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# Recent problems solved by 'drj'

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 Linear-equations/226263: 2x=x+41 solutions Answer 168535 by drj(1380)   on 2009-10-13 21:32:09 (Show Source): You can put this solution on YOUR website! Step 1. Subtract x from both sides of the equation Step 2. Check solution with original equation which is a true statement Step 3. ANSWER: The solution is I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J drjctu@gmail.com http://www.FreedomUniversity.TV http://www.Facebook.com/FreedomUniversity.TV http://www.Twitter.com/FreedomUTV
Numbers_Word_Problems/226268: The sum of four consecutive odd integers is 216 . Find the four integers
1 solutions

Answer 168534 by drj(1380)   on 2009-10-13 21:29:34 (Show Source):
You can put this solution on YOUR website!
The sum of four consecutive odd integers is 216 . Find the four integers

Step 1. Let n be the first odd integer.

Step 2. Let n+2, n+4, and n+6 be the next three consecutive odd integers

Step 3. Then, n+n+2+n+4+n+6=216 since the sum of the four consecutive odd integers is 216.

Step 4. Solving the equation in Step 4 yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=51. Graphical form: Equation was fully solved.Text form: n+n+2+n+4+n+6=216 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( n+n+2+n+4+n+6=216 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
It becomes .

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

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

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

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

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 4*n-204 =0
It becomes .
Result:
This is an equation! Solutions: n=51.

### Universal Simplifier and Solver

Done!

With n=51, then n+2=53, n+4=55, and n+6=57. Also 51+53+55+57=216 as a check...

Step 5. The four consecutive odd integers are 51, 53, 55, and 57

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV

Linear_Equations_And_Systems_Word_Problems/226249: The perimeter of a rectangle is 126 cm. The rectangle is twice as long as it is wide. What are its dimensions?
1 solutions

Answer 168529 by drj(1380)   on 2009-10-13 21:14:44 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 126 cm. The rectangle is twice as long as it is wide. What are its dimensions?

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

Step 2. Let w be the width.

Step 3. Let 2w be the length

Step 4. Then, P=w+w+2w+2w=126.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=21. Graphical form: Equation was fully solved.Text form: w+w+2w+2w=126 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( w+w+2w+2w=126 )` 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 .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

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

Look at .
Solved linear equation equivalent to 6*w-126 =0
It becomes .
Result:
This is an equation! Solutions: w=21.

### Universal Simplifier and Solver

Done!

For w=21 , then 2w=42 and P=2(21+42)=126 which is a true statement.

Step 6. ANSWER: The width is 21 cm and the length is 42 cm.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV

 Graphs/226245: Find the y- and x-intercepts for the equation. 4) f(x) = - 3 - 7x 1 solutions Answer 168526 by drj(1380)   on 2009-10-13 21:10:29 (Show Source): You can put this solution on YOUR website!Find the y- and x-intercepts for the equation. 4) f(x) = - 3 - 7x Step 1. Given y=f(x)=-3-7x, then x-intercepts occur when y=0. Then 0=-3-7x leads to Adding 7x to both sides of the equation Divide by 7 to both sides of the equation Step 2. Given y=-3x-7, y-intercepts occur when x=0, y=-3*x-7 or y=-7. Step 3. ANSWER: The x-intercept occurs at point (-3/7,0) and the y-intercept occurs at point(0,-7). I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J
Numbers_Word_Problems/226182: the sum of three consecutive integers is -129. find the integers.
1 solutions

Answer 168508 by drj(1380)   on 2009-10-13 19:52:14 (Show Source):
You can put this solution on YOUR website!
The sum of three consecutive integers is -129. Find the integers.

Step 1. Let n be the first integer.

Step 2. Let n+1 and n+2 be the next two consecutive integers.

Step 3. Then, n+n+1+n+2=-129 since the sum is -129.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=-44. Graphical form: Equation was fully solved.Text form: n+n+1+n+2=-129 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( n+n+1+n+2=-129 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
It becomes .

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

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

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

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

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 3*n+132 =0
It becomes .
Result:
This is an equation! Solutions: n=-44.

### Universal Simplifier and Solver

Done!

With n=-44, n+1=-43, and n+2=-42. Not the sum of these integers is -129.

Step 4. The integers are -44, -43, and -42.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Human-and-algebraic-language/226119: Mary is 3 years older than her brother Tom, and Tom is 4 years older than John. Three years ago Mary was twice as old as John. How old is each now?1 solutions Answer 168487 by drj(1380)   on 2009-10-13 18:40:38 (Show Source): You can put this solution on YOUR website!Mary is 3 years older than her brother Tom, and Tom is 4 years older than John. Three years ago Mary was twice as old as John. How old is each now? Step 1. Let x be the age of John. Step 2. Let x+4 be the age of Tom since Tom is 4 years older than John Step 3. Let x+4+3=x+7 be the age of Mary since she is 3 years old than Tom Step 4. Let x+4+3-3=x+4 be the age of Mary three years ago Step 5. Let x-3 be the age of John three years ago. Step 6. Then, x+4=2(x-3) since three years ago Mary was twice as old as John Step 7. Solving equation in Step 6 yields the following steps Add 6-x to both sides to get numbers only on one side and the variable x on the other side. John's age Then Tom's age and Mary's age. Check...if equation in Step 6 is true. Three years ago Mary was 14 years old which is twice the age of John who was 7 years old which satisfies Step 6. Step 8. ANSWER: John is 10 years old, Tom is 14 years old and Mary is 17 years old. 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
 Problems-with-consecutive-odd-even-integers/226096: Find two consecutive even integers whose sum is 1171 solutions Answer 168475 by drj(1380)   on 2009-10-13 17:43:48 (Show Source): You can put this solution on YOUR website!Find two consecutive even integers whose sum is 117. Step 1. Let n be the first even integer. Step 2. Let n+2 be the next consecutive even integer. Step 3. Then n+n+2=117 since two consecutive even integers whose sum is 117. Step 4. Solving yields the following steps. Divide by 2 to both sides of the equation but this is not an even integer. Step 5. ANSWER: There is no solution to this problem. Note the addition of two even integers will not yield an odd integer. I hope the above steps and explanation were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 test/226090: Graph the line that passes through the point(-1,2)and has slope –4/3. 1 solutions Answer 168473 by drj(1380)   on 2009-10-13 17:38:31 (Show Source): You can put this solution on YOUR website!Graph the line that passes through the point(-1,2)and has slope –4/3. Step 1. Starting with the (-1,2) or x=-1 and y=2, we move units to the RIGHT and units DOWN since the slope . This means we have another point at (-1+3,2-4) or (2, -2). Step 3. Use the two points (-1,2) and (2,-2) to plot the line. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J
 test/226092: Graph y=1/2x-3 by using the slope and y-intercept.1 solutions Answer 168469 by drj(1380)   on 2009-10-13 17:27:58 (Show Source): You can put this solution on YOUR website!Graph where m is the slope and b is the y-intercept when x=0 or at point (0,b). In this case, and or y-intercept at (0,-3) Step 2. Starting with the y-intercept at (0,-3) or x=0 and y=-3, we move two units to the right and one unit up since the slope is 1/2. This means we have another point at (0+2,-3+1) or (2, -2). Step 3. Use the two points (0,-3) and (2,-2) to plot the line. 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/226088: 6x-4= 1 How do you solve this one?1 solutions Answer 168465 by drj(1380)   on 2009-10-13 17:21:32 (Show Source): You can put this solution on YOUR website! How do you solve this one? Step 1. Add 4 to both sides of the equation Step 2. Divide 6 to both sides of the equation Step 3. Check solution with original equation which is a true statement Step 4. ANSWER: Solution 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
Linear-equations/226066: 2x+4y=15

1 solutions

Answer 168462 by drj(1380)   on 2009-10-13 17:17:39 (Show Source):
You can put this solution on YOUR website!

Step 1. I assume you want to plot this linear equation given in standard form.

Step 2. It takes two point to generate a line.

Step 3. Let x=0 then

Divide 4 to both sides of the equation

. So one point is (0,15/4).

Step 4. Let y=0, then

Divide 2 to both sides of the equation

. So another point is (15/2, 0).

Step 5. Use these two points (0,15/4) and (15/2,0) to plot the line.

 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. 15/2 = 7.5.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 15/4 = 3.75.Slope is -2/4 = -0.5. Equation in slope-intercept form: y=-0.5*x+3.75.

I hope the above steps were helpful.

Respectfully,
Dr J

Quadratic_Equations/226036: Use algrebra so solve (x-1)(x+2)=18
1 solutions

Answer 168461 by drj(1380)   on 2009-10-13 17:10:34 (Show Source):
You can put this solution on YOUR website!
Use algebra so solve (x-1)(x+2)=18

Step 1. Multiply out to get rid of the parenthesis.

Step 2. Subtract 18 from both sides of the equation

and or and

Step 4. We can also solve using the quadratic equation shown below:

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

 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=81 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, -5. Here's your graph:

...same as before.

Step 5. ANSWER: The solutions are x=-5 and x=4.

I hope the above steps were helpful.

Respectfully,
Dr J

Numbers_Word_Problems/225987: the sum of two numbers is 42. If the larger number is 3 more than triple the number find both numbers
1 solutions

Answer 168433 by drj(1380)   on 2009-10-13 15:21:52 (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 42. If the larger number is 3 more than triple the number find both numbers

Step 1. Let x be the larger number.

Step 2. Let 42-x be the other and smaller number.

Step 3. Then, x=3+3(42-x) where I assume you meant the larger number is 3 more than triple the smaller number.

Step 4. Solving the equation in Step 3 yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=32.25. Graphical form: Equation was fully solved.Text form: x=3+3*(42-x) simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( x=3+3*(42-x) )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

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

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

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

Look at .
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 4*x-129 =0
It becomes .
Result:
This is an equation! Solutions: x=32.25.

### Universal Simplifier and Solver

Done!

Let x=32.25, then 42-32.25=9.75. Check if equation is satisfied in Step 3.

32.25=3+3*9.75 which is a true statement.

I hope the above steps were helpful.

And good luck in your studies!

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

real-numbers/226000: For three consecutive odd integers, the sum of the least and greatest is 146. What is the sum of all three integers?
1 solutions

Answer 168431 by drj(1380)   on 2009-10-13 15:12:23 (Show Source):
You can put this solution on YOUR website!
For three consecutive odd integers, the sum of the least and greatest is 146. What is the sum of all three integers?

Step 1. Let be the first odd integer.

Step 2. Let and and be the next two consecutive integers.

Step 3. Let since the sum of the least and greatest is 146.

Step 4. Solving the equation in Step 3 yields the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=71. Graphical form: Equation was fully solved.Text form: n+n+4=146 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( n+n+4=146 )` 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 .
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 2*n-142 =0
It becomes .
Result:
This is an equation! Solutions: n=71.

### Universal Simplifier and Solver

Done!

With n=71, then n+2=73 and n+4=75 where the sum of the least and largest number is 146. The sum is 71+73+75=219

Step 8. ANSWER: The sum of the numbers is 219.

I hope the above steps were helpful.

And good luck in your studies!

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

 Expressions-with-variables/225995: The shorter leg of a right triangle is 20 yards. If the hypotenuse is 29 yards, how long is the other leg?1 solutions Answer 168430 by drj(1380)   on 2009-10-13 15:05:09 (Show Source): You can put this solution on YOUR website!The shorter leg of a right triangle is 20 yards. If the hypotenuse is 29 yards, how long is the other leg? Step 1. Use the Pythagorean Theorem which states that the sum of the squares of the legs (given legs a and) is equal to the square of the hypotenuse c. Step 2. Let a=20 and c=29, we can find the other leg b as follows Subtract from both sides of the equation Take the square root of b to both sides of the equation Step 3. ANSWER. The length of the other leg is 21 yards. I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J drjctu@gmail.com http://www.FreedomUniversity.TV http://www.Facebook.com/FreedomUniversity.TV http://www.Twitter.com/FreedomUTV
Numbers_Word_Problems/225986: the difference between two numbers is 22. If the larger number is 4 more than twice the smaller. Find the numbers

1 solutions

Answer 168426 by drj(1380)   on 2009-10-13 14:58:18 (Show Source):
You can put this solution on YOUR website!
The difference between two numbers is 22. If the larger number is 4 more than twice the smaller. Find the numbers

Step 1. Let x be one number

Step 2. Let 22+x be the larger number and since the difference between the two numbers is 22.

Step 3. Let 2x be twice the smaller.

Step 4. 22+x=4+2x since the larger number is 4 more than twice the smaller.

Step 5. Solving the equation in Step 4 leads to the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=18. Graphical form: Equation was fully solved.Text form: 22+x=4+2x simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 22+x=4+2x )` 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 .
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 .
Solved linear equation equivalent to -x+18 =0
It becomes .
Result:
This is an equation! Solutions: x=18.

### Universal Simplifier and Solver

Done!

With x=18, then 22+x=40

Check with equation four 22+x=4+2x or 40=4+2*18 or 40=40 which is a true statement.

Step 6. Then numbers are 18 and 40

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV

 Linear-systems/225910: -3=-4y+11 solutions Answer 168425 by drj(1380)   on 2009-10-13 14:51:15 (Show Source): You can put this solution on YOUR website! Step 1. Subtract 1 from both sides of the equation Step 2. Divide by -4 to both sides of the equation Step 3. ANSWER: The solution is I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J drjctu@gmail.com http://www.FreedomUniversity.TV http://www.Facebook.com/FreedomUniversity.TV http://www.Twitter.com/FreedomUTV
Quadratic_Equations/225944: THE PERIMETER IS 1280, THE WIDTH IS 90 LESS THAN THE LENGTH, WHAT IS THE LENGTH AND WIDTH?
1 solutions

Answer 168423 by drj(1380)   on 2009-10-13 14:47:21 (Show Source):
You can put this solution on YOUR website!
THE PERIMETER IS 1280, THE WIDTH IS 90 LESS THAN THE LENGTH, WHAT IS THE LENGTH AND WIDTH?

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

Step 2. Let w be the width.

Step 3. Let w+90 be the length since the width is 90 less than the length

Step 4. Then, P=w+w+w+90+w+90=1280.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=275. Graphical form: Equation was fully solved.Text form: w+w+w+90+w+90=1280 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( w+w+w+90+w+90=1280 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
It becomes .

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

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

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

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

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 4*w-1100 =0
It becomes .
Result:
This is an equation! Solutions: w=275.

### Universal Simplifier and Solver

Done!

For w=275 , then w+90=365 and P=2(275+365)=1280 which is a true statement.

Step 6. ANSWER: The length is 365 and the width is 275

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV

 Linear-systems/225957: Solve by method of elimination: 2x +3y =10 -3x+y =181 solutions Answer 168420 by drj(1380)   on 2009-10-13 14:39:04 (Show Source): You can put this solution on YOUR website!Solve by method of elimination: 2x +3y =10 Equation A -3x+y =18 Equation B Step 1. Multiply Equation B by 3 and subtract from Equation A to eliminate y terms Step 2. Divide by 11 to both sides of the equation Step 3. Substitute in Equation A to find y Step 4. Add 8 to both sides of the equation to find y Step 5. Divide by 3 to both sides of the equation Step 6. Check solution of and with Equation B which is a true statement. Step 7. ANSWER: The solution is (-4,6) or x=-4 and y=6 for the linear system of equations. I hope the above steps and explanation were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
 Surface-area/225978: find the area of a rectangle with base of 2yd and height 5ft1 solutions Answer 168415 by drj(1380)   on 2009-10-13 14:27:28 (Show Source): You can put this solution on YOUR website!Find the area of a rectangle with base of 2yd and height 5ft Step 1. Area A=b*h where b is the base and h is the height Step 2. 1 yard = 3 feet or 2 yards = 6 feet. Step 3. A=6*5=30 square feet Step 4. ANSWER: The area is 30 square feet. I hope the above steps and explanation were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
Equations/225967: solve x^4 + 6x^2 - 27 = 0
1 solutions

Answer 168413 by drj(1380)   on 2009-10-13 14:18:30 (Show Source):
You can put this solution on YOUR website!

Step 1. Let , then .

Step 2. Then,

Step 3. To solve equation in Step 2, use the quadratic formula

where a=1, b=6, and c=-27

 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=144 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3, -9. Here's your graph:

With and or and

So , , and where

Step 4. ANSWER: So , , and

I hope the above steps and explanation were helpful.

And good luck in your studies!

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

 Rectangles/225971: Perimeter of a rectangle. The perimeter of a rectangular backyard is 6x + 6 yards. If the width is x yards, find a binomial that represents the length.1 solutions Answer 168409 by drj(1380)   on 2009-10-13 14:08:14 (Show Source): You can put this solution on YOUR website!Perimeter of a rectangle. The perimeter of a rectangular backyard is 6x + 6 yards. If the width is x yards, find a binomial that represents the length. Step 1. Perimeter P means adding up all the sides of the rectangles. Step 2. Let L be the length and x be the width. Step 3. Then P=x+x+L+L=2x+2L Step 4. But P=6x+6=2x+2L. Solving for L yields the following steps: Subtract 2x from both sides of the equation Step 5. ANSWER. The length of the rectangle is I hope the above steps and explanation were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV
test/225969: Find the equation of the line containing the point (8, –39) and parallel to the line 6x+y= -4 .

1 solutions

Answer 168407 by drj(1380)   on 2009-10-13 14:01:17 (Show Source):
You can put this solution on YOUR website!
Find the equation of the line containing the point (8, –39) and parallel to the line 6x+y= -4 .

Step 1. We can find the slope by recognizing that parallel lines have the same slope. So we need to put the equation of the line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept b when x=0 or at point (0,b).
We can transform the given equation by subtracting -6x from both sides of the equation

Since is in slope-intercept form given as y=mx+b where the slope m=-6 and the y-intercept b=-4 when x=0 or at point (0,b) or (0,-4).

Step 2. Now we have to find the line with slope m=-6 going through point (8,-39).

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

Step 4. Let (x1,y1)=(8,-39) or x1=8 and y1=-39. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

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

Step 6. Multiply x-8 to both sides to get rid of denominator on right side of equation.

Subtract 39 from both sides of the equation

Step 7. ANSWER: The equation in slope-intercept form is

Note: the above equation can be rewritten as

And the graph is shown below which is consistent with the above steps.

 Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc Equation describes a sloping line. For any equation ax+by+c = 0, slope is .X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 9/6 = 1.5.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 9/1 = 9.Slope is -6/1 = -6. Equation in slope-intercept form: y=-6*x+9.

I hope the above steps and explanation were helpful.

And good luck in your studies!

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

test/225964: Point (1, –2) , m = –5.
1 solutions

Answer 168402 by drj(1380)   on 2009-10-13 13:49:46 (Show Source):
You can put this solution on YOUR website!
Point (1, –2) , m = –5.

I assume you want to write the slope intercept form of the equation of the line through the given point (1,-2) with the given slope m=-5.

Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).

Step 2. Now we have to find the line with slope m=-5 going through point (1,-2).

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

Step 4. Let (x1,y1)=(1,-2) or x1=1 and y1=-2. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

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

Step 6. Multiply x-1 to both sides to get rid of denominator on right side of equation.

Step 7. Add -2 to both sides of the equation

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

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

And the graph is shown below which is consistent with the above steps.

 Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc Equation describes a sloping line. For any equation ax+by+c = 0, slope is .X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 3/5 = 0.6.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 -5/1 = -5. Equation in slope-intercept form: y=-5*x+3.

I hope the above steps and explanation were helpful.

And good luck in your studies!

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

Proportions/225956: write in standard form the equation of the line with slope =-2 and passing through (4,1)
1 solutions

Answer 168398 by drj(1380)   on 2009-10-13 13:43:22 (Show Source):
You can put this solution on YOUR website!
Write in standard form the equation of the line with slope =-2 and passing through (4,1)

Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). Using the slope-intercept, we can translate it to the standard form given as Ax+By=C where A, B, and C are constants.

Step 2. Now we have to find the line with slope m=-2 going through point (4,1).

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

Step 4. Let (x1,y1)=(4,1) or x1=4 and y1=1. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

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

Step 6. Multiply x-4 to both sides to get rid of denominator on right side of equation.

Step 7. Add 1 to both sides of the equation

Step 7. ANSWER: The equation in slope-intercept form is where the slope m=-2 and the y-intercept b=9. The above equation can be rewritten in standard form by adding 2x to both sides as .

And the graph is shown below which is consistent with the above steps.

 Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc Equation describes a sloping line. For any equation ax+by+c = 0, slope is .X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 9/2 = 4.5.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 9/1 = 9.Slope is -2/1 = -2. Equation in slope-intercept form: y=-2*x+9.

I hope the above steps and explanation were helpful.

And good luck in your studies!

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

Numbers_Word_Problems/225878: The product of two positive consecutive numbers is 42. What is the larger number?
1 solutions

Answer 168371 by drj(1380)   on 2009-10-13 09:42:29 (Show Source):
You can put this solution on YOUR website!
The product of two positive consecutive numbers is 42. What is the larger number?

Step 1. Let n be the smaller positive number.

Step 2. Let n+1 be the next consecutive and larger positive number.

Step 3. Then n(n+1)=42 since their product is 42.

Step 4. Subtract 42 from both sides of the equation to get a quadratic.

Step 5. To solve, use the quadratic equation given below as

where a=1, b=1, and c=-42

 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: 6, -7. Here's your graph:

Selecting the positive solution n=6, then n+1=7. Also note their product is 42.

Step 6. ANSWER: The larger number is 7.

I hope the above steps were helpful.