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Effective Speed = 540+720 = 1260 mph
Distance = 1890 miles
Time = Distance / Speed
Time = 1890/1260
time = 1.5 hour.

After 1.5 hours two planes will be 1890 miles apart?


Check
======
Plane A Data
============
Speed = 540 mph
Time = 1.5 hour
Distance covered = ?
Distance = Speed * Time
Distance covered= 540 * 1.5 = 810 miles

Plane B Data
============
Speed = 720 mph
Time = 1.5 hour
Distance covered = ?
Distance = Speed * Time
Distance covered = 720 * 1.5 = 1080 miles

Total Distance between two planes after 1.5 hours = 1080+810 = 1890 miles

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Half the number y is equal to y minus ten.
1/2(y)=y-10
y/2=y-10
2*(y/2)=2*(y-10)
y=2y-20
y-2y=-20
-y=-20
Multiply by -1 both sides
y=20

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find equestion of the line which is perpindicular the line y=5x+9 and has y-intercept=6
Given
y=5x+9
Compare above equatoin with Standard Equation of the Straight line
y=mx+b
Slope m = 5
Since lines are perpendicular, multiplication of their slopes will result in (-1) therefore slope of the required line is (-1/5) and we have been given y-intercept 6 of the required line
y=-(1/5)x+6
y=-x/5+6
Above equation is the equatoin of the required line.
Red line = Given Line
Green line = Required Line

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Let
Present age of John = j
Present age of Chris = c

John is 10 years older than Chris.
j=c+10 ..........(1)
In 2 years
John will be = j + 2
Chris will be = c + 2
Then,
John will be twice as old as Chris.
j + 2 = 2(c + 2)
j + 2 = 2c + 4
j = 2c + 4 - 2
J = 2c + 2 .............(2)
Put the value of j from (1) to (2)
c+10 = 2c + 2 .............(2)
c-2c=2-10
-c=-8
Multiply by -1 both sides
c=8
Put the value of c in (1)
j = 8 + 10
j = 18



Present age of John = j = 18 years old
Present age of Chris = c = 8 years old

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Let
Present age of Dorthy = d
Present age of Rita = r

Dorthy is 14 years younger than Rita.
d=r-14.........(1)
Ten years ago
Dorthy age was = d-10
Rita age was = r-10
Then,
Rita was 3 times as old as Dorthy
r-10=3(d-10)
r-10=3d-30
r=3d-30+10
r=3d-20...........(2)
Plug in the value of d from (1) to (2)
r=3(r-14)-20
r=3r-42-20
r-3r=-62
-2r=-62
-2r/-2=-62/-2
r=31
Pulg in the value of r in (1)
d=r-14
d=31-14
d=17


Present age of Dorthy = d = 17 years old
Present age of Rita = r = 31 years old

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Let
Present age of Bill = x
Six year ago he was = x-6
Then
Bill was 1/4 of his present age
1/4x=x-6
x/4=x-6
x=4(x-6)
x=4x-24
x-4x=-24
-3x=-24
-3x/-3=-24/-3
x=8
Bill is 8 years old
Check
======
Bill present age 8 years
Six years ago = 8-6 = 2 (which is 1/4 of 8)

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Amount taken at 8% = x
Amount taken at 6% = 2000-x
Total interest paid = 136



Amount taken * interest rate + Amount taken * interest rate = Total interest paid
x*8% + (2000-x)*6% = 136
x*8/100 + (2000-x)*6/100 = 136
Multiply by 100 both sides
x*8 + (2000-x)*6 = 136 * 100
8x + 12000-6x=13600
8x - 6x=13600-12000
2x=1600
2x/2=1600/2
x=800


Amount taken at 8% = x = 800
Amount taken at 6% = 2000-x = 2000-800 = 1200

Check
800 * 8/100 + 1200 * 6/100 = 136
8*8 + 12*6 = 136
64+72 = 136
136=136

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Let
One odd integer = x+1
Other odd integer = x+3
Given Condition
(x+1)(x+3)=5((x+1)+(x+3))-1
x^2+3x+x+3=5(x+1+x+3)-1
x^2+4x+3=5(2x+4)-1
x^2+4x+3=10x+20-1
x^2+4x+3=10x+19
x^2+4x-10x+3-19=0
x^2-6x-16=0
x^2-8x+2x-16=0
x(x-8)+2(x-8)=0
(x-8)(x+2)=0
x-8=0 or x+2=0
x=8 or x=-2 (inadmissible)
x=8
One odd integer = x+1 = 8+1=9
Other odd integer = x+3 = 8+3 = 11
Check
======
Product of integers = 5 (sum of integers) -1
9*11=5(9+11)-1
99=5(20)-1
99=100-1
99=99

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Let
Amount invested at 14% = x
Amount invested at 16% = 8800-x
Given
Total interest on both investments = 1326
14% * (x) + 16% * (8800-x) = 1326
14/100 * (x) + 16/100 * (8800-x) = 1326
Multiply by 100 both sides
14 * (x) + 16 * (8800-x) = 1326 * 100
14x + 140800-16x = 132600
-2x=132600-140800
-2x=-8200
-2x/-2=-8200/-2
x=4100
Amount invested at 14% = x = 4100
Amount invested at 16% = 8800-x = 8800-4100 = 4700

Check
=====
4100 * 14/100 + 4700 * 16/100 = 1326
Multiply by 100 both sides
4100*14 + 4700*16 = 132600
57400+75200=132600
132600=132600

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Let
She bought = x radios
Price per radio = 1080/x
Number of Radio Gifted = 9
She sold = x-9
She sold $10 more than the original price = 1080/x + 10
Total Amount radios sold = (1080/x+10)*(x-9) = 1080-9720/x+10x-90 = (10x-9720/x+990)

Finally she broke even
Total amount radio sold = Final Amount
10x-9720/x+990 = 1080
10x-9720/x = 1080 - 990
10x-9720/x = 90
Multiply by x both sides
10x^2-9720= 90x
10x^2-90x-9720=0
10*(x^2-9x-972)=0
Divide by 10 both sides
x^2-9x-972=0
x^2-36x+27x-972=0
x(x-36)+27(x-36)
x-36=0 or x+27=0
x=36 or x=-27 (inadmissible)
She bought 36 radios
Price per radio = 1080/36 = 30
She sold = 36-9 = 27 radios
She sold 27 radios for $10 more than she paid for each radio = 30+10=40
Total Amount she received for selling 27 radios @ $40 = 27*40 = $1080

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x+4y=14 ..........(1)
x+3y=11 ..........(2)
Subtract (2) from (1)
x+4y=14
-x-3y=-11
--------------
y=3
Plug in the value of y in (1)
x+4y=14
x+4(3)=14
x+12=14
Subtract 12 from both sides
x+12-12=14-12
Cancel out 12 from Left Hand Side (LHS)
x=2
x,y = 2, 3


Check
======
Plug in the values of x and y in (1)
x+4y=14 ..........(1)
2+4(3)=14
2+12=14
14=14
Now
Plug in the values of x and y in (2)
x+3y=11 ..........(2)
2+3(3)=11
2+9=11
11=11

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2r-6=0
Add 6 both sides
2r-6+6=6
Cancel out 6 from LHS
2r=6
divide by 2 both sides
2r/2=6/2
r=3


Check
======
2r-6=0
2(3)-6=0
6-6=0
0=0

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Yes, you are right.
Answer is 5x^6/2

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: Graphical form: simplifies to Text form: 15x^3/6/x^-3 simplifies to 5*x^(6)/2 Cartoon (animation) form: For tutors: simplify_cartoon( 15x^3/6/x^-3 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Factors 15 and 6 have greatest common factor (GCF) of 3. Reducing fraction. It becomes . Look at . Reduce similar several occurrences of to It becomes . Look at . Removed extra sign in front of It becomes . Look at . Added fractions or integers together It becomes . Result: Universal Simplifier and Solver Done!

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a = 5cm
b = 6cm
c = ?
Use Pythagorean Theorem
c^2=a^2+b^2
c^2=(5)^2+(36)^2
c^2 = 25 +36
c^2 = 61
Taking sqrt both sides
sqrtc^2 = sqrt61
c=7.81cm
The length of diagonal is 7.81cm

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Standard Form of Equation of the line:
y=mx+b
Given
(y+2)=1/2 (x-4)
rearrage the above equation according to the standard form
y+2=(1/2)x-4(1/2)
y+2=(1/2)x-2
y=(1/2)x-2-2
y=(1/2)x-4
Compare above equation with the standard form equation
m=1/2 and b=-4
Since lines are parallel their slopes will be equal,therefore slope of the required line will be (1/2)
Now we have a point(1,3) and slope (1/2)of the line we can easily find required lines by putting these values in the equation of the straight line poin-slope form.
m=(y2-y1)/(x2-x1)
1/2=(y-3))/(x-1)
1*(x-1)=2(y-3)
x-1=2y-6
x-1+6=2y
x+5=2y
2y=x+5
2y/2=(x+5)/2
y=(1/2)x+5/2
Above equation is the Equation of Staright line in the Standard Form.

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Ce nter City East Parking Garage has a capacity of 251 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1221 cars, find the capacity for each garage
Let
The Capacity of Center City West Parking = x
The Capacity of Center City East Parking = x + 251
Parking Capacity of Both Centres = Total Parking Capacity
x+x+251=1221
2x+251=1221
2x=1221-251
2x=970
2x/2=970/2
x=485


The Capacity of Center City West Parking = x = 485
The Capacity of Center City East Parking = x + 251 = 485+251=736


Check
=====
Parking Capacity of Both Centres = Total Parking Capacity
485+736=1221
1221=1221

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-3x+2=7x-22
-3x-7x=-22-2
-10x=-24
-10x/-10=-24/-10
x=12/5

Check
====
-3(12/5)+2=7(12/5)-22
(-36+10)/5=(84/5)-22
-26/5=(84-110)/5
-26/5=-26/5

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A 68 foot pipe is cut into two pieces, one of the which is 12 ft less than the other.
What is the length of the shorter piece?
Let
One piece = x
Other piece = x-12
Sum of two pieces = Total length of entire piece
x+x-12=68
2x-12=68
2x=68+12
2x=80
x=80/2
x=40
One piece = x = 40 feet
Other piece = x-12 = 40-12 = 28 feet
Shorter piece = 28 feet

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The width of a rectangle is 4 more than the length,l. write an equation to describe the perimeter in term of w.

Perimeter = p
Lenght = l
Width = w
Given
l+4=w
l=w-4
Perimeter = p = 2 length + 2 width
p=2l+2w
p=2(w-4)+2w
p=2w-8+2w
p=4w-8
Perimeter in term of w

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Let
Amount invested at 7% = x
Amount invested at 9% = 15000-x
Given
Total interest on both investments = 1230

7% * (x) + 9% * (15000-x) = 1230
7/100 * x + 9/100 * (15000-x) = 1230
Multiply by 100 both sides
7*x + 9 * (15000-x) = 1230 * 100
7x+ 135000-9x = 123000
7x-9x = 123000-135000
-2x=-12000
-2x/-2=-12000/-2
x=6000

Amount invested at 7% = x = 6000
Amount invested at 9% = 15000-x = 15000 - 6000 = 9000
Check
=====
6000 * 7/100 + 9000 * 9/100 = 1230
60*7 + 90*9 = 1230
420 + 810 = 1230
1230=1230

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Let
Loan taken on 6% = x
Loan taken on 5% = x + 1000
Given
Total interest = 215

x*6% + (x+1000)*5% = 215
x*(6/100) + (x+1000)*(5/100) = 215
Multiply by 100 both sides
x*6 + (x+1000)*5=215*100
6x+5x+5000=21500
11x=21500 - 5000
11x=16500
11x/11=16500/11
x=1500

Loan taken on 6% = x = $1500
Loan taken on 5% = x + 1000 = 1500+1000 = $2500


Check
=====
1500 * 6/100 + 2500 * 5/100 = 215
15*6+25*5 = 215
90+125=215
215=215

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points (2, 7) and (–1, 3)
Slope of line = Rise in y / Rise in x
m = (y2-y1)/(x2-x1)
m=3-7/-1-2
m=-4/-3
m=4/3
Slope is 4/3

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Perimeter = P = 56
Length = l = 3w (Given)

Length = ?
Width = ?


Perimeter of rectangel = 2l + 2w

p = 2l + 2w
56 = 2(3w) + 2w
56 = 6w + 2w
56 = 8w
56/8=8w/8
7=w
w=7

Given
Length = l = 3w
Length = l = 3(7)
Length = 21


Perimeter = P = 56 ft.
Length = l = 21 ft.
Width = 7 ft

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Let
Number of Children = x
Number of Adults = x + 289
Adults + Children = 737
(x+289)+x=737
x+289+x=737
2x=737-289
2x=448
2x/2=448/2
x=224


Number of Children = x = 224
Number of Adults = x + 289 = 224+289=513

Check
======
Total Attendance = Adults + Children
737 = 513+224
737=737

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Solution set = 3, -2
x= 3, or -2
x=3 or x=-2
x-3=0 or x+2=0
Since either of above is equal to zero, therefore multiplicatoin of the both will equal to zero
(x-3)(x+2)=0
x^2+2x-3x-6=0
x^2-x-6=0
Required Quadratic Equation.

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Area of Square = side * side
Perimeter of Square = 4 * Side
Given
Area of Square = 9 sq ft.
side * side = 9
(side)^2=9
Take sqour root both sides
sqrt(side)^2=sqrt(9)
side=sqrt(3*3)
side=3 ft.
Perimeter of Square = 4 * Side
Perimeter of Square = 4 * 3
Perimeter of Square = 12 feet

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A garden is shaped like a rectangle whose perimeter is 88 ft. The length is 10 ft more than the width. Find the length and width.
P = 88 feet
L = W + 10
W = ?
L = ?
Perimeter of regtangle = 2 length + 2 width
P=2L + 2W
88 = 2 (W+10)+ 2W
88 = 2W+20+ 2W
88-20=4W
68=4W
68/4=W
17=W
W=17
Given
L=W+10 = 17+10 = 27 feet

Perimeter = 88 feet
Length = 27 feet
Width = 17 feet

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(5+k) / 2 = (2 + 6 + k)/3
(5+k) / 2 = (8 + k)/3
3(5+k)=2(8+k)
15+3k=16+2k
3k-2k=16-15
k=1


Check
======
(5+k) / 2 = (2 + 6 + k)/3
(5+1) / 2 = (2 + 6 + 1)/3
6/2=9/3
3=3

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Let
Socre of fifth exam = x
Avarage for five exams = (97+71+89+73+x)/5 = (324+x)/5
His exam average must be greater than or equal to 80 and less than 90
80≤(324+x)/5<90
Now
For 80≤(324+x)/5
80≤(324+x)/5
Multiply by 5
5*80≤5*(324+x)/5
400≤(324+x)
400-324≤x
76≤x
For
(324+x)/5<90
Multiply by 5
5*(324+x)/5<90*5
324+x<450
x<450-324
x<126
Range of x
76≤x<126
Range of marks is between 76 and 125
He must score marks between 76 and 125 in his fifth test to maintain an average which will give him a grade B.
If the total marks of an exam is 100 then range must be between 76 and 100.

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Change the minutes into hour
70 minutes = 70 * (1/60) hours
70 minutes = 7/6 hours
70 minutes = 1.17 hours
Speed = Distance / time = 24/1.17 = 20.51 mph

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Total Amount = $180,000
Total Interest = $14,600
Amount to be paid off at 9% = x
Amount to be paid off at 7% = 180,000 - x
Amount to be paid off at 9% * 9% + Amount to be paid off at 7% * 7% = Total Interest
x*9/100 + (180000-x)*7/100=14600
x*0.09+(180000-x)*0.07=14600
0.09x+12600-0.07x=14600
0.02x=14600-12600
0.02x=2000
x=2000/0.02
x=100,000

Amount to be paid off at 9% = x = $100,000
Amount to be paid off at 7% = 180,000 - 100,000 = $80,000

Check
======
100000 * 0.09 + 80000 * 0.07 = 14600
9000+5600=14600
14600=14600