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Recent problems solved by 'ichudov'

ichudov answered: 497 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509, >>Next

Graphs/7313: Please help me to graph this..
1)y=1/5x-5
2)y=-4/1x-7
1 solutions
Answer 4074 by ichudov(499) About Me  on 2005-08-16 08:54:37 (Show Source):

Linear-equations/7318: solve the following equation. express roots to the nearest hundredth.
2m^2-m-7=0
1 solutions
Answer 4073 by ichudov(499) About Me  on 2005-08-16 08:44:19 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation am%5E2%2Bbm%2Bc=0 (in our case 2m%5E2%2B-1m%2B-7+=+0) has the following solutons:

m%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A2%2A-7=57.

Discriminant d=57 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+57+%29%29%2F2%5Ca.

m%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+57+%29%29%2F2%5C2+=+2.13745860881769
m%5B2%5D+=+%28-%28-1%29-sqrt%28+57+%29%29%2F2%5C2+=+-1.63745860881769

Quadratic expression 2m%5E2%2B-1m%2B-7 can be factored:
2m%5E2%2B-1m%2B-7+=+2%28m-2.13745860881769%29%2A%28m--1.63745860881769%29
Again, the answer is: 2.13745860881769, -1.63745860881769. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-1%2Ax%2B-7+%29

Expressions-with-variables/7314: a + a/5 + 2/5*a
1 solutions
Answer 4072 by ichudov(499) About Me  on 2005-08-16 08:43:07 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: a%2Ba%2F5%2B2%2F5%2Aa simplifies to 8%2F5%2Aa
  • Text form: a+a/5+2/5*a simplifies to 8/5*a
  • Cartoon (animation) form: simplify_cartoon%28+a%2Ba%2F5%2B2%2F5%2Aa+%29
    For tutors: simplify_cartoon( a+a/5+2/5*a )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+a+%29%2Bhighlight_red%28+a%2F5+%29%2Bhighlight_red%28+2%2F5%2Aa+%29.
Eliminated similar terms highlight_red%28+a+%29,highlight_red%28+a%2F5+%29,highlight_red%28+2%2F5%2Aa+%29 replacing them with highlight_green%28+%281%2B1%2F5%2B2%2A1%2F5%29%2Aa+%29
It becomes highlight_green%28+%281%2B1%2F5%2B2%2A1%2F5%29%2Aa+%29.
Look at %281%2B1%2F5%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2F5%29%2Aa.
Multiplied numerator integers
It becomes %281%2B1%2F5%2Bhighlight_green%28+2+%29%2F5%29%2Aa.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1%2F5+%29%2Bhighlight_red%28+2%2F5+%29%29%2Aa.
Added fractions or integers together
It becomes %28highlight_green%28+8%2F5+%29%29%2Aa.
Look at highlight_red%28+%28highlight_red%28+8%2F5+%29%29%2Aa+%29.
Remove unneeded parentheses around factor highlight_red%28+8+%29,highlight_red%28+1%2F5+%29
It becomes highlight_green%28+8+%29%2Fhighlight_green%28+5+%29%2Aa.
Result: 8%2F5%2Aa

Universal Simplifier and Solver


Done!

Quadratic-relations-and-conic-sections/7324: Dear Sir/Madam,
I am confronted with the following problem:
"Find a polar equation which has the same graph as the
equation +x%5E2+-+2x+%2B+y%5E2+=+0+."
I assumed that this question wants you to complete the square, so I went ahead and did that.
1) +%28x-1%29%5E2+-+1+%2B+y%5E2+=+0+
2) +y%5E2+-+1+=+-%28x-1%29%5E2+
Meaning that the center of this circle is at (1, 1) correct? Either way, once you have this information, how do you put this into a polar equation? Or did I approach this question entirely wrong?
Thanks in advance.
Regards,
-Mike
1 solutions
Answer 4071 by ichudov(499) About Me  on 2005-08-16 08:41:48 (Show Source):
You can put this solution on YOUR website!
great job on both typing formulas in our formula system as well as getting to the solution. You are almost there.
%28x-1%29%5E2%2By%5E2+=+1
that's an equation of a circle with center in point x=1, y=0.
so, assuming that this is what you want, system%28+x=1%2B+cos%28+phi+%29%2C+y=sin%28+phi+%29+%29+.

Linear-systems/7336: find the value of m such that this question have no solutions:
3x-my=4
x+y=12
1 solutions
Answer 4070 by ichudov(499) About Me  on 2005-08-16 08:34:18 (Show Source):
You can put this solution on YOUR website!
that's a great problem. Start solving this system a little bit, it will help. Subtract 3 times the bottom equation, from top equation:
3x-my - 3(x+y) = 4-3*12
-my-3y = -32
remove minuses just to make it more readable
my+3y = 32
the value of m that makes this equation impossible (no solutions) is such am that makes the equation 0=32. 0=32 is an impossible equation.
-3 looks pretty good:
-3y+3y=32 is the same as 0 = 32.
so, the answer is m=-3.

Length-and-distance/7328: The ____ and the ____ are devices used to make linear measures.
1 solutions
Answer 4048 by ichudov(499) About Me  on 2005-08-15 23:09:20 (Show Source):
You can put this solution on YOUR website!
Would that be, perhaps, ruler and compass?

Distributive-associative-commutative-properties/7329: I need help with this problem: 8x+3-4x apply the distributive property and simplify the expression
1 solutions
Answer 4047 by ichudov(499) About Me  on 2005-08-15 23:07:46 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 8x%2B3-4x simplifies to 4%2Ax%2B3
  • Text form: 8x+3-4x simplifies to 4*x+3
  • Cartoon (animation) form: simplify_cartoon%28+8x%2B3-4x+%29
    For tutors: simplify_cartoon( 8x+3-4x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 8%2Ax%2Bhighlight_red%28+3+%29-4%2Ax.
Moved 3 to the right of expression
It becomes 8%2Ax-4%2Ax%2Bhighlight_green%28+3+%29.
Look at highlight_red%28+8%2Ax+%29-highlight_red%28+4%2Ax+%29%2B3.
Eliminated similar terms highlight_red%28+8%2Ax+%29,highlight_red%28+-4%2Ax+%29 replacing them with highlight_green%28+%288-4%29%2Ax+%29
It becomes highlight_green%28+%288-4%29%2Ax+%29%2B3.
Look at %28highlight_red%28+8+%29-highlight_red%28+4+%29%29%2Ax%2B3.
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2Ax%2B3.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2Ax+%29%2B3.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2Ax%2B3.
Result: 4%2Ax%2B3

Universal Simplifier and Solver


Done!

Numbers_Word_Problems/7330: Five decreased by eight is four times y
1 solutions
Answer 4046 by ichudov(499) About Me  on 2005-08-15 23:06:16 (Show Source):
You can put this solution on YOUR website!
that's a problem of translating english to algebrese.
five decreased by eight: 5-8
four times y: 4*y
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: y=-0.75.
  • Graphical form: Equation 5-8=4%2Ay was fully solved.
  • Text form: 5-8=4*y simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5-8=4%2Ay+%29
    For tutors: simplify_cartoon( 5-8=4*y )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+5+%29-highlight_red%28+8+%29=4%2Ay.
Added fractions or integers together
It becomes highlight_green%28+-3+%29=4%2Ay.
Look at highlight_red%28+-3+%29=4%2Ay.
Removed extra sign in front of -3
It becomes -highlight_green%28+3+%29=4%2Ay.
Look at -3=highlight_red%28+4%2Ay+%29.
Moved these terms to the left highlight_green%28+-4%2Ay+%29
It becomes -3-highlight_green%28+4%2Ay+%29=0.
Look at -highlight_red%28+3+%29-4%2Ay=0.
Moved -3 to the right of expression
It becomes -4%2Ay-highlight_green%28+3+%29=0.
Look at highlight_red%28+-4%2Ay-3+%29=0.
Solved linear equation highlight_red%28+-4%2Ay-3=0+%29 equivalent to -4*y-3 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=-0.75.

Universal Simplifier and Solver


Done!

Equations/7273: i need help on the following problem.....
1/2*(4x-8)=2(x+3)
I cant remember how you find X !!!
Thankyou
1 solutions
Answer 4013 by ichudov(499) About Me  on 2005-08-15 15:45:02 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 1%2F2%2A%284x-8%29=2%2A%28x%2B3%29 simplifies to -10=0
  • Text form: 1/2*(4x-8)=2*(x+3) simplifies to -10=0
  • Cartoon (animation) form: simplify_cartoon%28+1%2F2%2A%284x-8%29=2%2A%28x%2B3%29+%29
    For tutors: simplify_cartoon( 1/2*(4x-8)=2*(x+3) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+1+%29%2F2%2A%284%2Ax-8%29=2%2A%28x%2B3%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %284%2Ax-8%29%2F2=2%2A%28x%2B3%29.
Look at %284%2Ax-8%29%2F2=highlight_red%28+2%2A%28x%2B3%29+%29.
Moved these terms to the left highlight_green%28+-2%2A%28x%2B3%29+%29
It becomes %284%2Ax-8%29%2F2-highlight_green%28+2%2A%28x%2B3%29+%29=0.
Look at highlight_red%28+%284%2Ax-8%29%2F2+%29-2%2A%28x%2B3%29=0.
Expanded term 1%2F2 by using associative property on %284%2Ax-8%29
It becomes highlight_green%28+1%2F2%2A4%2Ax+%29-highlight_green%28+1%2F2%2A8+%29-2%2A%28x%2B3%29=0.
Look at 1%2Fhighlight_red%28+2+%29%2Ahighlight_red%28+4+%29%2Ax-1%2F2%2A8-2%2A%28x%2B3%29=0.
Factors 4 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+2+%29%2Ax-1%2F2%2A8-2%2A%28x%2B3%29=0.
Look at highlight_red%28+1+%29%2F1%2Ahighlight_red%28+2+%29%2Ax-1%2F2%2A8-2%2A%28x%2B3%29=0.
Multiplied numerator integers
It becomes highlight_green%28+2+%29%2F1%2Ax-1%2F2%2A8-2%2A%28x%2B3%29=0.
Look at 2%2F1%2Ax-1%2Fhighlight_red%28+2+%29%2Ahighlight_red%28+8+%29-2%2A%28x%2B3%29=0.
Factors 8 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 2%2F1%2Ax-1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+4+%29-2%2A%28x%2B3%29=0.
Look at 2%2F1%2Ax-highlight_red%28+1+%29%2F1%2Ahighlight_red%28+4+%29-2%2A%28x%2B3%29=0.
Multiplied numerator integers
It becomes 2%2F1%2Ax-highlight_green%28+4+%29%2F1-2%2A%28x%2B3%29=0.
Look at 2%2F1%2Ax-highlight_red%28+4%2F1+%29-2%2A%28x%2B3%29=0.
Moved -4%2F1 to the right of expression
It becomes 2%2F1%2Ax-2%2A%28x%2B3%29-highlight_green%28+4%2F1+%29=0.
Look at 2%2Fhighlight_red%28+1+%29%2Ax-2%2A%28x%2B3%29-4%2F1=0.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 2%2Ax-2%2A%28x%2B3%29-4%2F1=0.
Look at 2%2Ax-2%2A%28x%2B3%29-4%2Fhighlight_red%28+1+%29=0.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 2%2Ax-2%2A%28x%2B3%29-4=0.
Look at 2%2Ax-highlight_red%28+2%2A%28x%2B3%29+%29-4=0.
Expanded term -2 by using associative property on %28x%2B3%29
It becomes 2%2Ax-highlight_green%28+2%2Ax+%29-highlight_green%28+2%2A3+%29-4=0.
Look at 2%2Ax-2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+3+%29-4=0.
Multiplied numerator integers
It becomes 2%2Ax-2%2Ax-highlight_green%28+6+%29-4=0.
Look at 2%2Ax-2%2Ax-highlight_red%28+6+%29-highlight_red%28+4+%29=0.
Added fractions or integers together
It becomes 2%2Ax-2%2Ax%2Bhighlight_green%28+-10+%29=0.
Look at 2%2Ax-2%2Ax%2Bhighlight_red%28+-10+%29=0.
Removed extra sign in front of -10
It becomes 2%2Ax-2%2Ax-highlight_green%28+10+%29=0.
Look at highlight_red%28+2%2Ax+%29-highlight_red%28+2%2Ax+%29-10=0.
Eliminated similar terms highlight_red%28+2%2Ax+%29,highlight_red%28+-2%2Ax+%29 replacing them with highlight_green%28+%282-2%29%2Ax+%29
It becomes highlight_green%28+%282-2%29%2Ax+%29-10=0.
Look at highlight_red%28+%282-2%29%2Ax+%29-10=0.
Since highlight_red%28+%282-2%29%2Ax+%29 has zero as a factor, it should be replaced with a zero
Look at 0-10=0.
Added fractions or integers together
It becomes 0-10=0.
Look at highlight_red%28+0+%29-10=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes -10=0.
Result: -10=0

Universal Simplifier and Solver


Done!


As you can see, 10=0 is an impossible equation.

Polynomials-and-rational-expressions/7233: Hi, I am not sure where to start with this problem. Simplify 5x^2y-2x^2y(2+y)+8x^2y^2...... Thanks so much for any help... I'm just not sure where to start.... the part with the parentheses throws me off....
Thanks,
Ashley
1 solutions
Answer 4012 by ichudov(499) About Me  on 2005-08-15 15:30:09 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 5x%5E2y-2x%5E2y%2A%282%2By%29%2B8x%5E2y%5E2 simplifies to x%5E2%2Ay%2B6%2Ax%5E2%2Ay%5E2
  • Text form: 5x^2y-2x^2y*(2+y)+8x^2y^2 simplifies to x^2*y+6*x^2*y^2
  • Cartoon (animation) form: simplify_cartoon%28+5x%5E2y-2x%5E2y%2A%282%2By%29%2B8x%5E2y%5E2+%29
    For tutors: simplify_cartoon( 5x^2y-2x^2y*(2+y)+8x^2y^2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2Ax%5E2%2Ay-2%2Ax%5E2%2Ay%2A%28highlight_red%28+2+%29%2By%29%2B8%2Ax%5E2%2Ay%5E2.
Moved 2 to the right of expression
It becomes 5%2Ax%5E2%2Ay-2%2Ax%5E2%2Ay%2A%28y%2Bhighlight_green%28+2+%29%29%2B8%2Ax%5E2%2Ay%5E2.
Look at 5%2Ax%5E2%2Ay-highlight_red%28+2%2Ax%5E2%2Ay%2A%28y%2B2%29+%29%2B8%2Ax%5E2%2Ay%5E2.
Expanded term -2%2Ax%5E2%2Ay by using associative property on %28y%2B2%29
It becomes .
Look at .
Multiplied numerator integers
It becomes 5%2Ax%5E2%2Ay-2%2Ax%5E2%2Ay%2Ay-highlight_green%28+4+%29%2Ax%5E2%2Ay%2B8%2Ax%5E2%2Ay%5E2.
Look at .
Reduce similar several occurrences of highlight_red%28+y+%29 to highlight_green%28+y%5E2+%29
It becomes 5%2Ax%5E2%2Ay-2%2Ax%5E2%2Ahighlight_green%28+y%5E2+%29-4%2Ax%5E2%2Ay%2B8%2Ax%5E2%2Ay%5E2.
Look at .
Eliminated similar terms highlight_red%28+5%2Ax%5E2%2Ay+%29,highlight_red%28+-4%2Ax%5E2%2Ay+%29 replacing them with highlight_green%28+%285-4%29%2Ax%5E2%2Ay+%29
It becomes highlight_green%28+%285-4%29%2Ax%5E2%2Ay+%29-2%2Ax%5E2%2Ay%5E2%2B8%2Ax%5E2%2Ay%5E2.
Look at .
Eliminated similar terms highlight_red%28+-2%2Ax%5E2%2Ay%5E2+%29,highlight_red%28+8%2Ax%5E2%2Ay%5E2+%29 replacing them with highlight_green%28+%28-2%2B8%29%2Ax%5E2%2Ay%5E2+%29
It becomes %285-4%29%2Ax%5E2%2Ay%2Bhighlight_green%28+%28-2%2B8%29%2Ax%5E2%2Ay%5E2+%29.
Look at highlight_red%28+%285-4%29+%29%2Ax%5E2%2Ay%2B%28-2%2B8%29%2Ax%5E2%2Ay%5E2.
Remove extraneous '1' from product highlight_red%28+%285-4%29+%29
It becomes x%5E2%2Ay%2B%28-2%2B8%29%2Ax%5E2%2Ay%5E2.
Look at x%5E2%2Ay%2B%28-highlight_red%28+2+%29%2Bhighlight_red%28+8+%29%29%2Ax%5E2%2Ay%5E2.
Added fractions or integers together
It becomes x%5E2%2Ay%2B%28highlight_green%28+6+%29%29%2Ax%5E2%2Ay%5E2.
Look at x%5E2%2Ay%2Bhighlight_red%28+%28highlight_red%28+6+%29%29%2Ax%5E2%2Ay%5E2+%29.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes x%5E2%2Ay%2Bhighlight_green%28+6+%29%2Ax%5E2%2Ay%5E2.
Result: x%5E2%2Ay%2B6%2Ax%5E2%2Ay%5E2

Universal Simplifier and Solver


Done!

Age_Word_Problems/7246: Erin's age is 3 times Warren's. In 4 years she will be twice as old as he will be. how old is each now?
1 solutions
Answer 4009 by ichudov(499) About Me  on 2005-08-15 14:53:13 (Show Source):
You can put this solution on YOUR website!
Translation from English into algebrese:
Erin = 3*Warren
Erin+4 = 2*(Warren+4)
Erin-3*Warren = 0
Erin - 2*Warren = 4
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving -3*Warren to the right, we get:
1%2AErin+=+0+-+-3%2AWarren, or Erin+=+0%2F1+-+-3%2AWarren%2F1. Substitute that
into another equation:
1%2A%280%2F1+-+-3%2AWarren%2F1%29+%2B+-2%5CWarren+=+4 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

Money_Word_Problems/7241: I can not figure out the formula for the folliwng problem.
Robert inherited $4000 from grandmother. Part was invested at 5% while the rest was invested at 6.5%. The interest for the yearw as $227. How much was invested at 6.5%
1 solutions
Answer 4008 by ichudov(499) About Me  on 2005-08-15 14:46:19 (Show Source):
You can put this solution on YOUR website!
say he invested X at 5% and Y at 6.5%. X+Y is 4,000. Interest is 0.05X+0.065Y = 227.
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 1*Y to the right, we get:
1%2AX+=+4000+-+1%2AY, or X+=+4000%2F1+-+1%2AY%2F1. Substitute that
into another equation:
0.05%2A%284000%2F1+-+1%2AY%2F1%29+%2B+0.065%5CY+=+227 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

Rational-functions/6758: help me find the domain of 7x%2F%28x%2B4%29+ how and why?

1 solutions
Answer 3947 by ichudov(499) About Me  on 2005-08-13 23:07:37 (Show Source):
You can put this solution on YOUR website!
The domain is simply all points where the function is defined. The only way this one can be UNdefined is when the denominator is 0.
x+4 = 0 x=-4.
So, the domain is all values of x EXCEPT -4.

Mixture_Word_Problems/7101: Can anyone please help me?? Use definitions or identities to find the remaining five trigonometric functions of the acute angle.
cos=sqrt2/2
Thank you!!!
1 solutions
Answer 3892 by ichudov(499) About Me  on 2005-08-12 13:04:07 (Show Source):
You can put this solution on YOUR website!
If cos%28alpha%29+=+sqrt%282%29%2F2, then alpha is a 45 degree angle. Just FYI.
sin%28+alpha+%29+=+sqrt%28+1-%28cos%28alpha%29%29%5E2%29+=+sqrt%282%29%2F2. Go ahead and calculate tangent and cotangent.

Quadratic_Equations/7077: identify the root to the nearest tenth.
y=2x^4+x^2-3
1 solutions
Answer 3890 by ichudov(499) About Me  on 2005-08-12 10:11:57 (Show Source):
You can put this solution on YOUR website!
You need to solve equation
2x%5E4%2Bx%5E2-3+=+0
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=1,x=-1.
  • Graphical form: Equation 2x%5E4%2Bx%5E2-3=0 was fully solved.
  • Text form: 2x^4+x^2-3=0 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2x%5E4%2Bx%5E2-3=0+%29
    For tutors: simplify_cartoon( 2x^4+x^2-3=0 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+2%2Ax%5E4%2Bx%5E2-3+%29=0.
Equation highlight_red%28+2%2Ax%5E4%2Bx%5E2-3=0+%29 is a quadratic equation, if we substitute Z=x%5E2: and has solutions Z= 1 and solution x=root%28+2%2C+Z+%29: 1,-1
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=1,x=-1.

Universal Simplifier and Solver


Done!

logarithm/7037: solve:
-2logbase4x=logbase49
-2%2Alog%28+4%2C+x+%29+=+log%28+4%2C+9+%29

3 logbase2 x=-logbase2 27

thank you!
1 solutions
Answer 3863 by ichudov(499) About Me  on 2005-08-11 11:53:49 (Show Source):
You can put this solution on YOUR website!
I will solve one for you, and you do the rest, okay?

-2%2Alog%28+4%2C+x+%29+=+log%28+4%2C+9+%29

log%28+4%2C+x%5E-2+%29+=+log%28+4%2C+9+%29
x%5E-2+=+9
1%2Fx%5E2+=+9
x%5E2+=+1%2F9
x=1%2F3, x=-1%2F3

logarithm/7041: How can i write as sum, difference, or multiple of log:
ln%28+5x%2Froot%283%2C+x%5E2%2B1%29+%29+
I have tried so far: ln5x-⅓lnx²+1 Not sure if this is correct. Your help is greatly appreciated.
1 solutions
Answer 3862 by ichudov(499) About Me  on 2005-08-11 11:48:01 (Show Source):
You can put this solution on YOUR website!
Your answer is correct. ln of a fraction is the difference of logarithms (you got that), and log of cubic root is 1/3 of the log of its argument (you got that right also).

expressions/6788: Dear Tutor,
It would be really very nice of you to evaluate this question for me.
Evaluate:
2a-{4[b-3(a-2xb-2a)]-10(3b-5a)]
Thank you
1 solutions
Answer 3738 by ichudov(499) About Me  on 2005-08-08 08:44:10 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 2a-%284%2A%28b-3%2A%28a-2xb-2a%29%29-10%2A%283b-5a%29%29 simplifies to -60%2Aa%2B26%2Ab-24%2Axb
  • Text form: 2a-(4*(b-3*(a-2xb-2a))-10*(3b-5a)) simplifies to -60*a+26*b-24*xb
  • Cartoon (animation) form: simplify_cartoon%28+2a-%284%2A%28b-3%2A%28a-2xb-2a%29%29-10%2A%283b-5a%29%29+%29
    For tutors: simplify_cartoon( 2a-(4*(b-3*(a-2xb-2a))-10*(3b-5a)) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2Aa-highlight_red%28+%284%2A%28b-3%2A%28a-2%2Axb-2%2Aa%29%29-10%2A%283%2Ab-5%2Aa%29%29+%29.
Remove unneeded parentheses around terms highlight_red%28+-4%2A%28b-3%2A%28a-2%2Axb-2%2Aa%29%29+%29,highlight_red%28+10%2A%283%2Ab-5%2Aa%29+%29
It becomes .
Look at .
Eliminated similar terms highlight_red%28+a+%29,highlight_red%28+-2%2Aa+%29 replacing them with highlight_green%28+%281-2%29%2Aa+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -1
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes 2%2Aa-4%2A%28b-3%2A%28-highlight_green%28+1+%29%2Aa-2%2Axb%29%29%2B10%2A%283%2Ab-5%2Aa%29.
Look at 2%2Aa-4%2A%28b-3%2A%28-highlight_red%28+1+%29%2Aa-2%2Axb%29%29%2B10%2A%283%2Ab-5%2Aa%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes 2%2Aa-4%2A%28b-3%2A%28-a-2%2Axb%29%29%2B10%2A%283%2Ab-5%2Aa%29.
Look at 2%2Aa-4%2A%28b-highlight_red%28+3%2A%28-a-2%2Axb%29+%29%29%2B10%2A%283%2Ab-5%2Aa%29.
Expanded term -3 by using associative property on %28-a-2%2Axb%29
It becomes .
Look at 2%2Aa-highlight_red%28+4%2A%28b%2B3%2Aa%2B3%2A2%2Axb%29+%29%2B10%2A%283%2Ab-5%2Aa%29.
Expanded term -4 by using associative property on %28b%2B3%2Aa%2B3%2A2%2Axb%29
It becomes .
Look at .
Multiplied numerator integers
It becomes 2%2Aa-4%2Ab-highlight_green%28+12+%29%2Aa-4%2A3%2A2%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at .
Multiplied numerator integers
It becomes 2%2Aa-4%2Ab-12%2Aa-highlight_green%28+24+%29%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at .
Eliminated similar terms highlight_red%28+2%2Aa+%29,highlight_red%28+-12%2Aa+%29 replacing them with highlight_green%28+%282-12%29%2Aa+%29
It becomes highlight_green%28+%282-12%29%2Aa+%29-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+-10+%29%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at %28highlight_red%28+-10+%29%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Removed extra sign in front of -10
It becomes %28-highlight_green%28+10+%29%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at .
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes -highlight_green%28+10+%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at -10%2Aa-4%2Ab-24%2Axb%2Bhighlight_red%28+10%2A%283%2Ab-5%2Aa%29+%29.
Expanded term 10 by using associative property on %283%2Ab-5%2Aa%29
It becomes -10%2Aa-4%2Ab-24%2Axb%2Bhighlight_green%28+10%2A3%2Ab+%29-highlight_green%28+10%2A5%2Aa+%29.
Look at -10%2Aa-4%2Ab-24%2Axb%2Bhighlight_red%28+10+%29%2Ahighlight_red%28+3+%29%2Ab-10%2A5%2Aa.
Multiplied numerator integers
It becomes -10%2Aa-4%2Ab-24%2Axb%2Bhighlight_green%28+30+%29%2Ab-10%2A5%2Aa.
Look at -10%2Aa-4%2Ab-24%2Axb%2B30%2Ab-highlight_red%28+10+%29%2Ahighlight_red%28+5+%29%2Aa.
Multiplied numerator integers
It becomes -10%2Aa-4%2Ab-24%2Axb%2B30%2Ab-highlight_green%28+50+%29%2Aa.
Look at -highlight_red%28+10%2Aa+%29-4%2Ab-24%2Axb%2B30%2Ab-highlight_red%28+50%2Aa+%29.
Eliminated similar terms highlight_red%28+-10%2Aa+%29,highlight_red%28+-50%2Aa+%29 replacing them with highlight_green%28+%28-10-50%29%2Aa+%29
It becomes highlight_green%28+%28-10-50%29%2Aa+%29-4%2Ab-24%2Axb%2B30%2Ab.
Look at %28-10-50%29%2Aa-highlight_red%28+4%2Ab+%29-24%2Axb%2Bhighlight_red%28+30%2Ab+%29.
Eliminated similar terms highlight_red%28+-4%2Ab+%29,highlight_red%28+30%2Ab+%29 replacing them with highlight_green%28+%28-4%2B30%29%2Ab+%29
It becomes %28-10-50%29%2Aa%2Bhighlight_green%28+%28-4%2B30%29%2Ab+%29-24%2Axb.
Look at %28-highlight_red%28+10+%29-highlight_red%28+50+%29%29%2Aa%2B%28-4%2B30%29%2Ab-24%2Axb.
Added fractions or integers together
It becomes %28highlight_green%28+-60+%29%29%2Aa%2B%28-4%2B30%29%2Ab-24%2Axb.
Look at %28-60%29%2Aa%2B%28-highlight_red%28+4+%29%2Bhighlight_red%28+30+%29%29%2Ab-24%2Axb.
Added fractions or integers together
It becomes %28-60%29%2Aa%2B%28highlight_green%28+26+%29%29%2Ab-24%2Axb.
Look at %28highlight_red%28+-60+%29%29%2Aa%2B%2826%29%2Ab-24%2Axb.
Removed extra sign in front of -60
It becomes %28-highlight_green%28+60+%29%29%2Aa%2B%2826%29%2Ab-24%2Axb.
Look at highlight_red%28+%28-highlight_red%28+60+%29%29%2Aa+%29%2B%2826%29%2Ab-24%2Axb.
Remove unneeded parentheses around factor highlight_red%28+60+%29
It becomes -highlight_green%28+60+%29%2Aa%2B%2826%29%2Ab-24%2Axb.
Look at -60%2Aa%2Bhighlight_red%28+%28highlight_red%28+26+%29%29%2Ab+%29-24%2Axb.
Remove unneeded parentheses around factor highlight_red%28+26+%29
It becomes -60%2Aa%2Bhighlight_green%28+26+%29%2Ab-24%2Axb.
Result: -60%2Aa%2B26%2Ab-24%2Axb

Universal Simplifier and Solver


Done!

Geometry_Word_Problems/6771: In 1974, the French Army sent soldiers up in hot air balloons to observe enemy troop movements. One such balloon, L'Entrepenant, had a volume of 256 (pi)/3.
a)Solve the formula for the volume of a sphere (V=4/3 (pi)r (cubed) for r cubed. Then use this formula to calculate the radius of the L'Entrepenant balloon.
b) What was the diameter of the L'Entrepenant balloon?

UGH!
i appreciate your time- this is my step-daughter's homework problem and it has us both baffled!
1 solutions
Answer 3731 by ichudov(499) About Me  on 2005-08-07 20:30:44 (Show Source):
You can put this solution on YOUR website!
This is a problem of mostly translating English to algebrese.
What they say is that volume is 256%2Api%2F3.
They also mention that the volume of a sphere is 4%2F3%2Api%2Ar%5E3.
So, we have 256%2Api%2F3+=+4%2F3%2Api%2Ar%5E3.
Remove pi:
256%2F3=4%2F3%2Ar%5E3
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: r=4.
  • Graphical form: 256%2F3=4%2F3%2Ar%5E3 simplifies to %2B-1.33333333333333%2Ar%5E2-5.33333333333333%2Ar-21.3333333333333=0
  • Text form: 256/3=4/3*r^3 simplifies to +-1.33333333333333*r^2-5.33333333333333*r-21.3333333333333=0
  • Cartoon (animation) form: simplify_cartoon%28+256%2F3=4%2F3%2Ar%5E3+%29
    For tutors: simplify_cartoon( 256/3=4/3*r^3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 256%2F3=highlight_red%28+4%2F3%2Ar%5E3+%29.
Moved these terms to the left highlight_green%28+-4%2F3%2Ar%5E3+%29
It becomes 256%2F3-highlight_green%28+4%2F3%2Ar%5E3+%29=0.
Look at highlight_red%28+256%2F3+%29-4%2F3%2Ar%5E3=0.
Moved 256%2F3 to the right of expression
It becomes -4%2F3%2Ar%5E3%2Bhighlight_green%28+256%2F3+%29=0.
Look at highlight_red%28+-4%2F3%2Ar%5E3%2B256%2F3+%29=0.
Divided polynomial on the left by known factors (r-(4))
It becomes %2Bhighlight_green%28+-1.33333333333333%2Ar%5E2-5.33333333333333%2Ar-21.3333333333333+%29=0.
Result: %2B-1.33333333333333%2Ar%5E2-5.33333333333333%2Ar-21.3333333333333=0
This is an equation! Solutions: r=4.

Universal Simplifier and Solver


Done!
.
So, the radius is 4, and the diameter is twice more, or 8.

expressions/6772: how do you solve:
3%2F4%2A%285x%2B6y%29%2A17%2B85%2F2%2B4x-2y
1 solutions
Answer 3730 by ichudov(499) About Me  on 2005-08-07 20:15:28 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 3%2F4%2A%285x%2B6y%29%2A17%2B85%2F2%2B4x-2y simplifies to 271%2F4%2Ax%2B149%2F2%2Ay%2B85%2F2
  • Text form: 3/4*(5x+6y)*17+85/2+4x-2y simplifies to 271/4*x+149/2*y+85/2
  • Cartoon (animation) form: simplify_cartoon%28+3%2F4%2A%285x%2B6y%29%2A17%2B85%2F2%2B4x-2y+%29
    For tutors: simplify_cartoon( 3/4*(5x+6y)*17+85/2+4x-2y )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Multiplied numerator integers
It becomes highlight_green%28+51+%29%2F4%2A%285%2Ax%2B6%2Ay%29%2B85%2F2%2B4%2Ax-2%2Ay.
Look at 51%2F4%2A%285%2Ax%2B6%2Ay%29%2Bhighlight_red%28+85%2F2+%29%2B4%2Ax-2%2Ay.
Moved 85%2F2 to the right of expression
It becomes 51%2F4%2A%285%2Ax%2B6%2Ay%29%2B4%2Ax-2%2Ay%2Bhighlight_green%28+85%2F2+%29.
Look at highlight_red%28+51%2F4%2A%285%2Ax%2B6%2Ay%29+%29%2B4%2Ax-2%2Ay%2B85%2F2.
Expanded term 51%2F4 by using associative property on %285%2Ax%2B6%2Ay%29
It becomes .
Look at .
Multiplied numerator integers
It becomes highlight_green%28+255+%29%2F4%2Ax%2B51%2F4%2A6%2Ay%2B4%2Ax-2%2Ay%2B85%2F2.
Look at .
Factors 6 and 4 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .
Look at .
Multiplied numerator integers
It becomes 255%2F4%2Ax%2Bhighlight_green%28+153+%29%2F2%2Ay%2B4%2Ax-2%2Ay%2B85%2F2.
Look at highlight_red%28+255%2F4%2Ax+%29%2B153%2F2%2Ay%2Bhighlight_red%28+4%2Ax+%29-2%2Ay%2B85%2F2.
Eliminated similar terms highlight_red%28+255%2F4%2Ax+%29,highlight_red%28+4%2Ax+%29 replacing them with highlight_green%28+%28255%2A1%2F4%2B4%29%2Ax+%29
It becomes highlight_green%28+%28255%2A1%2F4%2B4%29%2Ax+%29%2B153%2F2%2Ay-2%2Ay%2B85%2F2.
Look at .
Eliminated similar terms highlight_red%28+153%2F2%2Ay+%29,highlight_red%28+-2%2Ay+%29 replacing them with highlight_green%28+%28153%2A1%2F2-2%29%2Ay+%29
It becomes %28255%2A1%2F4%2B4%29%2Ax%2Bhighlight_green%28+%28153%2A1%2F2-2%29%2Ay+%29%2B85%2F2.
Look at .
Multiplied numerator integers
It becomes %28highlight_green%28+255+%29%2F4%2B4%29%2Ax%2B%28153%2A1%2F2-2%29%2Ay%2B85%2F2.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+271%2F4+%29%29%2Ax%2B%28153%2A1%2F2-2%29%2Ay%2B85%2F2.
Look at .
Multiplied numerator integers
It becomes %28271%2F4%29%2Ax%2B%28highlight_green%28+153+%29%2F2-2%29%2Ay%2B85%2F2.
Look at %28271%2F4%29%2Ax%2B%28highlight_red%28+153%2F2+%29-highlight_red%28+2+%29%29%2Ay%2B85%2F2.
Added fractions or integers together
It becomes %28271%2F4%29%2Ax%2B%28highlight_green%28+149%2F2+%29%29%2Ay%2B85%2F2.
Look at highlight_red%28+%28highlight_red%28+271%2F4+%29%29%2Ax+%29%2B%28149%2F2%29%2Ay%2B85%2F2.
Remove unneeded parentheses around factor highlight_red%28+271+%29,highlight_red%28+1%2F4+%29
It becomes highlight_green%28+271+%29%2Fhighlight_green%28+4+%29%2Ax%2B%28149%2F2%29%2Ay%2B85%2F2.
Look at 271%2F4%2Ax%2Bhighlight_red%28+%28highlight_red%28+149%2F2+%29%29%2Ay+%29%2B85%2F2.
Remove unneeded parentheses around factor highlight_red%28+149+%29,highlight_red%28+1%2F2+%29
It becomes 271%2F4%2Ax%2Bhighlight_green%28+149+%29%2Fhighlight_green%28+2+%29%2Ay%2B85%2F2.
Result: 271%2F4%2Ax%2B149%2F2%2Ay%2B85%2F2

Universal Simplifier and Solver


Done!

Distributive-associative-commutative-properties/6719: I need Help!
1. -3 = 7 - 4y
2. 2x + 4(3x - 6) = 4 - (6x + 2)
3. 3(2x + 6) + 3x = -27
4. 4(x - 1) = -6(x + 2) + 48
Please Help
1 solutions
Answer 3701 by ichudov(499) About Me  on 2005-08-06 13:58:59 (Show Source):
You can put this solution on YOUR website!
I'll sove a couple for you, and you do the rest, okay?
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=1.3.
  • Graphical form: Equation 2x%2B4%2A%283x-6%29=4-%286x%2B2%29 was fully solved.
  • Text form: 2x+4*(3x-6)=4-(6x+2) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2x%2B4%2A%283x-6%29=4-%286x%2B2%29+%29
    For tutors: simplify_cartoon( 2x+4*(3x-6)=4-(6x+2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2Ax%2B4%2A%283%2Ax-6%29=4-highlight_red%28+%286%2Ax%2B2%29+%29.
Remove unneeded parentheses around terms highlight_red%28+-6%2Ax+%29,highlight_red%28+-2+%29
It becomes 2%2Ax%2B4%2A%283%2Ax-6%29=4-highlight_green%28+6%2Ax+%29-highlight_green%28+2+%29.
Look at 2%2Ax%2B4%2A%283%2Ax-6%29=highlight_red%28+4+%29-6%2Ax-highlight_red%28+2+%29.
Added fractions or integers together
It becomes 2%2Ax%2B4%2A%283%2Ax-6%29=highlight_green%28+2+%29-6%2Ax.
Look at 2%2Ax%2B4%2A%283%2Ax-6%29=highlight_red%28+2+%29-6%2Ax.
Moved 2 to the right of expression
It becomes 2%2Ax%2B4%2A%283%2Ax-6%29=-6%2Ax%2Bhighlight_green%28+2+%29.
Look at 2%2Ax%2B4%2A%283%2Ax-6%29=highlight_red%28+-6%2Ax%2B2+%29.
Moved these terms to the left highlight_green%28+6%2Ax+%29,highlight_green%28+-2+%29
It becomes 2%2Ax%2B4%2A%283%2Ax-6%29%2Bhighlight_green%28+6%2Ax+%29-highlight_green%28+2+%29=0.
Look at highlight_red%28+2%2Ax+%29%2B4%2A%283%2Ax-6%29%2Bhighlight_red%28+6%2Ax+%29-2=0.
Eliminated similar terms highlight_red%28+2%2Ax+%29,highlight_red%28+6%2Ax+%29 replacing them with highlight_green%28+%282%2B6%29%2Ax+%29
It becomes highlight_green%28+%282%2B6%29%2Ax+%29%2B4%2A%283%2Ax-6%29-2=0.
Look at %28highlight_red%28+2+%29%2Bhighlight_red%28+6+%29%29%2Ax%2B4%2A%283%2Ax-6%29-2=0.
Added fractions or integers together
It becomes %28highlight_green%28+8+%29%29%2Ax%2B4%2A%283%2Ax-6%29-2=0.
Look at highlight_red%28+%28highlight_red%28+8+%29%29%2Ax+%29%2B4%2A%283%2Ax-6%29-2=0.
Remove unneeded parentheses around factor highlight_red%28+8+%29
It becomes highlight_green%28+8+%29%2Ax%2B4%2A%283%2Ax-6%29-2=0.
Look at 8%2Ax%2Bhighlight_red%28+4%2A%283%2Ax-6%29+%29-2=0.
Expanded term 4 by using associative property on %283%2Ax-6%29
It becomes 8%2Ax%2Bhighlight_green%28+4%2A3%2Ax+%29-highlight_green%28+4%2A6+%29-2=0.
Look at 8%2Ax%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+3+%29%2Ax-4%2A6-2=0.
Multiplied numerator integers
It becomes 8%2Ax%2Bhighlight_green%28+12+%29%2Ax-4%2A6-2=0.
Look at 8%2Ax%2B12%2Ax-highlight_red%28+4+%29%2Ahighlight_red%28+6+%29-2=0.
Multiplied numerator integers
It becomes 8%2Ax%2B12%2Ax-highlight_green%28+24+%29-2=0.
Look at 8%2Ax%2B12%2Ax-highlight_red%28+24+%29-highlight_red%28+2+%29=0.
Added fractions or integers together
It becomes 8%2Ax%2B12%2Ax%2Bhighlight_green%28+-26+%29=0.
Look at 8%2Ax%2B12%2Ax%2Bhighlight_red%28+-26+%29=0.
Removed extra sign in front of -26
It becomes 8%2Ax%2B12%2Ax-highlight_green%28+26+%29=0.
Look at highlight_red%28+8%2Ax+%29%2Bhighlight_red%28+12%2Ax+%29-26=0.
Eliminated similar terms highlight_red%28+8%2Ax+%29,highlight_red%28+12%2Ax+%29 replacing them with highlight_green%28+%288%2B12%29%2Ax+%29
It becomes highlight_green%28+%288%2B12%29%2Ax+%29-26=0.
Look at %28highlight_red%28+8+%29%2Bhighlight_red%28+12+%29%29%2Ax-26=0.
Added fractions or integers together
It becomes %28highlight_green%28+20+%29%29%2Ax-26=0.
Look at highlight_red%28+%28highlight_red%28+20+%29%29%2Ax+%29-26=0.
Remove unneeded parentheses around factor highlight_red%28+20+%29
It becomes highlight_green%28+20+%29%2Ax-26=0.
Look at highlight_red%28+20%2Ax-26+%29=0.
Solved linear equation highlight_red%28+20%2Ax-26=0+%29 equivalent to 20*x-26 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=1.3.

Universal Simplifier and Solver


Done!

real-numbers/6722: how do you simplify 3/8*(16x-8)+2/3*(15y+12)
1 solutions
Answer 3700 by ichudov(499) About Me  on 2005-08-06 13:57:37 (Show Source):
You can put this solution on YOUR website!
you use my simplifier...
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 3%2F8%2A%2816x-8%29%2B2%2F3%2A%2815y%2B12%29 simplifies to 6%2Ax%2B10%2Ay%2B5
  • Text form: 3/8*(16x-8)+2/3*(15y+12) simplifies to 6*x+10*y+5
  • Cartoon (animation) form: simplify_cartoon%28+3%2F8%2A%2816x-8%29%2B2%2F3%2A%2815y%2B12%29+%29
    For tutors: simplify_cartoon( 3/8*(16x-8)+2/3*(15y+12) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+3%2F8%2A%2816%2Ax-8%29+%29%2B2%2F3%2A%2815%2Ay%2B12%29.
Expanded term 3%2F8 by using associative property on %2816%2Ax-8%29
It becomes .
Look at .
Factors 16 and 8 have greatest common factor (GCF) of 8. Reducing fraction.
It becomes .
Look at .
Multiplied numerator integers
It becomes highlight_green%28+6+%29%2F1%2Ax-3%2F8%2A8%2B2%2F3%2A%2815%2Ay%2B12%29.
Look at 6%2F1%2Ax-3%2Fhighlight_red%28+8+%29%2Ahighlight_red%28+8+%29%2B2%2F3%2A%2815%2Ay%2B12%29.
Factors 8 and 8 have greatest common factor (GCF) of 8. Reducing fraction.
It becomes .
Look at 6%2F1%2Ax-highlight_red%28+3+%29%2F1%2Ahighlight_red%28+1+%29%2B2%2F3%2A%2815%2Ay%2B12%29.
Multiplied numerator integers
It becomes 6%2F1%2Ax-highlight_green%28+3+%29%2F1%2B2%2F3%2A%2815%2Ay%2B12%29.
Look at 6%2F1%2Ax-highlight_red%28+3%2F1+%29%2B2%2F3%2A%2815%2Ay%2B12%29.
Moved -3%2F1 to the right of expression
It becomes 6%2F1%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-highlight_green%28+3%2F1+%29.
Look at 6%2Fhighlight_red%28+1+%29%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-3%2F1.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 6%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-3%2F1.
Look at 6%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-3%2Fhighlight_red%28+1+%29.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 6%2Ax%2B2%2F3%2A%2815%2Ay%2B12%29-3.
Look at 6%2Ax%2Bhighlight_red%28+2%2F3%2A%2815%2Ay%2B12%29+%29-3.
Expanded term 2%2F3 by using associative property on %2815%2Ay%2B12%29
It becomes 6%2Ax%2Bhighlight_green%28+2%2F3%2A15%2Ay+%29%2Bhighlight_green%28+2%2F3%2A12+%29-3.
Look at 6%2Ax%2B2%2Fhighlight_red%28+3+%29%2Ahighlight_red%28+15+%29%2Ay%2B2%2F3%2A12-3.
Factors 15 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes 6%2Ax%2B2%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+5+%29%2Ay%2B2%2F3%2A12-3.
Look at 6%2Ax%2Bhighlight_red%28+2+%29%2F1%2Ahighlight_red%28+5+%29%2Ay%2B2%2F3%2A12-3.
Multiplied numerator integers
It becomes 6%2Ax%2Bhighlight_green%28+10+%29%2F1%2Ay%2B2%2F3%2A12-3.
Look at 6%2Ax%2B10%2F1%2Ay%2B2%2Fhighlight_red%28+3+%29%2Ahighlight_red%28+12+%29-3.
Factors 12 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes 6%2Ax%2B10%2F1%2Ay%2B2%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+4+%29-3.
Look at 6%2Ax%2B10%2F1%2Ay%2Bhighlight_red%28+2+%29%2F1%2Ahighlight_red%28+4+%29-3.
Multiplied numerator integers
It becomes 6%2Ax%2B10%2F1%2Ay%2Bhighlight_green%28+8+%29%2F1-3.
Look at 6%2Ax%2B10%2F1%2Ay%2Bhighlight_red%28+8%2F1+%29-highlight_red%28+3+%29.
Added fractions or integers together
It becomes 6%2Ax%2B10%2F1%2Ay%2Bhighlight_green%28+5+%29.
Look at 6%2Ax%2B10%2Fhighlight_red%28+1+%29%2Ay%2B5.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 6%2Ax%2B10%2Ay%2B5.
Result: 6%2Ax%2B10%2Ay%2B5

Universal Simplifier and Solver


Done!

Systems-of-equations/6323: Complete the ordered pairs so that each is a solution to the given linear equation. Prenset your answer as an ordered pair. y = 3x + 6
(a) (0, ?) (b) (2, ?)
1 solutions
Answer 3688 by ichudov(499) About Me  on 2005-08-06 08:24:30 (Show Source):
You can put this solution on YOUR website!
In human language, your problem means "calculate y for x=0 and also for x=2".
calculate 3*0+6 and 3*2+6

logarithm/6701: I tried this natural log problem and keep comming up with the wrong awnser of .25 HELP! (please)
2e%5E%283x%29=4e%5E%285x%29 Am i just bad at algebra or is this somewhat complicated
1 solutions
Answer 3686 by ichudov(499) About Me  on 2005-08-06 06:19:08 (Show Source):
You can put this solution on YOUR website!
great job on typing the formula.
2e%5E%283x%29=4e%5E%285x%29
2e%5E%283x%29%2F4e%5E%285x%29=1
%281%2F2%29%2Ae%5E%283x-5x%29=1
e%5E%28-2x%29=2
take natural log of both sides
-2x=ln%28+2+%29
x=-ln%28+2+%29%2F2

Age_Word_Problems/6702: please me solve this equation:find for the unknown
1.3bx-2=4ax+3: find for the x
2.4x+3=10x+5
3.81x+13=100x-2
4.(x+2) (x+3)=(x+4) (x-2)
5.ax+5=bx-2
1 solutions
Answer 3685 by ichudov(499) About Me  on 2005-08-06 06:07:26 (Show Source):
You can put this solution on YOUR website!
i'll solve a couple and you do the rest, okay?
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=-0.333333333333333.
  • Graphical form: Equation 4x%2B3=10x%2B5 was fully solved.
  • Text form: 4x+3=10x+5 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4x%2B3=10x%2B5+%29
    For tutors: simplify_cartoon( 4x+3=10x+5 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2Ax%2B3=highlight_red%28+10%2Ax%2B5+%29.
Moved these terms to the left highlight_green%28+-10%2Ax+%29,highlight_green%28+-5+%29
It becomes 4%2Ax%2B3-highlight_green%28+10%2Ax+%29-highlight_green%28+5+%29=0.
Look at 4%2Ax%2Bhighlight_red%28+3+%29-10%2Ax-highlight_red%28+5+%29=0.
Added fractions or integers together
It becomes 4%2Ax%2Bhighlight_green%28+-2+%29-10%2Ax=0.
Look at 4%2Ax%2Bhighlight_red%28+-2+%29-10%2Ax=0.
Moved -2 to the right of expression
It becomes 4%2Ax-10%2Ax%2Bhighlight_green%28+-2+%29=0.
Look at 4%2Ax-10%2Ax%2Bhighlight_red%28+-2+%29=0.
Removed extra sign in front of -2
It becomes 4%2Ax-10%2Ax-highlight_green%28+2+%29=0.
Look at highlight_red%28+4%2Ax+%29-highlight_red%28+10%2Ax+%29-2=0.
Eliminated similar terms highlight_red%28+4%2Ax+%29,highlight_red%28+-10%2Ax+%29 replacing them with highlight_green%28+%284-10%29%2Ax+%29
It becomes highlight_green%28+%284-10%29%2Ax+%29-2=0.
Look at %28highlight_red%28+4+%29-highlight_red%28+10+%29%29%2Ax-2=0.
Added fractions or integers together
It becomes %28highlight_green%28+-6+%29%29%2Ax-2=0.
Look at %28highlight_red%28+-6+%29%29%2Ax-2=0.
Removed extra sign in front of -6
It becomes %28-highlight_green%28+6+%29%29%2Ax-2=0.
Look at highlight_red%28+%28-highlight_red%28+6+%29%29%2Ax+%29-2=0.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes -highlight_green%28+6+%29%2Ax-2=0.
Look at highlight_red%28+-6%2Ax-2+%29=0.
Solved linear equation highlight_red%28+-6%2Ax-2=0+%29 equivalent to -6*x-2 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-0.333333333333333.

Universal Simplifier and Solver


Done!


Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=-4.66666666666667.
  • Graphical form: Equation %28x%2B2%29%2A%28x%2B3%29=%28x%2B4%29%2A%28x-2%29 was fully solved.
  • Text form: (x+2)*(x+3)=(x+4)*(x-2) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%28x%2B2%29%2A%28x%2B3%29=%28x%2B4%29%2A%28x-2%29+%29
    For tutors: simplify_cartoon( (x+2)*(x+3)=(x+4)*(x-2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %28x%2B2%29%2A%28x%2B3%29=highlight_red%28+%28x%2B4%29%2A%28x-2%29+%29.
Moved these terms to the left highlight_green%28+-%28x%2B4%29%2A%28x-2%29+%29
It becomes %28x%2B2%29%2A%28x%2B3%29-highlight_green%28+%28x%2B4%29%2A%28x-2%29+%29=0.
Look at highlight_red%28+%28x%2B2%29%2A%28x%2B3%29+%29-%28x%2B4%29%2A%28x-2%29=0.
Expanded term %28x%2B3%29 by using associative property on %28x%2B2%29
It becomes .
Look at highlight_red%28+%28x%2B3%29%2Ax+%29%2B%28x%2B3%29%2A2-%28x%2B4%29%2A%28x-2%29=0.
Expanded term x by using associative property on %28x%2B3%29
It becomes .
Look at .
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes highlight_green%28+x%5E2+%29%2Bx%2A3%2B%28x%2B3%29%2A2-%28x%2B4%29%2A%28x-2%29=0.
Look at x%5E2%2Bx%2A3%2Bhighlight_red%28+%28x%2B3%29%2A2+%29-%28x%2B4%29%2A%28x-2%29=0.
Expanded term 2 by using associative property on %28x%2B3%29
It becomes .
Look at .
Multiplied numerator integers
It becomes x%5E2%2Bx%2A3%2B2%2Ax%2Bhighlight_green%28+6+%29-%28x%2B4%29%2A%28x-2%29=0.
Look at x%5E2%2Bx%2A3%2B2%2Ax%2Bhighlight_red%28+6+%29-%28x%2B4%29%2A%28x-2%29=0.
Moved 6 to the right of expression
It becomes x%5E2%2Bx%2A3%2B2%2Ax-%28x%2B4%29%2A%28x-2%29%2Bhighlight_green%28+6+%29=0.
Look at .
Eliminated similar terms highlight_red%28+x%2A3+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%283%2B2%29%2Ax+%29
It becomes x%5E2%2Bhighlight_green%28+%283%2B2%29%2Ax+%29-%28x%2B4%29%2A%28x-2%29%2B6=0.
Look at .
Added fractions or integers together
It becomes x%5E2%2B%28highlight_green%28+5+%29%29%2Ax-%28x%2B4%29%2A%28x-2%29%2B6=0.
Look at x%5E2%2Bhighlight_red%28+%28highlight_red%28+5+%29%29%2Ax+%29-%28x%2B4%29%2A%28x-2%29%2B6=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes x%5E2%2Bhighlight_green%28+5+%29%2Ax-%28x%2B4%29%2A%28x-2%29%2B6=0.
Look at x%5E2%2B5%2Ax-highlight_red%28+%28x%2B4%29%2A%28x-2%29+%29%2B6=0.
Expanded term -%28x-2%29 by using associative property on %28x%2B4%29
It becomes .
Look at x%5E2%2B5%2Ax-highlight_red%28+%28x-2%29%2Ax+%29-%28x-2%29%2A4%2B6=0.
Expanded term -x by using associative property on %28x-2%29
It becomes .
Look at x%5E2%2B5%2Ax-highlight_red%28+x+%29%2Ahighlight_red%28+x+%29%2Bx%2A2-%28x-2%29%2A4%2B6=0.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes x%5E2%2B5%2Ax-highlight_green%28+x%5E2+%29%2Bx%2A2-%28x-2%29%2A4%2B6=0.
Look at highlight_red%28+x%5E2+%29%2B5%2Ax-highlight_red%28+x%5E2+%29%2Bx%2A2-%28x-2%29%2A4%2B6=0.
Eliminated similar terms highlight_red%28+x%5E2+%29,highlight_red%28+-x%5E2+%29 replacing them with highlight_green%28+%281-1%29%2Ax%5E2+%29
It becomes highlight_green%28+%281-1%29%2Ax%5E2+%29%2B5%2Ax%2Bx%2A2-%28x-2%29%2A4%2B6=0.
Look at .
Eliminated similar terms highlight_red%28+5%2Ax+%29,highlight_red%28+x%2A2+%29 replacing them with highlight_green%28+%285%2B2%29%2Ax+%29
It becomes %281-1%29%2Ax%5E2%2Bhighlight_green%28+%285%2B2%29%2Ax+%29-%28x-2%29%2A4%2B6=0.
Look at highlight_red%28+%281-1%29%2Ax%5E2+%29%2B%285%2B2%29%2Ax-%28x-2%29%2A4%2B6=0.
Since highlight_red%28+%281-1%29%2Ax%5E2+%29 has zero as a factor, it should be replaced with a zero
Look at 0%2B%285%2B2%29%2Ax-%28x-2%29%2A4%2B6=0.
Added fractions or integers together
It becomes 0%2B%285%2B2%29%2Ax-%28x-2%29%2A4%2B6=0.
Look at 0%2B%28highlight_red%28+5+%29%2Bhighlight_red%28+2+%29%29%2Ax-%28x-2%29%2A4%2B6=0.
Added fractions or integers together
It becomes 0%2B%28highlight_green%28+7+%29%29%2Ax-%28x-2%29%2A4%2B6=0.
Look at highlight_red%28+0+%29%2B%287%29%2Ax-%28x-2%29%2A4%2B6=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes %287%29%2Ax-%28x-2%29%2A4%2B6=0.
Look at highlight_red%28+%28highlight_red%28+7+%29%29%2Ax+%29-%28x-2%29%2A4%2B6=0.
Remove unneeded parentheses around factor highlight_red%28+7+%29
It becomes highlight_green%28+7+%29%2Ax-%28x-2%29%2A4%2B6=0.
Look at 7%2Ax-highlight_red%28+%28x-2%29%2A4+%29%2B6=0.
Expanded term -4 by using associative property on %28x-2%29
It becomes 7%2Ax-highlight_green%28+4%2Ax+%29%2Bhighlight_green%28+4%2A2+%29%2B6=0.
Look at 7%2Ax-4%2Ax%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+2+%29%2B6=0.
Multiplied numerator integers
It becomes 7%2Ax-4%2Ax%2Bhighlight_green%28+8+%29%2B6=0.
Look at 7%2Ax-4%2Ax%2Bhighlight_red%28+8+%29%2Bhighlight_red%28+6+%29=0.
Added fractions or integers together
It becomes 7%2Ax-4%2Ax%2Bhighlight_green%28+14+%29=0.
Look at highlight_red%28+7%2Ax+%29-highlight_red%28+4%2Ax+%29%2B14=0.
Eliminated similar terms highlight_red%28+7%2Ax+%29,highlight_red%28+-4%2Ax+%29 replacing them with highlight_green%28+%287-4%29%2Ax+%29
It becomes highlight_green%28+%287-4%29%2Ax+%29%2B14=0.
Look at %28highlight_red%28+7+%29-highlight_red%28+4+%29%29%2Ax%2B14=0.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ax%2B14=0.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29%2B14=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ax%2B14=0.
Look at highlight_red%28+3%2Ax%2B14+%29=0.
Solved linear equation highlight_red%28+3%2Ax%2B14=0+%29 equivalent to 3*x+14 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-4.66666666666667.

Universal Simplifier and Solver


Done!

Polynomials-and-rational-expressions/6690: Can you please help me answer this equaton?
Combine:(3x^3-4x^2)+(-7-3x^3)-(-4x^2+2x)
1 solutions
Answer 3681 by ichudov(499) About Me  on 2005-08-05 23:51:14 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: %283x%5E3-4x%5E2%29%2B%28-7-3x%5E3%29-%28-4x%5E2%2B2x%29 simplifies to -2%2Ax-7
  • Text form: (3x^3-4x^2)+(-7-3x^3)-(-4x^2+2x) simplifies to -2*x-7
  • Cartoon (animation) form: simplify_cartoon%28+%283x%5E3-4x%5E2%29%2B%28-7-3x%5E3%29-%28-4x%5E2%2B2x%29+%29
    For tutors: simplify_cartoon( (3x^3-4x^2)+(-7-3x^3)-(-4x^2+2x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%283%2Ax%5E3-4%2Ax%5E2%29+%29%2B%28-7-3%2Ax%5E3%29-%28-4%2Ax%5E2%2B2%2Ax%29.
Remove unneeded parentheses around terms highlight_red%28+3%2Ax%5E3+%29,highlight_red%28+-4%2Ax%5E2+%29
It becomes .
Look at 3%2Ax%5E3-4%2Ax%5E2%2Bhighlight_red%28+%28-7-3%2Ax%5E3%29+%29-%28-4%2Ax%5E2%2B2%2Ax%29.
Remove unneeded parentheses around terms highlight_red%28+-7+%29,highlight_red%28+-3%2Ax%5E3+%29
It becomes .
Look at 3%2Ax%5E3-4%2Ax%5E2-7-3%2Ax%5E3-highlight_red%28+%28-4%2Ax%5E2%2B2%2Ax%29+%29.
Remove unneeded parentheses around terms highlight_red%28+4%2Ax%5E2+%29,highlight_red%28+-2%2Ax+%29
It becomes .
Look at 3%2Ax%5E3-4%2Ax%5E2-highlight_red%28+7+%29-3%2Ax%5E3%2B4%2Ax%5E2-2%2Ax.
Moved -7 to the right of expression
It becomes 3%2Ax%5E3-4%2Ax%5E2-3%2Ax%5E3%2B4%2Ax%5E2-2%2Ax-highlight_green%28+7+%29.
Look at highlight_red%28+3%2Ax%5E3+%29-4%2Ax%5E2-highlight_red%28+3%2Ax%5E3+%29%2B4%2Ax%5E2-2%2Ax-7.
Eliminated similar terms highlight_red%28+3%2Ax%5E3+%29,highlight_red%28+-3%2Ax%5E3+%29 replacing them with highlight_green%28+%283-3%29%2Ax%5E3+%29
It becomes highlight_green%28+%283-3%29%2Ax%5E3+%29-4%2Ax%5E2%2B4%2Ax%5E2-2%2Ax-7.
Look at %283-3%29%2Ax%5E3-highlight_red%28+4%2Ax%5E2+%29%2Bhighlight_red%28+4%2Ax%5E2+%29-2%2Ax-7.
Eliminated similar terms highlight_red%28+-4%2Ax%5E2+%29,highlight_red%28+4%2Ax%5E2+%29 replacing them with highlight_green%28+%28-4%2B4%29%2Ax%5E2+%29
It becomes %283-3%29%2Ax%5E3%2Bhighlight_green%28+%28-4%2B4%29%2Ax%5E2+%29-2%2Ax-7.
Look at highlight_red%28+%283-3%29%2Ax%5E3+%29%2B%28-4%2B4%29%2Ax%5E2-2%2Ax-7.
Since highlight_red%28+%283-3%29%2Ax%5E3+%29 has zero as a factor, it should be replaced with a zero
Look at 0%2B%28-4%2B4%29%2Ax%5E2-2%2Ax-7.
Added fractions or integers together
It becomes 0%2B%28-4%2B4%29%2Ax%5E2-2%2Ax-7.
Look at 0%2Bhighlight_red%28+%28-4%2B4%29%2Ax%5E2+%29-2%2Ax-7.
Since highlight_red%28+%28-4%2B4%29%2Ax%5E2+%29 has zero as a factor, it should be replaced with a zero
Look at 0%2B0-2%2Ax-7.
Added fractions or integers together
It becomes 0%2B0-2%2Ax-7.
Look at highlight_red%28+0+%29%2B0-2%2Ax-7.
Remove extraneous zero highlight_red%28+0+%29
It becomes 0-2%2Ax-7.
Look at highlight_red%28+0+%29-2%2Ax-7.
Remove extraneous zero highlight_red%28+0+%29
It becomes -2%2Ax-7.
Result: -2%2Ax-7

Universal Simplifier and Solver


Done!

Quadratic_Equations/6693: Can you tell me how to find the domain and range of this quadratic function?
y = -2x^2 - x + 4
Thanks!
1 solutions
Answer 3680 by ichudov(499) About Me  on 2005-08-05 23:49:43 (Show Source):
You can put this solution on YOUR website!
Since -2x%5E2-x%2B4 can be computed for every x (unlike, say, square root, which can only be computed for positive x), the domain is the entire set of real numbers.
The range can be guessed by looking at the graph
graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C+-2x%5E2-x%2B4%29+
It has its maximum right in the middle between the roots, which is x = -b/2a, or x=+-%28-1%29%2F%282%2A%28-2%29%29+=+-1%2F4. Now use substitution of x+=+-1%2F4 into expression -2x%5E2-x%2B4:
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: -2x%5E2-x%2B4 simplifies to 4.125
  • Text form: -2x^2-x+4 simplifies to 4.125
  • Cartoon (animation) form: simplify_cartoon%28+-2x%5E2-x%2B4+%29
    For tutors: simplify_cartoon( -2x^2-x+4 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -2%2Ahighlight_red%28+x+%29%5E2-x%2B4.
Replaced x with -0.25
It becomes -2%2Ahighlight_green%28+-0.25+%29%5E2-x%2B4.
Look at -2%2Ahighlight_red%28+-0.25+%29%5Ehighlight_red%28+2+%29-x%2B4.
Replace constants in factor: highlight_red%28+-0.25+%29,highlight_red%28+2+%29 with highlight_green%28+0.0625+%29
It becomes -2%2Ahighlight_green%28+0.0625+%29-x%2B4.
Look at -2%2A0.0625-highlight_red%28+x+%29%2B4.
Replaced x with -0.25
It becomes -2%2A0.0625-highlight_green%28+-0.25+%29%2B4.
Look at -2%2A0.0625-highlight_red%28+-0.25+%29%2Bhighlight_red%28+4+%29.
Added fractions or integers together
It becomes -2%2A0.0625%2Bhighlight_green%28+425%2F100+%29.
Look at -2%2A0.0625%2Bhighlight_red%28+425+%29%2Fhighlight_red%28+100+%29.
Factors 425 and 100 have greatest common factor (GCF) of 25. Reducing fraction.
It becomes -2%2A0.0625%2Bhighlight_green%28+17+%29%2Fhighlight_green%28+4+%29.
Look at -highlight_red%28+2%2A0.0625+%29%2Bhighlight_red%28+17%2F4+%29.
Replace constants in expression: highlight_red%28+-2%2A0.0625+%29,highlight_red%28+17%2F4+%29 with highlight_green%28+4.125+%29
It becomes highlight_green%28+4.125+%29.
Result: 4.125

Universal Simplifier and Solver


Done!


So, the domain is all numbers and the range is from minus infinity to 4.125.

Exponents/6694: (2^-2+2)^2
1 solutions
Answer 3679 by ichudov(499) About Me  on 2005-08-05 23:42:04 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: %282%5E-2%2B2%29%5E2 simplifies to 5.0625
  • Text form: (2^-2+2)^2 simplifies to 5.0625
  • Cartoon (animation) form: simplify_cartoon%28+%282%5E-2%2B2%29%5E2+%29
    For tutors: simplify_cartoon( (2^-2+2)^2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %28highlight_red%28+2+%29%5Ehighlight_red%28+-2+%29%2B2%29%5E2.
Replace constants in factor: highlight_red%28+2+%29,highlight_red%28+-2+%29 with highlight_green%28+0.25+%29
It becomes %28highlight_green%28+0.25+%29%2B2%29%5E2.
Look at %28highlight_red%28+0.25+%29%2Bhighlight_red%28+2+%29%29%5E2.
Added fractions or integers together
It becomes %28highlight_green%28+225%2F100+%29%29%5E2.
Look at highlight_red%28+%28225%2F100%29+%29%5Ehighlight_red%28+2+%29.
Replace constants in factor: highlight_red%28+%28225%2F100%29+%29,highlight_red%28+2+%29 with highlight_green%28+5.0625+%29
It becomes highlight_green%28+5.0625+%29.
Result: 5.0625

Universal Simplifier and Solver


Done!

Quadratic_Equations/6686: place the following equations in the standard form of a quadratic equation (ax^2+bx+c=0)
a. 4/x^2+3/x-10=0
b. 6+4/x-1=5/x-3
c. 3.5x+4.6/x=1.2

please help
1 solutions
Answer 3667 by ichudov(499) About Me  on 2005-08-05 19:22:35 (Show Source):
You can put this solution on YOUR website!
I'll solve this one and you try other ones (same idea)
a. 4/x^2+3/x-10=0
use y instead of 1/x.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 4y%5E2%2B3y%2B-10+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A4%2A-10=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C4+=+1.25
y%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C4+=+-2

Quadratic expression 4y%5E2%2B3y%2B-10 can be factored:
4y%5E2%2B3y%2B-10+=+4%28y-1.25%29%2A%28y--2%29
Again, the answer is: 1.25, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B-10+%29


so, my solver says y=5/4, -2. That means that x=1/y = 4/5, -1/2.

Quadratic_Equations/6687: use the quadratic formula to solve the following quadratic equations.
a. 3x^2+2x-8=0
b. 5x^2+7x=12

please help
1 solutions
Answer 3666 by ichudov(499) About Me  on 2005-08-05 19:20:51 (Show Source):
You can put this solution on YOUR website!
I'll do one and you do another, okay?
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B2x%2B-8+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A3%2A-8=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+100+%29%29%2F2%5C3+=+1.33333333333333
x%5B2%5D+=+%28-%282%29-sqrt%28+100+%29%29%2F2%5C3+=+-2

Quadratic expression 3x%5E2%2B2x%2B-8 can be factored:
3x%5E2%2B2x%2B-8+=+3%28x-1.33333333333333%29%2A%28x--2%29
Again, the answer is: 1.33333333333333, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B2%2Ax%2B-8+%29

Expressions-with-variables/6678: If the system 2x-5y=1 and -3x+7y=-3 is to be solved by elimination of x, and the first equation is multiplied by 3, then by which number should the second equation be multiplied?
*I think that the answer is 2.Is this correct?
1 solutions
Answer 3652 by ichudov(499) About Me  on 2005-08-05 14:45:32 (Show Source):
You can put this solution on YOUR website!
you are fully right, that way the coefficients in front of x would be the same except for the sign. you can then add them and eliminate x.