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Rectangles/209727: area of a rectangle is 243 m2. The height is nine less than 4 times the base. What is the perimeter?
1 solutions

Answer 162253 by drj(1380)   on 2009-09-18 23:01:40 (Show Source):
You can put this solution on YOUR website!
Area of a rectangle is 243 m^2. The height is nine less than 4 times the base. What is the perimeter?

Step 1. Let x be the base and 4x-9 be the height

Step 2. Perimeter P means adding up the four sides of a rectangle.

Step 3. Then

Step 4. Area=x*(4x-9)=243 or 4x^2-9x-243=0 or a quadratic equation.

Step 5. We can use the quadratic formula given as

where a=4, b=-9 and c=-243

 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=3969 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 9, -6.75. Here's your graph:

Select the positive number x=9.

Step 6. Then

Step 7. ANSWER: The perimeter is 81.

I just found this problem on 18 Sep 09, but I hope the above steps were helpful for review. Sorry about the late response.

And good luck in your studies!

Respectfully,
Dr J

 Radicals/214168: Find the real solution(s) of the equation involving rational exponents (x^2+6)^(2/3)=91 solutions Answer 162250 by drj(1380)   on 2009-09-18 22:49:51 (Show Source): You can put this solution on YOUR website!Find the real solution(s) of the equation involving rational exponents Step 1. Raise both sides of the equation by the power 3/2 where 1/2 in the exponent is the square root and for this example Step 2. Subtract 6 from both sides of the equation or 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

1 solutions

Answer 162248 by drj(1380)   on 2009-09-18 22:40:00 (Show Source):
You can put this solution on YOUR website!

Step 1. Square both sides of the equation

Step 2. Subtract x+6 from both sides of the equation to get a quadratic one.

Step 3. We can use the quadratic formula to solve this given as

where a=1, b=-19 and c=75

 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=61 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 13.4051248379533, 5.59487516204667. Here's your graph:

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

Step 2.

 Polynomials-and-rational-expressions/214784: Hello, I need help with simplifying this rational expression: x^2-100 over (x+10)^21 solutions Answer 162243 by drj(1380)   on 2009-09-18 22:15:11 (Show Source): You can put this solution on YOUR website!Simplify Step 1. Rewriting the numerator using the difference of squares (x-10)(x+10)=x^2-10^2 and rewriting the denominator as follows yields, Step 2. Canceling the (x+10) found in the numerator and denominator yields 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
 Proportions/214779: This question is from textbook intermediate algebra My teacher wants use to write a narrative description of what you would do to simplify. 1. (16) power of 1/2 I know the answer is four b/c I did it in the calculator but how does it get that. 1 solutions Answer 162242 by drj(1380)   on 2009-09-18 21:49:30 (Show Source): You can put this solution on YOUR website!(16) power of 1/2 I know the answer is four b/c I did it in the calculator but how does it get that. Step 1. The power of 1/2 means square root. Step 2. Now we know where in the exponent OR where and 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
 Linear-equations/214164: how do you graph how do you graph 1 solutions Answer 162236 by drj(1380)   on 2009-09-18 21:36:12 (Show Source): You can put this solution on YOUR website!How do you graph how do you graph Step 1. You can think of the above inequality consist of two inequalities. That is, and Step 2. Then, on the number line we have Step 3. Now, the graph is going from the red dot at 2/3 to the right pass the green dot to positive infinity or a positive large number. Step 4. The graph is going from the green dot at 5/2 to left pass the red dot to minus infinity or a negative large number. Step 5. ANSWER. Finally, combining these two graphs as described above in Steps 3 and 4 will overlap with each other. The overlap and solution is between 2/3 and 5/2 or between the red and green dots as shown in the graph. 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
 Trigonometry-basics/214777: what is: x is less than pi/7? using interval notation. 1 solutions Answer 162232 by drj(1380)   on 2009-09-18 21:23:54 (Show Source): You can put this solution on YOUR website!What is: x is less than ? using interval notation. I interpret your question as an inequality of or if you want only positive angles. I hope that was what you meant. 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
 Expressions-with-variables/214774: Western State College is 18 years older than Southern State. Western is also 2.5 times as old as southern. how old is each? choices for southern state's age: 12,14,181 solutions Answer 162230 by drj(1380)   on 2009-09-18 21:20:09 (Show Source): You can put this solution on YOUR website!Western State College is 18 years older than Southern State. Western is also 2.5 times as old as southern. How old is each? choices for southern state's age: 12,14,18 Step 1. Let x be the age of Southern State, x+18 is the age of Western State College. Step 2. 2.5x Western age is also 2.5 times as old as southern. Step 3. x+18=2.5x as given by Steps 1 and 2. Step 4. Subtract x to both sides of the equation in Step 3 Step 4. Multiply 2/3 to both sides of the equation to get x With x=12, then x+18=30 years old for Western Step 5. ANSWER: Southern State's age is 12 years old and Western State's age is 30 years old. 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
 Linear-systems/214764: Find slope-intercept form of the equation of the line with the following intercepts: x-intercept: -7 y-intercept: 51 solutions Answer 162226 by drj(1380)   on 2009-09-18 21:07:44 (Show Source): You can put this solution on YOUR website!Find slope-intercept form of the equation of the line with the following intercepts: x-intercept: -7 y-intercept: 5 Step 1. The slope-intercept form of the equation is given as y=mx+b where m is the slope and b is the y-intercept at point(0,5). For our example, b=5. Step 2. To find the slope we use the x-intercept which means it occurs at point (-7,0) or x=-7 and y=0. Step 3. Then Add 7m to both sides of equation Divide 7 to both sides of equation Step 4. ANSWER: The equation of the line is } 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
 Miscellaneous_Word_Problems/214761: a certain number is increased by 8 ans that sum is divided by 2. the result is 6 1/4 . find the number.1 solutions Answer 162216 by drj(1380)   on 2009-09-18 20:43:55 (Show Source): You can put this solution on YOUR website!A certain number is increased by 8 and that sum is divided by 2. The result is 6 1/4. Find the number. Step 1. Let x be the number. Step 2. that number is increased by 8 and that sum is divided by 2. Step 3. where we converted Step 4. Multiply 4 to get rid of denominators Step 5. Subtract 16 to both sides of equation Step 6. Divide 2 to both sides of equation to get x Step 7. ANSWER: The number is 9/2. 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
 Miscellaneous_Word_Problems/214759: sally has saved twice as much money as jon, jeremy has saved three times as much money as jon. find the amount each person saved if the total savings is \$180.001 solutions Answer 162207 by drj(1380)   on 2009-09-18 20:24:50 (Show Source): You can put this solution on YOUR website!Sally has saved twice as much money as Jon, Jeremy has saved three times as much money as Jon. Find the amount each person saved if the total savings is \$180.00 Step 1. Let x be the amount Jon saved, 2x be the amount Sally saved, and 3x be the amount Jeremy Saved. Step 2. x+2x+3x=180 Sum of amount each person saved is 180 dollars. Step 3. Solving yields divide 6 to both sides of equation Verify solution Step 4. ANSWER: Jon saved \$30, Sally saved \$60, and Jeremy saved \$90. 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
 Linear-systems/214758: write the equation in slope-intercept form of the line satisfying: m= 5/7, y-intercept (0,5) 1 solutions Answer 162204 by drj(1380)   on 2009-09-18 20:18:28 (Show Source): You can put this solution on YOUR website!Write the equation in slope-intercept form of the line satisfying: m= 5/7, y-intercept (0,5) The equation for the slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept at point (0,b). For this example the slope m is 5/7 and b is 5. Then the equation of the line is 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
test/214746: Galina spent \$3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the number of 30¢ stamps. How many stamps of each kind did Galina buy?
1 solutions

Answer 162202 by drj(1380)   on 2009-09-18 20:14:57 (Show Source):
You can put this solution on YOUR website!
Galina spent \$3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the number of 30¢ stamps. How many stamps of each kind did Galina buy?

Step 1. Let x be the number of 30 cents stamps.

Step 2. Let x-2 be the number of 20 cents stamps.

Step 3. Let 30x be the cost of buying x number of 30 cents stamps

Step 4. Let 20(x-2) be the cost of buying x-2 number of 20 cents stamps.

Step 5. 30x+20(x-2)=360 cents is the total cost of buying stamps.

Step 6. The following steps will solve the equation in Step 5:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=8. Graphical form: Equation was fully solved.Text form: 30x+20*(x-2)=360 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 30x+20*(x-2)=360 )` 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 .
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 50*x-400 =0
It becomes .
Result:
This is an equation! Solutions: x=8.

### Universal Simplifier and Solver

Done!

With x=8, then x-2=6

Step 7 The number of 30 cents stamps is 8 and the number of 20 cents stamps is 6.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Expressions-with-variables/214757: A clown weighs 60lb more than a trapeze artist. The trapeze artist weighs two thirds as much as the clown. How much does each weigh? Choice for the weight of the trapeze artist: 110, 120, 125.1 solutions Answer 162201 by drj(1380)   on 2009-09-18 20:08:46 (Show Source): You can put this solution on YOUR website!A clown weighs 60lb more than a trapeze artist. The trapeze artist weighs two thirds as much as the clown. How much does each weigh? Choice for the weight of the trapeze artist: 110, 120, 125. Step 1. Let x be the weight of the trapeze artist and x+60 is the weight of the clown. Step 2. Trapeze artist weights two thirds as much as the clown. Step 3. Solving equation in Step 2 yields Multiply by 3 to both sides of equation to get rid of denominator Subtract 2x to both sides of equation Then weight to clown is Step 4. Weight of trapeze artist is 120 pounds and weight of clown is 180 pounds. Step 5. ANSWER: Trapeze artist weighs 120 pounds. 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
 Expressions-with-variables/214752: This question is from textbook Algebra: Structure and Method Book 1 Two numbers differ by 57. Their sum is 185. Find the numbers. Choices for the smaller number: 29,30, 33.1 solutions Answer 162191 by drj(1380)   on 2009-09-18 19:05:16 (Show Source): You can put this solution on YOUR website!Two numbers differ by 57. Their sum is 185. Find the numbers. Choices for the smaller number: 29,30, 33. Step 1. Let x be one number and y be the other number. Step 2. Then based on the problem statement we have the following. Equation A Equation B Add Equations A and B to get Then y=185-121=64 ANSWER is 64 but it does not appear in your solutions. May need to double check to see if the above problem statement is correct. 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/214750: One-sixth of the smallest of three consecutive even integers is three less than one-tenth the sum of the other even integers. Find the integers. 1/6x +3 = 1/10 (x+2)+(x+4) 1/6x +3 = 1/10 (2x+6) 1/6x +3 -3 = 1/10 (2x+3) here is where I lose it, do not understand what to do with the fractions.1 solutions Answer 162190 by drj(1380)   on 2009-09-18 18:57:02 (Show Source): You can put this solution on YOUR website!One-sixth of the smallest of three consecutive even integers is three less than one-tenth the sum of the other even integers. Find the integers. Step 1. Let x be an even integer, x+2 and x+4 be the next two consecutive integers. Step 2. x+2+x+4 is the sum of the two even integers or 2x+6 Step 3. (2x+6)/10 is one-tenth of the sum of the other even integers. Step 4. x/6 is one-sixth of the smallest even itneger Step 5. as given by the problem statement. Step 6 Multiply 60 to both sides of the equation to get rid of the fractions. Add 144-10x to both sides Step 7. The numbers are 72, 74 and 76. 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
 Linear-systems/214749: given the function K(r)=10r+5 find each of the following K(4)= K(-9)= K(6.7)=1 solutions Answer 162188 by drj(1380)   on 2009-09-18 18:39:28 (Show Source): You can put this solution on YOUR website!given the function K(r)=10r+5 find each of the following 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
Linear_Equations_And_Systems_Word_Problems/214747: Harold had a summer lemonade stand where he sold small cups of lemonade for \$1.25 and large cups for \$2.50. If Harold sold a total of 155 cups of lemonade and collected a total of \$265, how many cups of each type did he sell?
1 solutions

Answer 162187 by drj(1380)   on 2009-09-18 18:37:05 (Show Source):
You can put this solution on YOUR website!
Harold had a summer lemonade stand where he sold small cups of lemonade for \$1.25 and large cups for \$2.50. If Harold sold a total of 155 cups of lemonade and collected a total of \$265, how many cups of each type did he sell?

Step 1. Let x number of small cups sold.

Step 2. Let y number of large cups sold.

Step 3. Let 1.25x be the cost of small cups sold.

Step 4. Let 2.50x be the cost of large cups sold.

Step 5. Then we have the following relationships:

where the total number of cups sold is 155

where the total cost of cups sold is \$265.

Step 6. The following steps will solve the system of equations in Step 5.

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 7. The number of small cups sold is 98 and the number of large cups sold is 57.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Percentage-and-ratio-word-problems/214735: A car salesperson earns a 12.5% commission on every car sold. The sales−person sells a car for \$17100. What is the commission (in dollars)? 1 solutions Answer 162184 by drj(1380)   on 2009-09-18 18:19:33 (Show Source): You can put this solution on YOUR website!A car salesperson earns a 12.5% commission on every car sold. The sales person sells a car for \$17100. What is the commission (in dollars)? Step 1. 12.5%=0.125 Definition of percent. Step 2. Multiply car cost by percent of commission will to get commission in dollars Step 3. ANSWER: The commission is \$2137.50. 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
Linear-systems/214740: 8x+3y=34
-5x+y=27
1 solutions

Answer 162181 by drj(1380)   on 2009-09-18 18:15:47 (Show Source):
You can put this solution on YOUR website!
8x+3y=34
-5x+y=27

The following will solve the system of equations using substitution.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 3*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

Linear-systems/214742: 5x+5y=-11
7x-2y=17
1 solutions

Answer 162179 by drj(1380)   on 2009-09-18 18:14:11 (Show Source):
You can put this solution on YOUR website!
5x+5y=-11
7x-2y=17

The following will solve the system of equations using substitution:

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

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

Linear-systems/214739: `6x+2y=8
-3x+y=20

1 solutions

Answer 162178 by drj(1380)   on 2009-09-18 18:12:35 (Show Source):
You can put this solution on YOUR website!
Equation A
Equation B

Step 1. Multiply Equation B by 2 and Add the two equations.

Step 2. This yields

or

Step 3. Substitue y=12 into equation A or B. Here's for Equation A

Step 4. ANSWER: The solution is x=-8/3 and y=12.

As a check here's the solution using SUBSTITUTION:

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

The results are the same as before.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Functions/214733: I have to find the composition of functions! I did 16 problems already with no problem but can't figure this one out. g(x)=(2x)^1/2 f(x)=x^2+1 find (Fog)(x) I would welcome any help!!!!!1 solutions Answer 162173 by drj(1380)   on 2009-09-18 18:03:52 (Show Source): You can put this solution on YOUR website!I have to find the composition of functions! I did 16 problems already with no problem but can't figure this one out. g(x)=(2x)^1/2 and f(x)=x^2+1. Then find (Fog)(x)=F(g(x)) Step 1. Substitute g(x)=2x^1/2 into f(x) as follows Step 2. Step 3. ANSWER: Fog(x)=F(g(x))=2x+1 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
 Number-Line/214729: wat is 29-58? inoe its -29 but i want to know the steps on how to get to get -29 1 solutions Answer 162172 by drj(1380)   on 2009-09-18 17:55:34 (Show Source): You can put this solution on YOUR website!What is 29-58? I know it's -29 but I want to know the steps on how to get to get -29. 29-58=29+(-58)=-29. Where we used the additive inverse of 58. Think of walking 29 forward steps and then 58 backward steps. The net result is that you went 29 steps backwards from where you started. 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
Linear-systems/214731: 6x+2y=8
-3x+y=20
8x+3y=34
-5x+y=27

1 solutions

Answer 162171 by drj(1380)   on 2009-09-18 17:51:15 (Show Source):
You can put this solution on YOUR website!
Using SUBSTITUTION, the following will solve the system of equations given as

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

Using SUBSTITUTION, the following will solve the system of equations given as

8x+3y=34
-5x+y=27

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 3*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

Numbers_Word_Problems/214726: What are the four consecutive even integers that equal 308?
1 solutions

Answer 162170 by drj(1380)   on 2009-09-18 17:43:26 (Show Source):
You can put this solution on YOUR website!
What are the four consecutive even integers that equal 308?

Step 1. Let n be an even integer, n+2, n+4, and n+6 be the next three consecutive integers.

Step 2. Then n+n+2+n+4+n+6=308 as given by the problem statement where the sum of the four consecutive integers equal to 308.

Step 3. The following steps will solve the equation in Step 2:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=74. Graphical form: Equation was fully solved.Text form: n+n+2+n+4+n+6=308 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( n+n+2+n+4+n+6=308 )` 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 .
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 4*n-296 =0
It becomes .
Result:
This is an equation! Solutions: n=74.

### Universal Simplifier and Solver

Done!

Step 4. The integers are: 74, 76, 78, and 80.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Proportions/214724: A sofa is 6 feet long. In a scale drawing, the sofa is 3 inches long. Find the scale of the drawing without units. 1 solutions Answer 162167 by drj(1380)   on 2009-09-18 17:36:23 (Show Source): You can put this solution on YOUR website!A sofa is 6 feet long. In a scale drawing, the sofa is 3 inches long. Find the scale of the drawing without units. Given the sofa is 6 feet long, the scale drawing 3 inches long. Let s be the scale ratio without units. Note 1 foot = 12 inches then 1/4 feet is 3 inches. I'll give two scale factors depending how you want the answer. APPROACH 1. Hence, s=6/3 or s=1/2. This means at if the length is 3 feet then the scale drawing is 3*(1/2)=1.5 inches. So this is a scale conversion of feet/inches (so this is not unitless) APPROACH 2. We can change the scale factor by changing the denominator to 1/4=3 inches. So s=6/(1/4)=24. So the scaling is 24 to 1. So 6 feet/24= 1/4 feet or 3 inches in the scale drawing. So this is unitless scale s since the conversion is feet/feet. 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
Graphs/214716: graph the system of unequalities
x+2y<6
2x+y<6
x>0
y>0
1 solutions

Answer 162163 by drj(1380)   on 2009-09-18 17:21:23 (Show Source):
You can put this solution on YOUR website!
Graph the system of unequalities

x+2y<6
2x+y<6
x>0
y>0

Graph of

 Solved by pluggable solver: Plot Any Inequality Graphing function :

Graph of

 Solved by pluggable solver: Plot Any Inequality Graphing function :

Graph of

 Solved by pluggable solver: Plot Any Inequality Graphing function :

Graph of

 Solved by pluggable solver: Plot Any Inequality Graphing function :

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

Numbers_Word_Problems/214714: The sum of three numbers is 120. The second number is 8 less than the first number, and the third is 4 more than the first number. This question is on a handout my child brought home. There is no ISBN
1 solutions

Answer 162159 by drj(1380)   on 2009-09-18 17:00:42 (Show Source):
You can put this solution on YOUR website!
The sum of three numbers is 120. The second number is 8 less than the first number, and the third is 4 more than the first number

Step 1. Let x be the first number

Step 2. Let x-8 be the second number since it's 8 less than the first number

Step 3. Let x+4 be the third number since it's 4 more than the first number

Step 4. Then, x+x-8+x+4=120 since we're given the sum of three numbers is 120.

Step 5. The following will solve the above equation in step 4.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=41.3333333333333. Graphical form: Equation was fully solved.Text form: x+x-8+x+4=120 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( x+x-8+x+4=120 )` 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 .
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 3*x-124 =0
It becomes .
Result:
This is an equation! Solutions: x=41.3333333333333.

### Universal Simplifier and Solver

Done!

With x=41.33333... or

So the numbers are , , and Note these numbers add up to 120.
I hope the above steps were helpful.