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Graphs/216390: graph the inequality 3x-2y>9
1 solutions

Answer 163392 by drj(1380)   on 2009-09-23 22:22:13 (Show Source):
You can put this solution on YOUR website!
Graph the inequality

Step 1. Let's put the inequality as a 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. Add 2y-9 to both sides of the inequality to yield

Step 3. Divide 2 to both sides of the inequality

or

 Solved by pluggable solver: Plot Any Inequality Graphing function :

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 Trigonmetry please visit http://www.FreedomUniversity.TV/courses/Trignometry.

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

Respectfully,
Dr J

 Rectangles/216380: the area of rectangle is 45 square inches. One demension is 5 inches. What is the perumeter.1 solutions Answer 163385 by drj(1380)   on 2009-09-23 22:12:09 (Show Source): You can put this solution on YOUR website!The area of rectangle is 45 square inches. One dimension is 5 inches. What is the perimeter. Step 1. Let where is the width and is the length. Step 2. Given inches, then inches. Step 3. Perimeter P means adding up all four sides or inches Step 4. ANSWER: The perimeter is 28 inches. 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 Trigonmetry please visit http://www.FreedomUniversity.TV/courses/Trignometry. Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs. Respectfully, Dr J
 Geometry_Word_Problems/216373: find the demensions of a rectangle , if the area equals 144 square in. and the length and the width are in the ratio of 2 to 1/2 .(hint : in order to eliminate the fraction , the ratio may be changed to 4 to 1 .) 1 solutions Answer 163380 by drj(1380)   on 2009-09-23 22:04:45 (Show Source): You can put this solution on YOUR website!Find the dimensions of a rectangle , if the area equals 144 square in. and the length and the width are in the ratio of 2 to 1/2. (hint : in order to eliminate the fraction , the ratio may be changed to 4 to 1. Step 1. Let A=Area = width * length = 144 square inches Step 2. Let w be the width and 4w be the length. Step 3. Then Step 4. Divide 4 to both sides of equation. Step 5. Take the square root yields or Step 6. Then ...Check the area ...which is a true statement. Step 7. ANSWER: The dimensions are 6 feet as the width and 24 feet as the length. 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 Trigonmetry please visit http://www.FreedomUniversity.TV/courses/Trignometry. Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs. Respectfully, Dr J
 Coordinate-system/216306: Graph the equation. y=-x squared+41 solutions Answer 163355 by drj(1380)   on 2009-09-23 20:42:59 (Show Source): You can put this solution on YOUR website!Graph Step 1. Form two columns: one for x and one for y. Try different values of x say -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Substitute x into the equation for y. For example when x=0, then y=0^2+4=4. So one point on the graph is (0,4) and see graph in Step 2. Try the other values of x. Step 2. Here's the graph: 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/216310: Find two consecutive odd integers in which the sum is equal to one or more than three times the smallest1 solutions Answer 163350 by drj(1380)   on 2009-09-23 20:38:13 (Show Source): You can put this solution on YOUR website!Find two consecutive odd integers in which the sum is equal to one or more than three times the smallest. Step 1. Let n be one odd integer and let n+2 be the next consecutive integer. Step 2. Let 3n be three times the smallest. Step 3. Then n+n+2=1+3n or 2n+2=1+3n. Then n=1 and n+2=3. Step 4. ANSWER: The numbers are 1 and 3. 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/216326: Two angles are supplementary. One angle measures 12 degrees more than the other. What is the measure of the angles. 1 solutions Answer 163347 by drj(1380)   on 2009-09-23 20:31:40 (Show Source): You can put this solution on YOUR website!Two angles are supplementary. One angle measures 12 degrees more than the other. What is the measure of the angles. Step 1. Supplementary angles means that two angles add up to 180 degrees. Step 2. Let x be one angle and let x+12 be its supplementary angle and one angle measures 12 degrees more than the other Step 3. Then x+x+12=180 or 2x+12=180. Subtracting 12 from both sides of the equation yields 2x=168. Dividing by 2 to both sides yields x=84 degrees. Then x+12=96. Also, note that 84+96 add up to 180 degrees. Step 4. ANSWER: The supplementary angles are 84 and 96 degrees. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J
 Radicals/216327: what you would do to simplify each one. 1. (16)^(1/2) 2. √1001 solutions Answer 163341 by drj(1380)   on 2009-09-23 20:27:59 (Show Source): You can put this solution on YOUR website!What you would do to simplify each one. 1. Since square root has an exponent of 1/2 and 4*4=16 2. Since 10*10=100. 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/216320: the length of a rectangle Is 6 feet more than three times the width. the area of the rectanle is 240 square feet. what are the dimensions?
1 solutions

Answer 163338 by drj(1380)   on 2009-09-23 20:26:03 (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 6 feet more than three times the width. The area of the rectangle is 240 square feet. What are the dimensions?

Step 1. Let w be the width and 3w+6 is the length since rectangle is 6 feet more than three times the width.

Step 2. Area = width * length = w(3w+6) = 240 square feet

Step 3. Then we can put the equation in Step 2 in quadratic form

Subtract 240 to both sides of the equation

Step 4. We can use the quadratic formula given as

where a=3, b=6, and c=-240

 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=2916 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 8, -10. Here's your graph:

So select the positive solution for positive dimensions:

and

Verify area.... ...which is a true statement.

Step 5. Dimensions of the rectangle are a width of 8 feet and a length of 30 feet.

I hope the above steps were helpful.

http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Respectfully,
Dr J

Matrices-and-determiminant/216281: find the intersection of these two lines...
3x=2+4y
2y=6-5x
I can not figure this out to save my life!!
1 solutions

Answer 163328 by drj(1380)   on 2009-09-23 20:08:22 (Show Source):
You can put this solution on YOUR website!
find the intersection of these two lines...

Equation A
Equation B

Step 1. Let's put the variable terms x and y on the left side and numbers on the right side of equation as given by Step 2.

Step 2. For Equation A, subtract 4y to both sides of the equation and; for equation B add 5x to both sides of the equation.

Equation A-1
Equation B-1

Step 3. Multiply 2 to both sides of Equation B-1 to get

Equation A-1
Equation B-2

Step 4. Add Equations A-1 and B-2 and note the y-terms cancel each other out leaving the x-terms on the left side.

or

Step 5. Substitute this value of x into either Equations A-1 or B-2. Let's choose Equation A-1.
Equation A-1

Multiply by 13 to both sides of equation to get rid of denominator

Add 52y-26 to both sides of equation

Divide 52 to both sides of the equation

Step 6. ANSWER: So x=14/13 and y=4/13 or the intersection point is (14/13,4/13).

We can verify the above result by substituting these values into both equations to see if it leads to a true statement.

Here's another approach to solving the linear system equations by substitution:

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

Same result as before.

I hope the above steps were helpful.

http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Respectfully,
Dr J

 Finance/216147: what is 18=5p+3?1 solutions Answer 163238 by drj(1380)   on 2009-09-23 17:00:40 (Show Source): You can put this solution on YOUR website!what is 18=5p+3? Step 1. Subtract 3 from both sides of equation to get p-terms on right side and numbers only on left side. Step 2. Divide 5 from both sides of the equation Check if or which is 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
Systems-of-equations/216118: How do you solve this(7a+3)+(-a-5)=-16?
1 solutions

Answer 163229 by drj(1380)   on 2009-09-23 16:46:51 (Show Source):
You can put this solution on YOUR website!
How do you solve this(7a+3)+(-a-5)=-16?

The following steps will solve this equation:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: a=-2.33333333333333. Graphical form: Equation was fully solved.Text form: (7a+3)+(-a-5)=-16 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( (7a+3)+(-a-5)=-16 )` 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 .
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 .
Solved linear equation equivalent to 6*a+14 =0
It becomes .
Result:
This is an equation! Solutions: a=-2.33333333333333.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Respectfully,
Dr J

 Linear-equations/216122: Find the equation of each line in y=mx+b form (-3,5) slope 1/51 solutions Answer 163225 by drj(1380)   on 2009-09-23 16:45:06 (Show Source): You can put this solution on YOUR website!Find the equation of each line in y=mx+b form (-3,5) slope 1/5 Step 1. The equation of the line given as y=mx+b is the slope-intercept form where m is the slope at b is the y-intercept when x=0 or at point (0,b). Step 2. Since the slope is , we have . To get the y-intercept b, substitute x=-3 and y=5 since this line passes through the point (-3,5). Multiply 5 to both sides to get rid of denominator. Add 3 to both sides of the equation Divide 5 to both sides of the equation Step 3. ANSWER: The equation is The graph is shown below. Note the y-intercept at x=0 and the slope of 1/5 which means five units to the left, then one unit up. 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/216107: answer this problem step by step:wright an equation for eac line. then graph the line. through (-2,1) and parallel to y = -3 + 11 solutions Answer 163218 by drj(1380)   on 2009-09-23 16:34:09 (Show Source): You can put this solution on YOUR website!answer this problem step by step:wright an equation for eac line. then graph the line. through (-2,1) and parallel to y = -3x + 1 Step 1. The line is in slope-intercept form given as y=mx+b where m is the slope and y-intercept is b at point (0,b). For this example, m=-3 and b=1. Step 2. Parallel lines have the same slope. So m=-3. Now we need to pass this line through (-2,1) or x=-2 and y=1. Then, to find b the y-intercept for this line substitute x and y values into the equation y=-3x+b (this is the line parallel to y=-3x+1. Subtract 6 from both sides of the equation Step 3. Now that we have slope and the y-intercept , then the equation becomes Step 4. ANSWER The graph of the two parallel lines is shown below and note the y-intercepts to determine which line is which. You should observe that the red line is described as and the green line is described 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
 Polynomials-and-rational-expressions/216079: (x-6x+9)/(x-3)1 solutions Answer 163206 by drj(1380)   on 2009-09-23 15:49:55 (Show Source): You can put this solution on YOUR website! Step 1. Look at the numerator . Step 2. Need to integers m and n whose sum is -6 and product is 9. Step 3. The two integers are -3 and -3. We can factor through grouping where -6x=-3x-3x. We can also recognize that the trinomial is a perfect square, that is . Nevertheless the following steps, will show the technique of grouping. Factor (x-3) from both groups Step 4. Now substitute the expression in Step 3 with Note we can cancel the factor (x-3) in the numerator and denominator. Step 4. 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
 Numbers_Word_Problems/215773: What are three consecutive integers such that the sum of twice the smallest and three times the largest is 126?1 solutions Answer 163199 by drj(1380)   on 2009-09-23 15:26:30 (Show Source): You can put this solution on YOUR website!What are three consecutive integers such that the sum of twice the smallest and three times the largest is 126? Step 1. Let n be an integer (smallest integer), n+1 and n+2 (largest integer) be the next two consecutive integers. Step 2. Let 2n be twice the smallest integer. Step 3. Let 3(n+2) be three times the largest integer. Step 4. Then since the sum of twice the smallest and three times the largest is 126. Step 5. The following steps will solve the equation in Step 4. Subtract 6 from both sides of the equation Divide 5 to both sides of the equation With , then and Check sum... which is a true statement. Step 6. ANSWER: The numbers are 24, 25, and 26. 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
Age_Word_Problems/215999: Tom is half as old as Ellen was three years ago.
In 10 years, Ellen will be one-and-one-half times as old as Tom.
Would you please show me the formula to use? And the answer?
Thank you.
1 solutions

Answer 163158 by drj(1380)   on 2009-09-23 12:24:04 (Show Source):
You can put this solution on YOUR website!
Tom is half as old as Ellen was three years ago.
In 10 years, Ellen will be one-and-one-half times as old as Tom.
Would you please show me the formula to use? And the answer?

Step 1. Let be Tom's current age and let be Ellen's age

Step 2. Let be Tom's age three years ago and be Ellen's age three years ago

Step 3. Let be Ellen's age three years ago since Tom is half of Ellen's age three years ago. Simply this equation as follows

Add 6-y to both sides of the equation to isolate x and y terms on one side and numbers on the right side

Step 4. Let be Ellen's age in ten years since Ellen will be one and one half times as old as Tom where , x+10 is Tom's age in ten years, and y+10 is Ellen's age in ten years.

Multiply by 2 to both sides of the equation to get rid of denominator

Subtract 3x-20 to both sides of the equation

Step 5. Now we have a linear system of equations from Steps 3 and 4 and is shown below:

Step 6. Now solve the linear system of equations in Step 5 using 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

So x=16 and y=29.

Check the ages three ago

and where Ellen is twice the age of Tom three years ago...so this is a true statement.

Check the ages ten years from now.

and or which is another true statement.

Step 7. So Tom is 16 years old and Ellen is 29 years old.

I hope the above steps were helpful.

http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Respectfully,
Dr J

 expressions/216002: This question is from textbook PREALGEBRA -20=-4X-6X1 solutions Answer 163150 by drj(1380)   on 2009-09-23 11:26:39 (Show Source): You can put this solution on YOUR website! Step 1. Combine the x-terms on the right side of the equation Step 2. Divide by -10 to both sides of the equation 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
 Linear-systems/215986: Could you help me solve this inequality 5w+2 < 8w+231 solutions Answer 163147 by drj(1380)   on 2009-09-23 11:22:30 (Show Source): You can put this solution on YOUR website!Could you help me solve this inequality Step 1. Subtract 5w to both sides of the inequality Step 2. Subtract 23 from both sides of the inequality Step 3. Divide 3 to both sides of the inequality. Step 4. The answer is or 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/215978: This question is from textbook Intermediate Algebra Write an equivalent expression using exponential notation and simplify (125x)^2/3 1 solutions Answer 163145 by drj(1380)   on 2009-09-23 11:15:35 (Show Source): You can put this solution on YOUR website!Write an equivalent expression using exponential notation and simplify where 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