window = 38 m let the height of office be h Let the vertical heightbetween the window and the office be x feet. height of office upto level of window= Tan 57 27' = x/38 angle of depression is 18 10' vertical height of window from the ground = (h-x) Tan 18 10' = (h-x)/38 Tan 57 27'+Tan 18 10' = (h-x)/38 + x/38 Tan 57 27'+Tan 18 10'= h/38 -x/38 +x/38 Tan 57 27'+Tan 18 10' = h/38 Tan 57.45 + Tan 18.17 = h/38 1.57 + 0.33 = h/38 1.9= h/38 h= 1.9 *38 h= 72.2 m ---------------- From point A angle of elevation = 30 deg From point B angle of elevation = 22 deg distance AB = 50 ft. let height of tree be h and distance from point A be x Tan 30 = h/x Cot 30 = x/h Point B Tan 22 = h/(50+x) cot 22 = (50+x)/h Cot 22- Cot 30 = 50/h +x/h - x/h 2.475-1.733= 50/h 0.742= 50/h h= 50/0.742 67.38 feet
 Numbers_Word_Problems/579854: I need help with the following problem: Three times the smallest of 3 consecutive even integers plus the sum of the other 2 is 66. Find the numbers. 1 solutions Answer 371081 by mananth(12270)   on 2012-02-28 22:41:34 (Show Source): You can put this solution on YOUR website!let the consequtive even numbers be x, x+2, x+4 3x+(x+2)+(x+4)=66 3x+x+2+x+4=66 5x+6=66 add -6 to both sides 5x=60 x=60/5 x= 12 The numbers are 12,14,16
 Triangles/579844: What is the value of x if the triangle is 15 square yards? Base of the triangle is x-5 Height of the triangle is 2x + 11 solutions Answer 371080 by mananth(12270)   on 2012-02-28 22:38:20 (Show Source): You can put this solution on YOUR website!Area of triangle = 1/2 * base * height 15= 1/2 * (x-5)(2x+1) multiply by 2 30 = (x-5)(2x+1) 30= x(2x+1)-5(2x+1) 30=2x^2+x-10x-5 30=2x^2-9x-5 add -30 0= 2x^2-9x-35 2x^2-9x-35=0 2x^2-14x+5x-35=0 2x(x-7)+5(x-7)=0 (x-7)(x+5)=0 x=7 OR -5 x=7 since the lengths cannot be negative.
 Geometry_Word_Problems/579849: If each side of a square is increased by 3 cm, the total area of both the new square and the original square will be 617 cm2 . Approximate to the nearest tenth of a centimeter the length of each side of the original square.1 solutions Answer 371077 by mananth(12270)   on 2012-02-28 22:29:19 (Show Source): You can put this solution on YOUR website!let side of square be x area = l*w= x^2 3 is added to its side Area of this square = (x+3)^2 x^2+(x+3)^2= 617 x^2+x^2+6x+9=617 2x^2+6x-617+9=0 2x^2+6x-608=0 /2 x^2+3x-304 =0 x^2+19x-16x-304=0 x(x+19)-16(x+19)=0 (x+19)(x-16)=0 x=-19 OR 16 ignore negative the length of side = 16cm
 Linear_Equations_And_Systems_Word_Problems/579833: if henry has 45 nickels and dimes totaling \$2.90, write an equation that can be used as part of a system of equations to determine how many nickels (n) and dimes (d) henry has.1 solutions Answer 371074 by mananth(12270)   on 2012-02-28 22:24:53 (Show Source): You can put this solution on YOUR website!let x be the nickels y the dimes x+y=45 0.05x+0.1y = 2.90 solve to get x & y