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# Recent problems solved by 'mananth'

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 Linear-equations/572898: Write the equation of the line that passes through the given point and is perpendicular to the given line. Write the answer in slope-intercept form. P(-9, 7), y + 8x = -19 1 solutions Answer 368583 by mananth(12270)   on 2012-02-14 22:24:06 (Show Source): You can put this solution on YOUR website!8x +y = -19 Find the slope of this line y = -8x-19 Compare this equation with y=mx+b, m= slope , & b= y intercept slope m = -8 The slope of a line perpendicular to the above line will be the negative reciprocal 1/8 m1*m2=-1 The slope of the required line will be 1/8 m= 1/8 ,point ( -9 , 7 ) Find b by plugging the values of m & the point in y=mx+b 7 = -9/ 8 + b b= -65/8 m= 1/8 The required equation is y = 1/ 8x-65/ 8 m.ananth@hotmail.ca
 percentage/572928: Could someone please help with this problem? "25 people like. 35 people don't like. What % like?"1 solutions Answer 368576 by mananth(12270)   on 2012-02-14 22:06:58 (Show Source): You can put this solution on YOUR website!"25 people like. 35 people don't like 25+35=60 (25/60)*100= 41.67% like
 Word_Problems_With_Coins/572915: a newspaper carrier has \$4.25 in change. He has seven more quarters than dimes but four times as many nickels as quarters. How many coins of each type does he have?1 solutions Answer 368571 by mananth(12270)   on 2012-02-14 21:58:34 (Show Source): You can put this solution on YOUR website!let dimes be x quarters = x+7 nickels = 4(x+7) the value = \$4.25 = 425cents value equation 10x+25(x+7)+5*4(x+7)=425 10x+25x+175+20x+140=425 55x+315=425 55x= 425-315 55x=110 x= 2 2 dimes quarters =(2+7)=9 nickels = 4(x+7)=4*9=36 CHECK 36*5 + 9*25+2*10= 180+225+20=425
 Travel_Word_Problems/572820: Travis paddles his kayak in the harbor at Morro Bay, California, where the incoming tide has caused a current in the water. From the point where he enters the water, he paddles 2 miles against the current, then turns around and paddles 2 miles back to where he started. His average speed when paddling with the current is 3 miles per hour faster than his speed against the current. If the complete trip (out and back) takes him 1.4 hours, find his average speed when he paddles against the current.1 solutions Answer 368542 by mananth(12270)   on 2012-02-14 20:33:59 (Show Source): You can put this solution on YOUR website!2/y + 2/(y-3)=1.4 2y-6+2y=1.4 4y-6=7/5(y(y-3) 5(4y-3)=7y^2-21y 20y-30=7y^2-21y 7y^2-41y+30=0 a= 7 , b= -41 , c= 30 b^2-4ac= 1681 + -840 b^2-4ac= 841 x1=( 41 + 29 )/ 14 x1= 5.00 x2=( 41 -29 ) / 14 x2= 0.86 speed with current = 5 mph speed against = 2 mph
 Linear_Equations_And_Systems_Word_Problems/572851: The sum of two numbers is 155. Their difference is 65. What are the numbers? Choose one answer. a. 40 and 115 b. 35 and 120 c. 55 and 100 d. 45 and 1101 solutions Answer 368533 by mananth(12270)   on 2012-02-14 20:07:22 (Show Source): You can put this solution on YOUR website!d. 45 and 110
 Percentage-and-ratio-word-problems/572864: Here is the word problem I am trying to write an equation for: " Mike received 73%, 71%, 79% and 75% on his first four math tests. What grade on his fifth test would allow him to make an average of at least 75%? Assume the test scores are whole numbers." Here is what I have tried so far: Let X represent fifth test score (73 +71+79+75 + X)/5 = 75 (298 + X)/5 = 75 59.6 + 1/5X = 75 X = (75 - 59.6)/5 X = 3.08 I know this is not correct but I am not sure what is wrong with my equation. Any help showing me how to set up the right equation would really help me. thanks 1 solutions Answer 368531 by mananth(12270)   on 2012-02-14 20:04:44 (Show Source): You can put this solution on YOUR website!Here is what I have tried so far: Let X represent fifth test score (73 +71+79+75 + X)/5 = 75 (298 + X)/5 = 75 59.6 + (1/5)X = 75 X = (75 - 59.6)*5 X = 77
 Miscellaneous_Word_Problems/572856: A car travels 400 miles on level terrain in the same amount of time it travels 160 miles on mountainous terrain. If the rate of the car is 30 miles per hour less in the mountains than on level ground, find its rate in the mountains.1 solutions Answer 368528 by mananth(12270)   on 2012-02-14 20:00:55 (Show Source): You can put this solution on YOUR website!Level x mph Mountain -30 slower x -30 mph Level 400 miles Mountain 160 miles Level time = Mountain time t=d/r 400 / x = 160 /( x -30 ) cross multiply 400 ( x -30 ) = 160 x 400 x + -12000 = 160 x 400 x - 160 x = 12000 400 x = 12000 / 360 x = 60 mph SPEED ON LEVEL speed in mountains = 60-30 = 30 MPH
 Polynomials-and-rational-expressions/572842: solve the equation for y (5/y-3)+ (10/y^2-y-6) = (y/y+2)] (five over y-3) plus (10 over y squared minus y minus 6) equals (y over y+2) 1.Im not sure if i did it right, i found the least common denominator which is (y-3)(y+2) and multiplied to the missing part of the least common denominator to the top to get: 5(y+2)/(y-3)(y+2) - 10/(y-3)(y+2) = y(y-3)/(y+2)(y-3) 2.Then i combined like terms and simplified to get 5y+20/(y-3)(y+2) = (y^2)-3y/(y+2)(y-3) 3. My final answer was 5y(y+4)/ (y+2)(y-3) Is it correct? 1 solutions Answer 368522 by mananth(12270)   on 2012-02-14 19:47:53 (Show Source): You can put this solution on YOUR website! Multiply by (y-3)(y+2) 5(y+2) +10 =y(y-3) 5y+10+10=y^2-3y 5y+20=y^2-3y y^2-8y-20=0 y^2-10y+2y-20=0 y(y-10)+2(y-10)=0 (y-10)(y+2)=0 y=10 OR -2
 test/572566: Substition method problem: 2x-5y=25 X-2y=101 solutions Answer 368445 by mananth(12270)   on 2012-02-14 08:54:25 (Show Source): You can put this solution on YOUR website!x-2y =10 .............1 y=10-x ---------2 Substitute y in (2) 2x-5y=25 2x-5(10 -x)= 25 2x-50+5x= 25 2x+5x =75 7x=75 / 7 x= 75/ 7 Plug the value of x in (1) 2x-5y = 25 2*75/ 7-5y=25 150/ 7 + -5y = 25 -5 y = 25/ 7 / -5 y= - 5/ 7 m.ananth@hotmail.ca
 Angles/572564: help me please for the solution,,,,,,, three angles of a triangle measure x+10, 2x+15, and 3x-13. what are the degree measures of the angles of the triangle?1 solutions Answer 368444 by mananth(12270)   on 2012-02-14 08:36:42 (Show Source): You can put this solution on YOUR website!x+10, 2x+15, and 3x-13. what are the degree measures of the angles of the triangle? The sum of the measures of the angles of triangle = 180 degrees x+10+2x+15+3x-13=180 6x+12=180 -12 -12 6x=168 /6 x=28 plug x in the angles and you will get the measures x+10 = 28+10=38 2x+16 = 2*28+15=71deg you work out the third
 Linear-equations/572513: I need help with the following problem: Solve by the subsitution method. 9x + 2y = -37 -3x + y = 191 solutions Answer 368443 by mananth(12270)   on 2012-02-14 08:25:50 (Show Source): You can put this solution on YOUR website!-3 x + 1 y = 19 .............1 1 y = 19 3 x ---------2 / 1 = y = 19 3 x Substitute y in (2) 9 x + 2 ( 19 3 x ) = 9 x + 38 + 6 x = -37 9 x 6 x = -75 15 x = -75 / 15 x= -5 Plug the value of x in (1) 9 x + 2 y = -37 9 * -5 + 2 y = -37 -45 + 2 y = -37 2 y = 8 / 2 y= 4 m.ananth@hotmail.ca
 Geometry_Word_Problems/572544: A square has a perimeter of 80 meters. what is its area? Please answer with a representation and checking.1 solutions Answer 368441 by mananth(12270)   on 2012-02-14 08:07:13 (Show Source): You can put this solution on YOUR website!Square - all sides are equal perimeter = 80 side length = 80/4 = 20m Area = side ^2 area = 20*20 = 400 sq.m
 Linear-equations/572546: how to find the y-intercept, slope and direction of the line of No. 1.) y=2x No. 2.) y=-2x+2 No. 3) y=1/2x-3 No. 4.)x-3y=5 And the last one No. 5.) 2x+4y=6 PLEASE ANSWER MY QUESTION. THANK YOU VERY MUCH. IT WILL BE VERY MUCH HELPFUL IF YOU ANSWER IT BECAUSE I CAN'T UNDERSTAND IT. 1 solutions Answer 368440 by mananth(12270)   on 2012-02-14 08:04:43 (Show Source): You can put this solution on YOUR website! 1.) y=2x compare with y= mx +c m= slope = 2 y intercept = c= 0 since the slope is positive the line rises from the left to the right. No. 2.) y=-2x+2 m=-2 = slope y intercept . Plug x = 0 y= 2 so y intercept = 2 the line passes through the y axis at 2 and goes up from 4th quadrant to 2nd. Quadrant No. 3) y=(1/2)x-3 slope = 1/2 y intercept =-3 rises up from III quadrant to I quadrant cutting the y axis at -3 No. 4.)x-3y=5 3y=x-6 y=(1/3)x-2 slope = 1/3 y intercept = -2 rises up from III quadrant to I quadrant cutting the y axis at -2 And the last one No. 5.) 2x+4y=6
 Triangles/571966: i have a question that says "Given the lengths of the three sides, tell whether each of these are right triangles or not" a)8,15,17 b)9,10,15 i am not sure how to work this out at all help?1 solutions Answer 368250 by mananth(12270)   on 2012-02-13 01:13:55 (Show Source): You can put this solution on YOUR website!If they are right triangles then it will follow the Pythagoras theorem The longest side is always the hypotenuse in a right triangle leg1^2+leg2^2=hypotenuse^2 leg1 & leg2 are the sides forming the right angle. 8,15,17 17 has to be the hyptenuse if it is a right triangle 8^2+15^2=289 17^2= 289 hence it is a right triangle. you can verify the second
 Travel_Word_Problems/571891: Mary made a 205 mile bike trip in 8 hours. Her speed varied directly as the speed of the tailwind and inversly as the square root of the degree of the incline. She traveled at 20 mph when the tailwind was 10 mph and the incline was 25 degrees.How fast (to the nearest tenth)would she travel with a 5 mph tailwind on a 36 degree incline? 1 solutions Answer 368243 by mananth(12270)   on 2012-02-12 22:54:32 (Show Source): You can put this solution on YOUR website!let t be the tail wind speed Let be the angle Speed Speed= 20= 20=k*10/5 20=2k /2 k=10 Speed = speed = speed= speed= 8.3 mph
 Linear-equations/571922: Dorothy invested her income tax refund in two separate accounts. She invested part of it at 7% and triple that amount at 11%. The total first-year interest from the two investments was \$120. How much did she invest at 7%? a. \$300 at 7% b. \$150 at 7% c. \$200 at 7% d. \$250 at 7% 1 solutions Answer 368240 by mananth(12270)   on 2012-02-12 22:33:28 (Show Source): You can put this solution on YOUR website!300 @ 7%
 Graphs/571903: Hello I've got 4 questions I really need your help with. Please help me. I need it asap. Thank you 1. Find the y-intercept and the x-intercept for the equation. -10x+y=14 What is the y-intercept? What is the x-intercept? 2. Graph the equation and identify the y-intercept. x+3y=12 3. Solve. 8y-8<7y-1 4. Find the slope if it exists. x+7y=14 m= 1 solutions Answer 368231 by mananth(12270)   on 2012-02-12 22:02:41 (Show Source): You can put this solution on YOUR website!1. Find the y-intercept and the x-intercept for the equation. -10x+y=14 rewrite equation in slope intercept form y=10x+14 compare with y= mx+b What is the y-intercept? 14 What is the x-intercept? plug y = 0 -10x=14 /-10 x=14/-10 x=-7/5 2. Graph the equation and identify the y-intercept. x+3y=12 3y=-x+12 when x= 0 y= 4 ,( 0 , 4 ) when y = 0 x= 12 ,( 12 , 0 ) y intercept=4 3. Solve. 8y-8<7y-1 +8 +8 8y<7y-1+8 8y<7y+7 /8 y<(7/8)y+7/8 4. Find the slope if it exists. x+7y=14 7y=-x+14 /7 y=-(1/7)x+2 m=-1/7
 Inequalities/571910: find the slope y = 0.25x + 91 solutions Answer 368224 by mananth(12270)   on 2012-02-12 21:38:37 (Show Source): You can put this solution on YOUR website!y = 0.25x + 9 compare this equation with slope intercept equation y=mx+b m= 0.25 = slope
 Rectangles/571847: In a rectangle, the length is fifthteen less than three times the width. If the perimeter is 34, what is the length?1 solutions Answer 368205 by mananth(12270)   on 2012-02-12 20:26:56 (Show Source): You can put this solution on YOUR website! Perimeter = 34 feet Length 1 ( 3 x -15 ) Width = 1 x ft Perimeter =2(L+W) Perimeter = 2((3x-15)+x) Perimeter = 2((3x-15+x) Perimeter = 2(6x-15+2x) 34=16x-30 34-=16x 34+30=8x 64=8x x=8ft Width plug x in the expression for length(3x-15) we get( 24-15) Length= =9 feet
 Geometry_Word_Problems/571849: A wire of length 8x is bent into the shape of a square. Express the area A of the square as a function of x.1 solutions Answer 368200 by mananth(12270)   on 2012-02-12 20:03:50 (Show Source): You can put this solution on YOUR website!Perimeter of square = 8x so length of side of square = 8x/4 = 2x Area = L*W = 2x*2x = 4x^2 sq. units
 Equations/571844: y + 6 = 3y - 10 -y -y --------------- 6 = 2y -10 +10 +10 --------------- 16 = 2y ------- 2 2 y= 8 but i needa do a check on this? 1 solutions Answer 368199 by mananth(12270)   on 2012-02-12 20:02:12 (Show Source): You can put this solution on YOUR website!You are right
 Linear_Equations_And_Systems_Word_Problems/571497: hey i really need some help with this question i have been trying for hours and still can't get it one number is nine less than twice another, and their sum is 42. find the two numbers thanks1 solutions Answer 368105 by mananth(12270)   on 2012-02-12 04:55:59 (Show Source): You can put this solution on YOUR website!let one number be x other number = 2x-9 x+2x-9=42 3x-9=42 +9 3x=51 /3 x=17 other number = 2x-9 2(17)-9=25 17 & 25 are the numbers
 Geometry_Word_Problems/571507: the lower base of a trapezoid is x+7 cm and the upper base is x+4 cm. if the distance between them is x cm and the area of the trapezoid is 20 sq. cm, find x1 solutions Answer 368104 by mananth(12270)   on 2012-02-12 04:50:10 (Show Source): You can put this solution on YOUR website!The area of a trapezoid is = 1/2 the sum of parallel sides * the height Area = Simplify (x^2+11x)/2 = 20 2x^2+11x=40 2x^2+11x-40=0 2x^2+16x-5x-40=0 2x(x+8)-5(x+6)=0 (2x+6)(x-5)=0 2x+6 =0 2x=-6 x=-3 OR x=5
 Linear-equations/571138: I need help solving this word problem...I have been trying for 2 hours. In 1920, the record for a certain race was 45.4 sec. In 1970, it was 44.4 sec. Let R(t)=the record in the race and t=the number of years since 1920. Find a linear function that fits the data R(t)= Round to nearest hundredth What is the predicted record for 2003____sec What is the predicted record for 2006? In what year will the predicted record be 43.50 seconds? Thanks so much!1 solutions Answer 367965 by mananth(12270)   on 2012-02-10 22:50:38 (Show Source): You can put this solution on YOUR website!year Record time 1920 45.4 seconds 1970 44.4 seconds Difference 50 -1 rate of reduction per year =-1 /50 = -0.02 R(t)= 45.4-0.020t 2003 t=83 R(t)= 45.4 + -0.020 * 83 R (83)= 43.74 seconds ------------ R(t)= 45.4-0.02t 43.5=45.4-0.02t 45.4-43.5=0.02t 1.9=0.02t t= 1.9/0.02 t=95 years 1920 +95 = 2015 year 2015 it will bve 43.5 seconds
 Polynomials-and-rational-expressions/571134: factor completely 7x^2-7x^2y-28x+28xy1 solutions Answer 367963 by mananth(12270)   on 2012-02-10 22:39:56 (Show Source): You can put this solution on YOUR website!7x^2-7x^2y-28x+28xy 7x^2(1-y)-28x(1-y) (1-y)(7x^2-28x) (1-y)*7x(x-4) 7x(x-4)(1-y)
 Pythagorean-theorem/571131: The hypotenuse of angle XYZ is 10 and length of one of its legs is 8. Find the length of the other leg. Show diagram and calculation.1 solutions Answer 367962 by mananth(12270)   on 2012-02-10 22:37:15 (Show Source): You can put this solution on YOUR website!Pythagoras theorem Hypotenuse ^2 = leg1^2+leg2^2 Leg1^2= Hypotenuse^2-leg2^2 Hypotenuse = 10 ft leg1= 8 ft leg2= ? ft Leg1^2= Hypotenuse^2-leg2^2 leg1^2= 10 ^2 - 8 ^2 leg1= leg1= 6 ft
 percentage/571132: what is the percentage discount if you take 10 dollars from 40 dollars1 solutions Answer 367960 by mananth(12270)   on 2012-02-10 22:29:08 (Show Source): You can put this solution on YOUR website!x% of 40 =10 x=(100*10)/40 x=25 25 %
 Functions/571130: Sorry I forgot to write out the pair of lines 3x+8=y 2y=6x-3 are these lines parallel?1 solutions Answer 367959 by mananth(12270)   on 2012-02-10 22:26:49 (Show Source): You can put this solution on YOUR website!3x+8=y y=3x+8 2y=6x-3 /2 y=3x-(3/2) compare both the lines with y= mx+b m the slope of both lines are 3 so the lines are parallel
 Linear_Equations_And_Systems_Word_Problems/571115: The length of a rectangle is fixed at 12 cm. What widths will make the perimeter greater than 86 cm? The width must be greater the ___ cm.1 solutions Answer 367958 by mananth(12270)   on 2012-02-10 22:24:40 (Show Source): You can put this solution on YOUR website!Perimeter = 2L+2W perimeter >86 L=12 2L=24 24+2W>86 -24 2w>62 /2 w>31 cm
 Pythagorean-theorem/571125: Name three(3) sets of Pythagorean triplets and prove that they are indeed Pythagorean triplets.1 solutions Answer 367957 by mananth(12270)   on 2012-02-10 22:19:56 (Show Source): You can put this solution on YOUR website!There are many many triplets PYthagoras theorem states the sum of squares of the adjacent sides = hypotenuse^2 leg1^2+leg2^2=hypotenuse^2 In a right triangle the largest side is aways the hypotenuse. First the basic one 3,4,5 3^2+4^2=5^2 (+16=25 25=25 ---- 5,12,13 5^2+12^2=13^2 25+144=169 169=169 ------------- Third one you can find
 Graphs/571119: What is the slope and y-intercept of 30x+5y=20 Thanks1 solutions Answer 367956 by mananth(12270)   on 2012-02-10 22:11:20 (Show Source): You can put this solution on YOUR website!30x+5y =20 5y= 20-30x /5 y=4-6x y=-6x+4 compare with y = mx+b m=-6 the slope b= 4 = y intercept