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Geometry_Word_Problems/225160: 10. Angles A and B are supplementary angles and angle A is 2⁰ more than 4 times angle B. Find the measures of angle A and angle B.
1 solutions

Answer 168078 by drj(1380)   on 2009-10-11 21:57:10 (Show Source):
You can put this solution on YOUR website!
Angles A and B are supplementary angles and angle A is 2⁰ more than 4 times angle B. Find the measures of angle A and angle B.

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

Step 2. Let A be one angle.

Step 3. Let B=180-A be its supplementary angle.

Step 4. Let A=2+4(180-A) since angle A is 2 degrees more than 4 times angle B=180-A.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: A=144.4. Graphical form: Equation was fully solved.Text form: A=2+4*(180-A) simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( A=2+4*(180-A) )` 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 .
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 5*A-722 =0
It becomes .
Result:
This is an equation! Solutions: A=144.4.

### Universal Simplifier and Solver

Done!

With A=144.4 then B=180-144.4=35.6 so check if equation in Step 4 is true... 144.4=2+4(35.6)...which it is.

Step 5. ANSWER: Angle A is 144.4 degrees and angle B is 35.6 degrees.

I hope the above steps and explanation were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

 Miscellaneous_Word_Problems/225137: Recall that the sum of the measures of the angles of a triangle is 180 degrees. In the triangle below, angle c has the same measure as angle b, and a measures 42 degrees less than angle b. Find the measure of each angle.1 solutions Answer 168075 by drj(1380)   on 2009-10-11 21:49:31 (Show Source): You can put this solution on YOUR website!Recall that the sum of the measures of the angles of a triangle is 180 degrees. In the triangle below, angle c has the same measure as angle b, and a measures 42 degrees less than angle b. Find the measure of each angle. Step 1. Given c=b Step 2. a=b-42 since angle a measures 42 less than angle b. Step 3. Then, b-42+b+b=180 since c=b and the three angles add to 180 degrees. and and Step 4. Check if the angles equal to 180...74+74+32=180 which it does. Step 6. ANSWER: Angle a is 32 degrees and angles b and c is each 74 degrees. I hope the above steps and explanation 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. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
Numbers_Word_Problems/225116: One number is 2 more than 5 times another. Their product is 3. Find the numbers.
1 solutions

Answer 168072 by drj(1380)   on 2009-10-11 21:23:45 (Show Source):
You can put this solution on YOUR website!
One number is 2 more than 5 times another. Their product is 3. Find the numbers.

Step 1. Let x be one number

Step 2. Let 2+5x be the other number since its 2 more than 5 times the first number.

Step 3. Then, since their product is 3.

Step 4. Turn this equation into a quadratic one in standard form as follows:

Subtract 3 from both sides

Simplify and arrange in descending order to get our quadratic equation

Step 4. To solve, use the quadratic formula given as

where a=5, b=2, and c=-3

 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=64 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.6, -1. Here's your graph:

With x=0.6 then 2+5x=2+5*0.6=5

With x=-1 then 2+5*(-1)=-3.

Step 5. ANSWER: The numbers are 0.6 and 5 as one pair and -1 and -3 as the other pair of numbers.

I hope the above steps and explanation were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

 test/225054: graph y=3x+11 solutions Answer 168068 by drj(1380)   on 2009-10-11 21:05:12 (Show Source): You can put this solution on YOUR website!Graph y=3x+1 Step 1. The equation is in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). Step 2. Comparing the given equation with y=mx+b shows that the slope m=3 and y-intercept is 1 when x=0 or at point (0,1). Step 3. To graph, start with the point (0,1) and the slope means for every one unit to the right we go three units up since the slope is 3. This means that one point is (0+1,1+3) or (1,4) is a point on the line. Step 4. Using the two points (0,1) and (1,4) we have the following graph of the line since it takes two points to make a line. I hope the above steps and explanation 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. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 test/225051: Find the equation of the line containing the point (4, 25) and perpendicular to the line 11x+55y=-12 . 1 solutions Answer 168066 by drj(1380)   on 2009-10-11 20:56:57 (Show Source): You can put this solution on YOUR website!Find the equation of the line containing the point (4, 25) and perpendicular to the line 11x+55y=-12. Step 1. Two lines are perpendicular if their product of the slopes is -1. In equation form m1*m2=-1 where m1 is the slope given by the first equation. And m2 is the slope of the line perpendicular to the first line. Step 2. We need to put the above given line in slope intercept form so we can find the slope of the given line. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept b when x=0 or at point (0,b). Step 3. The following steps puts the above equation in slope-intercept form Subtract 11 from both sides of the equation Divide by 5 to both sides of the equation Step 4. Comparing the last equation with y=mx+b, the slope m1=-1/5. Step 5. Therefore, the slope of the perpendicular line is since the product of the slopes between the two lines is -1 (or m1*m2=-1) Step 6. So now we have a perpendicular line with slope m2=5 that must pass through the point (4,25) Step 7. Given two points (x1,y1) and (x2,y2), then the slope m is given as Step 4. Let (x1,y1)=(4,25) or x1=4 and y1=25. Let other point be (x2,y2)=(x,y) or x2=x and y2=y. Step 5. Now we're given . Substituting above values and variables in the slope equation m yields the following steps: Step 6. Multiply x-4 to both sides to get rid of denominator on right side of equation. Add 25 to both sides of the equation Step 7. ANSWER: The equation of the perpendicular line in slope-intercept form is And the graph of the two lines are shown below. I hope the above steps and explanation 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. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 Graphs/225024: solve the system of equations by graphing. then classify 6x + y = 46 7x + 8y = 401 solutions Answer 168059 by drj(1380)   on 2009-10-11 20:34:33 (Show Source): You can put this solution on YOUR website!Solve the system of equations by graphing. Then classify 6x + y = 46 7x + 8y = 40 Step 1. Graph the two lines from above as shown below Step 2. Based on the graph the intersection point is (8,-2) or x=8 and y=-2. Step 3. Check if the solution (8,2) satisfies the above linear system of equations 6x + y = 46 or 6*8+-2=46 or 46=46 which is a true statement 7x + 8y = 40 or 7*8+8*(-2)=40 or 40=40 which is another true statement Step 4. ANSWER: The solution is (8,2). The equations are independent and consistent providing a unique solution. 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
 test/225057: Graph y=x/2-3 by using the slope and y-intercept.1 solutions Answer 168054 by drj(1380)   on 2009-10-11 20:28:10 (Show Source): You can put this solution on YOUR website!Graph y=x/2-3 by using the slope and y-intercept. 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. Comparing with , the slope and the y-intercept Step 3. Now the slope of for every two units you go the right, you go one unit up. To plot the line take the y-intercept at point (0,-3). So starting at point (0,-3) or x1=0 and y1=-3 we go two units to the right means x2=0+2=2 and 1 unit up means y2=-3+1=-2. So we have two points (0,-3) and (2,-2) used to plot the line. 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
Expressions-with-variables/225065: x+8y=76
-x+9y=77
1 solutions

Answer 168049 by drj(1380)   on 2009-10-11 20:19:27 (Show Source):
You can put this solution on YOUR website!
x+8y=76
-x+9y=77

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 8*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

drjctu@gmail.com

http://www.FreedomUniversity.TV

Miscellaneous_Word_Problems/225094: The perimeter of a standard high school basketball court is 268ft. The length is 34ft longer than the width. Find the dimensions of the court.
1 solutions

Answer 168048 by drj(1380)   on 2009-10-11 20:17:38 (Show Source):
You can put this solution on YOUR website!
The perimeter of a standard high school basketball court is 268ft. The length is 34ft longer than the width. Find the dimensions of the court.

Step 1. The perimeter P means adding up all the four sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let w+34 be the length since the length is 34 ft longer than the width.

Step 4. Then, P=w+w+w+34+w+34=268.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=50. Graphical form: Equation was fully solved.Text form: w+w+w+34+w+34=268 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( w+w+w+34+w+34=268 )` 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*w-200 =0
It becomes .
Result:
This is an equation! Solutions: w=50.

### Universal Simplifier and Solver

Done!

For w=50 , then w+34=84 and P=2(50+84)=268 which is a true statement.

Step 6. ANSWER: The width is 50 feet and he length is 84 feet.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV

 Functions/225073: rewrite the equation so that y is a function of x y/5-7=-2x How do you solve this?1 solutions Answer 168025 by drj(1380)   on 2009-10-11 19:35:53 (Show Source): You can put this solution on YOUR website!rewrite the equation so that y is a function of x Step 1. Add 7 to both sides of the equation Step 2. Multiply by 5 to both sides of the equation to get rid of denominator. Step 3. 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. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 Linear-equations/225062: Solve each system of equations by graphing. y=x-2 y=3x-81 solutions Answer 168020 by drj(1380)   on 2009-10-11 19:20:46 (Show Source): You can put this solution on YOUR website!Solve each system of equations by graphing. y=x-2 y=3x-8 Step 1. Graphing the system of equations is Step 2. Based on the graph, the intersection point is (3,1) Step 3. Check if the intersection point (3,1) satisfies the system of equations y=x-2 1=3-2 which is a true statement y=3x-8 1=3*3-8 which is another true statement Step 4. ANSWER: The solution is (3,1) or x=3 and y=1. 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
test/225022: Find the equation of the line that contains the points P1(–8, –12) and P2(9, –12).
1 solutions

Answer 168017 by drj(1380)   on 2009-10-11 19:12:55 (Show Source):
You can put this solution on YOUR website!
Find the equation of the line that contains the points P1(–8, –12) and P2(9,–12).

Step 1. We will put the equation of the line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).

Step 2. The slope of the line m is given as

where for our example is x1=-8, y1=-12, x2=9 and y2=-12 (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 3. Substituting the above values in the slope equation gives

Step 4. The slope is calculated as or

Step 5. Now use the slope equation of Step 2 and choose one of the given points. I'll choose point (9,-12). Letting y=y2 and x=x2 and substituting in the slope equation given as,

Step 6. Multiply both sides of equation by x-9 to get rid of denominator found on the right side of the equation

Step 9. ANSWER: The equation of the line is

See graph below to check the above steps.

 Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc This equation defines a horizontal line. There is no X intercept. Y intercept is

I hope the above steps were helpful.

Respectfully,
Dr J

 Linear-systems/225044: I am trying to help my daughter with her homework and need to know how to solve this equation.... 2k + 6 - K = 171 solutions Answer 168015 by drj(1380)   on 2009-10-11 18:45:45 (Show Source): You can put this solution on YOUR website!I am trying to help my daughter with her homework and need to know how to solve this equation.... 2k + 6 - k = 17 Step 1. Simplify by adding the like terms on the left side of the equation Step 2. Subtract 6 from obth sides of the equation to solve for k terms. Check solution...... which is a true statement. Step 3. ANSWER: Solution is 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
 Numbers_Word_Problems/225037: the width of a rectangle is one third of the length.If the perimeter is 20 cm,find the width.1 solutions Answer 168013 by drj(1380)   on 2009-10-11 18:37:47 (Show Source): You can put this solution on YOUR website!The width of a rectangle is one third of the length. If the perimeter is 20 cm,find the width. Step 1. The perimeter P means adding up all four sides of a rectangle. Step 2. Let w be the width Step 3. Let 3w be the length since the width is one-third the length Step 4. Then P=w+w+3w+3w=8w=20 since the perimeter P is 20 cm. Step 5. Solving the equation in Step 4 leads to the following steps Divide by 8 to both sides of the equation and 3w=15/2 and P=2(5/2+15/2)=20 which is a true statement. Step 6. ANSWER: The width is 5/2 cm. 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
 Linear_Algebra/225027: Solve by using elimination. This cant be solved right? x-4y=2 4x-16y=81 solutions Answer 168010 by drj(1380)   on 2009-10-11 18:30:40 (Show Source): You can put this solution on YOUR website!Solve by using elimination. This cant be solved right? x-4y=2 Multiply by 4 to both sides and you'll get 4x-16y=8 which is identical to the one below 4x-16y=8 ANSWER: Because these are equations are dependent (one equation is a multiple of the other, 4 in this case), there are many solutions that satisfies these equations. 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
 Numbers_Word_Problems/225035: Two numbers are in the ratio 1:11 and their sum is 15. Find the numbers. Thanks1 solutions Answer 168007 by drj(1380)   on 2009-10-11 18:24:29 (Show Source): You can put this solution on YOUR website!Two numbers are in the ratio 1:11 and their sum is 15. Find the numbers. Step 1. Let x be one number Step 2. Let 11x be the other number since the ratio is 1:11. Step 3. Then 11x+x=15 or 12x=15 then and which is atrue statement. Step 4. ANSWER: The numbers are and . 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/225001: graph and check: "graph the linear system and estimate the solution. Then check the solution algebraically. 2x+y=5 x+y=21 solutions Answer 167999 by drj(1380)   on 2009-10-11 18:07:15 (Show Source): You can put this solution on YOUR website!Graph and check: "graph the linear system and estimate the solution. Then check the solution algebraically. Step 1. Graph the linear system of equations Step 2. Based on the above graph, the intersection point is (3,-1). Step 3. Check if (3,-1) or x=3 and y=-1 satisfies the system of equaitons Given , then which is a true statment. Given , then which is a true statement. Step 4. ANSWER: The solution sis (3,-1) or x=3 and y=-1. 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
 Quadratic_Equations/224995: factor 6x^2+241 solutions Answer 167990 by drj(1380)   on 2009-10-11 17:39:25 (Show Source): You can put this solution on YOUR website!Factor Step 1. Look at numbers and find greatest factor which is 6 Step 2. Look to see if there are common terms in the variable x and in this case there is none. Step 3. ANSWER: I hope the above steps and explanation 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. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
Linear-equations/224990: find the slope intercept equation of the line that has the given characteristics
slope 4 and y intercept (0,3)
slope intercept equation is y=
1 solutions

Answer 167989 by drj(1380)   on 2009-10-11 17:28:00 (Show Source):
You can put this solution on YOUR website!
Find the slope intercept equation of the line that has the given characteristics

slope 4 and y intercept (0,3)

slope intercept equation is y=4x+3

Step 1. The equation in slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).
In your example we compare y=mx+b such that m=4 and b=3. Therefore, y=4x+3.

Step 2. Here's another way...now we have to find the line with slope m=4 going through point (0,3).

Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as

Step 4. Let (x1,y1)=(0,3) or x1=0 and y1=3. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given . Substituting above values and variables in the slope equation m yields the following steps:

Step 6. Multiply x to both sides to get rid of denominator on right side of equation.

Step 7. Add 3 to both sides of the equation

same as in Step 1.

Step 7. ANSWER: The equation in slope-intercept form is where the slope m=7 and the y-intercept b=-5.

Note: the above equation can be rewritten in standard form as

And the graph is shown below which is consistent with 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. -5/-7 = 0.714285714285714.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -5/1 = -5.Slope is --7/1 = 7. Equation in slope-intercept form: y=7*x+-5.

I hope the above steps and explanation were helpful.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Angles/224936: can you please help me figure out the supplement of a given angle is four times as large as a complement of the angle. Find the measure of the given angle. Please.

1 solutions

Answer 167973 by drj(1380)   on 2009-10-11 15:11:30 (Show Source):
You can put this solution on YOUR website!
Can you please help me figure out the supplement of a given angle is four times as large as a complement of the angle. Find the measure of the given angle. Please.

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. Then 180-x=4(90-x) since the supplement of a given angle is four times as large as a complement of the angle

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=4*(90-x) simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 180-x=4*(90-x) )` 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 .
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 3*x-180 =0
It becomes .
Result:
This is an equation! Solutions: x=60.

### Universal Simplifier and Solver

Done!

With x=60, then 180-x-120 and 90-60=30 and note that four times the complement of the angle is the supplement of the angle.

Step 7. ANSWER: The angle is 60 degrees. It complement is 30 degrees and its supplement is 120 degrees.

I hope the above steps were helpful.

And good luck in your studies!

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

 Circles/224919: what is the circumference of a circle with a diameter of 3cm?1 solutions Answer 167971 by drj(1380)   on 2009-10-11 15:06:29 (Show Source): You can put this solution on YOUR website!What is the circumference of a circle with a diameter of 3 cm? Step 1. The circumference C of a circle is given as where d is the diameter. Step 2. ANSWER: cm 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 http://www.FreedomUniversity.TV http://www.Facebook.com/FreedomUniversityTV http://www.Twitter.com/FreedomUTV
 Linear-equations/224926: is y+3=0 a linear equation?1 solutions Answer 167970 by drj(1380)   on 2009-10-11 15:02:16 (Show Source): You can put this solution on YOUR website!Is y+3=0 a linear equation? Yes. You can rewrite the above equation as y=-3. In Slope-Intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 at point (0,b). For this example, the slope m=0 or a horizontal line and the y-intercept is -3. The graph is shown below: 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 http://www.FreedomUniversity.TV http://www.Facebook.com/FreedomUniversityTV http://www.Twitter.com/FreedomUTV
Equations/224915: Solve this simultaneous equation:
y=5-4x²
y+3x=6
1 solutions

Answer 167967 by drj(1380)   on 2009-10-11 14:21:07 (Show Source):
You can put this solution on YOUR website!
Solve this simultaneous equation:
Equation 1
or Equation 2

Step 1. Set Equations 1 and 2 to be equal.

Step 2. Add to both sides of the equation

Step 3. To solve, use the quadratic formula given below

where a=4, b=-3, and c=1

 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 : . The discriminant -7 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -7 is + or - . The solution is Here's your graph:

Step 4. For each value of x found in Step 3, substitute each value into y=6-3x to get a total of 2 values for y. You now have two points as your solution to these equations. Your solutions will be complex numbers.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

http://www.FreedomUniversity.TV

x+y=10
y=3x²-2x-3
I have tried every way i can think of to solve this equation but i have failed. Please help me
1 solutions

Answer 167966 by drj(1380)   on 2009-10-11 14:10:44 (Show Source):
You can put this solution on YOUR website!
solve this simultaneous equation:
Equation 1
Equation 2

Step 1. In Equation 1, solve for and substitute y into Equation 2.

Step 2. Add x-10 to both sides of the equatiion

Step 3. To solve use the quadratic formula given below:

where a=3, b=-1, and c=-13

 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=157 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.25499401435694, -1.92166068102361. Here's your graph:

Step 4. Now, for each value of x found in Step 3, substitute into y=10-x to get two values for y.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

http://www.FreedomUniversity.TV