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Geometry_Word_Problems/223774: The perimeter of a rectangle is 60cm. If the length is decreased by 5 and the width is halved, the perimeter will decrease by 20cm. What are the length and width of the original rectangle?
1 solutions

Answer 167270 by drj(1380)   on 2009-10-08 16:07:03 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 60cm. If the length is decreased by 5 and the width is halved, the perimeter will decrease by 20cm. What are the length and width of the original rectangle?

Step 1. Perimeter P means adding up all 4 sides of a rectangle.

Step 2. Let w be the original width.

Step 3. Let L be the original length.

Step 4. Let w/2 be the width cut in half

Step 5. Let L-5 be the length reduced by 5

Step 6. Then, original perimeter P0=L+L+w+w=2L+2w=60

Step 7. Then, new perimeter or after adding 10 to both sides.

Step 8. Our linear system of equation is given in Steps 6 and 7 as

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 2*w to the right, we get:
, or . Substitute that
into another equation:
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

With and . And and which are true statements.

Step 5. ANSWER: The width is 10 cm and the length is 20 cm.

I hope the above steps were helpful.

Respectfully,
Dr J

Average/223783: x^2 + 8x = 9.
1 solutions

Answer 167268 by drj(1380)   on 2009-10-08 15:53:03 (Show Source):
You can put this solution on YOUR website!

Step 1. Subtract 9 from both sides of the equation to get a quadratic equation

Step 2. To solve, use the quadratic formula given as

where a=1, b=8, and c=-9

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=100 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1, -9. Here's your graph:

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV

 Linear-equations/223781: How would you put this expression in algebraic form? The difference of twice x and y is 61 solutions Answer 167267 by drj(1380)   on 2009-10-08 15:33:24 (Show Source): You can put this solution on YOUR website!How would you put this expression in algebraic form? The difference of twice x and y is 6 Step 1. Let 2x be twice x. Step 2. Let 2x-y be the difference of twice x and y. Step 3. Then 2x-y=6 since the difference of twice x and y is 6. Step 4. ANSWER: 2x-y=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 http://www.Facebook.com/FreedomUniversity.TV http://www.Twitter.com/FreedomUTV
Surface-area/223776: find the dimensions of the rectangle meeting the specified conditions
the perimeter is 320 cm and the width is 20 cm less than the length
1 solutions

Answer 167265 by drj(1380)   on 2009-10-08 15:30:47 (Show Source):
You can put this solution on YOUR website!
Find the dimensions of the rectangle meeting the specified conditions
the perimeter is 320 cm and the width is 20 cm less than the length

Step 1. Let L be the length

Step 2. Let L-20 be the width since it's 20 cm less than the length

Step 3. Perimeter P means adding up all 4 sides of the rectangle.

Step 4. Then, P=L+L+L-20+L-20=320 since perimeter is 320 cm.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: L=90. Graphical form: Equation was fully solved.Text form: L+L+L-20+L-20=320 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( L+L+L-20+L-20=320 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
It becomes .

Look at .
Eliminated similar terms ,,, replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Moved these terms to the left
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 4*L-360 =0
It becomes .
Result:
This is an equation! Solutions: L=90.

### Universal Simplifier and Solver

Done!

With and L-20=70}}}. Also which is a true statement.

Step 5. The dimensions are that the length is 90 cm and the width is 70 cm.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV

9x^2+6x-4=0
I have solved it down to -6 sqrt 180 / 18.
this is also the same as your sight gave me, but the answer key says this.
-1 sqrt 5 / 5
1 solutions

Answer 167250 by drj(1380)   on 2009-10-08 14:48:46 (Show Source):
You can put this solution on YOUR website!

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=180 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.412022659166597, -1.07868932583326. Here's your graph:

and

So, you are in the right track.

I hope the above steps were helpful.

Respectfully,
Dr J

 Numeric_Fractions/223758: how do you solve 8u-2=7u-4 ?1 solutions Answer 167245 by drj(1380)   on 2009-10-08 14:40:33 (Show Source): You can put this solution on YOUR website!How do you solve 8u-2=7u-4 ? Step 1. Subtract 7u from both sides of the equation Step 2. Add 2 to both sides of the equation to solve for u. Check............which is a true statement. Step 3. ANSWER: Solution is 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/223752: how do i find the equation for 3/4(6,-1)1 solutions Answer 167241 by drj(1380)   on 2009-10-08 14:35:50 (Show Source): You can put this solution on YOUR website!how do i find the equation for 3/4 (6,-1) Here, I assume you meant the slope is passing through the point (6,-1) Write an equation for the line described as slope and passes through (6,-1). Write equation in slope-intercept form. Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept b at x=0 or point (0,b). Here, the slope m=3/4. Step 2. The slope m is given as Step 3. Let (x1,y1)=(6,-1) or x1=6 and y1=-1. Let other point be (x2,y2)=(x,y) or x2=x and y2=y. Step 4. Now we're given . Substituting above values and variables in the slope equation m yields the following steps: Step 5. Multiply (x-6) to both sides to get rid of denominators on both sides of equation. Step 6. Now add -1 to both sides of equation to solve for y. Step 7. ANSWER: The equation is Here's a graph below and note the slope and y-intercept at x=0 or point (0,-7) and the x-intercept at y=0 or at point (51/3, 0)and note it is consistent with the equation when substituting these Note: the above equation can be rewritten in standard form as 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
1 solutions

Answer 167235 by drj(1380)   on 2009-10-08 14:20:57 (Show Source):
You can put this solution on YOUR website!

Use the quadratic formula to solve this and given below as

where a=2, b=-5 and c=3

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=1 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.5, 1. Here's your graph:

I hope the above steps were helpful.

Respectfully,
Dr J

 Surface-area/223747: WHAT IS THE VOLUM EOF A CUBOID WITH WIDTH 2CM, LENGTH 5CM AND HIEGHT 3CM?1 solutions Answer 167232 by drj(1380)   on 2009-10-08 14:14:37 (Show Source): You can put this solution on YOUR website!WHAT IS THE VOLUME OF A CUBOID WITH WIDTH 2 CM, LENGTH 5 CM AND HEIGHT 3 CM? Step 1. The volume V=width*length*height Step 2. Then, cubic centimeters. Step 3. ANSWER: The volume of a cuboid is 30 cubic centimeters. 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
Numbers_Word_Problems/223673: The sum of a number and two is three more than twice the same number
1 solutions

Answer 167229 by drj(1380)   on 2009-10-08 14:01:33 (Show Source):
You can put this solution on YOUR website!
The sum of a number and two is three more than twice the same number.

Step 1. Let n be the number

Step 2. Let n+2 be the sum of a number and 2.

Step 3. Let 2n+3 be three more than twice the number.

Step 4. Then n+2=2n+3 since the sum of a number and two is three more than twice the same number.

Step 5. Solving the equation in Step 4 yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=-1. Graphical form: Equation was fully solved.Text form: n+2=2n+3 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( n+2=2n+3 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved these terms to the left ,
It becomes .

Look at .
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
It becomes .

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Remove extraneous '1' from product
It becomes .

Look at .
Solved linear equation equivalent to -n-1 =0
It becomes .
Result:
This is an equation! Solutions: n=-1.

### Universal Simplifier and Solver

Done!

Step 6. ANSWER: The number is -1.

I hope the above steps were helpful.

Respectfully,
Dr J

 Sequences-and-series/223743: what is the general term for sequence 1,2,3,4,5,6.....1 solutions Answer 167227 by drj(1380)   on 2009-10-08 13:56:41 (Show Source): You can put this solution on YOUR website!what is the general term for sequence 1,2,3,4,5,6..... The general term for this example is "n". So if n=500 then the 500th term is 500. If the first term n=1 then, the first term is 1, etc. 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
1 solutions

Answer 167226 by drj(1380)   on 2009-10-08 13:53:46 (Show Source):
You can put this solution on YOUR website!

To solve, use the quadratic formula given as

where a=1, b=-2, and c=-13.

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=56 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.74165738677394, -2.74165738677394. Here's your graph:
\

I hope the above steps were helpful.

Respectfully,
Dr J

 Travel_Word_Problems/223682: A plane traveling at a constant speed is able to travel 750 miles in 5 hours. How fast is the plane flying?1 solutions Answer 167225 by drj(1380)   on 2009-10-08 13:51:22 (Show Source): You can put this solution on YOUR website!A plane traveling at a constant speed is able to travel 750 miles in 5 hours. How fast is the plane flying? Step 1. speed = distance / time Step 2. speed = 750 miles/ 5 hours = 150 miles per hour = 150 mph. Step 3. ANSWER: The plane's speed is 150 mph. 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
Problems-with-consecutive-odd-even-integers/223722: If the sum of three consecutive odd integers is 411, what is the first integer?

A 131
B 133
C 135
D 137
E 139
1 solutions

Answer 167224 by drj(1380)   on 2009-10-08 13:48:40 (Show Source):
You can put this solution on YOUR website!
If the sum of three consecutive odd integers is 411, what is the first integer?

A 131
B 133
C 135
D 137
E 139

Step 1. Let n be one odd integer.

Step 2. Let n+2 and n+4 be the next two odd consecutive integer.

Step 3. Then n+(n+2)+(n+4)=411 be the sum of three odd integers

Step 4. Solving n+(n+2)+(n+4)=411 yields the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=135. Graphical form: Equation was fully solved.Text form: n+(n+2)+(n+4)=411 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( n+(n+2)+(n+4)=411 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around terms ,
It becomes .

Look at .
Remove unneeded parentheses around terms ,
It becomes .

Look at .
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
Eliminated similar terms ,, replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Moved these terms to the left
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 3*n-405 =0
It becomes .
Result:
This is an equation! Solutions: n=135.

### Universal Simplifier and Solver

Done!

and

Check sum...135+137+139... which is a true statement

Step 5. ANSWER: The three consecutive odd integers are 135, 137, and 139. The first integer is 135 so the solution is C.

I hope the above steps were helpful.

Respectfully,
Dr J

 Probability-and-statistics/223726: In a standard deck of 52 playing cards, what is the probability of drawing an odd number? 1 solutions Answer 167219 by drj(1380)   on 2009-10-08 13:34:11 (Show Source): You can put this solution on YOUR website!In a standard deck of 52 playing cards, what is the probability of drawing an odd number? Step 1. Since over half of the cards are odd or 28 cards (counting the 8 face cards of Jacks and Kings as an odd number plus 20 cards (4 sets of the cards 1, 3, 5, 7, 9) then (ANSWER if you count face cards as either odd or even) Step 2. If you don't card the face cards as odd or even then you have 20 cards. (ANSWER if you don't count the face cards as either odd or even) 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
 Functions/223733: Simplify –y – (–y + 4). A. 2y + 4 B. –2y + (–4) C. –4 D. 4 = I got C, is it right ?? Thanks !1 solutions Answer 167214 by drj(1380)   on 2009-10-08 13:22:38 (Show Source): You can put this solution on YOUR website!Simplify –y – (–y + 4). A. 2y + 4 B. –2y + (–4) C. –4 D. 4 ANSWER: The solution is C. So you are correct. Good Job! 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
Rectangles/223729: The perimeter of a rectangle is 64 meters. the sum of the length and width is 32 meters. Find the length and width of the rectangle.
Tried 2x+2y= 64
x+y=32...now what? Thanks so much!
1 solutions

Answer 167213 by drj(1380)   on 2009-10-08 13:20:09 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 64 meters. The sum of the length and width is 32 meters. Find the length and width of the rectangle.

Step 1. Perimeter P means adding up all 4 sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 32-w be the length.

Step 4. Then, P=w+w+w-32+w-32=4w-64=64

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=32. Graphical form: Equation was fully solved.Text form: 4w-64=64 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 4w-64=64 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved these terms to the left
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 4*w-128 =0
It becomes .
Result:
This is an equation! Solutions: w=32.

### Universal Simplifier and Solver

Done!

With and . And which is a true statement. But the answer is not realistic.

Step 5. ANSWER: The width is 32 meters and the length is 0 meters to satisfy the problem statement. So you were on the right track but note your equations are also identical if you multiply one of them by 2.

I hope the above steps were helpful.

Respectfully,
Dr J

 Probability-and-statistics/223725: In a standard deck of 52 playing cards, what is the probability of drawing an even number?1 solutions Answer 167209 by drj(1380)   on 2009-10-08 13:12:38 (Show Source): You can put this solution on YOUR website!In a standard deck of 52 playing cards, what is the probability of drawing an even number? Step 1. Since almost half of the cards are even or 24 cards (counting the 4 face cards of queen as an even number plus 20 cards (4 sets of the cards 2,4,6,8,10) then (ANSWER if you count face cards as either odd or even) Step 2. If you don't card the face cards as odd or even then you have 20 cards. (ANSWER if you don't count the face cards as either odd or even) 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
Geometry_Word_Problems/223710: what is the length of a rectangle is twice its width if the width is increased by one meter and the length is diminished by three meters the area will be 12 square meters
1 solutions

Answer 167206 by drj(1380)   on 2009-10-08 12:57:27 (Show Source):
You can put this solution on YOUR website!
What is the length of a rectangle is twice its width if the width is increased by one meter and the length is diminished by three meters the area will be 12 square meters.

Step 1. Let w be the width

Step 2. Let 2w be the length.

Step 3. Let w+1 be the width increased by one meter.

Step 4. Let 2w-3 be the length diminished by three meters.

Step 5. The Area A=(w+1)(2w-3)=12 since the area will be 12 meters with these changed dimensions.

Step 6. Solving the equation in Step 5 will lead to a quadratic equation as follows:

Subtract 12 from both sides of the equation

Step 7. To solve, use the quadratic formula given as

where a=2, b=-1, and c=-15.

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=121 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3, -2.5. Here's your graph:

Selecting the positive solution given as , then . Check area A with width 3+1=4 and length 2w-3=3. So the area with these dimensions is 12 as given by the problem statement.

Step 8. ANSWER: The length is 6 meters.

I hope the above steps were helpful.

Respectfully,
Dr J

Angles/223720: Two angles are complementary if their sum is 90 degrees. If two complementary angles have the measures of x degrees and (2x - 3) degrees, find the measure of each angle.

1 solutions

Answer 167204 by drj(1380)   on 2009-10-08 12:47:10 (Show Source):
You can put this solution on YOUR website!
Two angles are complementary if their sum is 90 degrees. If two complementary angles have the measures of x degrees and (2x - 3) degrees, find the measure of each angle.

Then, x+2x-3=90

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=31. Graphical form: Equation was fully solved.Text form: x+2x-3=90 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( x+2x-3=90 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Moved these terms to the left
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 3*x-93 =0
It becomes .
Result:
This is an equation! Solutions: x=31.

### Universal Simplifier and Solver

Done!

With then,

ANSWER: The complementary angles are 31 degrees and 59 degrees.

I hope the above steps were helpful.

Respectfully,
Dr J

Linear-equations/223719: 7x-8-4x=25
1 solutions

Answer 167202 by drj(1380)   on 2009-10-08 12:44:26 (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=11. Graphical form: Equation was fully solved.Text form: 7x-8-4x=25 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 7x-8-4x=25 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved to the right of expression
It becomes .

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Moved these terms to the left
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 3*x-33 =0
It becomes .
Result:
This is an equation! Solutions: x=11.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

Respectfully,
Dr J

Unit_Conversion_Word_Problems/223711: the sum of of four times a number and three is the same as the difference of twice the number and eleven.find the number
1 solutions

Answer 167201 by drj(1380)   on 2009-10-08 12:43:26 (Show Source):
You can put this solution on YOUR website!
The the sum of of four times a number and three is the same as the difference of twice the number and eleven. Find the number.

Step 1. Let x be a number

Step 2. Let 4x+3 be the sum of four times a number and three.

Step 3. Let 2x-11 be the difference of twice the number and eleven.

Step 4. Set Steps 2 and 3 to be equal: since the the sum of of four times a number and three is the same as the difference of twice the number and eleven.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=-7. Graphical form: Equation was fully solved.Text form: 4x+3=2x-11 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 4x+3=2x-11 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved these terms to the left ,
It becomes .

Look at .
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Solved linear equation equivalent to 2*x+14 =0
It becomes .
Result:
This is an equation! Solutions: x=-7.

### Universal Simplifier and Solver

Done!

Step 5. ANSWER: The number is -7.

I hope the above steps were helpful.

Respectfully,
Dr J

 decimal-numbers/223712: Express this number in scientific notation 1,900,0001 solutions Answer 167200 by drj(1380)   on 2009-10-08 12:36:31 (Show Source): You can put this solution on YOUR website!Express this number in scientific notation where I counted the number of decimal places to the right of 1 which in this case is 6. 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
 decimal-numbers/223714: Express this number in decimal form (8.6 * 10^2)(4.6 * 10^-5)1 solutions Answer 167199 by drj(1380)   on 2009-10-08 12:34:13 (Show Source): You can put this solution on YOUR website!Express this number in decimal form 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
 decimal-numbers/223715: Express this number in decimal form without exponents. 8.1 * 10^2 divided by 0.9 * 10^-41 solutions Answer 167197 by drj(1380)   on 2009-10-08 12:32:06 (Show Source): You can put this solution on YOUR website!Express this number in decimal form without exponents. 8.1 * 10^2 divided by 0.9 * 10^-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
 decimal-numbers/223713: Express this number in decimal form without exponents 8.529 * 10^-51 solutions Answer 167195 by drj(1380)   on 2009-10-08 12:29:00 (Show Source): You can put this solution on YOUR website! where I moved the decimal point 5 places to the left. 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
Expressions-with-variables/223704: The length of a rectangle is 3 in. more than its width. The perimeter of the rectangle is 30 in.
a. Define a variable for width.
b. Write and expression for the length in terms of width.
c. Write an equation to find the width of the rectangle. Solve your equation.
d. What is the length of the rectangle?
1 solutions

Answer 167194 by drj(1380)   on 2009-10-08 12:21:45 (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 3 in. more than its width. The perimeter of the rectangle is 30 in.

Step 1. Perimeter P means adding up all 4 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=4w+6=30

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=6. Graphical form: Equation was fully solved.Text form: 4w+6=30 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 4w+6=30 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved these terms to the left
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 4*w-24 =0
It becomes .
Result:
This is an equation! Solutions: w=6.

### Universal Simplifier and Solver

Done!

With and . And which is a true statement

Step 5. ANSWER: The width is 6 inches and the length 9 inches yards.

I hope the above steps were helpful.

Respectfully,
Dr J

Human-and-algebraic-language/223660: The sum of two numbers is twelve. The total of three times the smaller number and six amounts to seven less than the product of four and the larger number. Find the two numbers.
1 solutions

Answer 167183 by drj(1380)   on 2009-10-08 10:49:15 (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is twelve. The total of three times the smaller number and six amounts to seven less than the product of four and the larger number. Find the two numbers.

Step 1. Let x be one number

Step 2. Let 12-x be the other number

Step 3. 3x+6=4*(12-x)-7 since the total of three times the smaller number and six amounts to seven less than the product of four and the larger number.

Step 4. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=5. Graphical form: Equation was fully solved.Text form: 3x+6=4*(12-x)-7 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 3x+6=4*(12-x)-7 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved to the right of expression
It becomes .

Look at .
Moved these terms to the left ,
It becomes .

Look at .
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
Expanded term by using associative property on
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Solved linear equation equivalent to 7*x-35 =0
It becomes .
Result:
This is an equation! Solutions: x=5.

### Universal Simplifier and Solver

Done!

With x=5, then 12-5=7

Check... or which is a true statement.

Step 5. ANSWER: The numbers are 5 and 7

I hope the above steps were helpful.

Respectfully,
Dr J

Linear-equations/223662: what is the solution to the equation -5x+4y=6 and 3x-y=2
1 solutions

Answer 167182 by drj(1380)   on 2009-10-08 10:45:10 (Show Source):
You can put this solution on YOUR website!
What is the solution to the equation -5x+4y=6 and 3x-y=2

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 4*y to the right, we get:
, or . Substitute that
into another equation:
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.