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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

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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!

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

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

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

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

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! For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra. 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)^3 1 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)=5x 1 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 For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra

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.