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# Recent problems solved by 'ichudov'

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

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)   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 (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=57 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.13745860881769, -1.63745860881769. Here's your graph:

Expressions-with-variables/7314: a + a/5 + 2/5*a
1 solutions

Answer 4072 by ichudov(499)   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

 Here's what you tried: Graphical form: simplifies to Text form: a+a/5+2/5*a simplifies to 8/5*aCartoon (animation) form: 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 .
Eliminated similar terms ,, replacing them with
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor ,
It becomes .
Result:

### 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 ." I assumed that this question wants you to complete the square, so I went ahead and did that. 1) 2) 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, -Mike1 solutions Answer 4071 by ichudov(499)   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. that's an equation of a circle with center in point x=1, y=0. so, assuming that this is what you want, .
 Linear-systems/7336: find the value of m such that this question have no solutions: 3x-my=4 x+y=121 solutions Answer 4070 by ichudov(499)   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)   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)   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

 Here's what you tried: Graphical form: simplifies to Text form: 8x+3-4x simplifies to 4*x+3Cartoon (animation) form: For tutors: `simplify_cartoon( 8x+3-4x )` 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 .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .
Result:

### Universal Simplifier and Solver

Done!

Numbers_Word_Problems/7330: Five decreased by eight is four times y
1 solutions

Answer 4046 by ichudov(499)   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

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

### DETAILED EXPLANATION

Look at .
It becomes .

Look at .
It becomes .

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

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

Look at .
Solved linear equation equivalent to -4*y-3 =0
It becomes .
Result:
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)   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

 Here's what you tried: Graphical form: simplifies to Text form: 1/2*(4x-8)=2*(x+3) simplifies to -10=0Cartoon (animation) form: 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 .
Remove extraneous '1' from product
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 .
Factors 4 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Factors 8 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .

Look at .
Multiplied numerator integers
It becomes .

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

Look at .
Remove extraneous '1' from product
It becomes .

Look at .
Remove extraneous '1' from product
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 .
Since has zero as a factor, it should be replaced with a zero

Look at .
It becomes .

Look at .
Remove extraneous zero
It becomes .
Result:

### 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)   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

 Here's what you tried: Graphical form: simplifies to Text form: 5x^2y-2x^2y*(2+y)+8x^2y^2 simplifies to x^2*y+6*x^2*y^2Cartoon (animation) form: 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 .
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 .
Reduce similar several occurrences of to
It becomes .

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

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

Look at .
Remove extraneous '1' from product
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .
Result:

### 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)   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:
, 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

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)   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:
, 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

 Rational-functions/6758: help me find the domain of how and why? 1 solutions Answer 3947 by ichudov(499)   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)   on 2005-08-12 13:04:07 (Show Source): You can put this solution on YOUR website!If , then alpha is a 45 degree angle. Just FYI. . 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)   on 2005-08-12 10:11:57 (Show Source):
You can put this solution on YOUR website!
You need to solve equation

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=1,x=-1. Graphical form: Equation was fully solved.Text form: 2x^4+x^2-3=0 simplifies to 0=0Cartoon (animation) form: 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 .
Equation is a quadratic equation, if we substitute : and has solutions Z= 1 and solution : 1,-1
It becomes .
Result:
This is an equation! Solutions: x=1,x=-1.

### Universal Simplifier and Solver

Done!

 logarithm/7037: solve: -2logbase4x=logbase49 3 logbase2 x=-logbase2 27 thank you!1 solutions Answer 3863 by ichudov(499)   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? ,
 logarithm/7041: How can i write as sum, difference, or multiple of log: 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)   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)   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

 Here's what you tried: Graphical form: simplifies to Text form: 2a-(4*(b-3*(a-2xb-2a))-10*(3b-5a)) simplifies to -60*a+26*b-24*xbCartoon (animation) form: 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 .
Remove unneeded parentheses around terms ,
It becomes .

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

Look at .
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Remove extraneous '1' from product
It becomes .

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

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

Look at .
Multiplied numerator integers
It becomes .

Look at .
Multiplied numerator integers
It becomes .

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

Look at .
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

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

Look at .
Multiplied numerator integers
It becomes .

Look at .
Multiplied numerator integers
It becomes .

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

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

Look at .
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .
Result:

### 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)   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 .
They also mention that the volume of a sphere is .
So, we have .
Remove pi:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: r=4. Graphical form: simplifies to Text form: 256/3=4/3*r^3 simplifies to +-1.33333333333333*r^2-5.33333333333333*r-21.3333333333333=0Cartoon (animation) form: 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 .
Moved these terms to the left
It becomes .

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

Look at .
Divided polynomial on the left by known factors (r-(4))
It becomes .
Result:
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:

1 solutions

Answer 3730 by ichudov(499)   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

 Here's what you tried: Graphical form: simplifies to Text form: 3/4*(5x+6y)*17+85/2+4x-2y simplifies to 271/4*x+149/2*y+85/2Cartoon (animation) form: 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 .

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 .
Factors 6 and 4 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .

Look at .
Multiplied numerator integers
It becomes .

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

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

Look at .
Multiplied numerator integers
It becomes .

Look at .
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor ,
It becomes .

Look at .
Remove unneeded parentheses around factor ,
It becomes .
Result:

### 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
1 solutions

Answer 3701 by ichudov(499)   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

 Here's what you tried: This is an equation! Solutions: x=1.3. Graphical form: Equation was fully solved.Text form: 2x+4*(3x-6)=4-(6x+2) simplifies to 0=0Cartoon (animation) form: 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 .
Remove unneeded parentheses around terms ,
It becomes .

Look at .
It becomes .

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

Look at .
Moved these terms to the left ,
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 .
Expanded term by using associative property on
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
It becomes .

Look at .
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 20*x-26 =0
It becomes .
Result:
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)   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

 Here's what you tried: Graphical form: simplifies to Text form: 3/8*(16x-8)+2/3*(15y+12) simplifies to 6*x+10*y+5Cartoon (animation) form: 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 .
Expanded term by using associative property on
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 .

Look at .
Factors 8 and 8 have greatest common factor (GCF) of 8. Reducing fraction.
It becomes .

Look at .
Multiplied numerator integers
It becomes .

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

Look at .
Remove extraneous '1' from product
It becomes .

Look at .
Remove extraneous '1' from product
It becomes .

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

Look at .
Factors 15 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Factors 12 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
It becomes .

Look at .
Remove extraneous '1' from product
It becomes .
Result:

### 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)   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) Am i just bad at algebra or is this somewhat complicated1 solutions Answer 3686 by ichudov(499)   on 2005-08-06 06:19:08 (Show Source): You can put this solution on YOUR website!great job on typing the formula. take natural log of both sides
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)   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

 Here's what you tried: This is an equation! Solutions: x=-0.333333333333333. Graphical form: Equation was fully solved.Text form: 4x+3=10x+5 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 4x+3=10x+5 )` 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 .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Solved linear equation equivalent to -6*x-2 =0
It becomes .
Result:
This is an equation! Solutions: x=-0.333333333333333.

### Universal Simplifier and Solver

Done!

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=-4.66666666666667. Graphical form: Equation was fully solved.Text form: (x+2)*(x+3)=(x+4)*(x-2) simplifies to 0=0Cartoon (animation) form: 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 .
Moved these terms to the left
It becomes .

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

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

Look at .
Reduce similar several occurrences of to
It becomes .

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

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

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

Look at .
Reduce similar several occurrences of to
It becomes .

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

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

Look at .
Since has zero as a factor, it should be replaced with a zero

Look at .
It becomes .

Look at .
It becomes .

Look at .
Remove extraneous zero
It becomes .

Look at .
Remove unneeded parentheses around factor
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 .
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+14 =0
It becomes .
Result:
This is an equation! Solutions: x=-4.66666666666667.

### Universal Simplifier and Solver

Done!

Combine:(3x^3-4x^2)+(-7-3x^3)-(-4x^2+2x)
1 solutions

Answer 3681 by ichudov(499)   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

 Here's what you tried: Graphical form: simplifies to Text form: (3x^3-4x^2)+(-7-3x^3)-(-4x^2+2x) simplifies to -2*x-7Cartoon (animation) form: 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 .
Remove unneeded parentheses around terms ,
It becomes .

Look at .
Remove unneeded parentheses around terms ,
It becomes .

Look at .
Remove unneeded parentheses around terms ,
It becomes .

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

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

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

Look at .
Since has zero as a factor, it should be replaced with a zero

Look at .
It becomes .

Look at .
Since has zero as a factor, it should be replaced with a zero

Look at .
It becomes .

Look at .
Remove extraneous zero
It becomes .

Look at .
Remove extraneous zero
It becomes .
Result:

### 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)   on 2005-08-05 23:49:43 (Show Source):
You can put this solution on YOUR website!
Since 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

It has its maximum right in the middle between the roots, which is x = -b/2a, or . Now use substitution of into expression :
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values

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

### DETAILED EXPLANATION

Look at .
Replaced x with -0.25
It becomes .

Look at .
Replace constants in factor: , with
It becomes .

Look at .
Replaced x with -0.25
It becomes .

Look at .
It becomes .

Look at .
Factors 425 and 100 have greatest common factor (GCF) of 25. Reducing fraction.
It becomes .

Look at .
Replace constants in expression: , with
It becomes .
Result:

### 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)   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

 Here's what you tried: Graphical form: simplifies to Text form: (2^-2+2)^2 simplifies to 5.0625Cartoon (animation) form: For tutors: `simplify_cartoon( (2^-2+2)^2 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Replace constants in factor: , with
It becomes .

Look at .
It becomes .

Look at .
Replace constants in factor: , with
It becomes .
Result:

### 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

1 solutions

Answer 3667 by ichudov(499)   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
 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=169 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.25, -2. Here's your graph:

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