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# Recent problems solved by 'drj'

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 Angles/222600: Find the measure of an angle if the measure of is complement is 53 degrees. Thank you for all the help and sorry if this has disturbed you in any way. 1 solutions Answer 166652 by drj(1380)   on 2009-10-06 17:00:47 (Show Source): You can put this solution on YOUR website!Find the measure of an angle if the measure of is complement is 53 degrees. Step 1. Complementary angles means two angles add up to 90 degrees. Step 2. Let x be the angle. Step 3. Let 90-x be its complement. Step 4. Given 90-x=53 or x=90-53=37. Step 5. ANSWER: The angle is 37 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
 Linear-systems/222598: Write the equation in the slope-intercept form and then find the slope m and y-intercept b of the corresponding line. -8x + 6y - 5 = -7 1 solutions Answer 166651 by drj(1380)   on 2009-10-06 16:58:37 (Show Source): You can put this solution on YOUR website!Write the equation in the slope-intercept form and then find the slope m and y-intercept b of the corresponding line. -8x + 6y - 5 = -7 Step 1. The slope-intercept form is y=mx+b where m is the slope and b is the y-intercept at x=0 or at point (0,b). Step 2. Solving yields the following steps. Add 8x+5 to both sides of the equation Divide 6 to both sides of the equation Step 3. The slope m=4/3 and y-intercept b=-1/3}}} Below is the graph and note the slope and y-intercept. 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/222591: y=2x-4 y=2x+41 solutions Answer 166647 by drj(1380)   on 2009-10-06 16:53:15 (Show Source): You can put this solution on YOUR website!y=2x-4 Equation A y=2x+4 Equation B Subtract Equation A from Equation B y-y=2x-2x+4-(-4) 0=8 ...Not a true statement. We also note that the lines are parallel since they have the same slope m=2 since the above equations are in slope-intercept form y=mx+b where m is the slope and b is the y-intercept when x=0 or at point(0,b). ANSWER: There is no solution since the two lines cannot intersect or are in parallel. 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/222592: 5.7m+2.25=19.351 solutions Answer 166643 by drj(1380)   on 2009-10-06 16:47:37 (Show Source): You can put this solution on YOUR website! Step 1. Subtract 2.25 from both sides of the equation Step 2. Divide by 5.7 to both sides of the equation Step 3. ANSWER: The solution is m=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
 Age_Word_Problems/222583: Carl is twice as old as Rita. Meg is 5 years older than Carl. If the combined age is 155, how old is Meg?1 solutions Answer 166642 by drj(1380)   on 2009-10-06 16:44:32 (Show Source): You can put this solution on YOUR website!Carl is twice as old as Rita. Meg is 5 years older than Carl. If the combined age is 155, how old is Meg? Step 1. Let x be the age of Rita. Step 2. Let 2x be the age of Carl since he is twice as old as Rita. Step 3. Let 2x+5 since Meg is 5 years older than Carl. Step 4. Then x+2x+2x+5=155 since their combined age is 155. Step 5. Solving the equation in Step 4 yields the following steps. Subtract 5 from both sides of the equation Divide by 5 to both sides of the equation , then and . Note that the combined age is 155. Step 6. ANSWER: The age of Meg is 65 years old. Note that Carl is 60 years old and Rita is 30 years old. 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
 real-numbers/222567: between them, terry and shelly have 50 cassettes. if shelly has more than two thirds as many cassettes as terry, at least how many cassettes does shelly have? at most how much does terry have1 solutions Answer 166639 by drj(1380)   on 2009-10-06 16:37:58 (Show Source): You can put this solution on YOUR website!Between them, Terry and Shelly have 50 cassettes. If Shelly has more than two thirds as many cassettes as Terry, at least how many cassettes does Shelly have? At most how much does Terry have? Step 1. Let be the number of cassettes Terry has. Step 2. Let be the number of cassettes Shelly has since she has more than two-thirds as many cassettes as Terry. Step 3. Then be the total of cassettes. Step 4. Solving for x yields the following steps: Multiply by to both sides of the equation to find x and and both add up to 50 cassettes. Step 5. ANSWER: Terry has 30 cassettes and Shelley has 20 cassettes. 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/222576: Angle A and angle B are complementary. The measure of angle B is 3 times the measure of A. Find the measure of angles A and B.1 solutions Answer 166631 by drj(1380)   on 2009-10-06 16:25:14 (Show Source): You can put this solution on YOUR website!Angle A and angle B are complementary. The measure of angle B is 3 times the measure of A. Find the measure of angles A and B. Step 1. Complementary angles means two angles add up to 90 degrees. Step 2. Let A be one angle. Step 3. Let B=90-A be its complement. Step 4. B=3A or 90-A=3A since the measure of B is 3 time the measure of A. Step 5. Solving yields the following steps Add A to both sides of the equation Divide 4 to both sides of the equation Then Step 6. ANSWER: The complementary angles are A=22.5 and B=67.5 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
 Exponents/222566: How do you write the number 1,203,487,386 in expanded form using exponets?1 solutions Answer 166625 by drj(1380)   on 2009-10-06 16:19:23 (Show Source): You can put this solution on YOUR website!How do you write the number 1,203,487,386 in expanded form using exponents? 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/222515: If jay and isabella have 59 movies together and jay has 13 more than isabella how many movies do each of them have1 solutions Answer 166591 by drj(1380)   on 2009-10-06 15:06:19 (Show Source): You can put this solution on YOUR website!If Jay and Isabella have 59 movies together and jay has 13 more than Isabella how many movies do each of them have Step 1. Let x be the number of movies Isabella has. Step 2. Let x+13 be the number of movies Jay has. Step 3. Then, x+x+13=59 since they both have 59 movies. Step 4. Solving yields the following steps Subtract 13 from both sides of the equation Divide 2 to both sides of the equation and and note total is . Step 5. ANSWER: Jay has 36 movies and Isabella has 23 movies. 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
 Probability-and-statistics/222511: find the 50th term in the arithmetic sequence 1,5,9,....1 solutions Answer 166588 by drj(1380)   on 2009-10-06 14:56:32 (Show Source): You can put this solution on YOUR website!Find the 50th term in the arithmetic sequence 1,5,9,.... Step 1. The constant for this sequence is 4 since 5-1=4 and 9-5=4. Step 2. Using this constant, we have 1+(n-1)*4 as the formula. We can check with n=1 or 1+(1-1)*4=1. With n=2, 1+(2-1)*4=5. With n=3, 1+(3-1)4=9. So it checks out. Step 3. With n=50, then 1+(50-1)*4=197. Step 4. ANSWER: The 50th term is 197. 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/222441: find three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number
1 solutions

Answer 166587 by drj(1380)   on 2009-10-06 14:52:10 (Show Source):
You can put this solution on YOUR website!
Find three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number.

Step 1. Let n be an integer.

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

Step 3. Let n+n+1=2n+1 be the sum of the two smallest integers.

Step 4. Let 2(2n+1) be twice the sum of the two smallest integers.

Step 5. Let 3(n+2) be three times the largest number

Step 6. Then using Steps 3 and 4, 2(2n+1)=3(n+2)+10 since twice the sum of the two smallest numbers is 10 more than three times the largest number.

Step 7. Solving yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=14. Graphical form: Equation was fully solved.Text form: 2*(2n+1)=3*(n+2)+10 simplifies to 0=0Cartoon (animation) form: For tutors: simplify_cartoon( 2*(2n+1)=3*(n+2)+10 ) If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

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

Look at .
Expanded term by using associative property on
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
It becomes .

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

Look at .
It becomes .

Look at .
Expanded term by using associative property on
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
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 n-14 =0
It becomes .
Result:
This is an equation! Solutions: n=14.

### Universal Simplifier and Solver

Done!

n=14, then n+1=15 and n+2=16

Check original equation or such that which is a true statement.

Step 8. ANSWER: The three consecutive integers are 14, 15, and 16.

I hope the above steps were helpful.

Respectfully,
Dr J

I hope the above steps were helpful.

Respectfully,
Dr J

 Geometry_Word_Problems/222404: two planes leave an airport at the same time and fly in opposite directions. one of the planes is flying at 450 mph, and the other is flying 550 mph. in how many hours will they be 2,000 miles apart?1 solutions Answer 166584 by drj(1380)   on 2009-10-06 14:42:00 (Show Source): You can put this solution on YOUR website!Two planes leave an airport at the same time and fly in opposite directions. One of the planes is flying at 450 mph, and the other is flying 550 mph. In how many hours will they be 2,000 miles apart? Step 1. time = distance/speed or distance=speed*time Step 2. Let x be the number of hours that the two planes will be 2000 miles apart. Step 3. Let 450x be the distance traveled by the plane at 450 mph. Step 4. Let 550x be the distance traveled by the plane at 500 mph. Step 5. 450x+550x=2000 be the total distance traveled by both planes. Step 6. Solving yields the following steps. Divide 1000 to both sides of the equation Check... 2*(550+450)=2000...which is a true statement. Step 7. ANSWER: The time will take 2 hours when they are 2000 miles apart. 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
Expressions-with-variables/222382: Solve by the substitution method.
6x+7y=-29
x=3-9y
What is the solution of the system? Type an ordered pair.
1 solutions

Answer 166582 by drj(1380)   on 2009-10-06 14:33:59 (Show Source):
You can put this solution on YOUR website!
Solve by the substitution method.

6x+7y=-29
x=3-9y or x+9y=3 after adding 9y to both sides of the equation.

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.

Respectfully,
Dr J

 expressions/222486: X=6, y=-4, a=3 6x - 5y + 4a evaluate.1 solutions Answer 166580 by drj(1380)   on 2009-10-06 14:30:23 (Show Source): You can put this solution on YOUR website!x=6, y=-4, a=3 6x - 5y + 4a Evaluate. 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
 percentage/222481: Amy paid \$80.83 for a pair of running shoes during a 15% off sale. What was the regular price?1 solutions Answer 166578 by drj(1380)   on 2009-10-06 14:27:15 (Show Source): You can put this solution on YOUR website!Amy paid \$80.83 for a pair of running shoes during a 15% off sale. What was the regular price? Step 1. 15% means 0.15. Step 2. Let x be the original price. Step 3. Let x-0.15x be dollar value that is 15% off. Step 4. Then 80.83=x-0.15x since Amy paid \$80.83 for a pair of running shoes during a 15% off sale/ Step 5. Solving yields the following steps Dividing 0.85 to both sides of the equation yields Step 6. ANSWER: The regular price is \$95.09. 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/222470: Show the graph y=-5x1 solutions Answer 166575 by drj(1380)   on 2009-10-06 14:21:07 (Show Source): You can put this solution on YOUR website!Show the graph Step 1. Two points are required to make a line. Try x=0, then y=-5*0=0 so one point is (0,0). Letting x=1, then y=-5*1=-5 and we have another point (1,-5). Step 2. Graph is shown below. 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
 Complex_Numbers/222474: a/4+5=5/2 1 solutions Answer 166572 by drj(1380)   on 2009-10-06 14:17:37 (Show Source): You can put this solution on YOUR website! Step 1. Multiply by 4 to both sides of the equation Step 2. Subtract 20 from both sides of the equation Check original equation......which is a true statement. Step 3. ANSWER:
 Quadratic_Equations/222390: how do i solve by factoring, x squared-13x+40=01 solutions Answer 166568 by drj(1380)   on 2009-10-06 14:13:52 (Show Source): You can put this solution on YOUR website!How do i solve by factoring, Step 1. Find two integers m and n whose sum and whose product is Step 2. After trial and error, the integers are m=-5 and n=-8. Step 3. Then using these integers we have Step 4. We have two solutions, and or and . Step 5. ANSWER: The answer is and . 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
 Complex_Numbers/222460: x/3-1/2=5/6 1 solutions Answer 166565 by drj(1380)   on 2009-10-06 14:06:38 (Show Source): You can put this solution on YOUR website! Step 1. Multiply 6 to both sides of the equation to get rid of denominators. Step 2. Add 3 from to both sides of the equation Step 3. Divide by 2 to both sides of the equation Check with original equation...... which is a true statement. 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
Angles/221642: the measure of the supplement of an angle exceeds three times the measure of the compliment by 30.
1 solutions

Answer 166199 by drj(1380)   on 2009-10-04 21:06:51 (Show Source):
You can put this solution on YOUR website!
The measure of the supplement of an angle exceeds three times the measure of the complement by 30.

Step 1. Supplementary angles means two angles add up to 180 degrees.

Step 2. Complementary angles means two angles add up to 90 degrees.

Step 3. Let x be the angle.

Step 4. Let 180-x be its supplementary angle.

Step 5. Let 90-x be its complementary angle.

Step 6. Let 3(90-x) be three times the complement.

Step 7. Then 180-x=3(90-x)+30 since the measure of the supplement of an angle exceeds three times the measure of the complement by 30.

Step 8. Solving the equation in Step 7 yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=60. Graphical form: Equation was fully solved.Text form: 180-x=3*(90-x)+30 simplifies to 0=0Cartoon (animation) form: For tutors: simplify_cartoon( 180-x=3*(90-x)+30 ) If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

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

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

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

Look at .
It becomes .

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

Look at .
Expanded term by using associative property on
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
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 .
Solved linear equation equivalent to 2*x-120 =0
It becomes .
Result:
This is an equation! Solutions: x=60.

### Universal Simplifier and Solver

Done!

With x=60, then 180-x=120 and 90-x=30.

Check equation 180-x=3(90-x)+30 of Step 7 or 120=3*30+30=120 which is a true statement

Step 9. ANSWER: The angle is 60, its supplement is 120 and its complement is 30.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J
drjctu@gmail.com
http://www.FreedomUniversity.TV

Linear-equations/221640: how do you solve for x and check the solution to the equation,

-0.3 + x-5(x + 1/10)= -0.8 + 5(-x+0.1)
1 solutions

Answer 166193 by drj(1380)   on 2009-10-04 20:53:14 (Show Source):
You can put this solution on YOUR website!
How do you solve for x and check the solution to the equation,

Step 1. Multiply by 10 to both sides of the equation to get rid of the decimal point and denominator

Step 2. Simplify as follows:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=0.5. Graphical form: Equation was fully solved.Text form: -3+10x-50x-5=-8-50x+5 simplifies to 0=0Cartoon (animation) form: For tutors: simplify_cartoon( -3+10x-50x-5=-8-50x+5 ) If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
It becomes .

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

Look at .
It becomes .

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

Look at .
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
It becomes .

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

Look at .
It becomes .

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

Look at .
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 .
Solved linear equation equivalent to 10*x-5 =0
It becomes .
Result:
This is an equation! Solutions: x=0.5.

### Universal Simplifier and Solver

Done!

Step 3. Check x=0.5 and substitute into original equation to see if you get a true statement.

a true statement.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV

 Word_Problems_With_Coins/221577: Donnie has \$5.10 in nickels, dimes, and quarters. He has an equal number of dimes and nickels, with the value of the quarters being \$2.40 more than the total value of the dimes and nickels. How many dimes does he have?1 solutions Answer 166163 by drj(1380)   on 2009-10-04 19:52:56 (Show Source): You can put this solution on YOUR website!Donnie has \$5.10 in nickels, dimes, and quarters. He has an equal number of dimes and nickels, with the value of the quarters being \$2.40 more than the total value of the dimes and nickels. How many dimes does he have? Step 1. Let x be the number of nickels Step 2. Let x be the number of dimes since they are equal in number with the nickels. Step 3. Let be the dollar values of nickels and dimes. Step 4. Let 0.25y be the dollar values of quarters. Step 5. since the value of the quarters being \$2.40 more than the total value of the dimes and nickels. Or rewriting it as Step 6. Also, as given by the problem since \$5.10 in nickels, dimes, and quarters. Step 7. Now, we have a linear system of equations in Steps 5 and 6 Equation A Equation B Adding Equations A and B quarters Then solving x from Equation B is or . Check Equation A if true or ...which is a true statement. Step 8. ANSWER: The number of nickels and dimes is 9 each and the number of quarters is 15. 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
 Graphs/221588: What is the slope and y-intercept of y = -2/3 x -121 solutions Answer 166160 by drj(1380)   on 2009-10-04 19:35:22 (Show Source): You can put this solution on YOUR website!What is the slope and y-intercept of y = -2/3 x -12 Step 1. The slope-intercept form is given at y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). Step 2. Given has a slope and y-intercept at Here's a graph of the above 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
 Word_Problems_With_Coins/221578: Jay's favorite book is 182 pages less than three times Mitchel's favorite book. If both books have the same number of pages, how many pages are in Jay's favorite book?1 solutions Answer 166158 by drj(1380)   on 2009-10-04 19:30:20 (Show Source): You can put this solution on YOUR website!Jay's favorite book is 182 pages less than three times Mitchel's favorite book. If both books have the same number of pages, how many pages are in Jay's favorite book? Step 1. Let x be the number of pages in Mitchel's book. Step 2. Let 3x be three times the number of pages in Mitchel's book Step 3. Let 3x-182 be the number of pages in Jay's book since it's 182 pages less than three times Mitchel's favorite book Step 4. Then, x=3x-182 since both books have the same number of pages Step 5. Solving the equation in Step 4 yields the following steps: Add 182-x to both sides of the equation Divide 2 to both sides of the equation The number of pages in Jay's book is 3x-182=3*91-182=91 Step 6. The number of pages in Jay's book is 91 pages. 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/221566: the width of a rectangle is 5ft less than the length. the area is 6ft^2

1 solutions

Answer 166150 by drj(1380)   on 2009-10-04 19:17:06 (Show Source):
You can put this solution on YOUR website!
The width of a rectangle is 5 ft less than the length. The area is 6ft^2

I assume you want to find the dimensions of the rectangle.

Step 1. Let L be the length.

Step 2. Let be the width.

Step 3. Area

Step 4. Solving A in Step 3 yields the following steps.

Subtract 6 from both sides to get a quadratic equation

Step 5. To solve equation in Step 5, use the quadratic formula given below

where a=1, b=-5, and c=-6

 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=49 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6, -1. Here's your graph:

Using the positive solution , then . Area A=6*1=6 which is a true statement.

Step 6. ANSWER: The dimensions of a rectangle are 6 feet and 1 feet.

I hope the above steps were helpful.

Respectfully,
Dr J

Rectangles/221567: the length of a rectangle is 12 meters longer than half the width. the area of the rectangle is 90 square meters. find the dimensions of the rectangle.
1 solutions

Answer 166147 by drj(1380)   on 2009-10-04 19:08:36 (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 12 meters longer than half the width. The area of the rectangle is 90 square meters. Find the dimensions of the rectangle.

Step 1. Let w be the width.

Step 2. Let be the length.

Step 3. Area

Step 4. Solving A in Step 3 yields the following steps.

Multiply 2 to both sides to get rid of denominator

Subtract 180 from both sides to get a quadratic equation

Step 5. To solve equation in Step 5, use the quadratic formula given below

where a=1, b=24, and c=-180

 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=1296 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6, -30. Here's your graph:

With , then . Area A=6*15=90 which is a true statement.

Step 6. ANSWER: The dimensions of a rectangle are 6 meters and 15 meters.

I hope the above steps were helpful.

Respectfully,
Dr J

Linear-systems/221568: 4x+2y=-6
2x+3y=-3
1 solutions

Answer 166144 by drj(1380)   on 2009-10-04 18:57:28 (Show Source):
You can put this solution on YOUR website!
4x+2y=-6
2x+3y=-3

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.

Respectfully,
Dr J

 Problems-with-consecutive-odd-even-integers/221523: Determine whether there are two consecutive odd integers such that 5 times the first exceeds 3 times the second by 54.1 solutions Answer 166139 by drj(1380)   on 2009-10-04 18:09:35 (Show Source): You can put this solution on YOUR website!Determine whether there are two consecutive odd integers such that 5 times the first exceeds 3 times the second by 54. Step 1. Let n be the first odd integer. Step 2. Let n+2 be then next consecutive odd integer. Step 3. Let 5n be 5 times the first odd integer. Step 4. Let 3(n+2) be 3 times the second odd integer. Step 5. Then, 5n=3(n+2)+54 since 5 times the first exceeds 3 times the second by 54 Step 6. Solving the equation in Step 5 yields the following steps: Subtract 3n from both sides of the equation Divide by 2 to both sides of the equation yields but n is an even integer. Step 8. ANSWER: Therefore there are no odd integers that satisfies the given problem statement. 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
Triangles/221519: The second angle of a triangle is 4 times as large as the first. The third angle is 120° more
than the sum of the other two angles. Find the measure of the second angle.
1 solutions

Answer 166134 by drj(1380)   on 2009-10-04 18:01:54 (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° more than the sum of the other two angles. Find the measure of the second angle.

Step 1. 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's 4 times as large as the first.

Step 4. Let x+4x=5x be the sum of the first and second angles.

Step 5. Let 5x+120 be the third angle since it's 120 degrees more than the sum of the other two angles.

Step 6. Then, x+4x+5x+120=180 since the three angles add up to 180

Step 7. Solving the equation in Step 6 yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=6. Graphical form: Equation was fully solved.Text form: x+4x+5x+120=180 simplifies to 0=0Cartoon (animation) form: For tutors: simplify_cartoon( x+4x+5x+120=180 ) If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

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

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

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

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 10*x-60 =0
It becomes .
Result:
This is an equation! Solutions: x=6.

### Universal Simplifier and Solver

Done!

With x=6, then 4x=24 and 5x+120=150. Note these angles add up to 180 degrees.

Step 8. ANSWER: The three angles are 6 degrees, 24 degrees and 150 degrees.