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# Recent problems solved by 'drj'

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 Travel_Word_Problems/213801: A boat can go 33 mph in still water.It take as long to go 300 milles uptream as it does to go downsteam 360 milles . How fast is the current?1 solutions Answer 161711 by drj(1380)   on 2009-09-16 11:14:30 (Show Source): You can put this solution on YOUR website!A boat can go 33 mph in still water. It take as long to go 300 miles upstream as it does to go downstream 360 miles . How fast is the current? Step 1. Let v be the velocity of the current. Step 2. Speed of boat in still water is 33 mph. Velocity going upstream is 33-v and velocity going downsteam is 33+v Step 3. Distance=Time*Velocity and Upstream time = Downstream time Step 4. Upstream time = Distance/Velocity=300/(33-v) Step 5. Downstream time = 360/(33+v) Step 6. Set expressions in Step 4 and 5 to be equal since time traveled upstream equals to time traveled downstream. Then Multiply by (33-v)(33+v) to both sides of equation to get rid of denominators. Divide by 60 to both sides of equation Add 6v-165 to both sides of equation Divide by 33 to both sides of equation Step 5. So velocity of current is 3 mph. 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
 Linear_Algebra/213825: Can someone please help me solve: how to solve f(x)=x^2+30 Thank you,1 solutions Answer 161709 by drj(1380)   on 2009-09-16 10:51:42 (Show Source): You can put this solution on YOUR website!How to solve f(x)=x^2+30 I assume you want to plot the above graph: Just take values of x and substitute in above equation: For example x=0 means f(x=0)=0^2+30=30 x=1 means f(x=1)=1^2+30=31 x=-1 means f(x=-1)=(-1)^2+30=31 etc. Here's a graph of the above equation... 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
 Travel_Word_Problems/214046: a car travels north for 6 hours and covers 300 kilomaters what is its speed1 solutions Answer 161706 by drj(1380)   on 2009-09-16 10:38:55 (Show Source): You can put this solution on YOUR website!A car travels north for 6 hours and covers 300 kilometers what is its speed Speed = Distance/Time Distance = 300 km Time = 6 hours Speed = 300/6 = 50 km/hr (ANSWER) 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/214097: Find two consecutive even integers such that three times the lesser integer, added to the larger integer, is 58.
1 solutions

Answer 161704 by drj(1380)   on 2009-09-16 10:32:10 (Show Source):
You can put this solution on YOUR website!
Find two consecutive even integers such that three times the lesser integer, added to the larger integer, is 58.

Step 1. Let n be an even integer and n+2 be the next consecutive even integer

Step 2. 3n be three times the lesser integer

Step 3. 3n+n+2 be three times the lesser integer added to the larger integer n+2

Step 4. 3n+n+2=58 be three times the less integer added to the larger integer n+2 is 58.

Step 5. The following steps will solve the equation 3n+n+2=58.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=14. Graphical form: Equation was fully solved.Text form: 3n+n+2=58 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 3n+n+2=58 )` 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 4*n-56 =0
It becomes .
Result:
This is an equation! Solutions: n=14.

### Universal Simplifier and Solver

Done!

Then n+2=16 when n=14

Check 3*14+16=58. So it works!!

Step 6. ANSWER: The integers are 14 and 16.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Trigonometry-basics/214091: Find the exact value of tan210 degree1 solutions Answer 161703 by drj(1380)   on 2009-09-16 10:24:09 (Show Source): You can put this solution on YOUR website!Find the exact value of tan 210 degree Step 1. The angle 210 degrees will fall in the third quadrant. This means that the x-coordinate is negative and the y-coordinate is negative. Also you can calculate using the 30-60-90 triangle since 210-180=30 degrees. You will need to draw a graph to see this more clearly. Step 2. So x-coordinate will be and y-coordinate is Step 3. Then we have Step 4. Answer 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
Length-and-distance/214089: the length of a rectangle garden is 5 m greater than the width. the area is 66m^2. find the dim. of the garden.
1 solutions

Answer 161700 by drj(1380)   on 2009-09-16 10:09:57 (Show Source):
You can put this solution on YOUR website!
The length of a rectangle garden is 5 m greater than the width. The area is 66m^2. Find the dimensions of the garden.

Step 1. Let w be the width and w+5 be the length.

Step 2. Let A=66=w(w+5) be the area of the rectangle.

Step 3. Solving for w yields the following steps

Subtract 66 from both sides of equation to yield a quadratic equation

We can use the quadratic formula given as

where

a=1, b=5 and c=-66

 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=289 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6, -11. Here's your graph:

Step 4. Based on the above steps, we select the positive solution 6. Now we have the width w=6 m and the length w+5=11 m. Area A=6*11=66 square meters as given in the problem

Step 5. ANSWER The dimensions of the rectangle are 6 m and 11 m.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Length-and-distance/214088: if an object is dropped the distance d it falls in 1 sec. is given by d=1/2gr^2 where g is approx. 32 ft. per sec. find the distance an object will fall in 6 sec.?1 solutions Answer 161697 by drj(1380)   on 2009-09-16 09:57:29 (Show Source): You can put this solution on YOUR website!If an object is dropped the distance d it falls in 1 sec. is given by where g is approx. 32 ft. per sec^2. find the distance an object will fall in 6 sec.? Given t= 6 sec, then ft. ANSWER is 576 ft where the object fell for 6 seconds. 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
 Numeric_Fractions/214087: y = 5x + 8xw Solve for x1 solutions Answer 161695 by drj(1380)   on 2009-09-16 09:50:58 (Show Source): You can put this solution on YOUR website! Solve for x Step 1. Factor out x on right side of equation. Step 2. Divide 5+8w to both sides of equation Step 3. ANSWER 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
 Numbers_Word_Problems/214083: If four times the sum of a number and 5 is divided by 3, the result is 16 1 solutions Answer 161693 by drj(1380)   on 2009-09-16 09:46:44 (Show Source): You can put this solution on YOUR website!If four times the sum of a number and 5 is divided by 3, the result is 16. Step 1. Let x be the number. Step 2. Four times the number and 5 is divided by 3 Step 3. The result is 16 Step 4. Multiply by 3 to both sides of equation to get rid of denominator Step 5. Subtract 20 from both sides of equation Step 6. Divide by 4 to both sides of equation Step 7 ANSWER is x=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
 Equations/214080: This question is from textbook Intermediate Algebra factor completely: 2x^2+20x+501 solutions Answer 161691 by drj(1380)   on 2009-09-16 09:33:54 (Show Source): You can put this solution on YOUR website!Factor completely: Step 1. We need to find two integers A and B that A*B=ac and A+B=b where in order to be factorable and a=2, b=20 and c=50 Step 2. In the above example, then A*B=(2)(50)=100 and A+B=20. Step 3. After trial and error the numbers are A=10 and B=10 Step 4. Using step 3, we can use grouping as follows where Step 5. Factor out 2x in first group and 10 in second group Step 6. Factor out (x+5) since it is common in both groups. ANSWER We can use the FOIL method to verify 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
 Equations/214081: This question is from textbook Intermediate Algebra factor completely: 3x^2-13x+141 solutions Answer 161690 by drj(1380)   on 2009-09-16 09:23:22 (Show Source): You can put this solution on YOUR website!Factor completely: Step 1. We need to find two integers A and B that A*B=ac and A+B=b where in order to be factorable and a=3, b=-13 and c=14 Step 2. In the above example, then A*B=(3)(14)=42 and A+B=-13. Step 3. After trial and error the numbers are A=-6 and B=-7 Step 4. Using step 3, we can use grouping as follows where Step 5. Factor out 3x in first group and -7 in second group Step 6. Factor out (x-2) since it is common in both groups. ANSWER We can use the FOIL method to verify 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
Rectangles/214050: If the AREA of a rectangle is 20m and the PERIMETER of the rectangle is 20m, what are the length and the width?
1 solutions

Answer 161687 by drj(1380)   on 2009-09-16 08:59:42 (Show Source):
You can put this solution on YOUR website!
If the AREA of a rectangle is 20 m^2 and the PERIMETER of the rectangle is 20 m, what are the length and the width?

Step 1. Area A=20=l*w where l is the length and w is the width for a rectangle.

Then l=20/w

Step 2. Perimeter P=20=l+l+2+2=2(l+w) where perimeter means adding up all four sides of a rectangle.

Step 3. Substitute the length l of Step 1 into Step 2 to get the following:

Simplify and multiply by w to both sides of equation to get rid of denominator

Subtract 10w to both sides of equation to get a quadratic equation.

where we can use the quadratic formula

where a=1 b=-10 and c=20

Step 4. The following steps will 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=20 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 7.23606797749979, 2.76393202250021. Here's your graph:

Step 5. ANSWER: Based on the above results, we have the width w=7.2361 m and the length l=2.7639 m. The numbers can also be reversed and note that these numbers satisfy the given area and perimeter.

So the sides of the rectangle are 7.2361 m and 2.7639 m.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Triangles/214077: Assume that is an acute angle. If sin A = 0.994, use a calculator to find the measure of to two decimal places.1 solutions Answer 161685 by drj(1380)   on 2009-09-16 08:37:10 (Show Source): You can put this solution on YOUR website!Assume that it is an acute angle. If sin A = 0.994, use a calculator to find the measure to two decimal places. Step 1. Step 2. Take the inverse or arcsin(A) to both sides of equation. Then arcsin(sin(A))=arcsin(0.994) A= 83.72 degrees. where arcsin(sin(A)))=A and arcsin(0.994)=83.72 degrees 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
 Equations/214019: You are given an endpoint and the midpoint of a line segment. Find the coordinates of the other endpoint. Each midpoint is denoted by M(x, y) C(-4,-5) M(3,-6) 1 solutions Answer 161664 by drj(1380)   on 2009-09-15 22:16:56 (Show Source): You can put this solution on YOUR website!You are given an endpoint and the midpoint of a line segment. Find the coordinates of the other endpoint. Each midpoint is denoted by M(x, y) C(-4,-5) M(3,-6) Let (x,y) be the other endpoint. Then for this example the midpoint is calculated by averaging the x and y coordinates of the endpoints. That is, and and and So the other endpoint is (10,-7) As a check between the two endpoints (10,-7) and (-4,-5), let's calculate the midpoint. is the x-coordinate for the midpoint. is the y-coordinate for the midpoint. So the midpoint is (3,-6) which is same as before. 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
 Rectangles/214015: what is the geatest possible area of a rectangle if its perimeter is 30 cm 1 solutions Answer 161662 by drj(1380)   on 2009-09-15 22:10:04 (Show Source): You can put this solution on YOUR website!What is the greatest possible area of a rectangle if its perimeter is 30 cm. The greatest possible area is when the sides are equal or a square and the perimeter is adding up the lengths of all four sides in this case. So let s be the side of the square. Then Perimeter P=4s or s=P/4=30/4=7.5 cm. The Area or 56.25 square centimeters. 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
 Geometric_formulas/214010: how do you solve this problem using the midpoint formula? R(2,6) M(-1,1)1 solutions Answer 161654 by drj(1380)   on 2009-09-15 21:53:22 (Show Source): You can put this solution on YOUR website!How do you solve this problem using the midpoint formula? R(2,6) M(-1,1) I assume R is one endpoint and the M is the midpoint Let (x,y) be the other endpoint. Then for this example the midpoint is calculated by averaging the x and y coordinates of the endpoints. That is, and and and So the other endpoint is (-4,-4) As a check between the two endpoints (-4,-4) and (2,6), let's calculate the midpoint. is the x-coordinate for the midpoint. is the y-coordinate for the midpoint. So the midpoint is (-1,1) which is same as before. 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/214006: You are given an endpoint and the midpoint of a line segment. Find the coordinates of the other endpoint. Each midpoint is denoted by M(x, y) B (5,7) M (-1,0) 1 solutions Answer 161651 by drj(1380)   on 2009-09-15 21:48:00 (Show Source): You can put this solution on YOUR website!You are given an endpoint and the midpoint of a line segment. Find the coordinates of the other endpoint. Each midpoint is denoted by M(x, y) B (5,7) M (-1,0) Let (x,y) be the other endpoint. Then for this example the midpoint is calculated by averaging the x and y coordinates of the endpoints. That is, and and and So the other endpoint is (-7,-7) As a check between the two endpoints (-7,-7) and (5,7), let's calculate the midpoint. is the x-coordinate for the midpoint. is the y-coordinate for the midpoint. So the midpoint is (-1,0) which is same as before. 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
 Numbers_Word_Problems/213997: The sum of two numbers is 84. The first is 9 more than 4 times the second. Find the first number.1 solutions Answer 161645 by drj(1380)   on 2009-09-15 21:25:39 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 84. The first is 9 more than 4 times the second. Find the first number. Step 1. Let x be the second number. Let 9+4x is be first number. Step 2. x+9+4x=84 The sum of two numbers is 84. Step 3. Simplify: 5x+9=84. Step 4. Subtract 9 to both sides of equation: 5x+9-9=84-9=75 Step 5. Simplify and divide by 5: 5x=75 or x=15. Then 9+4x=9+4(15)=69 Step 6. The first number is 69. 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
 real-numbers/213976: 3 divided by 5 times -6 times -151 solutions Answer 161642 by drj(1380)   on 2009-09-15 21:19:45 (Show Source): You can put this solution on YOUR website!3 divided by 5 times -6 times -15 where we factored 15=3*5. where 5/5=1 ANSWER IS 48 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
Linear-systems/213996: Please help me solve the substituation x+y=12 and x-y=-4. I can't figure out how to solve these
1 solutions

Answer 161640 by drj(1380)   on 2009-09-15 21:13:14 (Show Source):
You can put this solution on YOUR website!
Please help me solve the substitution x+y=12 and x-y=-4. I can't figure out how to solve these.

The following will solve the system of linear equations by substitution.

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

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

 Expressions-with-variables/213992: 1 solutions Answer 161634 by drj(1380)   on 2009-09-15 20:58:07 (Show Source): You can put this solution on YOUR website! 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
 Expressions-with-variables/213993: 1 solutions Answer 161633 by drj(1380)   on 2009-09-15 20:56:23 (Show Source): You can put this solution on YOUR website! 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
 Equations/213985: This question is from textbook kirra is two years older then reggie. reggie is six times as old as delia. the average of their ages is nine years and four months. how old is each of them?1 solutions Answer 161632 by drj(1380)   on 2009-09-15 20:53:52 (Show Source): You can put this solution on YOUR website!Kirra is two years older then Reggie. Reggie is six times as old as Delia. the average of their ages is nine years and four months. how old is each of them? Step 1. Let x be the age of Delia. Let 6x be the age of Reggie. Let 6x+2 be the age of Kirra Step 2. Let Average ages be A= years where 4/12=1/3 (4 months = 1/3 year) Step 3. or Delia's age. Then Reggie's age Kirra's age Step 4. ANSWER: Delia is 2 years old, Reggie is 12 years old and Kirra is 14 years old. As a check the average 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
 Length-and-distance/213979: Find the coodinates of the missing endpoint given that S is the midpoint of RT. T(-4,3),S(-1,5)1 solutions Answer 161625 by drj(1380)   on 2009-09-15 20:31:14 (Show Source): You can put this solution on YOUR website!Find the coordinates of the missing endpoint given that S is the midpoint of RT. T(-4,3),S(-1,5) Step 1. Let (x,y) be the endpoint. So the average of the x and y coordinates for the endpoints will be the midpoint. The following steps will show this Step 2. The x-coordinate for the midpoint S is -1. Then Step 2. The y-coordinate for the midpoint S is 5. Then Step 3. ANSWER: So the endpoint is (2,7) Step 4. As a check the other endpoint is (-4,3). Then the midpoint is calculated as so the x-coordinate of the midpoint is -1 so the y-coordinate of the midpoint is 5 The midpoint is then (-1,5) which was given. So it checks out! 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
 Polynomials-and-rational-expressions/213941: factor the polynomials. x^2+ x-201 solutions Answer 161599 by drj(1380)   on 2009-09-15 19:50:55 (Show Source): You can put this solution on YOUR website!Factor the polynomials. Note we need to find two numbers A and B such that A*B=-20 and A+B=1. After trial and error like A=1, B=-20 or A=2 and B=-20 the numbers that satisfy these relationships are A=5 and B=-4. where . We can check our factoring by using the FOIL method as well. 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
(18/w^2) - (10/w) + 1 = 0
Do not convert to decimal form.
1 solutions

Answer 161582 by drj(1380)   on 2009-09-15 19:11:41 (Show Source):
You can put this solution on YOUR website!
Solve by using the quadratic formula.

Do not convert to decimal form.

Step 1. Multiply by to get rid of denominators

OR

Step 2. Using the quadratic formula

where a=1, b=-10 and c=18 yields the following steps

 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=28 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 7.64575131106459, 2.35424868893541. Here's your graph:

Step 4. Based on the above steps we can simplify the solutions as follows

AND

Step 5. ANSWER: So solutions are and

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

Numbers_Word_Problems/213912: find the three consecutive odd integers such that the sum of the first two odd integers exceeds the third by 9.
1 solutions

Answer 161572 by drj(1380)   on 2009-09-15 18:53:56 (Show Source):
You can put this solution on YOUR website!
Find the three consecutive odd integers such that the sum of the first two odd integers exceeds the third by 9.

Step 1. Let n be an odd integer, n+2 and n+4 be the next two consecutive odd integers.

Step 2. Let n+n+2 is the sum of the first two integers

Step 3. Then, n+n+2=n+4+9 Since the sum of n+n+2 is 9 more than the third integer given as n+4

Step 4. Solve the above equation using the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: n=11. Graphical form: Equation was fully solved.Text form: n+n+2=n+4+9 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( n+n+2=n+4+9 )` 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 .
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 .
Remove extraneous '1' from product
It becomes .

Look at .
Solved linear equation equivalent to n-11 =0
It becomes .
Result:
This is an equation! Solutions: n=11.

### Universal Simplifier and Solver

Done!

Step 5. ANSWER: So the integers are 11, 13 and 15.

Check 11+13=24 which is 9 more than 15. So it checks!

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

Rectangles/213908: the perimeter of this rectangle is 74cm with length x+2 and with 3x. a.form an equation for the perimeter of the rectangle. b.solve your equation to find the length and with of the rectangle
1 solutions

Answer 161569 by drj(1380)   on 2009-09-15 18:40:35 (Show Source):
You can put this solution on YOUR website!
The perimeter of this rectangle is 74 cm with length x+2 and width 3x.

a. Form an equation for the perimeter of the rectangle.

b. Solve your equation to find the length and width of the rectangle.

Step 1. The perimeter of a rectangle P is when all the lengths of all 4 sides of a rectangle are added up.

Step 2. So . ANSWER to (a) is P=74=8x+4.

Step 3. Solving the equation for the perimeter yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=8.75. Graphical form: Equation was fully solved.Text form: 74=8x+4 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 74=8x+4 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

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

Look at .
It becomes .

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

Look at .
Solved linear equation equivalent to -8*x+70 =0
It becomes .
Result:
This is an equation! Solutions: x=8.75.

### Universal Simplifier and Solver

Done!

Step 4. ANSWER to b: With x= then length is l=8.75+2=10.75 cm and width is 3(8.75)=26.25 cm. Note perimeter is P=2(10.75+26.25)= 2*37=74 cm.

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

Rectangles/213893: the length of a rectangle is 8in.more than its width.the perimeter of the rectangle is 24 in. what are the width and length of the rectangle?
1 solutions

Answer 161564 by drj(1380)   on 2009-09-15 18:21:10 (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 8in. more than its width.the perimeter of the rectangle is 24 in. what are the width and length of the rectangle?

Step 1. Let l be the length where l=w+8 where w is the width.

Step 2. Perimeter of a rectangle is when the lengths of all four sides are summed together. Let P be the perimeter.

Step 3. Then we have

Step 4. Solving the above equation for w yields

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: w=2. Graphical form: Equation was fully solved.Text form: 24=w+8+w+8+w+w simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 24=w+8+w+8+w+w )` 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 .
Moved to the right of expression
It becomes .

Look at .
Solved linear equation equivalent to -4*w+8 =0
It becomes .
Result:
This is an equation! Solutions: w=2.

### Universal Simplifier and Solver

Done!

Step 5. So width w=2 inches and length l=2+8=10 inches. Note Perimeter P=2(10+2)=24 inches

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J

(18/w^2) - (10/w) + 1 = 0
1 solutions

Answer 161562 by drj(1380)   on 2009-09-15 18:14:23 (Show Source):
You can put this solution on YOUR website!
Solve by using the quadratic formula.

Step 1. Multiply above equation by to get rid of the denominator terms.

or

 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=28 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 7.64575131106459, 2.35424868893541. Here's your graph:

Based on the above steps the solutions simplify the solutions as follows:

I hope the above steps were helpful.

And good luck in your studies!

Respectfully,
Dr J