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# Recent problems solved by 'drj'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379, >>Next

 Equations/212887: solve equation 3b/2-1=1/81 solutions Answer 160809 by drj(1380)   on 2009-09-11 23:50:29 (Show Source): You can put this solution on YOUR website!solve equation Step 1. Multiply by 8 to both sides of equation to get rid of the fractions Step 2. Add 8 to both side of equation to isolate b on left side Step 3. Divide by 12 to both sides to get b and simplify ANSWER I hope the above steps were helpful. For Step-By-Step free 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
Inverses/212893: solve system of equations using the addition method
3a+2b=7
5a-3b=-1
(?,?)
1 solutions

Answer 160807 by drj(1380)   on 2009-09-11 23:42:38 (Show Source):
You can put this solution on YOUR website!
solve system of equations using the addition method
3a+2b=7
5a-3b=-1
(?,?)

The following steps solves the linear system using Substitition

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 2*b 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.

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

Respectfully,
Dr J

 Surface-area/212901: This question is from textbook Chemistry & Chemical Reactivity A compact disk has a diameter of 11.8 cm. What is the surface area of the disk in square centimeters? In square meters?1 solutions Answer 160806 by drj(1380)   on 2009-09-11 23:39:44 (Show Source): You can put this solution on YOUR website!A compact disk has a diameter of 11.8 cm. What is the surface area of the disk in square centimeters? In square meters? Step 1. The surface area is given as Surface area = pi * (radius)^2 = pi * (diameter/2)^2 = pi * (diameter)^2/4 Step 2. Let S = surface area, d= diameter and pi=3.14159 Step 3. S = pi * (11.8)^2/4 = 109.4 cm^2 (Answer in square centimeters) Step 4. Since 1 m = 100 cm, then (1 m)^2 = (100 cm)^2 = 10000 cm^2 Step 5. (109. cm^2)(1 m^2)/10000 cm^2)= (1.09/100) m^2 = 0.0109 m^2 (Answer in square meters) I hope the above steps were helpful. For Step-By-Step free 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/211851: What is the domain of p(x)=2x-21 solutions Answer 160760 by drj(1380)   on 2009-09-11 19:26:52 (Show Source): You can put this solution on YOUR website!What is the domain of p(x)=2x-2 The domain x is from -infinity to +infinity. I hope the above steps were helpful. For Step-By-Step free videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J
 Graphs/212835: Graph on a number line when x is a real number -21 solutions Answer 160758 by drj(1380)   on 2009-09-11 19:23:11 (Show Source): You can put this solution on YOUR website!Graph on a number line when x is a real number -2 The line segment greater than -2 from the red dot and going toward pass the green dot. I hope the above steps were helpful. For Step-By-Step free 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/212840: The sum of two numbers is 25. Twelve less than four times one of the numbers is 16 more than twice the other number. Find both Numbers.1 solutions Answer 160756 by drj(1380)   on 2009-09-11 19:14:30 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 25. Twelve less than four times one of the numbers is 16 more than twice the other number. Find both Numbers. Step 1. Let m be one number. Step 2. Let n be the other number Step 3. m+n=25 or n=25-m Step 4. 4n-12 (Twelve less than four times one of the numbers) Step 5. 2m+16 (16 more than twice the other number) Step 6. Set equation Steps 4 and 5 to be equal and find the numbers. Substitute n=25-m into above equation Add 4m-16 to both sides of equation to isolate m terms on right side and numbers on left side Divide by 6 to both sides Step 7. ANSWER: So m=12 and n=25-12=13 NOTE: Let's verify the above numbers with the problem statement: Twelve less than four times one of the numbers is 16 more than twice the other number. Find both Numbers. So it works! I hope the above steps were helpful. For Step-By-Step free 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/212833: How are whole numbers converted to fractions?1 solutions Answer 160751 by drj(1380)   on 2009-09-11 17:46:58 (Show Source): You can put this solution on YOUR website!Whole numbers can be converted to fractions my converting it into a ratio of two whole numbers. For example, {5=5/1} {2=10/5} I hope the above steps were helpful. For Step-By-Step free 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/212828: solve by the elimination method
0.3x-0.2y=4
0.2x+0.5y= -21/23
1 solutions

Answer 160747 by drj(1380)   on 2009-09-11 17:38:55 (Show Source):
You can put this solution on YOUR website!
Solve by the elimination method
0.3x-0.2y=4
0.2x+0.5y= -21/23
The following steps solves the problem using Substitutions:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 0.2*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.

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

Respectfully,
Dr J

Graphs/212830: I need help with this problem. I do not know where to begin.
what is the solution type in ordered pair if there is a solution or write no solution.
Solve
x+7y=4
x=9-7y
1 solutions

Answer 160746 by drj(1380)   on 2009-09-11 17:35:37 (Show Source):
You can put this solution on YOUR website!
I need help with this problem. I do not know where to begin.
what is the solution type in ordered pair if there is a solution or write no solution.

Solve

The following steps uses the substitution method:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 7*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.

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

Respectfully,
Dr J

Functions/212812: solve by substitution method
9x+4y= -55
-7x+y= 51
1 solutions

Answer 160732 by drj(1380)   on 2009-09-11 16:09:25 (Show Source):
You can put this solution on YOUR website!
Solve by substitution method

Use the following steps to solve the above system of equations:

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.

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

Respectfully,
Dr J

 Age_Word_Problems/212809: Four years ago, three times cecile's age was 42, her father's age now. How old is cecile now?1 solutions Answer 160730 by drj(1380)   on 2009-09-11 16:05:03 (Show Source): You can put this solution on YOUR website!Four years ago, three times Cecile's age was 42, her father's age now. How old is Cecile now? Step 1. Let n = current age of Cecile Step 2. Let 3(n-4) is three times Cecile's age four years ago Step 3. Now 3(n-4)=42 which is Cecile's father's age now Step 4. Solve n using the following steps: Add 12 to both sides of the equation to isolate 3n Divide by 3 to both sides to get n Step 5. Cecile's age is 18 years old. Note: Four years ago she was 14. 3(14)=42 which is her Father's age now. Hope this was helpful. For Step-By-Step free videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Aood luck in your studies! Respectfully, Dr J
 Linear-equations/211933: write the equation in the form y=mx+b 5x-y=71 solutions Answer 160729 by drj(1380)   on 2009-09-11 15:51:25 (Show Source): You can put this solution on YOUR website!Write the equation in the form y=mx+b Step 1. To solve for y add y to both sides of the equation Step 2. To isolate y, add -7 to both sides of the equation Step 3. Answer is y=5x-7 Hope this was helpful. For Step-By-Step free videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J
 Trigonometry-basics/211791: determine the greatest possible value for B if A= 30 degrees, a=5, and b=8 a)23.1 degrees b)53.1 degrees c)126.9 degrees d)96.9 degrees1 solutions Answer 160728 by drj(1380)   on 2009-09-11 15:40:35 (Show Source): You can put this solution on YOUR website!Determine the greatest possible value for B if A=30 degrees, a=5, and b=8 a)23.1 degrees b)53.1 degrees c)126.9 degrees d)96.9 degrees Step 1. Using the Law of Sines and substituting above values yields degrees Step 2. ANSWER is b or 53.13 degrees 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
 Proportions/212256: WHAT IS THE PERIMETER = 3 CENTIMETERS + 4CENTIMETER +5 CENTIMETER?1 solutions Answer 160724 by drj(1380)   on 2009-09-11 15:22:09 (Show Source): You can put this solution on YOUR website!For your example, it's adding up all the numbers you've shown. Since there are 3 you are finding the perimeter of a triangle. Answer is 12 cm. For a rectangle you would add up four sides where Perimeter P= 2(w+l) where w is the width and l is the length. Hope that was helpful? For Step-By-Step free 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/212783: GRAPH THE EQUATION y = 1/2x + 3/2
2) y = x + 2
x + 2y = 16 x= __________ y=_______
3) 2x = 5y - 3
6x - 15y = -3
4) 5X - 2Y = 36
3X + 4Y = 6
1 solutions

Answer 160713 by drj(1380)   on 2009-09-11 14:10:54 (Show Source):
You can put this solution on YOUR website!
GRAPH THE EQUATION y = 1/2x + 3/2
2) y = x + 2
x + 2y = 16 x= __________ y=_______
3) 2x = 5y - 3
6x - 15y = -3
4) 5X - 2Y = 36
3X + 4Y = 6
Since I didn't understand what you wrote, I answered some of the problems as best as I can in what you meant.

Step 1. Just a quick note. When you have an equation just plot two points x=0 and find y using the equation and x=0 and find x using the equation. Then draw a line between two point.
Graph y = 1/2x + 3/2
 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. 1.5/-0.5 = -3.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 1.5/1 = 1.5.Slope is --0.5/1 = 0.5. Equation in slope-intercept form: y=0.5*x+1.5.

Step 2. The following will solve y = x + 2

x + 2y = 16 x= __________ y=_______. Rewrite y=x+2 as -x+y=2

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 3. The following will solve 3) 2x = 5y - 3, 6x - 15y = -3

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 4. The following will solve 5X - 2Y = 36, 3X + 4Y = 6

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving -2*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 good luck in your studies!

Respectfully,
Dr J

 Trigonometry-basics/212761: in triangle ABC, A=27 degrees 35' , B=78 degrees 23' , and c=19.find a.round to the nearest tenth. a)8.6 b)9.2 c)12.8 d)19.41 solutions Answer 160701 by drj(1380)   on 2009-09-11 12:43:37 (Show Source): You can put this solution on YOUR website!In triangle ABC, A=27 degrees 35' , B=78 degrees 23' , and c= 19. Find a and round to the nearest tenth. a)8.6 b)9.2 c)12.8 d)19.4 Step 1. Convert angles A and B to decimal form (where 1 degree = 60 minutes) degrees degrees Step 2. Use a property of a triangle where sum of the angles of a triangle is 180 degrees to find angle C Step 2. To find c, Law of Sines Step 3. ANSWER IS 9.2 or (b) 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
Polynomials-and-rational-expressions/212773: need to find the slope of line containing points
p1(2,0) and p2(3,-2)
1 solutions

Answer 160694 by drj(1380)   on 2009-09-11 12:26:03 (Show Source):
You can put this solution on YOUR website!
need to find the slope of line containing points
p1(2,0) and p2(3,-2)

However, here are the steps showing you how you can check your work with one of the points.

Step 1. The slope of the line m is given as

where for our example is x1=2, y1=0, x2=3 and y2=-2 (think of ). You can choose the points the other way around but be consistent with the x and y coordinates. You will get the same result.

Step 2. Substituting the above values in the slope equation gives

Step 3. The slope is calculated as -2 or m=-2

Step 4. Now use the slope equation of step 1 and choose one of the given points. I'll choose point (3,-2). Letting y=y2 and x=x2 and substituting m=-3 in the slope equation given as,

Step 5. Multiply both sides of equation by x-3 to get rid of denomination found on the right side of the equation

Step 6. Now simplify and put the above equation into slope-intercept form.

Subtract 2 from both sides of the equation

ANSWER in slope-intercept form. m=-2 and y-intercept=4

Step 7. See if the other point (2,0) or x=2 and y=0 satisfies this equation

So the point (2,0) satisfies the equation and is on the line. In other words, you can use the other point to check your work.

Note; above equation can be also be transform into standard form as

See graph below to check the above steps.

 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. 4/2 = 2.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/1 = 4.Slope is -2/1 = -2. Equation in slope-intercept form: y=-2*x+4.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Trigonometry-basics/212763: determine the greatest possible value for B if A=30 degrees, a=5, and b=8 a)23.1 degrees b)53.1 degrees c)126.9 degrees d)96.9 degrees1 solutions Answer 160683 by drj(1380)   on 2009-09-11 12:03:14 (Show Source): You can put this solution on YOUR website!Determine the greatest possible value for B if A=30 degrees, a=5, and b=8 a)23.1 degrees b)53.1 degrees c)126.9 degrees d)96.9 degrees Step 1. Using the Law of Sines and substituting above values yields degrees Step 2. ANSWER is b or 53.13 degrees 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
 Trigonometry-basics/212762: determine the number of possible solutions if A=62 degrees, a=4, and b=6 a)none b)one c)two d)three1 solutions Answer 160682 by drj(1380)   on 2009-09-11 11:56:48 (Show Source): You can put this solution on YOUR website!The answer is b. Only one solution. If you were given only three angles there would many triangles that would satisfy the solution. 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
 Triangles/212760: This question is from textbook Amsco's Geometry name three things that are represented by a line1 solutions Answer 160680 by drj(1380)   on 2009-09-11 11:51:34 (Show Source): You can put this solution on YOUR website!The three things that could represent a line are: 1. Its slope. 2. The y-intercept 3. The x-intercept I hope the above items 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. Respectfully, Dr J
Graphs/212752: Solve by Substitution or Elimination: 2j-3k=3 with the problem just underneith the one above. j+k =14
Can you please explain how to get it? Thank you. -Leona
1 solutions

Answer 160677 by drj(1380)   on 2009-09-11 11:45:25 (Show Source):
You can put this solution on YOUR website!
Solve by Substitution or Elimination: 2j-3k=3 with the problem just underneith the one above. j+k =14

Step 1. We form a System of Equations

Step 2. The following steps solve the system of equations by substitution:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving -3*k 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 are helpful, Leona.

And good luck in your studies!

Respectfully,
Dr J

 Equations/212747: q#19 simplify: 2x-2{y-2(x+2(2x+3y))} 1 solutions Answer 160676 by drj(1380)   on 2009-09-11 11:39:46 (Show Source): You can put this solution on YOUR website!Simplify: Step 1. Work the innermost parenthesis first and then work outward to the next set of parenthesis. Step 3. Factor out 22 Step 4. ANSWER: 22(x+y) or 22x+22y 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. Respectfully, Dr J
 Miscellaneous_Word_Problems/212751: q#21 translate and simplify "three less than twice the sum of a number and five"1 solutions Answer 160675 by drj(1380)   on 2009-09-11 11:23:47 (Show Source): You can put this solution on YOUR website!Translate and simplify "three less than twice the sum of a number and five" Step 1. Let n be a number Step 2. n+5 (sum of number and five) Step 3. 2(n+5) twice the sum of number and five Step 4. 2(n+5)-3 three less than twice the sum of a number and five Step 5. Simplify 2(n+5)-3 Step 6. ANSWER is 2n+7 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. Respectfully, Dr J
 Bodies-in-space/212750: The height of this oversized container is 3m. Its diameteris 2m. The volume of this container is 1 solutions Answer 160674 by drj(1380)   on 2009-09-11 11:19:13 (Show Source): You can put this solution on YOUR website!The height of this oversized container is 3m. Its diameter is 2m. The volume of this container is V. Step 1. Volume of cylinder is V=pi*r^2*h where pi=3.14159, r is the radius, and h is the height and meter radius Step 2. Substitute values in equation } Step 3. Volume of cylinder is 2pi or 6.283. 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. Respectfully, Dr J
 Equations/212744: q#7 simplify: (-3^2(-2)^31 solutions Answer 160673 by drj(1380)   on 2009-09-11 11:11:58 (Show Source): You can put this solution on YOUR website!simplify: Step 1. Step 2. Step 3. 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. Respectfully, Dr J
 real-numbers/211906: 1/2(x-3)+(3/2)=5x1 solutions Answer 160670 by drj(1380)   on 2009-09-11 11:00:19 (Show Source): You can put this solution on YOUR website! Step 1. Multiply by 2 to both sides of equation to get rid of denominator Step 2. Add -x to both sides to get x terms on one side and numbers on the other side. Step 3. Divide by 9 to both sides to solve for x. Step 4. Answer is x=1/3 I hope the above steps were helpful. And good luck in your studies! Respectfully, Dr J For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.
Geometry_Word_Problems/211852: a rectangular room has an area of 665 square feet. Its length is three less than twice its width. what are the dimensions of the room?
1 solutions

Answer 160668 by drj(1380)   on 2009-09-11 10:45:49 (Show Source):
You can put this solution on YOUR website!
A rectangular room has an area of 665 square feet. Its length is three less than twice its width. what are the dimensions of the room?

Step 1. Let l = 2w-3 length of rectangle and let w be the width

Step 2. Let A = 655 square feet be the Area = (length)(width)

Step 3. Subtract 655 to both sides of equation to get 0 by left side

Step 4. Now we have a quadratic equation so we can use the quadratic formula given as

where a=2, b=-3 and c=-655.
The following steps solve the quadratic equation:

 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=5249 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 18.86249568668, -17.36249568668. Here's your graph:

Step 5. Choose the positive number for a positive length. In this case, the width is 18.86 ft and length is 2w+3 or 2(18.86)-3 or 34.72 ft.

Step 6. Answer is 18.86 ft for the width and 34.72 for the length. Multiply these two numbers to get an area of 655 square feet.

Hope the above steps were helpful. Good luck in your homework and studies!

Respectfully
Dr J

Hope you understood and followed the steps. Good luck in your studies. Dr J

 percentage/212734: How do u express something as a percentage of something.For eg: tax revenue as a percentage of GDP. I want the solution in algebric terms.1 solutions Answer 160663 by drj(1380)   on 2009-09-11 10:22:30 (Show Source): You can put this solution on YOUR website!How do you express something as a percentage of something.For eg: tax revenue as a percentage of GDP. I want the solution in algebraic terms. Step 1. Let T = Tax revenue and let P = Percent of Tax Revenue of GDP. Step 2. Form fraction Step 3. Multiply by 100 to get result as a percentage. The algebraic equation is ANSWER I hope the above steps were helpful. And good luck in your studies! Respectfully, Dr J For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.
 Travel_Word_Problems/212279: This question is from textbook Algebra 2 and Triginometry A train leaves Transylvania Station at 8:00 A.M. and travels eastward at a rate of 25 miles per hour. Two hours later another train leaves the station, traveling westward at a rate of 35 miles per hour. c) At what time will the trains be 370 miles apart?1 solutions Answer 160661 by drj(1380)   on 2009-09-11 10:10:35 (Show Source): You can put this solution on YOUR website!A train leaves Transylvania Station at 8:00 A.M. and travels eastward at a rate of 25 miles per hour. Two hours later another train leaves the station, traveling westward at a rate of 35 miles per hour. c) At what time will the trains be 370 miles apart? Step 1. Distance of train traveling eastward is 25x plus 25(2)=50 miles since it traveled for two hours before the other train started. So total distance traveled by eastward train is 25x+50 miles. And let x be the time traveled for both trains after two hours. That is, the total time traveled by the eastward train is x+2 and the westward train is x. Step 2. Distance traveled by westward train is 35x. Step 3. The distance traveled between the two trains is 370 miles which is equal to the sum of the distances described in Steps 1 and 2. So the equation is Step 4. Subtract 50 from both sides of equation to isolate x on one side. Step 5. Divide 60 from both sides of equation. hours Step 6. Time the trains are 370 miles apart occurs at 10 am + (5+1/3) hours or 3pm+(1/3) hour or 3:20 pm Note: hour is or approximately 20 minutes. I hope the above steps were helpful. And good luck in your studies! Respectfully, Dr J For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.