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# Recent problems solved by 'drj'

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1 solutions

Answer 160220 by drj(1380)   on 2009-09-09 11:54:57 (Show Source):
You can put this solution on YOUR website!
Solve for x in the following equation

Step 1. Square Both Sides of Equation

Step 2. Simplify to get a quadratic equation. Subtract 2x+5 from both sides of equation

Step 3. Now use the quadratic equation

where a=1, b=-8 and c=20 and follow steps below:

 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=16 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3, -1. Here's your graph:

Step 4. x=3 and x=-1 are solutions to the equation.

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

 Human-and-algebraic-language/212131: This question is from textbook Elementary and Intermediate Algebra Tickets for a concert were sold to adults for \$3 and to students for \$2. If the total receipts were \$824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?1 solutions Answer 160219 by drj(1380)   on 2009-09-09 11:42:52 (Show Source): You can put this solution on YOUR website!Tickets for a concert were sold to adults for \$3 and to students for \$2. If the total receipts were \$824 and twice as many adult tickets as student tickets were sold, then how many of each were sold? Step 1. Let x = number of tickets sold to adults Step 2. Let y = number of tickets sold to students Step 3. Total receipts = 824 Step 4. x=2y since twice as many adults tickets sold when compared to student tickets. y must be a smaller value than x. Step 5. Substitute x of Step 4 into Step 3. Step 6. 103 Student tickets were sold and 206 adult tickets were sold where x=2y=2*103=206. For Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.
Equations/212136: i need a solution to the ordinary differential equation
x"+2x'+2x=0
1 solutions

Answer 160217 by drj(1380)   on 2009-09-09 11:27:11 (Show Source):
You can put this solution on YOUR website!
I need a solution to the ordinary differential equation
x"+2x'+2x=0

Step 1. Assume the solution is

If this is true, then we need to solve for m.

Step 2. Take the derivatives of x:

x" =

x' =

Step 3. Substitute above derivatives and x into the given equation

x"+2x'+2x=

Step 4. Factor out

to get

Step 5. The only way to get 0 is that the quadratic expression is zero. That is,

Now, we can solve for m using the quadratic formula below.

where

a=1, b=2 and c=2

Step 6. See standard procedure of solving quadratic equation below:

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -4 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -4 is + or - . The solution is Here's your graph:

Step 7. Note the roots are complex. So your solution will consists of complex exponentials. Also, please ignore the graph since it's only applicable for real roots.

Using the above roots m1 and m2, the solution is

where the c1 and c2 are arbitrary constants. We need initial values to get values of c1 and c2.

I believe the above problem is above the skill level of algebra. However,
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Triangles/212135: the hypotenuse of a right triangle is twice as long as one of the legs and 6 inches longer than the other. what are the lengths of the sides of the triangle
1 solutions

Answer 160213 by drj(1380)   on 2009-09-09 11:06:00 (Show Source):
You can put this solution on YOUR website!
The hypotenuse of a right triangle is twice as long as one of the legs and 6 inches longer than the other. what are the lengths of the sides of the triangle

Step 1. Let x be length of one of the legs. Then x+6 is the length of the other leg. And length of hypotenuse is 2x.

Step 2. Pythagorean Theorem. Sum of the squares of the legs is equal to the square of the hypotenuse.

Simplify right side,

Subtract x^2 from both sides

Simplify left side and multiply out the square term of x+6

Subtract the left side of equation on both sides by itself to get zero on the left side. That is

Simplifying both sides of equation yields

Step 3. This is now a quadratic equation where we can use the quadratic formula.

where a=2, b=-12, c=-36

 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=432 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 8.19615242270663, -2.19615242270663. Here's your graph:

Step 4. Pick the positive number since we have only positive lengths. In this case, it's 8.196. so
Length of one leg

Length of other Leg

Length of hypotenuse.

You can use the Pythagorean Theorem to check if its close to verify your answer.

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

Miscellaneous_Word_Problems/212102: Find the x intercepts for the parabola y = x2 – 6x + 5.
Find the vertex of the parabola y = - 2x2 + 8x + 4

1 solutions

Answer 160210 by drj(1380)   on 2009-09-09 10:18:19 (Show Source):
You can put this solution on YOUR website!
Find the x intercepts for the parabola y = x2 – 6x + 5.
Step 1. For this problem y=0 since we want x-intercepts.

where a=1, b=-6 and c= 5
Step 3. The following steps shows how to solve the above equation in Step 2 where you will find x=1 and x=5. Note the parabola intercepts x-axis when y=6 at these points.
 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=16 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 5, 1. Here's your graph:

Problem: Find the vertex of the parabola y = - 2x2 + 8x + 4

Step 1. Graph is shown below and the vertex is at (2,12)
 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=96 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.449489742783178, 4.44948974278318. Here's your graph:

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 Travel_Word_Problems/212115: Bob is making a 40-kilometer boat trip. if he travels at 30 kilometers per hour for the first 10 kilometers, and then at 15 kilometers per hour for the rest of the trip, how many minutes more will it take him than if he tarvels the entire trip at 20 kilometers per hour?1 solutions Answer 160202 by drj(1380)   on 2009-09-09 09:53:39 (Show Source): You can put this solution on YOUR website!Bob is making a 40-kilometer boat trip. If he travels at 30 kilometers per hour for the first 10 kilometers, and then at 15 kilometers per hour for the rest of the trip, how many minutes more will it take him than if he travels the entire trip at 20 kilometers per hour? Step 1. Translate following into an equation: He travels at 30 kilometers per hour for the first 10 kilometers. We note that Distance=Velocity*Time hours minutes where 60 minutes = 1 hours minutes where Distance = 10 km, x is the time he travels at 30 kilometers per hours and 30x is the distance traveled. Step 2. 15 kilometers per hour for the rest of the trip which in this case is 10 kilometers = 40-30. hours minutes minutes Step 3. Add Step 1 and Step 2 for Total Time. Total time = 20 minutes + 40 minutes = 60 minutes = 1 hour Step 4. Last part of the problem means he travels 40 km at 20 kilometers per hour. hour hour minutes minutes where z is the amount of time for this part of the problem. Step 5. The amount of time in Step 3 is 60 minutes and amount of time in Step 4 is 30 minutes. So Step 3 is 30 minutes more than Step 4. For more Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.
 Miscellaneous_Word_Problems/212105: \$1500 is deposited every year in an account yielding 6% interest compounded annually, how much money will have been saved after 10 years? 1 solutions Answer 160195 by drj(1380)   on 2009-09-09 09:15:54 (Show Source): You can put this solution on YOUR website!\$1500 is deposited every year in an account yielding 6% interest compounded annually, how much money will have been saved after 10 years? Step 1. Money after First year = 1500*1.06 (Money after first year is bigger than initial investment. That's why 1.06 must be bigger than 1 where 6% is 0.06. Then add 1 to get 1.06) Step 2. Money after Second year = First Year*1.06= 1500*1.06*1.06 Step 3. Money after Third year = Second Year*1.06= 1500*1.06*1.06*1.06 Step 4. Base on Steps 1-3, there is a pattern. So after n years then the general formula is where n is the number of years and Pn is the amount of money after n years. In this case n=10 and payment after ten year is labelled as P10 Step 5. Solve equation in Step 4. now So Step 6. So at the end of 10 years an initial investment of \$1500 compounded annually at 6% is \$2686.27. You almost doubled your money. You should double your money at the end of 12 years. You can check by substituting n=12. Happy Investing! Dr J For Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra. For more questions in investing calculations, please contact Dr J at john@e-liteworks.com.
 Human-and-algebraic-language/212113: YOU PAY A TOLL IN EITHER ALL QUARTERS OR ALL DIMES. THE TOLL IS 3 MORE DIMES THAN QUARTERS. WHAT IS THE TOLL?1 solutions Answer 160192 by drj(1380)   on 2009-09-09 08:57:47 (Show Source): You can put this solution on YOUR website!YOU PAY A TOLL IN EITHER ALL QUARTERS OR ALL DIMES. THE TOLL IS 3 MORE DIMES THAN QUARTERS. WHAT IS THE TOLL? Step 1. Total cost = 10x = 25y where x is the number of dimes and y is the number of quarters Step 2. y=x-3 since toll is 3 more dimes than quarters. That is, number of quarters is less than number of times, Step 3. Substitute y of Step 2 into Step 1 . Step 4. Subtract 10x from both sides of equation to make left side = 0 Step 3. Now add 75 to both sides of equation to isolate x on one side. Step 6. Isolate x by dividing 15 to both sides of equation Step 7. x=5 (x is the number of dimes) so the cost of the toll is Total Cost = As a check with y as the number of quarters then , so Total Cost = So the answer also checks out with the number of quarters. For Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra. Contact Dr J for more info at john@e-liteworks.com
 Miscellaneous_Word_Problems/212107: Debbie plans on investing enough money so that she will have \$2000 at the end of two years. How much money will she have to invest now if her money will grow according to the following formula: 2000 = P (1.025)^4? 1 solutions Answer 160187 by drj(1380)   on 2009-09-09 08:27:02 (Show Source): You can put this solution on YOUR website!Debbie plans on investing enough money so that she will have \$2000 at the end of two years. How much money will she have to invest now if her money will grow according to the following formula: 2000 = P (1.025)^4? Step 1. Solve for P where P is the initial investment. Interest in this case is 2.5 % compounded semiannually since in this case it's compounded 4 times in 2 years Divide by to both sides of equation to isolate P. Step 2. P=\$1811.90
 Miscellaneous_Word_Problems/212106: Richard drove his rig at ‘x’ mph for 3 hours, then increased his speed to (x + 15) mph and drove 2 more hours. Write a polynomial that represents the total distance that he traveled. How much distance he covered if x = 45 Mph? 1 solutions Answer 160185 by drj(1380)   on 2009-09-09 08:13:09 (Show Source): You can put this solution on YOUR website!Richard drove his rig at ‘x’ mph for 3 hours, then increased his speed to (x + 15) mph and drove 2 more hours. Write a polynomial that represents the total distance that he traveled. How much distance he covered if x = 45 Mph? Step 1. Distance=Velocity * Time Total Distance in miles = where is the distance in miles traveling for 3 hours at x mph is the distance in miles traveling for 2 hours at x+15 mph Step 2. Substitute x=45 Mph into Total Distance equation of Step 1 Step 3. Total Distance traveled is 255 miles. For Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.
 Average/212108: what is the average of 35.741 solutions Answer 160184 by drj(1380)   on 2009-09-09 07:59:48 (Show Source): You can put this solution on YOUR website!I think what you meant is what is the average of 35 and 74? Step 1. Add 35 and 74. Step 2. Count the number of values. In this case it's 2. Step 3. Divide Total of 109 by 2. For Step-By-Step Videos in Introduction to Algebra, visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.
 Travel_Word_Problems/212069: Russ and Janet are running. Russ runs at 7mph, Janet at 5mph. If the run has a staggered start, and Janet starts first with Russ starting 10 minutes later, how long before he catches up with her?1 solutions Answer 160157 by drj(1380)   on 2009-09-08 23:47:05 (Show Source): You can put this solution on YOUR website!Russ and Janet are running. Russ runs at 7mph, Janet at 5mph. If the run has a staggered start, and Janet starts first with Russ starting 10 minutes later, how long before he catches up with her? Step 1. Find distance Janet travels just before Russ starts running. (5 miles/hour) * (1 hour/60 minutes) * (10 minutes) = miles Step 2. You need to realize that Russ and Janet must travel the same distance when Russ catches up. distance = velocity * time Step 3. Russ traveled where x is the time (in hours) he traveled Step 4. Janet traveled where same x is the time she traveled Step 5. Set equations equal: Step 3 = Step 4 Step 6. Subtract 5x from both sides of equation in previous step. Step 7. Divide by 2 to solve for x Step 8. Answer is hour or minutes where 60 minutes = 1 hour For Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.
 Functions/212060: x+15/6-2x+8/2=-41 solutions Answer 160153 by drj(1380)   on 2009-09-08 23:28:12 (Show Source): You can put this solution on YOUR website!x+15/6-2x+8/2=-4 Step 1. To solve for x collect like terms on left side. Simplify 8/2=4. Step 2. Subtract to both sides of equation to isolate x by itself on the left side (left side is now -x when canceling terms) (simplify left side) (simplify right side -4-4=-8) (put in common denominator) (multiply by -1 to both sides of equation toget final answer below)
 Equations/212059: I was givien the following problem: Write the equation 2x+3y=9 in function form and find f(-1) and f(6) 1 solutions Answer 160143 by drj(1380)   on 2009-09-08 22:32:21 (Show Source): You can put this solution on YOUR website!I was givien the following problem: Write the equation 2x+3y=9 in function form and find f(-1) and f(6) Step 1. Solve for y, such that y=f(x) where f(x) is a function of x. Step 2. Subtract 2x in both sides of equation Step 3. Divide 3 in both sides of equation Step 4. f(-1) implies x=-1 Step 5. f(6) implies x=6 For Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra. For other technical topics having Step-By-Step videos in Trigonometry, Differential Equations, and Circuit Analysis and Design 1, please visit http://FreedomUniversity.TV.
Miscellaneous_Word_Problems/212048: This question is from textbook
The height of a triangle is 5 centimeters longer than three times its base. Find the base of the triangle if its area is 6 square centimeters
1 solutions

Answer 160139 by drj(1380)   on 2009-09-08 22:14:54 (Show Source):
You can put this solution on YOUR website!
The height of a triangle is 5 centimeters longer than three times its base. Find the base of the triangle if its area is 6 square centimeters

Step 1. Area of Triangle =

where x=base, h=height and A=area of is one-half times base times height

Step 2. (The height of a triangle is 5 centimeters longer than three times its base)

Step 3. Substitute height in Step 2 into equation in Step 1.

Step 4. Multiply 2 in both sides of last equation in Step 3 to get rid of denominator.

Simplify by subtracting 12 from both sides of equation yields

Step 5. The last equation of Step 4 is simply a quadratic equation. Then use the quadratic formula:

where a=3, b=5, and c=-12

 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: 1.33333333333333, -3. Here's your graph:

Step 6. Pick the positive number in the quadratic equation. In this case, we have the base x= 1.3333=4/3.

height is then centimeters
Area is then square centimeters. This is the same answer to our given answer. So it check out.

For Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra. For other technical topics having Step-By-Step videos in Trigonometry, Differential Equations, and Circuit Analysis and Design 1, please visit http://FreedomUniversity.TV.

Quadratic_Equations/211995: a farmer wants to set up a pigpen using 40 feet of fence to enclose a rectangular area of 51 square feet. what are the dimensions of the pigpen?
1 solutions

Answer 160116 by drj(1380)   on 2009-09-08 20:59:44 (Show Source):
You can put this solution on YOUR website!
A farmer wants to set up a pigpen using 40 feet of fence to enclose a rectangular area of 51 square feet. what are the dimensions of the pigpen?

1. Perimeter of a rectangle is 2x+2y=40 where x=one side of rectangle and y=the adjacent side of x. We can simplify this as x+y=20 where we divided 2 on both sides of the equation. That is,

2. Area=xy=51 where area of rectangle is height times width.

3. Substitute y in Step 1 into Step 2.

Multiplying the terms will yield:

4. Put everything on the left side to the right. That is, add -20x+x^2 from both sides of the equation to make the left side equal to zero.

Simplifying will yield

Finally, the above equation is equivalent to

4. Now this is just a Quadratic Equation so we can use the formula

where a=1, b=-20 and c=51

5. Use the following steps to solve the quadratic equation.

 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=196 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 17, 3. Here's your graph:

6. The rectangular sides are 3 and 17. As a check 3*17=51 (Area is 51 square feet) and Perimeter is 2*(3+17)=40 ft. So everything checks out.

For Step-by-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.Tv/courses/IntroAlgebra

 Equations/211998: Tony has twice as much money as Alicia. She has \$16 less than Ralph. Together they have \$200. How much money does each have? 1 solutions Answer 160110 by drj(1380)   on 2009-09-08 20:25:27 (Show Source): You can put this solution on YOUR website!Tony has twice as much money as Alicia. She has \$16 less than Ralph. Together they have \$200. How much money does each have? Step 1. Let x=amount of dollars that Alicia has. Step 2. Tony has twice as much as Alicia or 2x dollars Step 3. Ralph has x+16 dollars since Alicia has \$16 less than Ralph. Step 4. Since the total amount is \$200 among Alicia, Tony and Ralph, add Steps 1-3. x+2x+x+16=200. This yields. 4x+16=200 or 4x=184 where I subtracted 16 from both sides of the equation. Step 5. Solving x=184/4=46 dollars. a. Alicia has 46 dollars b. Tony has 46*2=92 dollars. c Ralph has 46+16=62 dollars. d. Total should be \$200. So, 46+92+62=200. So it checks out. For Step-By-Step Videos in Introductory Algebra and more word problems, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.
Linear_Equations_And_Systems_Word_Problems/211973: Mike bought some kilograms of apples and some kilograms of oranges and spent
\$27.25. The apples cost \$3.10 per kilogram and oranges cost \$4.95 per kilogram.
If apples become \$1.55 more expensive and oranges become \$1.15 chaper he will
spend \$30. How many ograms of apples and oranges did Mike buy?
1 solutions

Answer 160107 by drj(1380)   on 2009-09-08 19:33:51 (Show Source):
You can put this solution on YOUR website!
Mike bought some kilograms of apples and some kilograms of oranges and spent
\$27.25. The apples cost \$3.10 per kilogram and oranges cost \$4.95 per kilogram.
If apples become \$1.55 more expensive and oranges become \$1.15 cheaper he will
spend \$30. How many kilograms of apples and oranges did Mike buy?

1. Let x=number of kilograms of apples and y=number of kilograms of oranges.

2. Cost of apples = x*\$3.10 =3.10x

3. Cost of oranges= y*4.95=4.95y

4. Total cost = 27.25 = 3.10x+4.95y

5. Let's look at "If apples become \$1.55 more expensive and oranges become \$1.15 cheaper he will spend \$30."

a. For apples 3.10+1.55=4.65

b. For oranges 4.95-1.15=3.80

c. New total cost = 30 = 4.65x+3.80y

d. Note we still have the same number of apples x and oranges y.

6. So now we have two equations and two unknowns

a. 27.25 = 3.10x+4.95y

b. 30 = 4.65x+3.80y

Need to solve for x and y. The steps below will show x=4 and y=3

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 4.95*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

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Rate-of-work-word-problems/211955: The question is:
Find two positive integers tha differ by 4 and whose product is 221. I know the answer is 13 and 17, but would like to know how to arrive at that algebraicly.
1 solutions

Answer 160105 by drj(1380)   on 2009-09-08 19:06:12 (Show Source):
You can put this solution on YOUR website!
The question is:

Find two positive integers that differ by 4 and whose product is 221. I know the answer is 13 and 17, but would like to know how to arrive at that algebraically.

Step 1. Two Positive Integers that differ by 4. Say n is one positive integer. Since the two numbers differ by 4, then the other must can be either n+4 or n-4. We'll choose n+4 but you can use n-4 and get similar results.

Step 2. Product is 221. This means that n(n+4)=221.

Step 3. Multiply the equation is step 2. . This will reduce to a quadratic equation given as

where we subtracted 221 from both sides of the equation in the first equation of Step 3.

where a=1, b=4 and c=-221

The steps are shown below. The solutions to the quadratic equation equation below are 13 and -17 and will intercept the x-axis in the parabola such that y=0. However, please ignore the graph for the moment since solution exceeded the limits for the graph.

Step 4a. Since we want a positive numbers then choose n=13. Therefore n+4=17.

 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=900 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 13, -17. Here's your graph:

For step-by-step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.Tv/courses/IntroAlgebra

 Polynomials-and-rational-expressions/211947: This question is from textbook Mathematics1 How do you tell what degree a polynomial is?1 solutions Answer 160104 by drj(1380)   on 2009-09-08 18:14:45 (Show Source): You can put this solution on YOUR website!Degree of polynomial is the term which has the highest exponent. for example the polynomial : has degree 3. I also have free step-by-step videos in Introduction to Algebra at http://www.FreedomUniversity.TV/courses/IntroAlgebra. Spread the word to your friends.
Quadratic_Equations/211918: This question is from textbook Intoductery Algebra

Thank you.
1 solutions

Answer 160097 by drj(1380)   on 2009-09-08 17:14:26 (Show Source):
You can put this solution on YOUR website!

Step 1. For this case completing the square was not needed. Let's get rid of the denominator by multiplying the denominator to both sides of the equation.

The equation OR which will now be

Step 2. Now let's subtract -4 from both sides of the equation.

(note: the answer is just the ) plus or minus sqrt(11)

Step 3. So this is now a quadratic equation where

a=1, b=0, and c=-11 where we will use the quadratic formula

Step 4. See the steps below to solve this.

 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=44 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3.3166247903554, -3.3166247903554. Here's your graph:

Note: Step-By-Step Videos in Pre-Algebra can be found at http://www.FreedomUniversity.Tv/courses/IntroAlgebra.

Linear-equations/211912: How do you figure out this problem: -5x(2x-1)=3(x+4)
1 solutions

Answer 160094 by drj(1380)   on 2009-09-08 16:52:03 (Show Source):
You can put this solution on YOUR website!
How do you figure out this problem: -5x(2x-1)=3(x+4)

Step 1. Multiply everything out on both sides of the equation. After we mess around with the equation, we will get a quadratic equation. Here it goes:

-5x(2x-1)=3(x+4) will yield: -10x^2+5x=3x+12.

Step 2. Now let's put everything on the right side so that the left side is zero. I like a positive number for the x^2 term.

Step 2a. Add 10x^2 to both sides of equation in Step 1:

10x^2-10x^2+5x=10x^2+3x+12

Note: The 10x^2 terms cancel out on the left side.

Step 2b. Simplify equation in step 2a.

5x=10x^2+3x+12

Step 3. Subtract 5x both sides of equation in Step 2b to make left side =0.

5x-5x=10x^2+3x-12-5x

Note: Collect like terms and simplify 3x-5x=-2x

Step 3a. Simplify to yield our final equation

0=10x^2-2x-12 OR 10x^2-2x-12=0

Step 4. Now we have a quadratic equation in step 3a.

where a=10, b=-2, and c=-12.

Step 5. Substitute a, b, and c in the formula. The steps are shown below:

Note when the quadratic equation is a parabola when the values of x are real numbers. See graph where it intersects the x-axis. This is when y=0, hence our quadratic equation.

 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=484 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.2, -1. Here's your graph:

For Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra

Quadratic_Equations/211828: This question is from textbook Introductory Algebra
Find the x-intercept.
y=x^2+4x-1
1 solutions

Answer 160037 by drj(1380)   on 2009-09-08 12:24:02 (Show Source):
You can put this solution on YOUR website!
Find the x-intercept.
y=x^2+4x-1

Step 1. The x-intercept occurs when y=0. So let's set y=0=x^2+4x-1.

Step 2. Now use the quadratic formula given as:

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

Step 3. Substitute above values in quadratic formula and you get the following. Note the values of x where y=0 and observe them on the graph.

Also, note a quadratic equation is basically a parabola if the value of x are real numbers.

 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=20 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.23606797749979, -4.23606797749979. Here's your graph:

If you have any questions, I have a video also on the quadratic equation and you can contact Dr J at john@e-liteworks.com or visit my website at http://www.FreedomUniversity.TV for more step-by-step videos in math.