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Rectangles/224571: the length of a rectangle is three centimeters greater than the width. If the perimeter equals 54 centimeters.
1 solutions
Answer 167753 by drj(1380) About Me  on 2009-10-10 12:33:08 (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is three centimeters greater than the width. If the perimeter equals 54 centimeters.

Step 1. The perimeter P means adding up all the four sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let w+3 be the length

Step 4. Then, P=w+w+w+3+w+3=54.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: w=12.
  • Graphical form: Equation w%2Bw%2Bw%2B3%2Bw%2B3=54 was fully solved.
  • Text form: w+w+w+3+w+3=54 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2Bw%2B3%2Bw%2B3=54+%29
    For tutors: simplify_cartoon( w+w+w+3+w+3=54 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at w%2Bw%2Bw%2Bhighlight_red%28+3+%29%2Bw%2Bhighlight_red%28+3+%29=54.
Added fractions or integers together
It becomes w%2Bw%2Bw%2Bhighlight_green%28+6+%29%2Bw=54.
Look at w%2Bw%2Bw%2Bhighlight_red%28+6+%29%2Bw=54.
Moved 6 to the right of expression
It becomes w%2Bw%2Bw%2Bw%2Bhighlight_green%28+6+%29=54.
Look at .
Eliminated similar terms highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+w+%29 replacing them with highlight_green%28+%281%2B1%2B1%2B1%29%2Aw+%29
It becomes highlight_green%28+%281%2B1%2B1%2B1%29%2Aw+%29%2B6=54.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2Aw%2B6=54.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2Aw+%29%2B6=54.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2Aw%2B6=54.
Look at 4%2Aw%2B6=highlight_red%28+54+%29.
Moved these terms to the left highlight_green%28+-54+%29
It becomes 4%2Aw%2B6-highlight_green%28+54+%29=0.
Look at 4%2Aw%2Bhighlight_red%28+6+%29-highlight_red%28+54+%29=0.
Added fractions or integers together
It becomes 4%2Aw%2Bhighlight_green%28+-48+%29=0.
Look at 4%2Aw%2Bhighlight_red%28+-48+%29=0.
Removed extra sign in front of -48
It becomes 4%2Aw-highlight_green%28+48+%29=0.
Look at highlight_red%28+4%2Aw-48+%29=0.
Solved linear equation highlight_red%28+4%2Aw-48=0+%29 equivalent to 4*w-48 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=12.

Universal Simplifier and Solver


Done!



For w=12 , then w+3=15 and P=2(12+15)=54 which is a true statement.

Step 6. ANSWER: The width is 12 cm and the length is 15 cm.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV
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logarithm/224573: condense each expression to a single logarithm
log%283%2C%28a%29%29%2Blog%283%2C%28b%29%29%2B5%2Alog%283%2C%28c%29%29 I am stuck on this question
1 solutions
Answer 167751 by drj(1380) About Me  on 2009-10-10 12:29:00 (Show Source):
You can put this solution on YOUR website!
condense each expression to a single logarithm

log3a+log3b+5log3c

The sum of the logarithms of each term is the log of their products.

Also 5log(3c)=log(3c)+log(3c)+log(3c)+log(3c)+log(3c)=log(3c*3c*3c*3c*3c)=log((3c)^5)



ANSWER: log%28%283a%29%29%2Blog%28%283b%29%29%2B5log%28%283c%29%29=log%28%282187abc%5E5%29%29

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

http://www.FreedomUniversity.TV
http://www.Facebook.com/FreedomUniversityTV
http://www.Twitter.com/FreedomUTV

Radicals/224569: Please help


sq root of 1-3x = x+1

I am supposed to solve the radical equation for the given variable.

1 solutions
Answer 167749 by drj(1380) About Me  on 2009-10-10 12:21:40 (Show Source):
You can put this solution on YOUR website!
sqrt%281-3x%29=x%2B1

Step 1. Square both sides of the equation to get rid of the square root sign.

%28sqrt%281-3x%29%29%5E2=%28x%2B1%29%5E2

1-3x=x%5E2%2B2x%2B1

Step 2. Add -1+3x to both sides of the equation to get a quadratic equation

1-3x-1%2B3x=x%5E2%2B2x%2B1-1%2B3x

0=x%5E2%2B5x

Step 3. Factor out the x

x%28x%2B5%29=0

x=0 and x%2B5=0 or x=-5

Step 4. ANSWER: The solutions are x=0 and x=-5

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

http://www.FreedomUniversity.TV
http://www.Facebook.com/FreedomUniversityTV
http://www.Twitter.com/FreedomUTV

Human-and-algebraic-language/224248: the length of a rectangle is increased by 120% and its width is decreased by 20%, what is the resulting percentage increase or decrease in the area? Justify your answer algebraically.
1 solutions
Answer 167745 by drj(1380) About Me  on 2009-10-10 11:05:51 (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is increased by 120% and its width is decreased by 20%, what is the resulting percentage increase or decrease in the area? Justify your answer algebraically.

Step 1. 120% means 1.2 and 20% means 0.20

Step 2. Let L be the original length and 1.20L be the increased length.

Step 3. Let w be the original width and (1-0.2)w=0.8w be the reduced width.

Step 4. Let w*L be the original area.

Step 5. Then, (0.8w)*(1.20L)=0.96w*L = (1-0.04)w*L

Step 6. ANSWER: The area is 96% of the original area or the area is reduced by 4%.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J



Angles/224487: the supplementary angle of a 160 degree angle has how many degrees? i have absolutely no idea
1 solutions
Answer 167743 by drj(1380) About Me  on 2009-10-10 10:59:22 (Show Source):
You can put this solution on YOUR website!
The supplementary angle of a 160 degree angle has how many degrees? i have absolutely no idea

Step 1. Supplementary angles means two angles add up 180 degrees.

Step 2. Let 160 be the angle and its supplementary angle is 180-160=20 degrees.

Step 3. ANSWER. Given the angle of 160 degrees, then its supplementary angle is 20 degrees since they both add up to 180 degrees.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J


Linear-systems/224489: find three consecutive even integers such that twice largest integer exceeds the sum of the sum of the first two by 6.
1 solutions
Answer 167742 by drj(1380) About Me  on 2009-10-10 10:54:02 (Show Source):
You can put this solution on YOUR website!
Find three consecutive even integers such that twice largest integer exceeds the sum of the sum of the first two by 6.

Step 1. Let n be the first even integer.

Step 2. Let n+2 and n+4 be the next two even integers.

Step 3. Let 2(n+4)=2n+8 be twice the largest integer.

Step 4. Let n+n+2=2n+2 be the sum of the first two.

Step 5. Then, 2n+8=2n+2+6 since twice largest integer exceeds the sum of the sum of the first two by 6.

Step 6. Solving the equation in Step 5 yields the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: Equation 2n%2B8=2n%2B2%2B6 was fully solved.
  • Text form: 2n+8=2n+2+6 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2n%2B8=2n%2B2%2B6+%29
    For tutors: simplify_cartoon( 2n+8=2n+2+6 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2An%2B8=2%2An%2Bhighlight_red%28+2+%29%2Bhighlight_red%28+6+%29.
Added fractions or integers together
It becomes 2%2An%2B8=2%2An%2Bhighlight_green%28+8+%29.
Look at 2%2An%2B8=highlight_red%28+2%2An%2B8+%29.
Moved these terms to the left highlight_green%28+-2%2An+%29,highlight_green%28+-8+%29
It becomes 2%2An%2B8-highlight_green%28+2%2An+%29-highlight_green%28+8+%29=0.
Look at 2%2An%2Bhighlight_red%28+8+%29-2%2An-highlight_red%28+8+%29=0.
Added fractions or integers together
It becomes 2%2An%2Bhighlight_green%28+0+%29-2%2An=0.
Look at 2%2An%2Bhighlight_red%28+0+%29-2%2An=0.
Moved 0 to the right of expression
It becomes 2%2An-2%2An%2Bhighlight_green%28+0+%29=0.
Look at 2%2An-2%2An%2Bhighlight_red%28+0+%29=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes 2%2An-2%2An=0.
Look at highlight_red%28+2%2An+%29-highlight_red%28+2%2An+%29=0.
Eliminated similar terms highlight_red%28+2%2An+%29,highlight_red%28+-2%2An+%29 replacing them with highlight_green%28+%282-2%29%2An+%29
It becomes highlight_green%28+%282-2%29%2An+%29=0.
Look at highlight_red%28+%282-2%29%2An+%29=0.
Since highlight_red%28+%282-2%29%2An+%29 has zero as a factor, it should be replaced with a zero
Look at 0=0.
Added fractions or integers together
It becomes 0=0.
Result: 0=0

Universal Simplifier and Solver


Done!



Step 7. ANSWER: The three consecutive integers can be anything that the satisfies equation in Step 5.

For example 2, 4, 6 will yield 2(6)=2+4+6 which is a true statement

Another example, 20, 22, 24 will yield 2(24)=20+22+6 which is another true statement

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Quadratic_Equations/224467: The height of an object thrown in the air is given by h = t2 – 7t + 3, where h is in feet and t is the time in seconds the object has been in motion. At what time (to the nearest tenth) is the object 10 feet in the air?
1 solutions
Answer 167739 by drj(1380) About Me  on 2009-10-10 10:42:51 (Show Source):
You can put this solution on YOUR website!
The height of an object thrown in the air is given by h=t%5E2-7t%2B3, where h is in feet and t is the time in seconds the object has been in motion. At what time (to the nearest tenth) is the object 10 feet in the air?

Step 1. Substitute h=10 into h=t%5E2-7t%2B3.

Step 2. Then, 10=t%5E2-7t%2B3 which is quadratic equation with two solutions.

The final quadratic equation is t%5E2-7t-7=0 after subtracting 10 from both sides of the equation.

Step 3. To solve, use the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=-7, and c=-7

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-7x%2B-7+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-7%29%5E2-4%2A1%2A-7=77.

Discriminant d=77 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+77+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+77+%29%29%2F2%5C1+=+7.88748219369606
x%5B2%5D+=+%28-%28-7%29-sqrt%28+77+%29%29%2F2%5C1+=+-0.887482193696061

Quadratic expression 1x%5E2%2B-7x%2B-7 can be factored:
1x%5E2%2B-7x%2B-7+=+1%28x-7.88748219369606%29%2A%28x--0.887482193696061%29
Again, the answer is: 7.88748219369606, -0.887482193696061. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B-7+%29



Selecting the positive time is 7.9 seconds

Step 4. ANSWER: The time is 7.9 seconds.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Travel_Word_Problems/224504: is a car moves with an average speed of 60 km/h an hour , it will travel a distance of 60 km.
a. how far would it travel if it moved at this rate for 4 h?
b. for 10m h?

i tried as u said to try and i think it is for a. averagespeed=distancecovered over time , 60 x 4=240 , 240 % 4 =6o maybe ... i want the answer today plzzz and thank u :)
1 solutions
Answer 167732 by drj(1380) About Me  on 2009-10-10 10:26:48 (Show Source):
You can put this solution on YOUR website!
If a car moves with an average speed of 60 km/hour , it will travel a distance of 60 km in 1 hour.
a. How far would it travel if it moved at this rate for 4 h?
b. for 10 h?

Step 1. distance+=+speed+%2A+time and speed=distance%2Ftime

Step 2. For Problem a, 60 km/hr * 4 hr = 240 km.

Step 3. For Problem b, 60 km/hr *10 hr= 600 km.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Travel_Word_Problems/224529: A train travels 120 km in the same time that a plane covers 336 km. If the speed of the the plane is 10 km per hour less than 3 times the speed of the train, find both speeds.
1 solutions
Answer 167729 by drj(1380) About Me  on 2009-10-10 10:21:23 (Show Source):
You can put this solution on YOUR website!
A train travels 120 km in the same time that a plane covers 336 km. If the speed of the the plane is 10 km per hour less than 3 times the speed of the train, find both speeds.

Step 1. distance+=+speed+%2A+time and speed+=+distance%2Ftime

Step 2. Let 120%2Ft be the speed of the train where t is the time traveled in 120 km.

Step 3. Let 336%2Ft be the speed of the plane traveled in 336 km with the same time t.

Step 4. Then 336%2Ft=3%2A120%2Ft-10 since the speed of the the plane is 10 km per hour less than 3 times the speed of the train,

Step 5. Multiply by t to both sides of the equation.

t%2A336%2Ft=t%2A3%2A120%2Ft-t%2A10

336=360-10t

Add 10t-336

336%2B10t-336=360-10t%2B10t-336

10t=24

Divide 10 to both sides of the equation

10t%2F10=24%2F10

t=2.4 Then 120%2F2.4=50 and 336%2F2.4=140

Also, note that the plane's speed is 10km/hour less than 3 times the speed of the train.

Step 6. ANSWER: The speed of the train is 50 km/hr and the plane's speed is 140 km/hr.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Graphs/224441: solve the system of equations by graphing. Then Classify the system.
x+y=13
x-y= -5
1 solutions
Answer 167692 by drj(1380) About Me  on 2009-10-09 22:54:34 (Show Source):
You can put this solution on YOUR website!
Solve the system of equations by graphing. Then Classify the system.
x+y=13
x-y= -5

Step 1. Graph the two lines as shown below

graph%28400%2C+400%2C+-10%2C10%2C-15%2C15%2C13-x%2C+x%2B5%29

Step 2. Based on the graph the solution is x=4, y=9 or point (4,9)

Step 3. Check if (4,9) satisfies the original solutin

4+9=13 which is a true statement
4-9=-5 which is a true statement

Step 4. ANSWER: The solution is (4,9). So the system of equations are independent, consistent and unique.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Linear_Algebra/224442: Suppose you need to solve a system of equations in which both equations represent lines. How many solutions can your system have?
How many solutions does the following equations have?
8x+4y=8
2x-2y=-4
1 solutions
Answer 167691 by drj(1380) About Me  on 2009-10-09 22:48:11 (Show Source):
You can put this solution on YOUR website!
Suppose you need to solve a system of equations in which both equations represent lines. How many solutions can your system have? None, One, and Many
How many solutions does the following equations have? One. The lines intersect at one point as shown below at (0,2)

8x+4y=8
2x-2y=-4

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++8%5Cx+%2B+4%5Cy+=+8%2C%0D%0A++++2%5Cx+%2B+-2%5Cy+=+-4+%29%0D%0A++We'll use substitution. After moving 4*y to the right, we get:
8%2Ax+=+8+-+4%2Ay, or x+=+8%2F8+-+4%2Ay%2F8. Substitute that
into another equation:
2%2A%288%2F8+-+4%2Ay%2F8%29+%2B+-2%5Cy+=+-4 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J
Linear_Algebra/224440: Suppose you need to solve a system of equations in which both equations represent lines. How many solutions can your system have?
How many solutions does the following equations have?
8x+4y=8
2x-2y=-4
1 solutions
Answer 167690 by drj(1380) About Me  on 2009-10-09 22:45:28 (Show Source):
You can put this solution on YOUR website!
Suppose you need to solve a system of equations in which both equations represent lines. How many solutions can your system have? None, One, and Many
How many solutions does the following equations have? One. The lines intersect at one point as shown below at (0,2)

8x+4y=8
2x-2y=-4

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++8%5Cx+%2B+4%5Cy+=+8%2C%0D%0A++++2%5Cx+%2B+-2%5Cy+=+-4+%29%0D%0A++We'll use substitution. After moving 4*y to the right, we get:
8%2Ax+=+8+-+4%2Ay, or x+=+8%2F8+-+4%2Ay%2F8. Substitute that
into another equation:
2%2A%288%2F8+-+4%2Ay%2F8%29+%2B+-2%5Cy+=+-4 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J
Graphs/224445: Solve the equation with graphing then classify
5x-y=10
5x+6y= -25
1 solutions
Answer 167689 by drj(1380) About Me  on 2009-10-09 22:41:53 (Show Source):
You can put this solution on YOUR website!
Solve the equation with graphing then classify

5x-y=10
5x+6y= -25

1. Graphing the two leads to the following picture:

graph%28600%2C600%2C+-5%2C+5%2C+-10%2C+10%2C+5x-10%2C+-5x%2F6-25%2F6%29

2. ANSWER: Based on the graph, the two lines intersect at point (1,-5) or x=1 and y=-5.

Check if the point (1,-5) satisfies the equations:

5x-y=10 so 5*1-(-5) then 5+5=10 which is a true statement.

5x+6y= -25 so then 5*1+6*(-5)=5-30=-25 which is a true statement.

So the intersection point (1,-5) is a solution to the system of equations.

I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Average/224458: 7x^2 = 21 Please help me solve.
1 solutions
Answer 167685 by drj(1380) About Me  on 2009-10-09 22:14:55 (Show Source):
You can put this solution on YOUR website!
7x^2 = 21 Please help me solve.

Step 1. Divide 7 to both sides of the equation

7x%5E2%2F7=21%2F7

x%5E2=3

Step 2. Take the square root to both sides of the equation

x=sqrt%283%29 and x=-sqrt%283%29

Step 3. ANSWER: Solutions are sqrt%283%29 and -sqrt%283%29

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

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Average/224463: x^4 + 7x^2 – 8 = 0 Please help me with this. Thanks
1 solutions
Answer 167684 by drj(1380) About Me  on 2009-10-09 22:07:58 (Show Source):
You can put this solution on YOUR website!
x%5E4%2B7x%5E2-8=0

x%5E4%2B7x%5E2-8=%28x%5E2%2B8%29%2A%28x%5E2-1%29=0

x%5E2%2B8=0 and x%5E2-1=0

x%5E2=-8 and x%5E2=1

Take the square root to both sides of the equation

x1=i%2A2sqrt%282%29 where i=sqrt%28-1%29
x2=-i%2A2sqrt%282%29
x3=1
x4=-1

ANSWER: The solutions are: x1=i%2A2sqrt%282%29, x2=-i%2A2sqrt%282%29, x3=1 and x4=-1

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Age_Word_Problems/224465: Mr. Escalate said "five less than one forth of my age is 12 how old am I?"
1 solutions
Answer 167683 by drj(1380) About Me  on 2009-10-09 22:01:36 (Show Source):
You can put this solution on YOUR website!
Mr. Escalate said "five less than one forth of my age is 12 how old am I?"

Step 1. Let x be the age of Mr. Escalate

Step 2. Let x/4 be one-forth of the his age.

Step 3. Then x%2F4-5=12 since five less than one fourth of his age is 12.

Step 4. Add 5 to both sides of the equation

x%2F4-5%2B5=12%2B5

x%2F4=17
Step 5. Multiply 4 to both sides of the equation

4x%2F4=4%2A17

x=68

Step 6. ANSWER: The age of Mr Escalate is 68 years old.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Linear-equations/224364: Solve the system by graphing the equations.
3y-3=0
x+2y=10
1 solutions
Answer 167644 by drj(1380) About Me  on 2009-10-09 20:14:27 (Show Source):
You can put this solution on YOUR website!
Solve the system by graphing the equations.
3y-3=0
x+2y=10
1. Graphing the two leads to the following picture:

graph%28600%2C600%2C+-20%2C+20%2C+-5%2C+10%2C+1%2C+-x%2F2%2B5%29

2. ANSWER: Based on the graph, the two lines intersect at point (-8, 3) or x=8 and y=1.

Check if the point (8,1) satisfies the equations:

3y-3=0 so at y=1 then 3*1-3=0 which is a true statement.

x+2y=10 so at x=8 and y=1 then 8+2*1=-8+2=10 which is a true statement.

So the intersection point (8,1) is a solution to the system of equations.

I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Expressions-with-variables/224381: -1x+5=2x+8
1 solutions
Answer 167620 by drj(1380) About Me  on 2009-10-09 18:14:11 (Show Source):
You can put this solution on YOUR website!
-1x%2B5=2x%2B8

Step 1. Add x-8 or to both sides of the equation

-1x%2B5%2Bx-8=2x%2B8%2Bx-8

-3=3x

Step 2. Divide 3 to both sides of the equation

-3%2F3=3x%2F3

-1=x

Step 3. Check solution with original equation

%28-1%29%28-1%29%2B5=2%28-1%29%2B8

1%2B5=-2%2B8

6=6 which is a true statement

Step 4. ANSWER: Solution is x=-1

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

http://www.FreedomUniversity.TV





Linear-systems/224344: Graph the linear system and tell how many solutions it has. If there is exactly one solution, give the solution.
-3X+4Y=-16
-6X=-8Y-32
1 solutions
Answer 167613 by drj(1380) About Me  on 2009-10-09 17:00:19 (Show Source):
You can put this solution on YOUR website!
Graph the linear system and tell how many solutions it has. If there is exactly one solution, give the solution.

-3X+4Y=-16 Equation 1 or multiplying -6X+8Y=-32 after multiplying 2.
-6X=-8Y-32 or -6X+8Y=-32 Equation 2


Equations 1 (after multiplying 2 to both sides of the equation) and Equation 2 are identical so there are an infinite many number of solutions.

The graph follows below

graph%28400%2C400%2C+-10%2C10%2C-10%2C+10%2C+3x%2F4-4%29

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

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Linear-systems/224340: Graph the linear system and tell how many solutions it has. If there is exactly one solution, give the solution
4X-5Y=2
8X+Y=4
1 solutions
Answer 167611 by drj(1380) About Me  on 2009-10-09 16:55:17 (Show Source):
You can put this solution on YOUR website!
Graph the linear system and tell how many solutions it has. If there is exactly one solution, give the solution
4X-5Y=2
8X+Y=4

Step 1. Graphing the above linear system of equations yields the following

graph%28600%2C600%2C+-10%2C10%2C-10%2C10%2C+4x%2F5-1%2F2%2C+-8x%2B4%29

Step 2. Based on the above graph the intersection point is (0.5, 0) or x=0.5 and y=0.

Check if this point (0.5, 0) satisfies the above system of equations and it does.

Step 3. ANSWER: The intersection point (0.5, 0) is a solution to the above system of equations.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

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Graphs/224332: Solve the system of equations by graphing:

2y-6=0
x+8y=16
1 solutions
Answer 167608 by drj(1380) About Me  on 2009-10-09 16:44:54 (Show Source):
You can put this solution on YOUR website!
Solve the system of equations by graphing:

2y-6=0
x+8y=16

1. Graphing the two leads to the following picture:

graph%28600%2C600%2C+-20%2C+20%2C+-5%2C+10%2C+3%2C+-x%2F8%2B2%29

2. ANSWER: Based on the graph, the two lines intersect at point (-8, 3) or x=-8 and y=3.

Check if the point (-8,3) satisfies the equations:

2y-6=0 so at y=3 then 2*3-6=0 which is a true statement.

x+8y=16 so at x=-8 and y=3 then -8+8*3=-8+24=16 which is a true statement.

So the intersection point (-8,3) is a solution to the system of equations.

I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Equations/224329: Find equation of the line with points m=6/7 (4,-3)
1 solutions
Answer 167605 by drj(1380) About Me  on 2009-10-09 16:36:05 (Show Source):
You can put this solution on YOUR website!
Find equation of the line with points m=6/7 (4,-3)

Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point(0,b).

Step 2. The slope m is given as

m=%28y2-y1%29%2F%28x2-x1%29

Step 3. Let (x1,y1)=(4, -3) or x1=4 and y1=-3 . Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 4. Now we're given the slope m=6%2F7. Substituting above values and variables in the slope equation m yields the following steps:

m=%28y2-y1%29%2F%28x2-x1%29

6%2F7=%28y-%28-3%29%29%2F%28x-4%29

6%2F7=%28y%2B3%29%2F%28x-4%29

Step 5. Multiply x-4 to both sides to get rid of denominator on right side of equation.

6%28x-4%29%2F7=y%2B3

6x%2F7-24%2F7=y%2B3

Step 6. Now subtract 3 from both sides of equation to solve for y.

6x%2F7-24%2F7-3=y%2B3-3

6x%2F7-45%2F7=y

Note: the above equation can be rewritten as

6x-7y=45

And the graph is shown below which is consistent with the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 6+x+%2B+-7+y+=+45 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-6%2F-7.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 45/6 = 7.5.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 45/-7 = -6.42857142857143.
  • Slope is -6/-7 = 0.857142857142857.
  • Equation in slope-intercept form: y=0.857142857142857*x+-6.42857142857143.




I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV




Miscellaneous_Word_Problems/224323: The length of a new rectangular playing field is 5 yards longer than double the width. If the perimeter of the rectangular playing field is 340 yards, what are its dimensions? I just want to know how to figure the answer out. Please and thank you in advanced!
1 solutions
Answer 167599 by drj(1380) About Me  on 2009-10-09 16:14:36 (Show Source):
You can put this solution on YOUR website!
The length of a new rectangular playing field is 5 yards longer than double the width. If the perimeter of the rectangular playing field is 340 yards, what are its dimensions?

Step 1. The perimeter P means adding up all the four sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 2w+5 be the length

Step 4. Then, P=w+w+2w+5+2w+5=340.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: w=55.
  • Graphical form: Equation w%2Bw%2B2w%2B5%2B2w%2B5=340 was fully solved.
  • Text form: w+w+2w+5+2w+5=340 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+w%2Bw%2B2w%2B5%2B2w%2B5=340+%29
    For tutors: simplify_cartoon( w+w+2w+5+2w+5=340 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at w%2Bw%2B2%2Aw%2Bhighlight_red%28+5+%29%2B2%2Aw%2Bhighlight_red%28+5+%29=340.
Added fractions or integers together
It becomes w%2Bw%2B2%2Aw%2Bhighlight_green%28+10+%29%2B2%2Aw=340.
Look at w%2Bw%2B2%2Aw%2Bhighlight_red%28+10+%29%2B2%2Aw=340.
Moved 10 to the right of expression
It becomes w%2Bw%2B2%2Aw%2B2%2Aw%2Bhighlight_green%28+10+%29=340.
Look at .
Eliminated similar terms highlight_red%28+w+%29,highlight_red%28+w+%29,highlight_red%28+2%2Aw+%29,highlight_red%28+2%2Aw+%29 replacing them with highlight_green%28+%281%2B1%2B2%2B2%29%2Aw+%29
It becomes highlight_green%28+%281%2B1%2B2%2B2%29%2Aw+%29%2B10=340.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Aw%2B10=340.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Aw+%29%2B10=340.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Aw%2B10=340.
Look at 6%2Aw%2B10=highlight_red%28+340+%29.
Moved these terms to the left highlight_green%28+-340+%29
It becomes 6%2Aw%2B10-highlight_green%28+340+%29=0.
Look at 6%2Aw%2Bhighlight_red%28+10+%29-highlight_red%28+340+%29=0.
Added fractions or integers together
It becomes 6%2Aw%2Bhighlight_green%28+-330+%29=0.
Look at 6%2Aw%2Bhighlight_red%28+-330+%29=0.
Removed extra sign in front of -330
It becomes 6%2Aw-highlight_green%28+330+%29=0.
Look at highlight_red%28+6%2Aw-330+%29=0.
Solved linear equation highlight_red%28+6%2Aw-330=0+%29 equivalent to 6*w-330 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=55.

Universal Simplifier and Solver


Done!



For w=55 , then 2w+5=115 and P=2(55+115)=340 which is a true statement.

Step 6. ANSWER: The width is 55 yards and length is 115 yards.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

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Systems-of-equations/224314: please help me solve by elimination
5x+6y=3
10x+12y=6
answer is ordered pair integers or fractions
1 solutions
Answer 167590 by drj(1380) About Me  on 2009-10-09 15:31:20 (Show Source):
You can put this solution on YOUR website!
Phelp me solve by elimination

5x+6y=3 (Equation 1) or multiplying by 2 to both sides of the equation yields 10x+12y=6
10x+12y=6 (Equation 2)

Answer is ordered pair integers or fractions

Equation 1 is identical to Equation 2 if you multiply Equation 1 by 2. Therefore you have an infinite set of solutions. When I do multiply Equation 1 by 2 and subtract Equation 2 from multiplied version of Equation 1, I get 0=0 on both sides of the equation while eliminating both the x and y terms.

ANSWER: There are an infinite set of solutions satisfying the system of equations.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

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http://www.Facebook.com/FreedomUniversityTV
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Travel_Word_Problems/224308: Two planes leave an airport at 8 a.m., one flying north at 480 km/h and the other flying south at 520 km/h. At what time will they be 3000 km apart?
1 solutions
Answer 167588 by drj(1380) About Me  on 2009-10-09 15:24:07 (Show Source):
You can put this solution on YOUR website!
Two planes leave an airport at 8 a.m., one flying north at 480 km/h and the other flying south at 520 km/h. At what time will they be 3000 km apart?

Step 1. Let x be the amount of time for the planes to be 3000 km.

Step 2. Let distance=speed*time.

Step 3. Let 480x be the distance traveled at 480 km/h.

Step 4. Let 520x be the distance traveled at 520 km/h.

Step 5. Then 480x+520x=3000 be the total distance of 3000 km traveled by both planes.

Step 6. Solving the equation in Step 5 yields the following steps

1000x=3000

Divide 1000 to both sides of the equation

1000x%2F1000=3000%2F1000

x=3 hours. So 3 hours ahead of 10 a.m. is 1 p.m.

Step 7. ANSWER: The planes will be 3000 km at 1 p.m.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

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Problems-with-consecutive-odd-even-integers/224200: If three times the smaller of two consecutive integers is added to four times the larger, the result is 39. Find the smaller integer.
1 solutions
Answer 167578 by drj(1380) About Me  on 2009-10-09 14:41:58 (Show Source):
You can put this solution on YOUR website!
If three times the smaller of two consecutive integers is added to four times the larger, the result is 39. Find the smaller integer.

Step 1. Let n be the smaller integer.

Step 2. Let n+1 be the larger and next consecutive integer.

Step 3. Let 3n be three times the smaller integer.

Step 4. Let 4(n+1) be four times the larger integer.

Step 5. Then 3n+4(n+1)=39 since three times the smaller of two consecutive integers is added to four times the larger will result in 39.

Step 6. Solving the equation in Step yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: n=5.
  • Graphical form: Equation 3n%2B4%2A%28n%2B1%29=39 was fully solved.
  • Text form: 3n+4*(n+1)=39 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3n%2B4%2A%28n%2B1%29=39+%29
    For tutors: simplify_cartoon( 3n+4*(n+1)=39 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2An%2B4%2A%28n%2B1%29=highlight_red%28+39+%29.
Moved these terms to the left highlight_green%28+-39+%29
It becomes 3%2An%2B4%2A%28n%2B1%29-highlight_green%28+39+%29=0.
Look at 3%2An%2Bhighlight_red%28+4%2A%28n%2B1%29+%29-39=0.
Expanded term 4 by using associative property on %28n%2B1%29
It becomes 3%2An%2Bhighlight_green%28+4%2An+%29%2Bhighlight_green%28+4%2A1+%29-39=0.
Look at 3%2An%2B4%2An%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+1+%29-39=0.
Multiplied numerator integers
It becomes 3%2An%2B4%2An%2Bhighlight_green%28+4+%29-39=0.
Look at 3%2An%2B4%2An%2Bhighlight_red%28+4+%29-highlight_red%28+39+%29=0.
Added fractions or integers together
It becomes 3%2An%2B4%2An%2Bhighlight_green%28+-35+%29=0.
Look at 3%2An%2B4%2An%2Bhighlight_red%28+-35+%29=0.
Removed extra sign in front of -35
It becomes 3%2An%2B4%2An-highlight_green%28+35+%29=0.
Look at highlight_red%28+3%2An+%29%2Bhighlight_red%28+4%2An+%29-35=0.
Eliminated similar terms highlight_red%28+3%2An+%29,highlight_red%28+4%2An+%29 replacing them with highlight_green%28+%283%2B4%29%2An+%29
It becomes highlight_green%28+%283%2B4%29%2An+%29-35=0.
Look at %28highlight_red%28+3+%29%2Bhighlight_red%28+4+%29%29%2An-35=0.
Added fractions or integers together
It becomes %28highlight_green%28+7+%29%29%2An-35=0.
Look at highlight_red%28+%28highlight_red%28+7+%29%29%2An+%29-35=0.
Remove unneeded parentheses around factor highlight_red%28+7+%29
It becomes highlight_green%28+7+%29%2An-35=0.
Look at highlight_red%28+7%2An-35+%29=0.
Solved linear equation highlight_red%28+7%2An-35=0+%29 equivalent to 7*n-35 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=5.

Universal Simplifier and Solver


Done!



With n=5, then n+1=6 and check the sum 3*5+4*6=15+24=39...which is a true statement.

Step 7. ANSWER: The integers are 5 and 6

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV
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Linear-equations/224207: Find the slope from the equation.
-2y-10+2x=0
1 solutions
Answer 167574 by drj(1380) About Me  on 2009-10-09 14:36:07 (Show Source):
You can put this solution on YOUR website!
Find the slope from the equation.

-2y-10%2B2x=0

Step 1. The slope-intercept from is given as y=mx+b where m is the slope and b is the y-intercept at x=0 or at point (0,b).

Step 2. Put the given equation in slope intercept form.

Add 2y to both sides of the equation

-2y-10%2B2x%2B2y=0%2B2y

-10%2B2x=2y

Divide by to 2 both sides of the equation

-10%2F2%2B2x%2F2=y

-5%2B2x=y or y=2x-5

Step 3. Comparing y=2x%2B5 with y=mx%2Bb we see the slope m=2 and the y-intercept b=-5 when x=0 or at point (0,b) or (0,-5).

Step 4. ANSWER: The slope m=2.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV
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Coordinate-system/224300: Two rectangles are similar. One has a length of 13 cm and a width of 10 cm, and the other has a width of 7 cm. Find the length of the second rectangle. Round to the nearest tenth if necessary.
1 solutions
Answer 167569 by drj(1380) About Me  on 2009-10-09 14:27:50 (Show Source):
You can put this solution on YOUR website!
Two rectangles are similar. One has a length of 13 cm and a width of 10 cm, and the other has a width of 7 cm. Find the length of the second rectangle. Round to the nearest tenth if necessary.

Step 1. Two rectangles are similar when the sides are in the same proportion.

Step 2. That is, Length%2FWidth=13%2F10=L%2F7 where L is the length of the second rectangle

Step 3. Solving for L by multiplying 7 to both sides of the equation in Step 2 yields L=13%2A7%2F10=5.10 cm

Step 4. ANSWER: The length of the second rectangle is 5.10 cm.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

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Numbers_Word_Problems/224304: what is the sum of the first 5000 odd numbers
1 solutions
Answer 167566 by drj(1380) About Me  on 2009-10-09 14:21:44 (Show Source):
You can put this solution on YOUR website!
What is the sum of the first 5000 odd numbers?

Step 1. So we need to add the first 5000 odd numbers from 1-9999.

Step 2. We note that 1+9999=10,0000 and 3+9997=10,000 5+9995=10,000 and so on.

Step 3. So we will have 2500 pairs of these numbers adding to 10,000.

Step 4. Then 2500*10000=25000000.

Step 5. ANSWER: The sum of the first 5000 odd numbers is 25 million.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV
http://www.Facebook.com/FreedomUniversityTV
http://www.Twitter.com/FreedomUTV






Linear-equations/224285: how do i find the slope and y intercept of 9y+2x+2=19+2x
1 solutions
Answer 167548 by drj(1380) About Me  on 2009-10-09 13:38:49 (Show Source):
You can put this solution on YOUR website!
How do i find the slope and y intercept of 9y+2x+2=19+2x

Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point(0,b).

Step 2. The following steps will put the equation in slope-intercept form.

9y%2B2x%2B2=19%2B2x

Subtract 2x+2 from both sides of the equation

9y%2B2x%2B2-2x-2=19%2B2x-2x-2

9y=17

Divide by 9 to both sides of the equation

9y%2F9=17%2F9

y=17%2F9

Step 3. So comparing y=17%2F9=0x%2B17%2F9 with y=mx%2Bb then the slope m=0 and y-intercept b=17%2F9 when x=0 or at point (0,17/9).

Step 4. ANSWER: The slope m=0 and the y-intercept b=17/9

I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV


Coordinate-system/224286: Use the factor to convert 90 seconds to minutes. Im not sure how to do this?
1 solutions
Answer 167539 by drj(1380) About Me  on 2009-10-09 13:20:57 (Show Source):
You can put this solution on YOUR website!
Use the factor to convert 90 seconds to minutes. I'm not sure how to do this?

Step 1. We note that 60 seconds = 1 minute

Step 2. 90 seconds * 1 minute/60 seconds = 90/60 minutes = 1.5 minutes

where the seconds cancel since it appears both in the numerator and denominator.

Step 3. ANSWER is 1.5 minutes which is equivalent to 90 seconds.
I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

http://www.FreedomUniversity.TV