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 Distributive-associative-commutative-properties/223600: factor by grouping 7a^2-2bc-7ab+2ac1 solutions Answer 167180 by drj(1380)   on 2009-10-08 10:31:05 (Show Source): You can put this solution on YOUR website! Step 1. Rearrange the order of terms so we can start grouping Step 2. Now factor out 7a from the first group and 2c from the second group. Step 3. We see that (a-b) is a common factor in the two groups, so factor it out... Step 4. 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
 Linear-equations/223654: Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and as dependent or independent. 5x-4y=-28 4y-5x=28 What is the solution of the system of equations? A. A point B. No solution C. Infinitely many solutions Is the system consistent or inconsistent? Are the equations dependent or independent?1 solutions Answer 167178 by drj(1380)   on 2009-10-08 10:22:56 (Show Source): You can put this solution on YOUR website!Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and as dependent or independent. 5x-4y=-28 Equation 1 4y-5x=28 Equation 2 or writing as -5x+4y=28 multiplying by -1 to both sides leads to an identical Equation 1. That is, Equations 1 and 2 are identical. What is the solution of the system of equations? A. A point B. No solution C. Infinitely many solutions (ANSWER) Is the system consistent or inconsistent? consistent Are the equations dependent or independent? dependent 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/223655: a rectangle carpet has a perimeter of 236 inches. The length of the carpet is 22 inches more than the width. what are the carpets dimensions...?
1 solutions

Answer 167177 by drj(1380)   on 2009-10-08 10:18:47 (Show Source):
You can put this solution on YOUR website!
A rectangle carpet has a perimeter of 236 inches. The length of the carpet is 22 inches more than the width. what are the carpets dimensions...?

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

Step 2. Let w be the width.

Step 3. Let w+22 be the length.

Step 4. Then, P=w+w+w+22+w+22=4w+44=236

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=48. Graphical form: Equation was fully solved.Text form: 4w+44=236 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 4w+44=236 )` 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 .
Added fractions or integers together
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 4*w-192 =0
It becomes .
Result:
This is an equation! Solutions: w=48.

Universal Simplifier and Solver

Done!

With and . And which is a true statement

Step 5. ANSWER: The width is 48 inches and the length is 70 inches.

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

Word_Problems_With_Coins/223618: John has \$2.05 in dimes and quarters. There are 3 more dimes than quarters. Find
the number of dimes and quarters. –setup system of equations and give the
solution
1 solutions

Answer 167174 by drj(1380)   on 2009-10-08 10:06:44 (Show Source):
You can put this solution on YOUR website!
John has \$2.05 in dimes and quarters. There are 3 more dimes than quarters. Find
the number of dimes and quarters. –setup system of equations and give the
solution

Step 1. Let x be the number of quarters.

Step 2. Let 0.25x be the dollar value of quarters.

Step 3. Let y be the number of dimes.

Step 4. Let 0.10y be the dollar value of dimes.

Step 5. Then 0.25x+0.10y=2.05 be the total dollar value.

Step 6. Also, y=x+3 since there are 3 more dimes than quarters

Step 7. Our linear system of equation is given in Steps 4 and 5 shown below:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 0.1*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

So x=5 and y=8. The difference is 3 and the total dollar value is 0.25*5+0.10*8=2.05 which is a true statement.

Step 8. ANSWER: The number of quarters is 5 and the number of dimes is 8.

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/223628: the perimeter of a rectangle is 140 m. The length is 4 m more than twice the width. Find the dimensions.
1 solutions

Answer 167172 by drj(1380)   on 2009-10-08 09:54:30 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 140 m. The length is 4 m more than twice the width. Find the dimensions.

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

Step 2. Let w be the width.

Step 3. Let 2w+4 be the length since it's 4 more than twice the width

Step 4. Then, P=w+w+2w+4+2w+4=6w+8=140

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=22. Graphical form: Equation was fully solved.Text form: 6w+8=140 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 6w+8=140 )` 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 .
Added fractions or integers together
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 6*w-132 =0
It becomes .
Result:
This is an equation! Solutions: w=22.

Universal Simplifier and Solver

Done!

With and . And which is a true statement

Step 5. ANSWER: The width is 22 meters and the length is 48 meters.

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/223646: The perimeter of a rectangle is 900 yards. What are the dimensions of the rectangle if the length is 30 yards more than the width?
1 solutions

Answer 167170 by drj(1380)   on 2009-10-08 09:50:41 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 900 yards. What are the dimensions of the rectangle if the length is 30 yards more than the width?

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

Step 2. Let w be the width.

Step 3. Let w+30 be the length.

Step 4. Then, P=w+w+w+30+w+30=4w+60=900

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=210. Graphical form: Equation was fully solved.Text form: 4w+60=900 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 4w+60=900 )` 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 .
Added fractions or integers together
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 4*w-840 =0
It becomes .
Result:
This is an equation! Solutions: w=210.

Universal Simplifier and Solver

Done!

With and . And which is a true statement

Step 5. ANSWER: The width is 210 yards and the length is 240 yards.

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/223553: the difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. find both numbers
1 solutions

Answer 167128 by drj(1380)   on 2009-10-08 00:57:39 (Show Source):
You can put this solution on YOUR website!
The difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. Find both numbers

Step 1. Let x be one smaller number

Step 2. Let y be the larger number.

Step 3. Then -x+y=12 since the difference of two numbers is 12.

Step 4. since two fifths of the greater number is six more than one third of the lesser number

Multiply by 15 to get rid of the denominators.

Subtract 5x from both sides of the equation

Step 5. So here's our system of linear equations From Steps 3 and 4:

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

Step 6. The numbers are 18 and 30.

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/223573: the perimeter of a rectangular field is 1,200 feet and the field is 50 feet longer than it is wide. what is the length, i feet, of the field?
1 solutions

Answer 167126 by drj(1380)   on 2009-10-08 00:50:50 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangular field is 1,200 feet and the field is 50 feet longer than it is wide. what is the length, in feet, of the field?

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

Step 2. Let w be the width.

Step 3. Let w+50 be the length.

Step 4. Then, P=1200=w+w+w+50+w+50.

Step 5. Solving leads to the following steps...

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=275. Graphical form: Equation was fully solved.Text form: 1200=w+w+w+50+w+50 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 1200=w+w+w+50+w+50 )` If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Added fractions or integers together
It becomes .

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

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

Look at .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

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

Look at .
Added fractions or integers together
It becomes .

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

Look at .
Solved linear equation equivalent to -4*w+1100 =0
It becomes .
Result:
This is an equation! Solutions: w=275.

Universal Simplifier and Solver

Done!

then and which is a true statement.

Step 6. ANSWER: The length of the field is 325 yards.

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/223562: Hi, I don't know how to do consecutive odd/even integers.
Such as this problem:

Find three consecutive integers whose sum is 36.

I know it's x+(x+2)+(x+3). Am I right? After all, they are 'consecutive', they are not odd or even.

Then the other one is:

Find two consecutive even integers whose sum is 126.

I did the first one, x+x+2=126
Then I subtracted two from both sides, and got x+x=124. Then I added like terms and got 2x=124. And then I simply divided by 2. And got 62.
I did the last question from another guy who answered another guy. But he didn't explain HOW to get the other one. I know the other answer is 64...but I do not know how to get it!
Please explain it clearly as I have an Algebra Test tomorrow, and I want to ace it.

Thanks. :)

1 solutions

Answer 167124 by drj(1380)   on 2009-10-08 00:42:32 (Show Source):
You can put this solution on YOUR website!
Find three consecutive integers whose sum is 36.

Step 1. Let n be the first integer.

Step 2. Let n+1 and n+2 be the next two consecutive integers.

Step 3. Then n+n+1+n+2=36 since the sum is 36.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=11. Graphical form: Equation was fully solved.Text form: n+n+1+n+2=36 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( n+n+1+n+2=36 )` If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Added fractions or integers together
It becomes .

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

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

Look at .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

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

Look at .
Added fractions or integers together
It becomes .

Look at .
It becomes .

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

Universal Simplifier and Solver

Done!

So , and Note integers add up to 36

Step 4. ANSWER: The integers are 11, 12, and 13.

Find two consecutive even integers whose sum is 126.

Step 1. Let n be the first even integer

Step 2. Let n+2 be the next consecutive even integers

Step 3. Then, n+n+2=126 since the sum is 126.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=62. Graphical form: Equation was fully solved.Text form: n+n+2=126 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( n+n+2=126 )` 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 .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

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

Look at .
Added fractions or integers together
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 2*n-124 =0
It becomes .
Result:
This is an equation! Solutions: n=62.

Universal Simplifier and Solver

Done!

and

Step 4. ANSWER: The consecutive even integers are 62 and 64

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

 Percentage-and-ratio-word-problems/223560: a bus is carrying 180 passengers which is 9/10 its capacity. What is its capacity?1 solutions Answer 167120 by drj(1380)   on 2009-10-08 00:18:04 (Show Source): You can put this solution on YOUR website!A bus is carrying 180 passengers which is 9/10 its capacity. What is its capacity? The capacity is or ANSWER: The capacity is 200. 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/223557: Please solve 6(5g+2)=30g1 solutions Answer 167119 by drj(1380)   on 2009-10-08 00:15:45 (Show Source): You can put this solution on YOUR website!Please solve 6(5g+2)=30g Step 1. Multiply out the terms to get rid of the parenthesis. Step 2. Subtract 30g from both sides of the equation This is not a true statement. Step 3. There is no solution to this 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
 Exponents/223259: Find each root cubed root of 8x^6y^31 solutions Answer 166980 by drj(1380)   on 2009-10-07 17:52:30 (Show Source): You can put this solution on YOUR website!Find each root cubed root of 8 x^6 y^3 cube root of 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_And_Systems_Word_Problems/223257: the second number is 3 less than twice the first number. Their sum is 57. Find the second number.1 solutions Answer 166978 by drj(1380)   on 2009-10-07 17:49:29 (Show Source): You can put this solution on YOUR website!The second number is 3 less than twice the first number. Their sum is 57. Find the second number. Step 1. Let n be the first number. Step 2. Let 2n-3 be the second number Step 3. Then n+2n-3=57 since the sum of the two numbers is 57. Step 4. Solving the equation in Step 3 Add 3 to both sides of the equation Divide 3 to both sides of the equation and . Note the sum is 57. Step 5. ANSWER: The second number is 37. 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/223253: If a wheel travels 1 mile in 1 minute, at a rate of 600 revolutions per minute, what is the diameter of the wheel, in feet? 1 solutions Answer 166977 by drj(1380)   on 2009-10-07 17:44:52 (Show Source): You can put this solution on YOUR website!If a wheel travels 1 mile in 1 minute, at a rate of 600 revolutions per minute, what is the diameter of the wheel, in feet? Step 1. Let d be the diameter of the wheel. Step 2. Let be the circumference of the wheel for one revolution Step 3. Note 1 mile = 5280 feet Step 4. Then 1 mile = 5280 ft= 600*pi*d since 600 revolutions occur in one minute. Step 5. Solving for feet Step 6. ANSWER: The diameter of the wheel is 2.80 feet. 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/223250: Having trouble with this problem. 2a+3a-13=a+31 solutions Answer 166975 by drj(1380)   on 2009-10-07 17:30:58 (Show Source): You can put this solution on YOUR website!Having trouble with this problem. 2a+3a-13=a+3 Step 1. Combine like terms and numbers Step 2. Add 13 to both sides of the equation to get number on the right side. Step 3. Subtract a to both sides of the equation to get a-terms on the left side. Step 4. Divide 4 to both sides of the equation Check............ which is a true statement. Step 5. 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
 Systems-of-equations/223154: how do you solve this equation by graphing x-y=3 x+y=51 solutions Answer 166970 by drj(1380)   on 2009-10-07 17:22:08 (Show Source): You can put this solution on YOUR website!How do you solve this equation by graphing x-y=3 x+y=5 Step 1. Plot the above equation using the slope intercept form 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. Put x-y=3 in slope intercept form or y=x-3 where we added y-3 to both sides of the equation. Here the slope m=1 and b=-3. Step 3. Put x+y=5 in slope intercept form where y=-x+5 where we added -x to both sides of the equation. Here the slope is m=-1 and b=5. Step 4. ANSWER: Based on the above graph, the two lines intersect at point (4,1) or x=4 and y=1. We can check by substituting in the original equations: or which is a true statement or which is also a true statement. So the point (4,1) is a solution to the system of equations. 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
Polynomials-and-rational-expressions/223191: If the sides of a square are lengthened by 8 cm, the area become 256cm^2. Find the length of the original square.
The length of the original square is ? cm.

1 solutions

Answer 166965 by drj(1380)   on 2009-10-07 17:10:22 (Show Source):
You can put this solution on YOUR website!
If the sides of a square are lengthened by 8 cm, the area become 256cm^2. Find the length of the original square.

The length of the original square is ? cm.

Step 1. Let x be the length of the original side of the square.

Step 2. Let x+8 be the length having an area of 256 square centimeters.

Step 3. Area A=(x+8)^2=256 since the area of the square is the square of its side x+8.

Step 4. Solving equation in Step 3 yields the following steps:

Subtract 256 from both sides of the equation

Step 5. To solve, use the quadratic formula given as

where a=1, b=16, and c=-192.

 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=1024 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 8, -24. Here's your graph:

Choosing the positive solution x=8. Note

Step 6. ANSWER: The length of the side of the original square is 8 cm.

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/223232: 9x-5(3x-12)=301 solutions Answer 166958 by drj(1380)   on 2009-10-07 17:01:37 (Show Source): You can put this solution on YOUR website!9x-5(3x-12)=30 Step 1. Multiply out the terms to get rid of the parenthesis and be careful or aware of the minus sign: Step 2. Combine the x-terms and add 60 to both sides of the equation Divide by -6 to both sides of the equation Check.............a true statement. Step 3. 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
 Pythagorean-theorem/223128: Find the area of a triangle with a base of 8 yd and a height of 19.1 yd. 1 solutions Answer 166899 by drj(1380)   on 2009-10-07 14:33:11 (Show Source): You can put this solution on YOUR website!Find the area of a triangle with a base of 8 yd and a height of 19.1 yd. The area A of a triangle is given as where b is the base and h is the height ANSWER: Area is 76.4 square yards 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
 expressions/223027: Solve. 8x-(6x+4)=12 The solution of x = ___1 solutions Answer 166866 by drj(1380)   on 2009-10-07 11:46:03 (Show Source): You can put this solution on YOUR website!Solve. The solution of x = ___ Step 1. Get rid of the parenthesis by distributing the negative (=-1) and combine line terms Step 2. Add 4 to both sides of the equation Step 3. Divide 8 to both sides of the equation Step 4. ANSWER. The solution is x=8. 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/223025: The problem isn't explaining it enough for me to understand here's the question
Solve the following system of equations by any method you wish
X + y = 6
Y = 2x – 3

1 solutions

Answer 166864 by drj(1380)   on 2009-10-07 11:42:27 (Show Source):
You can put this solution on YOUR website!
The problem isn't explaining it enough for me to understand here's the question
Solve the following system of equations by any method you wish

x + y = 6
y = 2x – 3 or -2x+y=-3

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 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

 Travel_Word_Problems/222988: The second angle of a triangle is 4 times as large as the first. The third angle is 120 degrees more than the sum of the two angles. Find the measure of the second angle.1 solutions Answer 166863 by drj(1380)   on 2009-10-07 11:40:54 (Show Source): You can put this solution on YOUR website!The second angle of a triangle is 4 times as large as the first. The third angle is 120 degrees more than the sum of the two angles. Find the measure of the second angle. Step 1. The three angles of a triangle add up to 180 degrees. Step 2. Let x be the first angle. Step 3. Let 4x be the second angle since it is 4 times as large as the first. Step 4. Let x+4x=5x be the sum of the first two angles. Step 5. Let 5x+120 be the third angle since it is 120 degrees more than the sum of the two angles. Step 6. Then, x+4x+5x+120=180 degrees. Step 7. Solving the equation in Step 6 yields the following steps Subtract 120 from both sides of the equation Divide 10 to both sides of the equation . Then and . Note these three angles add up to 180 degrees. Step 8. ANSWER: The second angle is 24 degrees. 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
Age_Word_Problems/222991: Kimberly is twice as old as Ryan. In 4 years, she will be 7 years older than Ryan. How old is Kimberly now?

1 solutions

Answer 166862 by drj(1380)   on 2009-10-07 11:32:56 (Show Source):
You can put this solution on YOUR website!
Kimberly is twice as old as Ryan. In 4 years, she will be 7 years older than Ryan. How old is Kimberly now?

Step 1. Let x be the age of Ryan

Step 2. Let 2x be the age of Kimberly

Step 3. Let x+4 be the age of Ryan in 4 years

Step 4. Let 2x+4 be the age of Kimberly in 4 years.

Step 5. 2x+4=x+4+7 since Kimberly will be 7 years older than Ryan in four years.

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

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: 2x+4=x+4+7 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 2x+4=x+4+7 )` If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Added fractions or integers together
It becomes .

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

Look at .
Added fractions or integers together
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 .
Remove extraneous '1' from product
It becomes .

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

Universal Simplifier and Solver

Done!

With then

Step 7. ANSWER: Kimberly is 14 years old.

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

 Human-and-algebraic-language/222997: The perimeter of a rectangle is 44 meters. The length is 2 meters more than the three times the width. Find the length.1 solutions Answer 166860 by drj(1380)   on 2009-10-07 11:25:48 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 44 meters. The length is 2 meters more than the three times the width. Find the length. Step 1. The perimeter P means adding up all four sides of a rectangle. Step 2. Let w be the width Step 3. Let 3w be three times the width Step 4. Let 3w+2 be the length since it is 2 meters more than three times the width Step 5. Then P=w+w+3w+2+3w+2=8w+4=44 since the perimeter P is 44 meters. Step 6. Solving the equation in Step 4 leads to the following steps Subtract four from both sides Divide by 8 to both sides of the equation and 3w+2=15+2=17 and P=2(5+17)=44 which is a true statement. Step 7. The length is 17 meters. 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
 Problems-with-consecutive-odd-even-integers/223001: Find three consecutive even integers whose sum is 36.1 solutions Answer 166856 by drj(1380)   on 2009-10-07 11:18:47 (Show Source): You can put this solution on YOUR website!Find three consecutive even integers whose sum is 36. Step 1. Let n be an even integer. Step 2. Let n+2 and n+4 be the next two consecutive even integers. Step 3. Then n+n+2+n+4=36 since the sum of these three even integers is 36. Step 4. Solving yields the following steps Subtract 6 from both sides of the equation Divide by 3 to both sides of the equation nad . Not these three even integers add up to 36. Step 5. ANSWER: The three consecutive even integers are 10, 12, and 14. 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