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Multiply and Simplify (2t+3)^2 - (t-1)(t+1)
Please show me the steps to solving this.
What form is used?
How do I know what to do first?
Thank you,
Jill
1 solutions
Answer 253981 by mananth(12270)   on 2010-10-13 08:53:49 (Show Source):
You can put this solution on YOUR website!(2t+3)^2 - (t-1)(t+1)
(2t+3)^2-(t^2-1) .............( (a+b)(a-b)= a^2-b^2) here a =t & b =1)
(4t^2+12t+9)-(t^2-1)...........( (a+b)^2 = a^2+2ab+b^2; a= 2t and b =3)
4t^2+12t+9-t^2+1
group the similar terms & simplify
4t^2-t^2+12t+9+1
3t^2+12t+10
...
In such problems first solve the terms in the brackets and then simplify
..
m.ananth@hotmail.ca
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Linear_Equations_And_Systems_Word_Problems/355671: If the numerator and denominator of a fraction is increased by 2 the fraction beomes 5/7 and if the denominator is decreased by 1 the fraction becomes 3/4. Find fraction.
1 solutions
Answer 253951 by mananth(12270) on 2010-10-13 05:43:28 (Show Source):
You can put this solution on YOUR website!let x be the numerator
y the denominator
x+2/y+2 =5/7
7(x+2)=5(y+2)
7x+14=5y+10
7x-5y=-4.....................1
..
x/y-1 = 3/4
4x=3(y-1)
4x=3y-3
4x-3y=-3.....................2
..
multiply equation1 by -4 and equation 2 by 7 and add them to eliminate x
-28x+20y=16
28x-21y=-21
-y=-5
y=5
..
plug value of y in equation 1
7x-25=-4
7x=21
/7
x=3
so the fraction is 3/5
...
m.ananth@hotmail.ca
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Volume/355663: The surface area of a cube is 294 cm squared. What is the length of its side?
1 solutions
Answer 253950 by mananth(12270) on 2010-10-13 05:36:04 (Show Source):
You can put this solution on YOUR website!the cube has 6 faces
let length of side be l
area of one face = l^2
area of 6 faces = 6l^2
6l^2=294
l^2=294/6
l^2=49
l=7 cm
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m.ananth@hotmail.ca
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Age_Word_Problems/355636: Please Help me solve this problem.
Maylen is 20 years older than her daughter Hazel. In ten years time she will be twice as old as her daughter. How old are Maylene and Hazel ?
Thanks ~
1 solutions
Answer 253949 by mananth(12270) on 2010-10-13 05:26:02 (Show Source):
You can put this solution on YOUR website!let hazel be x years
maylene = x+20
...
ten years later their ages will be
hazel = x+10
Maylene = x+20+10=x+30
x+30=2(x+10)
x+30 = 2x+20
2x-x=20-10
x=10 hazels age
Maylene = x+20
Maylene will be 30 years
...
m.ananth@hotmail.ca
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Angles/355656: What is the measure of an angle if the measure of its supplement is 39 degree more than twice the measure of its complement?
1 solutions
Answer 253948 by mananth(12270) on 2010-10-13 05:06:42 (Show Source):
You can put this solution on YOUR website!let the angle be x
the complement will be 90-x deg
the supplement = 180-x
..
180-x = 2(90-x)+39
180-x=180-2x+39
180-180-39=-2x+x
-x=-39
x= 39 the measure of the angle
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m.ananth@hotmail.ca
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Geometry_Word_Problems/355651: PROBLEM 1. If the area of an equilateral triangle is 36 suare centimeter, find its side length and height.
PROBLEM 2. If a gallon of paint covers 400 square feet, how much gallons are needed to paint two walls each having dimensions 38ft x 25ft.
1 solutions
Answer 253947 by mananth(12270) on 2010-10-13 05:01:28 (Show Source):
You can put this solution on YOUR website!the area of equilateral triangle = 36m^2
the area = sqrt3/4 * s^2=36
4*36/sqrt3=s^2
144/sqrt3 =s^2
83.13=s^2
s= 9.11 cm
...
dimensions wall = 38 by 25
Area = 38*25= 950 ft^2
2 walls = 1900 ft^2
..
area = 1900 ft^2
400ft2 /gallon
..
1900/400 = 4.75 gallons
m.ananth@hotmail.ca
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Percentage-and-ratio-word-problems/355644: A shirt is on sale at a 20% discount. The sales tax is 5%. A new sales clerk simply takes 15% off the original price. Is this correct? Why?
1 solutions
Answer 253946 by mananth(12270) on 2010-10-13 04:41:46 (Show Source):
You can put this solution on YOUR website!let the shirt cost $x
20% discount
so the shirt will cost 0.8x
..
add 5%sales tax on 0.8x
0.05*0.8x=0.04x
0.8x+0.04x=0.84x is the price...
...
price is $x
less 15%
0.15x is reduced.
so the price will be x-0.15x
=0.85x.
This is incorrect. He will be charging more.
...
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/355645: The price of regular rice is $1 per pound; that of premium rice is $2. Mix 300 pounds of regular rice with 400 pounds of premium rice. What is the price of the mixture?
1 solutions
Answer 253945 by mananth(12270) on 2010-10-13 04:32:28 (Show Source):
You can put this solution on YOUR website!The price of regular rice is $1 per pound; 300 pounds
that of premium rice is $2. :: 400 pounds
...
300*1 +400*2 = 700*x
300+800= 700x
1100=700x
/700
1100/700 =x
x=1.57
Mix cost = $1.57
...
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/355647: Mary and Jane shop at an office supplies store. Mary spends $20 on 10 pens and
10 notebooks. Jane spends $15 on 5 pens and 8 notebooks. Find the prices of the
stationery.
1 solutions
Answer 253943 by mananth(12270) on 2010-10-13 04:20:29 (Show Source):
You can put this solution on YOUR website!let price of pen be $x
price of notebook be $y/10
...
10x+10y=20
x+y=2.......................1
5x+8y=15....................2
multiply equation 1 by -5 and add it to equation2
-5x-5y=-10
add to 2
8y-5y=15-10
3y=5
/3
y = 5/3
...
plug value of y in equation 1
x+5/3 = 2
(3x+5)/3=2
3x+5 =6
3x=6-5
3x=1
x= 0.33
...
Pen costs 33 cents
notebook costs $1.67
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m.ananth@hotmail.ca
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Angles/355631: A triangle has three angles A, B,C. Angle A is 38 less than three times angle C, and angle B is 14 more than twice angle C. Find the measures of all the angles.
1 solutions
Answer 253941 by mananth(12270) on 2010-10-13 02:32:19 (Show Source):
You can put this solution on YOUR website!let angle c be x deg
Angle b =2x+14
Angle a= 3x-38
...
x+2x+14+3x-38=180
6x-24=180
6x=204
/6
x=34 deg. Angle C
Angle b = 2x+14 = 68+14=82 deg
Angle a =3x-38=102-38=64 deg
...
m.ananth@hotmail.ca
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Linear_Algebra/355612: HARD!! algebra (Linear Systems) question?
An Airplane cruises at 120km/h in still air. One day, when the wind was blowing steady rom the west, the airplane travelled west (flying into the wind) and landed at its desination after 1.5h. The airplane's return trip (flying with the wind) was only 1.0 h long. On both legs, the airplane travelled at its cruising speed. (meausred with respect to the air surrounding the airplane).
Part A
Write a System of equations that would allow you to determine the speed of the wind blowing that day and the distance traveled each way
Part B
When solving the system of equations graphically, what equations would you enter into the equation editor (to make graphs on your calculator)
Part C
Indicate what the X and the Y represent
Well.... im stumpped...
y=1.5(120 - x)= 180 -1.5x ?? then what
y=1.0(120 + x)=120 + 1.0x ??
I'm so confused please can someone help me:(
1 solutions
Answer 253940 by mananth(12270) on 2010-10-13 02:23:53 (Show Source):
You can put this solution on YOUR website!speed of plane in still air = 120mph
let speed of wind be x mph
against wind the speed will be 120-x mph
with wind the speed will be 120+x mph
..
distance trraveled forward = (120-x)*1.5
distance traveled return = (120+x)*1
x+120 = 180-1.5x
2.5x=60
x=60/2.5
x= 24 mph the speed of wind
...
the x axis represents the wind speed
the y axis represents the cruising speed.
Green line represents against wind
red line represents with wind.
they intesect at x = 24 the wind speed
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Numbers_Word_Problems/355609: if the digits of a two digit number are reversed, the number is increased by 36. The sum of the digit in the number is three times their difference. What is the number?
1 solutions
Answer 253927 by mananth(12270) on 2010-10-13 00:12:41 (Show Source):
You can put this solution on YOUR website!let the digit in tens place be x
& in the units place be y
..
10y+x=10x+y+36
9y-9x=36
/9
y-x=4.....................1
...
x+y=3(x-y)
x+y=3x-3y
2x-4y=0
/2
x-2y=0....................2
Add equation1 & 2
-y=4
y=-4
plug value of y in 1
y-x=4
-4-x=4
x=-8
...
-84 is the number
...
m.ananth@hotmail.ca
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Proportions/355610: I am having trouble getting the correct answer to this problem. The problem is
1/x+3 = -2x/x+5
This is how I worked it. The answer is -5/2, -1 but I keep getting -5/6
x+3(-2x) = x+5(1)
x-6x = x+5
-6x = 5
divide through by -6 and get -5/6.
What am I missing?
1 solutions
Answer 253924 by mananth(12270) on 2010-10-13 00:04:17 (Show Source):
You can put this solution on YOUR website!1/x+3 = -2x/x+5
..
x+5=-2x(x+3)
x+5=-2x^2-6x
-5
x+5-5 = -2x^2-6x-5
x=-2x^2-6x -5
2x^2+7x+5=0
2x^2+2x+5x+5=0
2x(x+1)+5(x+1)=0
(2x+5)(x+1)=0
x= -5/2 OR x=-1
...
m.ananth@hotmail.ca
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Travel_Word_Problems/355504: two motorcycles travel toward each other from Chicago and Indianapolis, which are about 350 km apart, at rates of 110 and 90 km/h. They started at the same time. in how many hours will they meet?
1 solutions
Answer 253912 by mananth(12270) on 2010-10-12 23:17:16 (Show Source):
You can put this solution on YOUR website!speed of A = 110
speed of B = 90
...
they are travelling towards each other.
add the speeds
110+90 =200 km/h
...
distance = 350 km
..
time = distance/speed
time = 350/200
=1.75 hours
mananth@hotmail.ca
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Linear_Algebra/355553: What is the equation of the line that passes through the points (−2, 2) and (0, 5)?
1 solutions
Answer 253908 by mananth(12270) on 2010-10-12 23:03:44 (Show Source):
You can put this solution on YOUR website!points (-2,2) (0,5)
slope m = y2-y1/x2-x1
slope = 5-2/0+2
= 3/2
...
equation = (y-y1)=m(x-x1)
use the first point
(y-2)=3/2(x+2)
2(y-2)=3(x+2)
2y-4 = 3x+6
2y= 3x+10
y = 3/2 *x +5is the equation of the line
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Equations/355530: A side of a square is 10 meters longer than the side of an equilateral triangle. The perimeter of the square is 3 times the perimeter of the triangle. Find the length of each side of the triangle.
1 solutions
Answer 253886 by mananth(12270) on 2010-10-12 21:29:53 (Show Source):
You can put this solution on YOUR website!square side = 10 meters
perimeter of square = 4*L = 40 meters
...
let side of triangle be x
perimeter of triangle = 3x
...
40 = 3x *3
9x =40
x= 40/9
x= 4.44 meters length of side of triangle
..
m.ananth@hotmail.ca
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Mixture_Word_Problems/355521: a painter needs to have 24 gallons of paint that contains 30% solvent. how many gallons of paint containing 20% solvent ahd how many gallons containing 60% solvent should be mixed to obtain the desired paint?
1 solutions
Answer 253884 by mananth(12270) on 2010-10-12 21:24:57 (Show Source):
You can put this solution on YOUR website! paint containing 20% solvent :let this be x gallons
paint containing 60% solvent :this will be 24-x gallons
Mixture : 24 gallons of paint that contains 30% solvent.
...
0.2x+0.6(24-x) = 24*0.3
0.2x+14.4-0.6x=7.2
-0.4x=-7.2
divide by -0.4
x= -7.2/0.4
x=18
18 gallons of 20%
6 gallons of 60% will be required.
...
m.ananth@hotmail.ca
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Geometry_Word_Problems/355471: If the sides of a square are decreased by 2cm, the area is decreased by 36cm2. What were the dimensions of the original square?
1 solutions
Answer 253876 by mananth(12270) on 2010-10-12 20:15:21 (Show Source):
You can put this solution on YOUR website!let side of square be x
Area = x^2
it is decreased by 2
so new length = x-2
area = (x-2)^2
..
The area decreases by 36 m^2
x^2-(x-2)^2=36
x^2-x^2+2x-4=36
2x-4 = 36
2x=40
x= 20 m
...
side = 20m
...
m.ananth@hotmail.ca
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Problems-with-consecutive-odd-even-integers/355146: How do you find a set of four consecutive odd integers that are positive and whose sum is at most 25?
1 solutions
Answer 253685 by mananth(12270) on 2010-10-12 09:39:28 (Show Source):
You can put this solution on YOUR website!let the numbers be x,x+2,x+4,x+6
...
x+x+2+x+4+x+6<=25
4x+12,=25
4x<=25-12
4x<=13
x<=13/4
x<=3.2
you need odd +ve integers
1,3,5,7 sum <25
3,5,7,9 sum <24
...
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/355113: An inlet pump can fill a reservoir in 10 hours. An outlet pump can drain the same reservoir in 30 hours. How long would it take to fill the reservoir if both pumps were in use at the same time? Thank You
1 solutions
Answer 253684 by mananth(12270) on 2010-10-12 09:33:18 (Show Source):
You can put this solution on YOUR website!inlet pump fills in 10 hours
so it does 1/10 of the job in 1 hour.
outlet pump takes 30 hours
so it can do 1/30 of the job in 1 hour.
..
when both are open they will do 1/10 -1/30 of the job in 1 hour
=2/30 = 1/15 of the job in one hour.
so the tank will fill in 15 hours when both are on.
....
m.ananth@hotmail.ca
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Graphs/355142: please explain how you get the answer
find the slope and the y-intercept of the line 4x=-2y+7
thank you
1 solutions
Answer 253679 by mananth(12270) on 2010-10-12 09:23:33 (Show Source):
You can put this solution on YOUR website!4x=-2y+7
rewrite the equation in the slope intercept form
y =mx+b
2y=-4x+7
/2
y=-2x +7/2
...
m is the slope
so m= -2
..
to get the y intercept plug x=0
so y = -2*0+7/2
y= 7/2
7/2 is the intercept.
...
m.ananth@hotmail.ca
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