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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) About Me  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) About Me  on 2012-02-14 22:06:58 (Show Source):
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"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) About Me  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) About Me  on 2012-02-14 20:33:59 (Show Source):
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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 %09sqrt%28%09841%09%29=%0929%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
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 110
1 solutions

Answer 368533 by mananth(12270) About Me  on 2012-02-14 20:07:22 (Show Source):
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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) About Me  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) About Me  on 2012-02-14 20:00:55 (Show Source):
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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) About Me  on 2012-02-14 19:47:53 (Show Source):
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%285%2F%28y-3%29%29%2B+%2810%2F%28y%5E2-y-6%29%29+=+%28y%2F%28y%2B2%29%29
%285%2F%28y-3%29%29%2B+%2810%2F%28%28y-3%29%28y%2B2%29%29%29+=+%28y%2F%28y%2B2%29%29
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=10
1 solutions

Answer 368445 by mananth(12270) About Me  on 2012-02-14 08:54:25 (Show Source):
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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) About Me  on 2012-02-14 08:36:42 (Show Source):
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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 = 19
1 solutions

Answer 368443 by mananth(12270) About Me  on 2012-02-14 08:25:50 (Show Source):
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-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) About Me  on 2012-02-14 08:07:13 (Show Source):
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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) About Me  on 2012-02-14 08:04:43 (Show Source):
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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) About Me  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) About Me  on 2012-02-12 22:54:32 (Show Source):
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let t be the tail wind speed
Let theta be the angle
Speed alpha+%28t%2F%28sqrt%28theta%29%29%29
Speed= +%28k%2At%2F%28sqrt%28theta%29%29%29
20=k%2A10%2Fsqrt%2825%29
20=k*10/5
20=2k
/2
k=10
Speed =+%28k%2At%2F%28sqrt%28theta%29%29%29
speed = 10%2A5%2F%28sqrt%2836%29%29
speed= 25%2F3
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) About Me  on 2012-02-12 22:33:28 (Show Source):


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) About Me  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 + 9
1 solutions

Answer 368224 by mananth(12270) About Me  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) About Me  on 2012-02-12 20:26:56 (Show Source):
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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) About Me  on 2012-02-12 20:03:50 (Show Source):
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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) About Me  on 2012-02-12 20:02:12 (Show Source):
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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
thanks
1 solutions

Answer 368105 by mananth(12270) About Me  on 2012-02-12 04:55:59 (Show Source):
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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 x
1 solutions

Answer 368104 by mananth(12270) About Me  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 = %281%2F2%29%2A%28x%2B4%2Bx%2B7%29%2Ax

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) About Me  on 2012-02-10 22:50:38 (Show Source):
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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+28xy
1 solutions

Answer 367963 by mananth(12270) About Me  on 2012-02-10 22:39:56 (Show Source):
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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) About Me  on 2012-02-10 22:37:15 (Show Source):
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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= sqrt%0936%09
leg1= 6 ft


percentage/571132: what is the percentage discount if you take 10 dollars from 40 dollars
1 solutions

Answer 367960 by mananth(12270) About Me  on 2012-02-10 22:29:08 (Show Source):
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x% of 40 =10
%28x%2F100+%29%2A+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) About Me  on 2012-02-10 22:26:49 (Show Source):
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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) About Me  on 2012-02-10 22:24:40 (Show Source):
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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) About Me  on 2012-02-10 22:19:56 (Show Source):
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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
Thanks
1 solutions

Answer 367956 by mananth(12270) About Me  on 2012-02-10 22:11:20 (Show Source):
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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