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(18/w^2) - (10/w) + 1 = 0
1 solutions

Answer 161562 by drj(1380)   on 2009-09-15 18:14:23 (Show Source):
You can put this solution on YOUR website!
Solve by using the quadratic formula.

Step 1. Multiply above equation by to get rid of the denominator terms.

or

 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=28 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 7.64575131106459, 2.35424868893541. Here's your graph:

Based on the above steps the solutions simplify the solutions as follows:

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Linear-systems/213899: This question is from textbook algebra 2 how to solve linear systems algebraically problem: 6x-y=-2 -18x+3y=41 solutions Answer 161560 by drj(1380)   on 2009-09-15 18:02:03 (Show Source): You can put this solution on YOUR website! or Step 1. Let's rewrite the second equation where we can again rearrange by adding 18x to both sides of the equation to yield or dividing by 3 to both sides of the equation, we have Step 2. Now compare the following equivalent system of equations The above equations are in slope intercept form where m=6 for both equations. Step 3. ANSWER: When the equations of lines have the same slope there is NO SOLUTION since they cannot intersect at a point. 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
 Linear-equations/213898: find an equation for the line with y intercept 0 that is parallel yo y=2x-5.1 solutions Answer 161559 by drj(1380)   on 2009-09-15 17:45:34 (Show Source): You can put this solution on YOUR website!Find an equation for the line with y intercept 0 that is parallel yo y=2x-5. Step 1. Lines are parallel is when the slopes are equal. The slope of y=2x-5 is in slope intercept form given as y=mx+b where m is the slope and b is the y-intercept. For this example slope m=2 and y-intercept b=-5 Step 2. So the slope is m=2. We are given b=0 for the problem statement for the unknown line. Step 3. Therefore, the equation is y=2x (ANSWER) and is parallel with y=2x-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
Matrices-and-determiminant/213891: 2x+3y=-3
x+2y=2
This is the problem and my daughters teacher gave her this: -2R1+R2
Please explain how this is done
1 solutions

Answer 161557 by drj(1380)   on 2009-09-15 17:15:42 (Show Source):
You can put this solution on YOUR website!
2x+3y=-3
x+2y=2

The following solves the system of linear equations by substitution.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 3*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 and I don't understand the statement: -2R1+R2

And good luck in your studies!

Respectfully,
Dr J

Trigonometry-basics/213877: find x-intercept and y- intercept and graph
3x-2y+8=0
1 solutions

Answer 161556 by drj(1380)   on 2009-09-15 17:12:56 (Show Source):
You can put this solution on YOUR website!
Find x-intercept and y- intercept and graph

Step 1. x-intercept occurs when y=0 and y-intercept occurs when x=0.

Step 2. So at x=0 then

So y-intercept is 4 at point (0,4)

Step 3. At y=0 then

So x-intercept is -8/3 at point (-8/3,0)

Step 4. Here's the graph and note the x-intercept and y-intercept points on the graph.

 Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc Equation describes a sloping line. For any equation ax+by+c = 0, slope is .X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -8/3 = -2.66666666666667.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -8/-2 = 4.Slope is -3/-2 = 1.5. Equation in slope-intercept form: y=1.5*x+4.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Rectangles/213863: The perimeter of a square is 36 centimeters. Find the length of the diagonal.1 solutions Answer 161547 by drj(1380)   on 2009-09-15 16:19:29 (Show Source): You can put this solution on YOUR website!The perimeter of a square is 36 centimeters. Find the length of the diagonal. Step 1. Let P be the perimeter of a square which means adding up all four sides. Step 2. Let s be the side of a square. Step 3 Then 4s=36 or s=9 centimeters after dividing by 4 to both sides of equation. Step 4. Use Pythagorean Theorem to find diagonal which says that the sum of the square of the legs (=s^2+s^2=2s^2) is equal to square of the hypotenuse (diagonal in this case and letting d be the diagonal). Step 5. ANSWER: The length of diagonal is 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
 Angles/213862: two angles of a triangle measure 15 degree and 85 degree what is the measure for the third angle1 solutions Answer 161542 by drj(1380)   on 2009-09-15 16:08:01 (Show Source): You can put this solution on YOUR website!Two angles of a triangle measure 15 degree and 85 degree what is the measure for the third angle Step 1. The sum of the angles in a triangle is equal to 180 degrees. Step 2. Let x by the unknown third angle. Then Step 3. Subtract 100 from both sides of equation to get x ANSWER 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/213859: A rectangle is 10 inches long and 8 inches wide, what is the length of the diangonal?1 solutions Answer 161538 by drj(1380)   on 2009-09-15 15:59:33 (Show Source): You can put this solution on YOUR website!A rectangle is 10 inches long and 8 inches wide, what is the length of the diagonal? Step 1. Use the Pythagorean Theorem where the sum of the squares of the legs (length and width) is equal to the square of the hypotenuse (diagonal). Step 2. Let d be the diagonal, then ANSWER 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
Linear-systems/213849: What is the answer to this equation: 5x=+10-6x+3=6-2x-2 and can you tell me how you solved it please and thank you
1 solutions

Answer 161536 by drj(1380)   on 2009-09-15 15:55:18 (Show Source):
You can put this solution on YOUR website!
What is the answer to this equation: 5x+10-6x+3=6-2x-2 and can you tell me how you solved it please and thank you

The following steps will solve the following equation:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=-9. Graphical form: Equation was fully solved.Text form: 5x+10-6x+3=6-2x-2 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 5x+10-6x+3=6-2x-2 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
It becomes .

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It becomes .

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Eliminated similar terms , replacing them with
It becomes .

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Remove extraneous '1' from product
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Moved these terms to the left ,
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Moved to the right of expression
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Eliminated similar terms , replacing them with
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Remove extraneous '1' from product
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Solved linear equation equivalent to x+9 =0
It becomes .
Result:
This is an equation! Solutions: x=-9.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

Numbers_Word_Problems/213852: The sum of four consecutive even integers is 276. Find the four integers
1 solutions

Answer 161534 by drj(1380)   on 2009-09-15 15:49:01 (Show Source):
You can put this solution on YOUR website!
The sum of four consecutive even integers is 276. Find the four integers.

Step 1. Let n be one even integer, n+2 the next consecutive integer, n+4 and n+6 are the next two consecutive integers.

Step 2. So n+n+2+n+4+n+6=276 as given by the problem statement.

Step 3. Solve using the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=66. Graphical form: Equation was fully solved.Text form: n+n+2+n+4+n+6=276 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( n+n+2+n+4+n+6=276 )` 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 .
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*n-264 =0
It becomes .
Result:
This is an equation! Solutions: n=66.

### Universal Simplifier and Solver

Done!

Step 4. So the even integers are 66, 68, 70, 72. These integers add up to 276.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

Equations/213816: 2x +3y=6
1 solutions

Answer 161528 by drj(1380)   on 2009-09-15 15:10:10 (Show Source):
You can put this solution on YOUR website!

Here I assume you want to plot the line.

Step 1. Let's put it in slope-intercept form y=mx+b where m is the slope and b is the y-intercepts

Step 2. Subtract -2x from both sides of equation.

Step 3. Divide 3 to both sides of equation

Step 4. So y=-2x/3+2 where slope m=-2/3 and y-intercept b=2.

 Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc Equation describes a sloping line. For any equation ax+by+c = 0, slope is .X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/2 = 3.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/3 = 2.Slope is -2/3 = -0.666666666666667. Equation in slope-intercept form: y=-0.666666666666667*x+2.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

Linear-systems/213833: x/2=3+(x-30/5)
1 solutions

Answer 161525 by drj(1380)   on 2009-09-15 14:28:13 (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=6. Graphical form: Equation was fully solved.Text form: x/2=3+(x-30/5) simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( x/2=3+(x-30/5) )` 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 .
Factors 30 and 5 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes .

Look at .
It becomes .

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Moved to the right of expression
It becomes .

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It becomes .

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Moved these terms to the left ,
It becomes .

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Eliminated similar terms , replacing them with
It becomes .

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It becomes .

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Remove unneeded parentheses around factor ,
It becomes .

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

Look at .
Solved linear equation equivalent to -0.5*x+3 =0
It becomes .
Result:
This is an equation! Solutions: x=6.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

Linear-systems/213834: x/2=3+(x-30/5)
1 solutions

Answer 161524 by drj(1380)   on 2009-09-15 14:26:50 (Show Source):
You can put this solution on YOUR website!

Let's solve and simplify the above equation.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=6. Graphical form: Equation was fully solved.Text form: x/2=3+(x-30/5) simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( x/2=3+(x-30/5) )` 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 .
Factors 30 and 5 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes .

Look at .
It becomes .

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

Look at .
It becomes .

Look at .
Moved these terms to the left ,
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 .
Remove extraneous '1' from product
It becomes .

Look at .
Solved linear equation equivalent to -0.5*x+3 =0
It becomes .
Result:
This is an equation! Solutions: x=6.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Trigonometry-basics/213742: A Building AB, is observed across a street from the window of a house 7 metres above the ground. If the angle of elevation of the top of the building is 23degrees and the angle of depression of the foot of the building is 26degrees, calculate the height of the building.1 solutions Answer 161506 by drj(1380)   on 2009-09-15 11:25:04 (Show Source): You can put this solution on YOUR website!A Building AB, is observed across a street from the window of a house 7 metres above the ground. If the angle of elevation of the top of the building is 23degrees and the angle of depression of the foot of the building is 26degrees, calculate the height of the building. Step 1. Let d be the distance to the building from the window. Given depression angle is 26 degrees and the height of the window is 7 meters, then we have the opposite side is 7 and the adjacent side is x. In this case, we have metres Step 2. Let x = be the height above seven metre reference, then total height of building h=x+. Then from the window looking at the building we have an angle of elevation of 23 degrees. Then the opposite side is x and the adjacent side is d. We have Step 3. Then h=6.07+7=13.07 or 13.07 metres I hope the above steps were helpful. And good luck in your studies! 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. Respectfully, Dr J
Equations/213777: 1. x^3+216=0

2. 5x^3+30x^2+45x=0

3. 1/x^2+8/x+15=0

1 solutions

Answer 161503 by drj(1380)   on 2009-09-15 11:06:12 (Show Source):
You can put this solution on YOUR website!
1. x^3+216=0

Subtracting 216 from both sides of equation

2. 5x^3+30x^2+45x=0

where we have x=0, 5x+15=0 and x+3=0. Solving yields

x=0, x=-3 and x=-3, or solve quadratic equation using following steps,

 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=0 is zero! That means that there is only one solution: . Expression can be factored: Again, the answer is: -3, -3. Here's your graph:

3. 1/x^2+8/x+15=0 Multiply by x^2 to get rid of denominator

where we have 5x+1=0 and 3x+1=0. Solving yields

So x=(-1/5) and x=(-1/3)

We can also use the quadratic formula as follows:

 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=4 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.2, -0.333333333333333. Here's your graph:

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Functions/213768: Is a circle a 'function' - it does not pass the vertical line test. tks! 1 solutions Answer 161494 by drj(1380)   on 2009-09-15 09:48:06 (Show Source): You can put this solution on YOUR website!Is a circle a 'function' - it does not pass the vertical line test. tks! Yes. You are correct. But it is an equation like centered at (0,0) or radius 1. So at x=0 then y has two possible values at +1 and -1. Hope that was helpful!. I hope the above steps were helpful. And good luck in your studies! 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. Respectfully, Dr J
 logarithm/211994: find an expression or equation that is equivalent to the one given: log(3)-log(3)91 solutions Answer 161483 by drj(1380)   on 2009-09-15 08:43:53 (Show Source): You can put this solution on YOUR website!Find an expression or equation that is equivalent to the one given: log(3)-log(3)9 Factor out log(3) to get (1-9)log(3)=-8log(3)= -3.187 ANSWER 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
 Sequences-and-series/211895: what is the 20th term for this set of numbers? 12, 19,26, 331 solutions Answer 161482 by drj(1380)   on 2009-09-15 08:40:03 (Show Source): You can put this solution on YOUR website!What is the 20th term for this set of numbers? 12, 19,26, 33 Step 1. Look for a pattern. In this case the next number is 7 greater than the previous number. Step 2. Here's a formula for this set of numbers: so if n=1 then expression is 12 if n=2 then expression is 19. Step 3. Let n=20, then Step 4. ANSWER: The 20th term is 145 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/213731: Two angles are complementary. The larger of the two is 9 degrees more than twice the smaller. Find the 2 angles.
1 solutions

Answer 161481 by drj(1380)   on 2009-09-15 08:31:14 (Show Source):
You can put this solution on YOUR website!
Two angles are complementary. The larger of the two is 9 degrees more than twice the smaller. Find the 2 angles.

Step 1. Complementary angles is when 2 angles add up to 90 degrees.

Step 2. x is one angle and 2x+9

Step 3. Then x+2x+9=90

Step 4. Solve the above equation using the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=27. Graphical form: Equation was fully solved.Text form: x+2x+9=90 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( x+2x+9=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-81 =0
It becomes .
Result:
This is an equation! Solutions: x=27.

### Universal Simplifier and Solver

Done!

Step 5. ANSWER: The angles are x=27 degrees and 2x+9=2(27)+9=63 degrees

I hope the above steps were helpful.

Respectfully,
Dr J

Equations/213745: -4(a+1)-3a=7(2a-3)+3
1 solutions

Answer 161480 by drj(1380)   on 2009-09-15 08:26:39 (Show Source):
You can put this solution on YOUR website!

The following steps will solve the above problem

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: a=0.666666666666667. Graphical form: Equation was fully solved.Text form: -4*(a+1)-3a=7*(2a-3)+3 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( -4*(a+1)-3a=7*(2a-3)+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 .
Expanded term by using associative property on
It becomes .

Look at .
Multiplied numerator integers
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Moved to the right of expression
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It becomes .

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Eliminated similar terms , replacing them with
It becomes .

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It becomes .

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Remove unneeded parentheses around factor
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Expanded term by using associative property on
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Multiplied numerator integers
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Multiplied numerator integers
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Eliminated similar terms , replacing them with
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Remove unneeded parentheses around factor
It becomes .

Look at .
Solved linear equation equivalent to -21*a+14 =0
It becomes .
Result:
This is an equation! Solutions: a=0.666666666666667.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

Respectfully,
Dr J

 Equations/213746: 1/5(2x-7)=3/10x+51 solutions Answer 161478 by drj(1380)   on 2009-09-15 08:23:30 (Show Source): You can put this solution on YOUR website! Step 1. Multiply by 10 to both sides of equation to get rid of denominator. Step 2. add 14-3x to both sides of equation to isolate x on left side and number on right side of equation ANSWER 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
 Finance/213753: 5/8x+3/5=81 solutions Answer 161476 by drj(1380)   on 2009-09-15 08:16:03 (Show Source): You can put this solution on YOUR website! Step 1. Multiply by 40 to both sides to get rid of denominator Step 2. Subtract 24 from both sides of equation. Step 3. Divide by 25 to both sides of equation. 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
 Equations/213726: Gold has a density of 19.3g/cm^3. What is the mass in kilograms of one cubic meter of gold?1 solutions Answer 161457 by drj(1380)   on 2009-09-14 23:48:59 (Show Source): You can put this solution on YOUR website!Gold has a density of 19.3g/cm^3. What is the mass in kilograms of one cubic meter of gold? Step 1. 1 kg = 1000 g and 1 m = 100 cm Step 2. 19.3 g/cm^3 * 1kg/1000g * ((100)^3 cm^3/(1 m^3))* 1 m^3 = 19.3*1000000/1000 = 19.3*1000 kg = 1.93 x 10^4 kg Step 3. ANSWER is 19,300 kg 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/211951: 3x-y=-13
2x+y=-9
1 solutions

Answer 161455 by drj(1380)   on 2009-09-14 23:37:24 (Show Source):
You can put this solution on YOUR website!

The following solves the system of equations by substitution.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving -1*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.

Respectfully,
Dr J

Linear-equations/213723: This question is from textbook algebra one interactions course 2
use x- and y intercepts to draw the graph for 3x - y = 6
1 solutions

Answer 161454 by drj(1380)   on 2009-09-14 23:34:37 (Show Source):
You can put this solution on YOUR website!
Use x- and y intercepts to draw the graph for 3x - y = 6

Step 1. The y-intercept occurs when x=0. We have

so we have (0,-6) as one point on the line

Step 2. The x-intercept occurs when y=0. We have

{{x=2}}} so we have (2,0) as another point on the line.

Step 3. Using these points, we can graph as follows:

 Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc Equation describes a sloping line. For any equation ax+by+c = 0, slope is .X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/3 = 2.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/-1 = -6.Slope is -3/-1 = 3. Equation in slope-intercept form: y=3*x+-6.

Step 4. Observe the points (2,0) and (0,-6) that are on the line and how it intercepts the axis.

I hope the above steps were helpful.

Respectfully,
Dr J

 Equations/213688: The speed limit on a certain highway is 72 km/h. What is the speed in cm/s?1 solutions Answer 161451 by drj(1380)   on 2009-09-14 23:14:14 (Show Source): You can put this solution on YOUR website!The speed limit on a certain highway is 72 km/h. What is the speed in cm/s? Step 1. 1000 m = 1 km and 100 cm= 1 m or 10000 cm = 1 km Step 2. 72 km/h * 1000 m/km * 100 cm/m = 7,200,000 cm/h (note the units cancel in km and m when multiplying the units together. Step 3. Answer is 7.2 million cm/h 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/213715: This question is from textbook MATHPOWER 11
Solve by elimination. Check each solution.
21. 6x-5y=-3
2y-9x=-1
1 solutions

Answer 161449 by drj(1380)   on 2009-09-14 23:08:01 (Show Source):
You can put this solution on YOUR website!

Step 1. Rearrange to align the x and y terms.

multiply by 3 to both sides to get 18x
multiply by 2 to both sides to get -18x

Eq 1
Eq 2

Step 2. Adding above equations Eq 1 and Eq 2 yields

or y=1

Step 3. Substitute y=1 into 6x-5y=-3 yields

Step 4. The solution is and .

Step 5. To verify, the following will solve the linear systems using substitution.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving -5*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

Step 6. Same result...the solution is and .

I hope the above steps were helpful.

Respectfully,
Dr J

 Polynomials-and-rational-expressions/213564: Simplify the rational expression: 6y - -- 461 solutions Answer 161368 by drj(1380)   on 2009-09-14 18:43:58 (Show Source): You can put this solution on YOUR website!Simplify the rational expression: 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
Sequences-and-series/213568: Please help me find 2 consecutive even integers whose sum is 217. The best I got was 106.6 and 108.8 but still fall short. I have these a lot and need to know how to find these with a simple math trick or formula. (Algebra 1) Thanks
1 solutions

Answer 161365 by drj(1380)   on 2009-09-14 18:34:48 (Show Source):
You can put this solution on YOUR website!
Find 2 consecutive even integers whose sum is 217.

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

Step 2. Note: The sum of two even integers is always even. So in this example there is no solution since 217 is odd.

Step 3. Solve anyway as n+n+2=217 or 2n+2=217

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: n=107.5. Graphical form: Equation was fully solved.Text form: 2n+2=217 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 2n+2=217 )` 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 2*n-215 =0
It becomes .
Result:
This is an equation! Solutions: n=107.5.

Done!