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Sequences-and-series/213568: Please help me find 2 consecutive even integers whose sum is 217. The best I got was 106.6 and 108.8 but still fall short. I have these a lot and need to know how to find these with a simple math trick or formula. (Algebra 1) Thanks
1 solutions

Answer 161365 by drj(1380)   on 2009-09-14 18:34:48 (Show Source):
You can put this solution on YOUR website!
Find 2 consecutive even integers whose sum is 217.

Step 1. Let n be one odd integer and n+2 be the next consecutive odd integer

Step 2. Note: The sum of two even integers is always even. So in this example there is no solution since 217 is odd.

Step 3. Solve anyway as n+n+2=217 or 2n+2=217

Step 4. Solving yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=107.5. Graphical form: Equation was fully solved.Text form: 2n+2=217 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 2n+2=217 )` 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 .
It becomes .

Look at .
Solved linear equation equivalent to 2*n-215 =0
It becomes .
Result:
This is an equation! Solutions: n=107.5.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

Respectfully,
Dr J

 Inequalities/213581: 24 - 7n < 11n - 12 1 solutions Answer 161358 by drj(1380)   on 2009-09-14 18:18:56 (Show Source): You can put this solution on YOUR website! Step. 1. Add 7n+12 to both sides of equation to get n terms on right side and numbers on the left side of equation. Step 2. Divide by 18 to both sides of equation or 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. Good luck in your studies! Respectfully, Dr J
Trigonometry-basics/213539: find the distance between the lines with equations y=3x-9 and y = 3x - 4.
a)5/4
b)5 sqrt(10)/2
c)sqrt(10)/2
d)13 sqrt(10)/2
1 solutions

Answer 161347 by drj(1380)   on 2009-09-14 17:38:58 (Show Source):
You can put this solution on YOUR website!
Find the distance between the lines with equations 3x - y = 9 and y = 3x - 4.
a)5/4
b)5 sqrt(10)/2
c) sqrt(10)/2
d) 13 sqrt(10)/2

Step 1. Here's a graph of the two equations:

Step 2. We need a line that's perpendicular to the two parallel lines and then use the point where it intercepts the axis. The slope of the above two lines is 3 and the perpendicular line has a slope of -1/3. The reason being is the fact that the product of the slope for two perpendicular lines is equal to -1.

Step 3. So let's pass the perpendicular line through (0,-4) and then we need to solve y=3x-4 line and figure out where it intersects the the other parallel line.

So our equation in slope intercept form is y=mx+b=-4=-0/3+b. So b=-4. The the equation of the perpendicular line is:

Here a graph of the situation

Step 4. For visually simplicity, let's pick a point say (0,-4) as one point. We can find the other point, using a system of equations

The following steps will solve this system of equations

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 1*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

Step 5. Based on the above the other point (1.5 and -4.5)

Step 6. The distance between (0,-4) and (1.5, -4.5) is therefore,

Step 7. The answer is c or 1.58.

I hope the above steps were helpful and it's probably long. I'll see if there is a shorter way. But that's my approach for now.

Respectfully,
Dr J

 Quadratic_Equations/213552: how can i telln if a graph opens up or down by looking at the equation1 solutions Answer 161337 by drj(1380)   on 2009-09-14 17:02:39 (Show Source): You can put this solution on YOUR website!How can I tell if a graph opens up or down by looking at the equation For the quadratic equation: if a>0 it will open up. if a<0 it will open down. Let's look at an example: for a=2, b=2 and c=1 for a=-2, b=2 and c=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
Linear-systems/213501: x+5/2+x-1/2=x-1/3
1 solutions

Answer 161299 by drj(1380)   on 2009-09-14 15:11:21 (Show Source):
You can put this solution on YOUR website!

The following steps solves the above equation:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=-2.33333333333333. Graphical form: Equation was fully solved.Text form: x+5/2+x-1/2=x-1/3 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( x+5/2+x-1/2=x-1/3 )` 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 .
Factors 4 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .

Look at .
Remove extraneous '1' from product
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 .
Moved to the right of expression
It becomes .

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

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

Look at .
Solved linear equation equivalent to x+2.33333333333333 =0
It becomes .
Result:
This is an equation! Solutions: x=-2.33333333333333.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

Respectfully,
Dr J

 Radicals/213509: what is the equation of the line with an undefined slope and x intercept =21 solutions Answer 161297 by drj(1380)   on 2009-09-14 15:06:59 (Show Source): You can put this solution on YOUR website!What is the equation of the line with an undefined slope and x intercept =2 Step 1. The general equation is y=mx+b where m is the slope and b is the y-intercept. The equation called the slope-intercept form. Step 2. We are given that the x-intercept is 2 which means at x=2 then y=0. Step 3. Substitute in the general equation to find b Step 4. With b=-2m substitute in equation of Step 1. OR 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. Good luck in your studies! Respectfully, Dr J
 Square-cubic-other-roots/213487: This question is from textbook factor using the difference of two squares formula x^2 - 1001 solutions Answer 161283 by drj(1380)   on 2009-09-14 13:13:12 (Show Source): You can put this solution on YOUR website!Factor using the difference of two squares formula ANSWER is (x-10)(x+10) 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
 Expressions-with-variables/213485: if 2t+(s-r)/3= t what is s in terms of r and t?1 solutions Answer 161281 by drj(1380)   on 2009-09-14 13:11:26 (Show Source): You can put this solution on YOUR website!If 2t+(s-r)/3= t what is s in terms of r and t? Step 1. Let's get rid of denominator by multiplying 3 to both sides of equation: Step 2. Add -6t+r to both sides of equation to get s. ANSWER Step 3. So s=-3t+r 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
 Distributive-associative-commutative-properties/213484: equivalent expression with out parentases -(-9+8y) 1 solutions Answer 161279 by drj(1380)   on 2009-09-14 13:01:03 (Show Source): You can put this solution on YOUR website!Equivalent expression with out parenthesis -(-9+8y) Step 1. Think of the - sign outside the parenthesis as -1 and then distribute. Step 2. -(-9+9y)=(-1)*(-9+8y)=(-1)*(-9)+(-1)*(8y)=9-8y 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
 Equations/213480: Suppose that the length of a certain rectangle is 9 meters less than two times its width. The perimeter of the rectangle is 42 meters. Find the length and width of the rectangle.1 solutions Answer 161277 by drj(1380)   on 2009-09-14 12:55:48 (Show Source): You can put this solution on YOUR website!Suppose that the length of a certain rectangle is 9 meters less than two times its width. The perimeter of the rectangle is 42 meters. Find the length and width of the rectangle. Step 1. Let l = 2w-9 be the length of rectangle and let w be the width Step 2. Let P = 42 meters be the perimeter. Perimeter means adding the 4 sides of a rectangle. So, Step 3. Add 18 to both sides of equation to get 4w by itself Step 4. Divide 6 to both sides of equation Step 5. w = 10 meters is the width of the rectangle and length is 11 m since l=2w-9=11 Check P=2w+2l=2(10)+2(11)=20+22=42 So w = 10 meters and l = 11 meters is the solution. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trig Vids please visit http://www.FreedomUniversity.TV/courses/Trigonometry And GOOD LUCK in your studies! Respectfully Dr J
Travel_Word_Problems/213418: Bob leaves at 9am heading due north at 9mph. Tom leaves at 9:30am heading due south at 4mph. At what time will Bob and Tom be 10 miles apart?
1 solutions

Answer 161270 by drj(1380)   on 2009-09-14 12:38:27 (Show Source):
You can put this solution on YOUR website!
Bob leaves at 9am heading due north at 9mph. Tom leaves at 9:30am heading due south at 4mph. At what time will Bob and Tom be 10 miles apart?

Step 1. Bob traveled for one-half hour before Tom leaves at 9:30 am. Let this distance be d0=9*0.5=4.5 miles.

Step 2. So Total Distance traveled by Bob dBob=4.5+9t where t is the amount of time at which Bob and Tom are 10 miles apart.

Step 3. Total Distance traveled by Tom is dTom = 4*t.

Step 4. But dBob+dTom = 10 miles

Step 5. So substitute equation in Steps 2 and 3 into Step 4.

Solving this equation will yield the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: t=0.423076923076923. Graphical form: Equation was fully solved.Text form: 4.5+9t+4*t=10 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 4.5+9t+4*t=10 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

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

Look at .
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 .
Factors 55 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes .

Look at .
Solved linear equation equivalent to 13*t-5.5 =0
It becomes .
Result:
This is an equation! Solutions: t=0.423076923076923.

### Universal Simplifier and Solver

Done!

Step 6. t=0.42307 hours or t = 0.42307*60 minutes/hour = 25.42 minutes.

Step 7. Time is therefore 9:30 am plus 25.42 minutes or 9:55 am.

I hope the above steps were helpful.

Respectfully,
Dr J

Linear-systems/213471: This question is from textbook Introductory and Intermediate Algebra
How to solve out 3/5t-1/10t=t-5/2
1 solutions

Answer 161269 by drj(1380)   on 2009-09-14 12:20:36 (Show Source):
You can put this solution on YOUR website!

The following steps will solve the above equation

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: t=5. Graphical form: Equation was fully solved.Text form: 3t/5-t/10=t-5/2 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 3t/5-t/10=t-5/2 )` 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 .

Look at .
Factors 5 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes .

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

Look at .
Solved linear equation equivalent to -0.5*t+2.5 =0
It becomes .
Result:
This is an equation! Solutions: t=5.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

Respectfully,
Dr J

 Square-cubic-other-roots/213474: I do not know how to enter a square root symbol on the computer so I will just put into words. multiply property of radicals to simplify square root of 20xy^6z^31 solutions Answer 161268 by drj(1380)   on 2009-09-14 12:18:39 (Show Source): You can put this solution on YOUR website!Multiply property of radicals to simplify where , , and 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. Good luck in your studies! Respectfully, Dr J
 Square-cubic-other-roots/213475: I don't know how to enter the square root symbol on the computer so I am just going to put into words. MULTIPLY PROPERTY OF RADICALS TO SIMPLIFY 5 square root of 181 solutions Answer 161266 by drj(1380)   on 2009-09-14 12:02:17 (Show Source): You can put this solution on YOUR website!USE MULTIPLY PROPERTY OF RADICALS TO SIMPLIFY 5 square root of 18 ANSWER is 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
expressions/213470: This question is from textbook
solve. 7x - 3(4 - 2x)= 2(x-3)- (5-x)
1 solutions

Answer 161265 by drj(1380)   on 2009-09-14 11:58:57 (Show Source):
You can put this solution on YOUR website!
7x - 3(4 - 2x)= 2(x-3)- (5-x)

The following steps will simplify and solve the above equation.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=0.1. Graphical form: Equation was fully solved.Text form: 7x-3*(4-2x)=2*(x-3)-(5-x) simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 7x-3*(4-2x)=2*(x-3)-(5-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 .
Remove unneeded parentheses around terms ,
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 .
Moved to the right of expression
It becomes .

Look at .
It becomes .

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

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
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 10*x-1 =0
It becomes .
Result:
This is an equation! Solutions: x=0.1.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

Respectfully,
Dr J

 test/213467: A pitcher can throw a baseball 95 miles per hour. The ball travels at that speed for 56 feet, until it arrives at the batter. How many seconds, correct to the nearest thousandth of a second, does the batter have from the moment the ball is thrown, until it arrives.1 solutions Answer 161261 by drj(1380)   on 2009-09-14 11:26:07 (Show Source): You can put this solution on YOUR website!A pitcher can throw a baseball 95 miles per hour. The ball travels at that speed for 56 feet, until it arrives at the batter. How many seconds, correct to the nearest thousandth of a second, does the batter have from the moment the ball is thrown, until it arrives Step 1. Step 2. Time = 95 mph/56 feet * (5280 feet/mile) (1 hour/3600 seconds) = 2.488 seconds = 2.5 seconds. where 1 mile = 5280 feet, 1 hour = 60 minutes = 3600 seconds Step 3. Answer is 2.5 seconds. 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
 Travel_Word_Problems/213469: Marc drives 420 miles in 7 hours. What is his average speed in mph?1 solutions Answer 161259 by drj(1380)   on 2009-09-14 11:21:02 (Show Source): You can put this solution on YOUR website!Marc drives 420 miles in 7 hours. What is his average speed in mph? Step 1. Step 2 speed = 420 miles/7 hours = 60 mile per hour = 60 mph 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
 Miscellaneous_Word_Problems/213411: #20 FIND THREE CONSECUTIVE ODD INTEGERS SUCH THAT FOUR TIMES THE MIDDLE INTEGER IS TWICE THE SUM OF THE OTHER TWO INTEGERS1 solutions Answer 161258 by drj(1380)   on 2009-09-14 11:19:07 (Show Source): You can put this solution on YOUR website!FIND THREE CONSECUTIVE ODD INTEGERS SUCH THAT FOUR TIMES THE MIDDLE INTEGER IS TWICE THE SUM OF THE OTHER TWO INTEGERS Step 1. Let n be an odd integer, n+2 be the next consecutive odd or middle integer, and n+4 be the second consecutive odd integer Step 2. 4(n+2)=2(n+n+4) since middle integer is twice the sum of n+n+4 Step 3. The above result means any 3 consecutive odd integers will satisfy the above equation or problem statement. For example, 1, 3, 5 implies 4(3)=2(1+5) or 12=12 3, 5, 7 implies 4(5)=2(3+7) or 20=20 5, 7, 9 implies 4(7)=2(5+9) or 28=28 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
 Travel_Word_Problems/213465: A car travels at a speed of 47 mph. How far would it travel in 6 hours?1 solutions Answer 161254 by drj(1380)   on 2009-09-14 11:06:11 (Show Source): You can put this solution on YOUR website!A car travels at a speed of 47 mph. How far would it travel in 6 hours? Step 1. Distance = speed * time or d=s*t Step 2. Distance = (47 miles/hour)(6 hours)= 282 miles (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. Good luck in your studies! Respectfully, Dr J
Polynomials-and-rational-expressions/213464: q=10-2p
q=20+3p
1 solutions

Answer 161253 by drj(1380)   on 2009-09-14 11:03:45 (Show Source):
You can put this solution on YOUR website!

Set above equations to be equal q=q

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: p=-2. Graphical form: Equation was fully solved.Text form: 10-2p=20+3p simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 10-2p=20+3p )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

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

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

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

Look at .
It becomes .

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

Look at .
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 -5*p-10 =0
It becomes .
Result:
This is an equation! Solutions: p=-2.

### Universal Simplifier and Solver

Done!

With p=-2, then q=14=10-2(-2). ANSWER is p=-2 and q=14.

I hope the above steps were helpful.

Respectfully,
Dr J

Triangles/213461: The second angle of a triangular kite is four times as large as the first. The third angle is 5 more than the sum of the other two angles. Find the measure of the second angle.
1 solutions

Answer 161252 by drj(1380)   on 2009-09-14 10:55:58 (Show Source):
You can put this solution on YOUR website!
The second angle of a triangular kite is four times as large as the first. The third angle is 5 more than the sum of the other two angles. Find the measure of the second angle.

Step 1. Let a be the first angle, 4a is the second angle, and 5+a+4a=5+5a be the third angle where a+5a=5a is the sum of the other two angles

Step 2. Sum of the angles of a triangle is equal to 180. So

The following steps solve the above equation.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: a=17.5. Graphical form: Equation was fully solved.Text form: a+4a+5+5a=180 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( a+4a+5+5a=180 )` 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 .

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 10*a-175 =0
It becomes .
Result:
This is an equation! Solutions: a=17.5.

### Universal Simplifier and Solver

Done!

I hope the above steps were helpful.

Respectfully,
Dr J

 Equations/213412: #11 SIMPLIFY (2.1)(0.6)(-3.5) 1 solutions Answer 161251 by drj(1380)   on 2009-09-14 10:34:16 (Show Source): You can put this solution on YOUR website!SIMPLIFY (2.1)(0.6)(-3.5) ANSWER I hope the above steps were helpful. 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
 Volume/213419: What is the volume of a paper cup with a diameter of 2 inches and 5 tall converted to centimeters.1 solutions Answer 161250 by drj(1380)   on 2009-09-14 10:30:31 (Show Source): You can put this solution on YOUR website!What is the volume of a paper cup with a diameter of 2 inches and 5 tall converted to centimeters. Step 1. Note that 1 inch = 2.54 centimeters. Step 2. Assume Volume of cup is equal to volume of cylinder. Step 3. Volume of cylinder where d/2 is the radius, d is the diameter, h is the height Step 4. 1 inch cube = (2.54)^3 centimeters cube or 16.387 cm^3. So cubic centimeters ANSWER I hope the above steps were helpful. 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
 Length-and-distance/213430: A box measures 1 metre X 1 metre X 1 metre. What would a box need to measure to hold twice the volume of this box?1 solutions Answer 161248 by drj(1380)   on 2009-09-14 10:22:29 (Show Source): You can put this solution on YOUR website!A box measures 1 metre X 1 metre X 1 metre. What would a box need to measure to hold twice the volume of this box? Volume of the box is V=s^3 where s is the edge of the box and they are equal in this case. Given V=2 means that Therefore, to get twice the volume the dimensions of the box would be 1.26 metre x 1.26 metre x 1.26 metre I hope the above steps were helpful. 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
Quadratic_Equations/213428: f(x)=-3x^2 make a table and a graph

1 solutions

Answer 161246 by drj(1380)   on 2009-09-14 10:17:33 (Show Source):
You can put this solution on YOUR website!
f(x)=-3x^2 make a table and a graph

Here's the list of points:
x......y=-3x^2
-5 -75
-4 -48
-3 -27
-2 -12
-1 -3
0 0
1 3
2 12
3 27
4 48
5 75

Here's the graph:

 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=0 is zero! That means that there is only one solution: . Expression can be factored: Again, the answer is: -0, -0. Here's your graph:

Note: The vertex is (0,0)

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

1 solutions

Answer 161242 by drj(1380)   on 2009-09-14 10:11:42 (Show Source):
You can put this solution on YOUR website!

The above equation is in slope intercept form or y=-mx+b where m is the slope and b is the y-intercept which occurs when x=0. In this example, slope=m=-1 and y-intercept=b=3.

I assume you want a plot of this equation, so here's a plot which shows the slope of -1 and y-intercept of 3 at x=0:

 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. 3/1 = 3.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 3/1 = 3.Slope is -1/1 = -1. Equation in slope-intercept form: y=-1*x+3.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Angles/213452: An angle is equal to 5 times its complement,determine its measure ?1 solutions Answer 161233 by drj(1380)   on 2009-09-14 09:33:16 (Show Source): You can put this solution on YOUR website!An angle is equal to 5 times its complement,determine its measure ? Step 1. Complementary angles are those angles when they add up to 90 degrees. Step 2. Let x be the angle and let 5x be its complement. Step 3. Then Divide by 6 to both sides of equation to get x Step 4. The angle is 15 degrees and its complement is 75 degrees. 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
Quadratic_Equations/213438: (x^2⁄2)- 4 – 6x = - 4
I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. Thankyou for you time. Your are appreshated.
1 solutions

Answer 161220 by drj(1380)   on 2009-09-14 09:02:53 (Show Source):
You can put this solution on YOUR website!

The following steps will simplify and solve the equation.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=12,x=0. Graphical form: Equation was fully solved.Text form: (x^2)/2-4-6x=-4 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( (x^2)/2-4-6x=-4 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around factor
It becomes .

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

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

Look at .
It becomes .

Look at .
Remove extraneous zero
It becomes .

Look at .
Equation is a quadratic equation: 0.5*x^2-6*x =0, and has solutions 12,0
It becomes .
Result:
This is an equation! Solutions: x=12,x=0.

### Universal Simplifier and Solver

Done!

You can also use the quadratic formula given as

where a=1/2, b=-6, and c=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=36 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 12, 0. Here's your graph:

I hope the above steps were helpful.