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# Recent problems solved by 'drj'

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 Graphs/218090: use the intercepts to graph the equation -x+5y=101 solutions Answer 164283 by drj(1380)   on 2009-09-27 22:11:42 (Show Source): You can put this solution on YOUR website!Use the intercepts to graph the equation -x+5y=10 Step 1. Intercepts means one of the coordinates is zero. The y-intercept b occurs when x=0 or at point (0,b) and the x-intercept a occurs when y=0 or at (a,0) Step 2. At x=0, then -x+5y=10 or -0+5y=10 or y=2 after dividing by 5 to both sides of the equation. So we have (0,2) as one point Step 3. At y=0, then -x+5y=10 or -x+5*0=10 or x=-10. And we have another point at (-10,0). Use these two points to graph as shown below: I hope the above steps and explanation were helpful. For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry. Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs. Respectfully, Dr J http://www.FreedomUniversity.TV
Systems-of-equations/218096: -7x+5y=-14
8x-3y=16
1 solutions

Answer 164281 by drj(1380)   on 2009-09-27 21:53:02 (Show Source):
You can put this solution on YOUR website!
-7x+5y=-14
8x-3y=16

The following will solve the above equation 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 and explanation were helpful.

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

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

Respectfully,
Dr J

http://www.FreedomUniversity.TV

 Linear-equations/218072: find the x and y intercepts of the graph of -2x-4y=-201 solutions Answer 164276 by drj(1380)   on 2009-09-27 21:31:35 (Show Source): You can put this solution on YOUR website!Find the x and y intercepts of the graph of -2x-4y=-20 Step 1. The intercepts occur when the one of the coordinates is zero. The y-intercept is when x=0 or at point (0,b) where b is the y-intercept. The x-intercept is when y=0 or at point (a,0) where a is the x-intercept. Step 2. So let x=0, then -2*0-4y-20 or 4y=20 or y=5 after dividing by 4 to both sides. Therefore, the y-intercept is 5. Step 3. So let y=0, then -2x-4*0-20 or 2x=20 or x=10 after dividing by 10 to both sides. Therefore, the x-intercept is 10. Step 4. ANSWER: The x-intercept is 10 and the y-intercept is 5. I hope the above steps and explanation were helpful. For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry. Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs. Respectfully, Dr J http://www.FreedomUniversity.TV
 Finance/218078: four consecutive integers whose sum is 581 solutions Answer 164274 by drj(1380)   on 2009-09-27 21:24:07 (Show Source): You can put this solution on YOUR website!Four consecutive integers whose sum is 58. Step 1. Let n be an integer Step 2. Let n+1, n+2, and n+3 be the next three consecutive integers. Step 3. Then, n+n+1+n+2+n+3=58 since the sum of four consecutive integers is 58. Step 4. Solving, 4n+6=58, yields the following steps: Subtract 6 from both sides of the equation. Divide 4 to both sides of the equation. Then , and Check if sum is 58....13+14+15+16=29+29=58....which is a true statement. Step 5. ANSWER: Numbers are 13, 14, 15, and 16. I hope the above steps and explanation were helpful. For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry. Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs. Respectfully, Dr J http://www.FreedomUniversity.TV
Human-and-algebraic-language/218082: The supplement of an angle exceeds five times the complement of an angle by 10 degrees. Find the angle.
1 solutions

Answer 164272 by drj(1380)   on 2009-09-27 21:16:20 (Show Source):
You can put this solution on YOUR website!
The supplement of an angle exceeds five times the complement of an angle by 10 degrees. Find the angle.

Step 1. Complementary angles is when two angles add up to 90 degrees.

Step 2. Supplementary angles is when two angles add up to 180 degrees.

Step 3. Let x be the angle.

Step 4. Let 90-x its complementary angle.

Step 5. Let 180-x be its supplementary angle.

Step 6. Let 5(90-x) be five times the complement

Step 7. 180-x=5(90-x)+10 since the supplement of an angle exceeds five times the complement of an angle by 10 degrees. Find the angle.

Step 8. Solving yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=70. Graphical form: Equation was fully solved.Text form: 180-x=5*(90-x)+10 simplifies to 0=0Cartoon (animation) form: For tutors: simplify_cartoon( 180-x=5*(90-x)+10 ) 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 4*x-280 =0
It becomes .
Result:
This is an equation! Solutions: x=70.

### Universal Simplifier and Solver

Done!

With x=70, then 90-x=20 and 180-x=110.

Check...180-x=5(90-x)+10 or 110=5*20+10=110...which is a true statement.

Step 9. ANSWER: The angle is 70 degrees.

I hope the above steps and explanation were helpful.

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

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

Respectfully,
Dr J

 Graphs/217960: Graph using the slope and the y-intercept x+5y=10 1 solutions Answer 164233 by drj(1380)   on 2009-09-27 19:02:29 (Show Source): You can put this solution on YOUR website!Graph using the slope and the y-intercept x+5y=10 Step 1. The slope-intercept from is given as y=mx+b where m is the slope and b is the y-intercept at x=0 or at point (0,b). Step 2. Put the given equation in slope intercept form. Subtract x from both sides of the equation Divide 5 to both sides of equation Step 3. The equation has a slope m=-1/5 and y-intercept b=2. Now the slope of for every five unit you go the right, you go one unit down. To plot the line take the y-intercept at point (0,2). So starting at point (0,2) or x1=0 and y1=2 we go five unit to the right means x2=0+5=5 and 1 unit down means y2=2-1=1. So we have two points (0,2) and (5,1). I hope the above explanation was useful. 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
 Graphs/217950: 3. Use the intercepts to graph the equation: x-2=y 1 solutions Answer 164219 by drj(1380)   on 2009-09-27 18:29:44 (Show Source): You can put this solution on YOUR website!3. Use the intercepts to graph the equation: Step 1. We can put this in standard form given as where we added 2-y to both sides of the equation Step 2. Now the intercepts occur when one of the coordinates is equal to zero, that is, x=0 or y=0. Step 3. Let x=0, then we have the y-intercept given as So for x=0, we have y=-2 and therefore point (0,-2) can be used to plot the line. Step 4. Let y=0, the we have the x-intercept given as So for y=0 we have x=2 and therefore another point (2,0) can be used to plot the line. Step 5. It takes two points to draw a line and these point from Steps 3 and 4 is (0,-2) and (2,0) Step 6. Graph the line as shown below using the intercepts point in Step 5. 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
 Equations/217865: Is -2/3 a solution of 3x + 6 =4?1 solutions Answer 164169 by drj(1380)   on 2009-09-27 15:41:12 (Show Source): You can put this solution on YOUR website!Is -2/3 a solution of 3x + 6 =4? To find out if this is a solution substitute the value in the equation and see if it leads a true statement. which is a true statement. I hope the above steps were helpful. For free Step-By-Step Videos on Intrduction 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 drjctu@gmail.com
 Numbers_Word_Problems/217829: The sum of two consecutive intergers is 237. Find the two intergers.1 solutions Answer 164158 by drj(1380)   on 2009-09-27 14:18:44 (Show Source): You can put this solution on YOUR website!The sum of two consecutive integers is 237. Find the two integers. Step 1. Let n be an integer. Step 2. Let n+1 be the next consecutive integer. Step 3. Then n+n+1=237 since the sum of two consecutive integers is 237. Step 4. Solving yields the following steps Subtract 1 from both sides of the equation. Divide by 2 to both sides of the equation. and Step 4. ANSWER: The integers are 118 and 119. 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 drjctu@gmail.com http://www.FreedomUniversity.TV http://www.Facebook.com/FreedomUniversity.TV http://www.Twitter.com/FreedomUTV
 Linear-systems/217789: Use the intercept method to graph x-y=3. help1 solutions Answer 164155 by drj(1380)   on 2009-09-27 14:14:37 (Show Source): You can put this solution on YOUR website!Use the intercept method to graph x-y=3. Step 1. Intercepts occur when one of the coordinates is equal to 0. So the y-intercept occurs at x=0 and the x-intercept occurs at y=0. Step 2. It takes two points to make a line. So use these intercepts points Step 3. When x=0, then 0-y=3 or y=-3. So we have point (0,-3). Step 4. When y=0, then x-0=3 or x=3. So we have another point (3,0). Step 5. Graph the line as shown below using these two points found in Steps 3 and 4. Note x-y=3 can be written as y=x-3 in slope-intercept form where slope m=1 and y-intercept b=-3. 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 drjctu@gmail.com http://www.FreedomUniversity.TV http://www.Facebook.com/FreedomUniversity.TV http://www.Twitter.com/FreedomUTV
Expressions-with-variables/217816: 2n+3n+7=-41
1 solutions

Answer 164148 by drj(1380)   on 2009-09-27 13:53:41 (Show Source):
You can put this solution on YOUR website!
2n+3n+7=-41

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=-9.6. Graphical form: Equation was fully solved.Text form: 2n+3n+7=-41 simplifies to 0=0Cartoon (animation) form: For tutors: simplify_cartoon( 2n+3n+7=-41 ) 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 .
Solved linear equation equivalent to 5*n+48 =0
It becomes .
Result:
This is an equation! Solutions: n=-9.6.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

And good luck in your studies!

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

Equations/217812: How do i solve problems like this (5x+6=2x+15)

1 solutions

Answer 164146 by drj(1380)   on 2009-09-27 13:52:17 (Show Source):
You can put this solution on YOUR website!
How do I solve problems like this 5x+6=2x+15?

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=3. Graphical form: Equation was fully solved.Text form: 5x+6=2x+15 simplifies to 0=0Cartoon (animation) form: For tutors: simplify_cartoon( 5x+6=2x+15 ) 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 .
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 3*x-9 =0
It becomes .
Result:
This is an equation! Solutions: x=3.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

And good luck in your studies!

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

 Quadratic-relations-and-conic-sections/217702: x^2+y^2=1 x+y=-1 can you give me the steps to solve this problem using simple words because i do not understand the steps they show me in my book1 solutions Answer 164132 by drj(1380)   on 2009-09-27 12:34:53 (Show Source): You can put this solution on YOUR website! This is an equation of a circle centered at point (0,0) with radius 1. This is an equation of a line with slope m=-1 and y-intercept at b=-1 or at point (0,-1). Step 1. Let's solve for x in Subtract -y to both sides of the equation } Step 2. Substitute into but and Step 3. Subtract 1 to both sides of the equation Then and Step 4. Find x-coordinates when and At , then . One intersection point is (-1,0). At then . One intersection point is (0,-1). Step 5. Then intersection points are (-1,0) and (0,-1) Here are the graphs of the circle and line and note they have two common points. 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
 Equations/217758: Write an equation for the line described as slope=-3/5 and passes through (7,6). Write in slope intercept form.1 solutions Answer 164120 by drj(1380)   on 2009-09-27 11:50:58 (Show Source): You can put this solution on YOUR website!Write an equation for the line described as slope=-3/5 and passes through (7,6). Write in slope intercept form. Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept b at x=0 or point (0,b). Here, the slope m=-3/5. Step 2. The slope m is given as Step 3. Let (x1,y1)=(6,7) or x1=7 and y1=6. Let other point be (x2,y2)=(x,y) or x2=x and y2=y. Step 4. Now we're given . Substituting above values and variables in the slope equation m yields the following steps: Step 5. Multiply (x-7) to both sides to get rid of denominators on both sides of equation. Step 6. Now add +6 to both sides of equation to solve for y. Step 7. ANSWER: The equation is Here's a graph below and note the slope and y-intercept at x=0 or point (0, 51/5) and the x-intercept at y=0 or at point (17, 0)and note it is consistent with the equation when substituting these Note: the above equation can be rewritten in standard form as I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J
 Permutations/217737: 1. In how many ways can 5 questions be selected out of 8 questions?1 solutions Answer 164116 by drj(1380)   on 2009-09-27 11:21:25 (Show Source): You can put this solution on YOUR website!1. In how many ways can 5 questions be selected out of 8 questions? Step 1. This is a combination problem where we have the following formula for this problem. where n! means n factorial or n*(n-1)*....1 and n=8 and x=5 for this example. Step 2. Then, Step 3. ANSWER: There are 6720 ways to select 5 out of 8 questions. 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
 Exponents/217747: how to convert 25/49 to exponential form?1 solutions Answer 164112 by drj(1380)   on 2009-09-27 11:11:24 (Show Source): You can put this solution on YOUR website!How to convert 25/49 to exponential form? 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
 Quadratic_Equations/217731: can you tell me what 6 ordered pairs are for this problem x2+4x+4?1 solutions Answer 164109 by drj(1380)   on 2009-09-27 11:04:37 (Show Source): You can put this solution on YOUR website!Can you tell me what 6 ordered pairs are for this problem ? Step 1. Let's define . Step 2. Form two columns one for x and the for y. Try different values of x and substitute into equation in Step 1. We'll try points -4, -3, -2, -1, 0, 1, 2, 3, 4 to get 9 ordered pairs...extra credit :) so ordered pair is (x,y) so ordered pair is (-4,4) so ordered pair is (-3,1) so ordered pair is (-2,0) so ordered pair is (-1,1) so ordered pair is (0,4) so ordered pair is (1,9) so ordered pair is (2,16) so ordered pair is (3,25) so ordered pair is (4,36) Step 3. ANSWER: Ordered pairs for this example are: (-4,4), (-3,1), (-2,0), (-1,1), (0,4), (1,9), (2,16), (3,25), (4,36) Here's a graph of the equation and see note there are ordered pairs as given above. 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