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Sequences-and-series/213568: Please help me find 2 consecutive even integers whose sum is 217. The best I got was 106.6 and 108.8 but still fall short. I have these a lot and need to know how to find these with a simple math trick or formula. (Algebra 1) Thanks
1 solutions
Answer 161365 by drj(1380) About Me  on 2009-09-14 18:34:48 (Show Source):
You can put this solution on YOUR website!
Find 2 consecutive even integers whose sum is 217.

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

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

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

Step 4. Solving yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: n=107.5.
  • Graphical form: Equation 2n%2B2=217 was fully solved.
  • Text form: 2n+2=217 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2n%2B2=217+%29
    For tutors: simplify_cartoon( 2n+2=217 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2An%2B2=highlight_red%28+217+%29.
Moved these terms to the left highlight_green%28+-217+%29
It becomes 2%2An%2B2-highlight_green%28+217+%29=0.
Look at 2%2An%2Bhighlight_red%28+2+%29-highlight_red%28+217+%29=0.
Added fractions or integers together
It becomes 2%2An%2Bhighlight_green%28+-215+%29=0.
Look at 2%2An%2Bhighlight_red%28+-215+%29=0.
Removed extra sign in front of -215
It becomes 2%2An-highlight_green%28+215+%29=0.
Look at highlight_red%28+2%2An-215+%29=0.
Solved linear equation highlight_red%28+2%2An-215=0+%29 equivalent to 2*n-215 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=107.5.

Universal Simplifier and Solver


Done!



Step 5. ANSWER: NO SOLUTION

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

Inequalities/213581: 24 - 7n < 11n - 12
1 solutions
Answer 161358 by drj(1380) About Me  on 2009-09-14 18:18:56 (Show Source):
You can put this solution on YOUR website!
24+-+7n+%3C+11n+-+12

Step. 1. Add 7n+12 to both sides of equation to get n terms on right side and numbers on the left side of equation.
24+-+7n%2B7n%2B12+%3C+11n+-+12%2B7n%2B12

36%3C18n

Step 2. Divide by 18 to both sides of equation

36%2F18%3C18n%2F18

2%3Cn or n%3E2 Answer.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Trigonometry-basics/213539: find the distance between the lines with equations y=3x-9 and y = 3x - 4.
a)5/4
b)5 sqrt(10)/2
c)sqrt(10)/2
d)13 sqrt(10)/2
1 solutions
Answer 161347 by drj(1380) About Me  on 2009-09-14 17:38:58 (Show Source):
You can put this solution on YOUR website!
Find the distance between the lines with equations 3x - y = 9 and y = 3x - 4.
a)5/4
b)5 sqrt(10)/2
c) sqrt(10)/2
d) 13 sqrt(10)/2

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

graph%28+300%2C+400%2C+-5%2C+5%2C+-10%2C+10%2C+y=3x-9%2C+y=3x-4%29

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

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

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

y=-1%2Ax%2F3%2B4%2F3
Here a graph of the situation

graph%28+300%2C+400%2C+-5%2C+5%2C+-10%2C+10%2C+y=3x-4%2C+y=3x-9%2C+y=%28-x%2F3%29-4%29

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

y=%28-x%2F3%29-4

y=3x-9

The following steps will solve this system of equations


Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 1*y to the right, we get:
0.333333333333333%2Ax+=+-4+-+1%2Ay, or x+=+-4%2F0.333333333333333+-+1%2Ay%2F0.333333333333333. Substitute that
into another equation:
-3%2A%28-4%2F0.333333333333333+-+1%2Ay%2F0.333333333333333%29+%2B+1%5Cy+=+-9 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



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

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

d=sqrt%28%280-1.5%29%5E2%2B%28-4-%28-4.5%29%29%29

d=sqrt%282.25%2B0.25%29

d=sqrt%282.5%29=sqrt%2810%2F4%29%29

d=sqrt%2810%29%2F2

d=1.58

Step 7. The answer is c or 1.58.


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

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J



Quadratic_Equations/213552: how can i telln if a graph opens up or down by looking at the equation
1 solutions
Answer 161337 by drj(1380) About Me  on 2009-09-14 17:02:39 (Show Source):
You can put this solution on YOUR website!
How can I tell if a graph opens up or down by looking at the equation

For the quadratic equation: ax%5E2%2Bbx%2Bc=0 if a>0 it will open up. if a<0 it will open down.

Let's look at an example:

2x%5E2%2B4x%2B1=0 for a=2, b=2 and c=1

graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+2x%5E2%2B2x%2B1+%29

-2x%5E2%2B4x%2B1=0 for a=-2, b=2 and c=1

graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+-2x%5E2%2B2x%2B1+%29

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Linear-systems/213501: x+5/2+x-1/2=x-1/3
1 solutions
Answer 161299 by drj(1380) About Me  on 2009-09-14 15:11:21 (Show Source):
You can put this solution on YOUR website!
x%2B5%2F2%2Bx-1%2F2=x-1%2F3

The following steps solves the above equation:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=-2.33333333333333.
  • Graphical form: Equation x%2B5%2F2%2Bx-1%2F2=x-1%2F3 was fully solved.
  • Text form: x+5/2+x-1/2=x-1/3 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2B5%2F2%2Bx-1%2F2=x-1%2F3+%29
    For tutors: simplify_cartoon( x+5/2+x-1/2=x-1/3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%2Bhighlight_red%28+5%2F2+%29%2Bx-highlight_red%28+1%2F2+%29=x-1%2F3.
Added fractions or integers together
It becomes x%2Bhighlight_green%28+4%2F2+%29%2Bx=x-1%2F3.
Look at x%2Bhighlight_red%28+4%2F2+%29%2Bx=x-1%2F3.
Moved 4%2F2 to the right of expression
It becomes x%2Bx%2Bhighlight_green%28+4%2F2+%29=x-1%2F3.
Look at x%2Bx%2Bhighlight_red%28+4+%29%2Fhighlight_red%28+2+%29=x-1%2F3.
Factors 4 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes x%2Bx%2Bhighlight_green%28+2+%29%2Fhighlight_green%28+1+%29=x-1%2F3.
Look at x%2Bx%2B2%2Fhighlight_red%28+1+%29=x-1%2F3.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes x%2Bx%2B2=x-1%2F3.
Look at highlight_red%28+x+%29%2Bhighlight_red%28+x+%29%2B2=x-1%2F3.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x+%29 replacing them with highlight_green%28+%281%2B1%29%2Ax+%29
It becomes highlight_green%28+%281%2B1%29%2Ax+%29%2B2=x-1%2F3.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2Ax%2B2=x-1%2F3.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2Ax%2B2=x-1%2F3.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2Ax+%29%2B2=x-1%2F3.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2Ax%2B2=x-1%2F3.
Look at 2%2Ax%2B2=highlight_red%28+x-1%2F3+%29.
Moved these terms to the left highlight_green%28+-x+%29,highlight_green%28+1%2F3+%29
It becomes 2%2Ax%2B2-highlight_green%28+x+%29%2Bhighlight_green%28+1%2F3+%29=0.
Look at 2%2Ax%2Bhighlight_red%28+2+%29-x%2Bhighlight_red%28+1%2F3+%29=0.
Added fractions or integers together
It becomes 2%2Ax%2Bhighlight_green%28+7%2F3+%29-x=0.
Look at 2%2Ax%2Bhighlight_red%28+7%2F3+%29-x=0.
Moved 7%2F3 to the right of expression
It becomes 2%2Ax-x%2Bhighlight_green%28+7%2F3+%29=0.
Look at highlight_red%28+2%2Ax+%29-highlight_red%28+x+%29%2B7%2F3=0.
Eliminated similar terms highlight_red%28+2%2Ax+%29,highlight_red%28+-x+%29 replacing them with highlight_green%28+%282-1%29%2Ax+%29
It becomes highlight_green%28+%282-1%29%2Ax+%29%2B7%2F3=0.
Look at highlight_red%28+%282-1%29+%29%2Ax%2B7%2F3=0.
Remove extraneous '1' from product highlight_red%28+%282-1%29+%29
It becomes x%2B7%2F3=0.
Look at highlight_red%28+x%2B7%2F3+%29=0.
Solved linear equation highlight_red%28+x%2B7%2F3=0+%29 equivalent to x+2.33333333333333 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-2.33333333333333.

Universal Simplifier and Solver


Done!



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

Radicals/213509: what is the equation of the line with an undefined slope and x intercept =2
1 solutions
Answer 161297 by drj(1380) About Me  on 2009-09-14 15:06:59 (Show Source):
You can put this solution on YOUR website!
What is the equation of the line with an undefined slope and x intercept =2

Step 1. The general equation is y=mx+b where m is the slope and b is the y-intercept. The equation called the slope-intercept form.

Step 2. We are given that the x-intercept is 2 which means at x=2 then y=0.

Step 3. Substitute in the general equation to find b

y=mx%2Bb

0=m%282%29%2Bb

b=-2m

Step 4. With b=-2m substitute in equation of Step 1.

y=mx-2m OR y=m%28x-2%29 ANSWER

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Square-cubic-other-roots/213487: This question is from textbook
factor using the difference of two squares formula
x^2 - 100
1 solutions
Answer 161283 by drj(1380) About Me  on 2009-09-14 13:13:12 (Show Source):
You can put this solution on YOUR website!
Factor using the difference of two squares formula
x%5E2+-+100=+x%5E2-10%5E2=%28x-10%29%28x%2B10%29

ANSWER is (x-10)(x+10)

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Expressions-with-variables/213485: if 2t+(s-r)/3= t what is s in terms of r and t?
1 solutions
Answer 161281 by drj(1380) About Me  on 2009-09-14 13:11:26 (Show Source):
You can put this solution on YOUR website!
If 2t+(s-r)/3= t what is s in terms of r and t?

Step 1. Let's get rid of denominator by multiplying 3 to both sides of equation:

2t%2B%28s-r%29%2F3=+t

2%2A3%2At%2B%28s-r%29%2A3%2F3=+3%2At

6t%2B%28s-r%29=+3%2At

6t%2Bs-r=3t

Step 2. Add -6t+r to both sides of equation to get s.

6t%2Bs-r-6t%2Br=3t-6t%2Br

s=-3t%2Br ANSWER

Step 3. So s=-3t+r


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J





Distributive-associative-commutative-properties/213484: equivalent expression with out parentases -(-9+8y)
1 solutions
Answer 161279 by drj(1380) About Me  on 2009-09-14 13:01:03 (Show Source):
You can put this solution on YOUR website!
Equivalent expression with out parenthesis -(-9+8y)

Step 1. Think of the - sign outside the parenthesis as -1 and then distribute.

Step 2. -(-9+9y)=(-1)*(-9+8y)=(-1)*(-9)+(-1)*(8y)=9-8y

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Equations/213480: Suppose that the length of a certain rectangle is 9 meters less than two times its width. The perimeter of the rectangle is 42 meters. Find the length and width of the rectangle.
1 solutions
Answer 161277 by drj(1380) About Me  on 2009-09-14 12:55:48 (Show Source):
You can put this solution on YOUR website!
Suppose that the length of a certain rectangle is 9 meters less than two times its width. The perimeter of the rectangle is 42 meters. Find the length and width of the rectangle.

Step 1. Let l = 2w-9 be the length of rectangle and let w be the width

Step 2. Let P = 42 meters be the perimeter. Perimeter means adding the 4 sides of a rectangle. So,

P=2w-9%2B2w-9%2Bw%2Bw

P=6w-18

P=6w-18=42

Step 3. Add 18 to both sides of equation to get 4w by itself


P=6w%2B18-18=42%2B18

6w=60

Step 4. Divide 6 to both sides of equation

6w%2F6=60%2F6

w=+10+

Step 5. w = 10 meters is the width of the rectangle and length is 11 m since

l=2w-9=11

Check P=2w+2l=2(10)+2(11)=20+22=42 So w = 10 meters and l = 11 meters is the solution.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trig Vids please visit http://www.FreedomUniversity.TV/courses/Trigonometry

And GOOD LUCK in your studies!

Respectfully
Dr J

Linear_Equations_And_Systems_Word_Problems/213482: Which is a solution of -8x + 5 > 11?
PLEASE HELP ME WITH MY 2 QUESTIONS :) THANK YOU
1 solutions
Answer 161273 by drj(1380) About Me  on 2009-09-14 12:46:22 (Show Source):
You can put this solution on YOUR website!
Which is a solution of -8x + 5 > 11?

Step 1. Add 8x-11 to both sides of the equation.

Step 2. -8x+5+8x-11 > 11+8x-11 OR -6>8x

Step 3. Divide 8 on both sides to get x by itself

-6%2F8%3E8x%2F8

x%3E-6%2F8=-3%2F4

x%3E-3%2F4

x%3E-0.75

number_line%28+600%2C+-10%2C+10%2C+-0.75%2C+10%29

ANSWER: Where the solution goes from the red dot at -0.75 toward pass the green dot.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J





Travel_Word_Problems/213418: Bob leaves at 9am heading due north at 9mph. Tom leaves at 9:30am heading due south at 4mph. At what time will Bob and Tom be 10 miles apart?
1 solutions
Answer 161270 by drj(1380) About Me  on 2009-09-14 12:38:27 (Show Source):
You can put this solution on YOUR website!
Bob leaves at 9am heading due north at 9mph. Tom leaves at 9:30am heading due south at 4mph. At what time will Bob and Tom be 10 miles apart?

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

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

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

Step 4. But dBob+dTom = 10 miles

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

4.5%2B9t%2B4%2At=10 Solving this equation will yield the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: t=0.423076923076923.
  • Graphical form: Equation 4.5%2B9t%2B4%2At=10 was fully solved.
  • Text form: 4.5+9t+4*t=10 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4.5%2B9t%2B4%2At=10+%29
    For tutors: simplify_cartoon( 4.5+9t+4*t=10 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+4.5+%29%2B9%2At%2B4%2At=10.
Moved 4.5 to the right of expression
It becomes 9%2At%2B4%2At%2Bhighlight_green%28+4.5+%29=10.
Look at highlight_red%28+9%2At+%29%2Bhighlight_red%28+4%2At+%29%2B4.5=10.
Eliminated similar terms highlight_red%28+9%2At+%29,highlight_red%28+4%2At+%29 replacing them with highlight_green%28+%289%2B4%29%2At+%29
It becomes highlight_green%28+%289%2B4%29%2At+%29%2B4.5=10.
Look at %28highlight_red%28+9+%29%2Bhighlight_red%28+4+%29%29%2At%2B4.5=10.
Added fractions or integers together
It becomes %28highlight_green%28+13+%29%29%2At%2B4.5=10.
Look at highlight_red%28+%28highlight_red%28+13+%29%29%2At+%29%2B4.5=10.
Remove unneeded parentheses around factor highlight_red%28+13+%29
It becomes highlight_green%28+13+%29%2At%2B4.5=10.
Look at 13%2At%2B4.5=highlight_red%28+10+%29.
Moved these terms to the left highlight_green%28+-10+%29
It becomes 13%2At%2B4.5-highlight_green%28+10+%29=0.
Look at 13%2At%2Bhighlight_red%28+4.5+%29-highlight_red%28+10+%29=0.
Added fractions or integers together
It becomes 13%2At-highlight_green%28+55%2F10+%29=0.
Look at 13%2At-highlight_red%28+55+%29%2Fhighlight_red%28+10+%29=0.
Factors 55 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes 13%2At-highlight_green%28+11+%29%2Fhighlight_green%28+2+%29=0.
Look at highlight_red%28+13%2At-11%2F2+%29=0.
Solved linear equation highlight_red%28+13%2At-11%2F2=0+%29 equivalent to 13*t-5.5 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: t=0.423076923076923.

Universal Simplifier and Solver


Done!



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

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


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J





Linear-systems/213471: This question is from textbook Introductory and Intermediate Algebra
How to solve out 3/5t-1/10t=t-5/2
1 solutions
Answer 161269 by drj(1380) About Me  on 2009-09-14 12:20:36 (Show Source):
You can put this solution on YOUR website!
3t%2F5-t%2F10=t-5%2F2

The following steps will solve the above equation

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: t=5.
  • Graphical form: Equation 3t%2F5-t%2F10=t-5%2F2 was fully solved.
  • Text form: 3t/5-t/10=t-5/2 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3t%2F5-t%2F10=t-5%2F2+%29
    For tutors: simplify_cartoon( 3t/5-t/10=t-5/2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+3%2At%2F5+%29-highlight_red%28+t%2F10+%29=t-5%2F2.
Eliminated similar terms highlight_red%28+3%2At%2F5+%29,highlight_red%28+-t%2F10+%29 replacing them with highlight_green%28+%283%2A1%2F5-1%2F10%29%2At+%29
It becomes highlight_green%28+%283%2A1%2F5-1%2F10%29%2At+%29=t-5%2F2.
Look at %28highlight_red%28+3+%29%2Ahighlight_red%28+1+%29%2F5-1%2F10%29%2At=t-5%2F2.
Multiplied numerator integers
It becomes %28highlight_green%28+3+%29%2F5-1%2F10%29%2At=t-5%2F2.
Look at %28highlight_red%28+3%2F5+%29-highlight_red%28+1%2F10+%29%29%2At=t-5%2F2.
Added fractions or integers together
It becomes %28highlight_green%28+5%2F10+%29%29%2At=t-5%2F2.
Look at highlight_red%28+%28highlight_red%28+5%2F10+%29%29%2At+%29=t-5%2F2.
Remove unneeded parentheses around factor highlight_red%28+5+%29,highlight_red%28+1%2F10+%29
It becomes highlight_green%28+5+%29%2Fhighlight_green%28+10+%29%2At=t-5%2F2.
Look at highlight_red%28+5+%29%2Fhighlight_red%28+10+%29%2At=t-5%2F2.
Factors 5 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes highlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2At=t-5%2F2.
Look at highlight_red%28+1+%29%2F2%2At=t-5%2F2.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes t%2F2=t-5%2F2.
Look at t%2F2=highlight_red%28+t-5%2F2+%29.
Moved these terms to the left highlight_green%28+-t+%29,highlight_green%28+5%2F2+%29
It becomes t%2F2-highlight_green%28+t+%29%2Bhighlight_green%28+5%2F2+%29=0.
Look at highlight_red%28+t%2F2+%29-highlight_red%28+t+%29%2B5%2F2=0.
Eliminated similar terms highlight_red%28+t%2F2+%29,highlight_red%28+-t+%29 replacing them with highlight_green%28+%281%2F2-1%29%2At+%29
It becomes highlight_green%28+%281%2F2-1%29%2At+%29%2B5%2F2=0.
Look at %28highlight_red%28+1%2F2+%29-highlight_red%28+1+%29%29%2At%2B5%2F2=0.
Added fractions or integers together
It becomes %28-highlight_green%28+1%2F2+%29%29%2At%2B5%2F2=0.
Look at highlight_red%28+%28-highlight_red%28+1%2F2+%29%29%2At+%29%2B5%2F2=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F2+%29
It becomes -highlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2At%2B5%2F2=0.
Look at -highlight_red%28+1+%29%2F2%2At%2B5%2F2=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -t%2F2%2B5%2F2=0.
Look at highlight_red%28+-t%2F2%2B5%2F2+%29=0.
Solved linear equation highlight_red%28+-t%2F2%2B5%2F2=0+%29 equivalent to -0.5*t+2.5 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: t=5.

Universal Simplifier and Solver


Done!



I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Square-cubic-other-roots/213474: I do not know how to enter a square root symbol on the computer so I will just put into words.
multiply property of radicals to simplify
square root of 20xy^6z^3
1 solutions
Answer 161268 by drj(1380) About Me  on 2009-09-14 12:18:39 (Show Source):
You can put this solution on YOUR website!
Multiply property of radicals to simplify

sqrt%2820xy%5E6z%5E3%29

sqrt%2820xy%5E6z%5E3%29=sqrt%284%2A5x%2A%28y%5E3%29%5E2%2A6z%5E2%2Az%29


sqrt%2820xy%5E6z%5E3%29=2%2Ay%5E3%2Az%2Asqrt%285x%2A6%2Az%29 where sqrt%284%29=2, sqrt%28%28y%5E3%29%5E2%29=y%5E3, and sqrt%28z%5E2%29=z

sqrt%2820xy%5E6z%5E3%29=%282y%5E3z%29sqrt%2830xz%29 ANSWER


I hope the above steps were helpful.

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Square-cubic-other-roots/213475: I don't know how to enter the square root symbol on the computer so I am just going to put into words.
MULTIPLY PROPERTY OF RADICALS TO SIMPLIFY
5 square root of 18
1 solutions
Answer 161266 by drj(1380) About Me  on 2009-09-14 12:02:17 (Show Source):
You can put this solution on YOUR website!
USE MULTIPLY PROPERTY OF RADICALS TO SIMPLIFY
5 square root of 18
5%2Asqrt%2818%29=5%2Asqrt%289%2A2%29=5%2A3%2Asqrt%282%29=15%2Asqrt%282%29

ANSWER is 15sqrt%282%29


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

expressions/213470: This question is from textbook
solve. 7x - 3(4 - 2x)= 2(x-3)- (5-x)
1 solutions
Answer 161265 by drj(1380) About Me  on 2009-09-14 11:58:57 (Show Source):
You can put this solution on YOUR website!
7x - 3(4 - 2x)= 2(x-3)- (5-x)

The following steps will simplify and solve the above equation.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=0.1.
  • Graphical form: Equation 7x-3%2A%284-2x%29=2%2A%28x-3%29-%285-x%29 was fully solved.
  • Text form: 7x-3*(4-2x)=2*(x-3)-(5-x) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+7x-3%2A%284-2x%29=2%2A%28x-3%29-%285-x%29+%29
    For tutors: simplify_cartoon( 7x-3*(4-2x)=2*(x-3)-(5-x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 7%2Ax-3%2A%28highlight_red%28+4+%29-2%2Ax%29=2%2A%28x-3%29-%285-x%29.
Moved 4 to the right of expression
It becomes 7%2Ax-3%2A%28-2%2Ax%2Bhighlight_green%28+4+%29%29=2%2A%28x-3%29-%285-x%29.
Look at 7%2Ax-3%2A%28-2%2Ax%2B4%29=2%2A%28x-3%29-highlight_red%28+%285-x%29+%29.
Remove unneeded parentheses around terms highlight_red%28+-5+%29,highlight_red%28+x+%29
It becomes 7%2Ax-3%2A%28-2%2Ax%2B4%29=2%2A%28x-3%29-highlight_green%28+5+%29%2Bhighlight_green%28+x+%29.
Look at 7%2Ax-3%2A%28-2%2Ax%2B4%29=2%2A%28x-3%29-highlight_red%28+5+%29%2Bx.
Moved -5 to the right of expression
It becomes 7%2Ax-3%2A%28-2%2Ax%2B4%29=2%2A%28x-3%29%2Bx-highlight_green%28+5+%29.
Look at 7%2Ax-3%2A%28-2%2Ax%2B4%29=highlight_red%28+2%2A%28x-3%29%2Bx-5+%29.
Moved these terms to the left highlight_green%28+-2%2A%28x-3%29+%29,highlight_green%28+-x+%29,highlight_green%28+5+%29
It becomes .
Look at highlight_red%28+7%2Ax+%29-3%2A%28-2%2Ax%2B4%29-2%2A%28x-3%29-highlight_red%28+x+%29%2B5=0.
Eliminated similar terms highlight_red%28+7%2Ax+%29,highlight_red%28+-x+%29 replacing them with highlight_green%28+%287-1%29%2Ax+%29
It becomes highlight_green%28+%287-1%29%2Ax+%29-3%2A%28-2%2Ax%2B4%29-2%2A%28x-3%29%2B5=0.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Ax-3%2A%28-2%2Ax%2B4%29-2%2A%28x-3%29%2B5=0.
Look at .
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Ax-3%2A%28-2%2Ax%2B4%29-2%2A%28x-3%29%2B5=0.
Look at 6%2Ax-highlight_red%28+3%2A%28-2%2Ax%2B4%29+%29-2%2A%28x-3%29%2B5=0.
Expanded term -3 by using associative property on %28-2%2Ax%2B4%29
It becomes 6%2Ax%2Bhighlight_green%28+3%2A2%2Ax+%29-highlight_green%28+3%2A4+%29-2%2A%28x-3%29%2B5=0.
Look at 6%2Ax%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+2+%29%2Ax-3%2A4-2%2A%28x-3%29%2B5=0.
Multiplied numerator integers
It becomes 6%2Ax%2Bhighlight_green%28+6+%29%2Ax-3%2A4-2%2A%28x-3%29%2B5=0.
Look at 6%2Ax%2B6%2Ax-highlight_red%28+3+%29%2Ahighlight_red%28+4+%29-2%2A%28x-3%29%2B5=0.
Multiplied numerator integers
It becomes 6%2Ax%2B6%2Ax-highlight_green%28+12+%29-2%2A%28x-3%29%2B5=0.
Look at 6%2Ax%2B6%2Ax-highlight_red%28+12+%29-2%2A%28x-3%29%2Bhighlight_red%28+5+%29=0.
Added fractions or integers together
It becomes 6%2Ax%2B6%2Ax%2Bhighlight_green%28+-7+%29-2%2A%28x-3%29=0.
Look at 6%2Ax%2B6%2Ax%2Bhighlight_red%28+-7+%29-2%2A%28x-3%29=0.
Moved -7 to the right of expression
It becomes 6%2Ax%2B6%2Ax-2%2A%28x-3%29%2Bhighlight_green%28+-7+%29=0.
Look at 6%2Ax%2B6%2Ax-2%2A%28x-3%29%2Bhighlight_red%28+-7+%29=0.
Removed extra sign in front of -7
It becomes 6%2Ax%2B6%2Ax-2%2A%28x-3%29-highlight_green%28+7+%29=0.
Look at highlight_red%28+6%2Ax+%29%2Bhighlight_red%28+6%2Ax+%29-2%2A%28x-3%29-7=0.
Eliminated similar terms highlight_red%28+6%2Ax+%29,highlight_red%28+6%2Ax+%29 replacing them with highlight_green%28+%286%2B6%29%2Ax+%29
It becomes highlight_green%28+%286%2B6%29%2Ax+%29-2%2A%28x-3%29-7=0.
Look at %28highlight_red%28+6+%29%2Bhighlight_red%28+6+%29%29%2Ax-2%2A%28x-3%29-7=0.
Added fractions or integers together
It becomes %28highlight_green%28+12+%29%29%2Ax-2%2A%28x-3%29-7=0.
Look at highlight_red%28+%28highlight_red%28+12+%29%29%2Ax+%29-2%2A%28x-3%29-7=0.
Remove unneeded parentheses around factor highlight_red%28+12+%29
It becomes highlight_green%28+12+%29%2Ax-2%2A%28x-3%29-7=0.
Look at 12%2Ax-highlight_red%28+2%2A%28x-3%29+%29-7=0.
Expanded term -2 by using associative property on %28x-3%29
It becomes 12%2Ax-highlight_green%28+2%2Ax+%29%2Bhighlight_green%28+2%2A3+%29-7=0.
Look at 12%2Ax-2%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+3+%29-7=0.
Multiplied numerator integers
It becomes 12%2Ax-2%2Ax%2Bhighlight_green%28+6+%29-7=0.
Look at 12%2Ax-2%2Ax%2Bhighlight_red%28+6+%29-highlight_red%28+7+%29=0.
Added fractions or integers together
It becomes 12%2Ax-2%2Ax%2Bhighlight_green%28+-1+%29=0.
Look at 12%2Ax-2%2Ax%2Bhighlight_red%28+-1+%29=0.
Removed extra sign in front of -1
It becomes 12%2Ax-2%2Ax-highlight_green%28+1+%29=0.
Look at highlight_red%28+12%2Ax+%29-highlight_red%28+2%2Ax+%29-1=0.
Eliminated similar terms highlight_red%28+12%2Ax+%29,highlight_red%28+-2%2Ax+%29 replacing them with highlight_green%28+%2812-2%29%2Ax+%29
It becomes highlight_green%28+%2812-2%29%2Ax+%29-1=0.
Look at %28highlight_red%28+12+%29-highlight_red%28+2+%29%29%2Ax-1=0.
Added fractions or integers together
It becomes %28highlight_green%28+10+%29%29%2Ax-1=0.
Look at highlight_red%28+%28highlight_red%28+10+%29%29%2Ax+%29-1=0.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes highlight_green%28+10+%29%2Ax-1=0.
Look at highlight_red%28+10%2Ax-1+%29=0.
Solved linear equation highlight_red%28+10%2Ax-1=0+%29 equivalent to 10*x-1 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=0.1.

Universal Simplifier and Solver


Done!





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/213467: A pitcher can throw a baseball 95 miles per hour. The ball travels at that speed for 56 feet, until it arrives at the batter. How many seconds, correct to the nearest thousandth of a second, does the batter have from the moment the ball is thrown, until it arrives.
1 solutions
Answer 161261 by drj(1380) About Me  on 2009-09-14 11:26:07 (Show Source):
You can put this solution on YOUR website!
A pitcher can throw a baseball 95 miles per hour. The ball travels at that speed for 56 feet, until it arrives at the batter. How many seconds, correct to the nearest thousandth of a second, does the batter have from the moment the ball is thrown, until it arrives

Step 1. Time+=+Distance%2FSpeed

Step 2. Time = 95 mph/56 feet * (5280 feet/mile) (1 hour/3600 seconds) = 2.488 seconds = 2.5 seconds.

where 1 mile = 5280 feet, 1 hour = 60 minutes = 3600 seconds

Step 3. Answer is 2.5 seconds.


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Travel_Word_Problems/213469: Marc drives 420 miles in 7 hours. What is his average speed in mph?
1 solutions
Answer 161259 by drj(1380) About Me  on 2009-09-14 11:21:02 (Show Source):
You can put this solution on YOUR website!
Marc drives 420 miles in 7 hours. What is his average speed in mph?

Step 1. speed=%28distance%2Ftime%29

Step 2 speed = 420 miles/7 hours = 60 mile per hour = 60 mph


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Miscellaneous_Word_Problems/213411: #20
FIND THREE CONSECUTIVE ODD INTEGERS SUCH THAT FOUR TIMES THE MIDDLE INTEGER IS TWICE THE SUM OF THE OTHER TWO INTEGERS
1 solutions
Answer 161258 by drj(1380) About Me  on 2009-09-14 11:19:07 (Show Source):
You can put this solution on YOUR website!
FIND THREE CONSECUTIVE ODD INTEGERS SUCH THAT FOUR TIMES THE MIDDLE INTEGER IS TWICE THE SUM OF THE OTHER TWO INTEGERS

Step 1. Let n be an odd integer, n+2 be the next consecutive odd or middle integer, and n+4 be the second consecutive odd integer

Step 2. 4(n+2)=2(n+n+4) since middle integer is twice the sum of n+n+4

4%28n%2B2%29=2%282n%2B4%29

4n%2B8=4n%2B8

0=0

Step 3. The above result means any 3 consecutive odd integers will satisfy the above equation or problem statement. For example,

1, 3, 5 implies 4(3)=2(1+5) or 12=12

3, 5, 7 implies 4(5)=2(3+7) or 20=20

5, 7, 9 implies 4(7)=2(5+9) or 28=28


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Travel_Word_Problems/213465: A car travels at a speed of 47 mph. How far would it travel in 6 hours?
1 solutions
Answer 161254 by drj(1380) About Me  on 2009-09-14 11:06:11 (Show Source):
You can put this solution on YOUR website!
A car travels at a speed of 47 mph. How far would it travel in 6 hours?

Step 1. Distance = speed * time or d=s*t

Step 2. Distance = (47 miles/hour)(6 hours)= 282 miles (ANSWER)

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Polynomials-and-rational-expressions/213464: q=10-2p
q=20+3p
1 solutions
Answer 161253 by drj(1380) About Me  on 2009-09-14 11:03:45 (Show Source):
You can put this solution on YOUR website!
q=10-2p
q=20%2B3p

Set above equations to be equal q=q

10-2p=20%2B3p

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: p=-2.
  • Graphical form: Equation 10-2p=20%2B3p was fully solved.
  • Text form: 10-2p=20+3p simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+10-2p=20%2B3p+%29
    For tutors: simplify_cartoon( 10-2p=20+3p )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+10+%29-2%2Ap=20%2B3p.
Moved 10 to the right of expression
It becomes -2%2Ap%2Bhighlight_green%28+10+%29=20%2B3p.
Look at -2%2Ap%2B10=highlight_red%28+20+%29%2B3%2Ap.
Moved 20 to the right of expression
It becomes -2%2Ap%2B10=3%2Ap%2Bhighlight_green%28+20+%29.
Look at -2%2Ap%2B10=highlight_red%28+3%2Ap%2B20+%29.
Moved these terms to the left highlight_green%28+-3%2Ap+%29,highlight_green%28+-20+%29
It becomes -2%2Ap%2B10-highlight_green%28+3%2Ap+%29-highlight_green%28+20+%29=0.
Look at -2%2Ap%2Bhighlight_red%28+10+%29-3%2Ap-highlight_red%28+20+%29=0.
Added fractions or integers together
It becomes -2%2Ap%2Bhighlight_green%28+-10+%29-3%2Ap=0.
Look at -2%2Ap%2Bhighlight_red%28+-10+%29-3%2Ap=0.
Moved -10 to the right of expression
It becomes -2%2Ap-3%2Ap%2Bhighlight_green%28+-10+%29=0.
Look at -2%2Ap-3%2Ap%2Bhighlight_red%28+-10+%29=0.
Removed extra sign in front of -10
It becomes -2%2Ap-3%2Ap-highlight_green%28+10+%29=0.
Look at -highlight_red%28+2%2Ap+%29-highlight_red%28+3%2Ap+%29-10=0.
Eliminated similar terms highlight_red%28+-2%2Ap+%29,highlight_red%28+-3%2Ap+%29 replacing them with highlight_green%28+%28-2-3%29%2Ap+%29
It becomes highlight_green%28+%28-2-3%29%2Ap+%29-10=0.
Look at %28-highlight_red%28+2+%29-highlight_red%28+3+%29%29%2Ap-10=0.
Added fractions or integers together
It becomes %28highlight_green%28+-5+%29%29%2Ap-10=0.
Look at %28highlight_red%28+-5+%29%29%2Ap-10=0.
Removed extra sign in front of -5
It becomes %28-highlight_green%28+5+%29%29%2Ap-10=0.
Look at highlight_red%28+%28-highlight_red%28+5+%29%29%2Ap+%29-10=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes -highlight_green%28+5+%29%2Ap-10=0.
Look at highlight_red%28+-5%2Ap-10+%29=0.
Solved linear equation highlight_red%28+-5%2Ap-10=0+%29 equivalent to -5*p-10 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: p=-2.

Universal Simplifier and Solver


Done!



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


I hope the above steps were helpful.

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.

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Respectfully,
Dr J

Triangles/213461: The second angle of a triangular kite is four times as large as the first. The third angle is 5 more than the sum of the other two angles. Find the measure of the second angle.
1 solutions
Answer 161252 by drj(1380) About Me  on 2009-09-14 10:55:58 (Show Source):
You can put this solution on YOUR website!
The second angle of a triangular kite is four times as large as the first. The third angle is 5 more than the sum of the other two angles. Find the measure of the second angle.

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

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

a%2B4a%2B5%2B5a=180

The following steps solve the above equation.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: a=17.5.
  • Graphical form: Equation a%2B4a%2B5%2B5a=180 was fully solved.
  • Text form: a+4a+5+5a=180 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+a%2B4a%2B5%2B5a=180+%29
    For tutors: simplify_cartoon( a+4a+5+5a=180 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at a%2B4%2Aa%2Bhighlight_red%28+5+%29%2B5%2Aa=180.
Moved 5 to the right of expression
It becomes a%2B4%2Aa%2B5%2Aa%2Bhighlight_green%28+5+%29=180.
Look at highlight_red%28+a+%29%2Bhighlight_red%28+4%2Aa+%29%2Bhighlight_red%28+5%2Aa+%29%2B5=180.
Eliminated similar terms highlight_red%28+a+%29,highlight_red%28+4%2Aa+%29,highlight_red%28+5%2Aa+%29 replacing them with highlight_green%28+%281%2B4%2B5%29%2Aa+%29
It becomes highlight_green%28+%281%2B4%2B5%29%2Aa+%29%2B5=180.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%2Bhighlight_red%28+5+%29%29%2Aa%2B5=180.
Added fractions or integers together
It becomes %28highlight_green%28+10+%29%29%2Aa%2B5=180.
Look at highlight_red%28+%28highlight_red%28+10+%29%29%2Aa+%29%2B5=180.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes highlight_green%28+10+%29%2Aa%2B5=180.
Look at 10%2Aa%2B5=highlight_red%28+180+%29.
Moved these terms to the left highlight_green%28+-180+%29
It becomes 10%2Aa%2B5-highlight_green%28+180+%29=0.
Look at 10%2Aa%2Bhighlight_red%28+5+%29-highlight_red%28+180+%29=0.
Added fractions or integers together
It becomes 10%2Aa%2Bhighlight_green%28+-175+%29=0.
Look at 10%2Aa%2Bhighlight_red%28+-175+%29=0.
Removed extra sign in front of -175
It becomes 10%2Aa-highlight_green%28+175+%29=0.
Look at highlight_red%28+10%2Aa-175+%29=0.
Solved linear equation highlight_red%28+10%2Aa-175=0+%29 equivalent to 10*a-175 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: a=17.5.

Universal Simplifier and Solver


Done!




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/213412: #11
SIMPLIFY
(2.1)(0.6)(-3.5)



1 solutions
Answer 161251 by drj(1380) About Me  on 2009-09-14 10:34:16 (Show Source):
You can put this solution on YOUR website!
SIMPLIFY (2.1)(0.6)(-3.5)
ANSWER %282.1%29%2A%280.6%29%2A%28-3.5%29=%2812.6%29%2A%28-3.5%29=+-44.1

I hope the above steps were helpful.

And good luck in your studies!

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

Respectfully,
Dr J

Volume/213419: What is the volume of a paper cup with a diameter of 2 inches and 5 tall converted to centimeters.
1 solutions
Answer 161250 by drj(1380) About Me  on 2009-09-14 10:30:31 (Show Source):
You can put this solution on YOUR website!
What is the volume of a paper cup with a diameter of 2 inches and 5 tall converted to centimeters.

Step 1. Note that 1 inch = 2.54 centimeters.

Step 2. Assume Volume of cup is equal to volume of cylinder.

Step 3. Volume of cylinder V=pi%2A%28d%2F2%29%5E2%2Ah where d/2 is the radius, d is the diameter, h is the height

V=pi%2A%282%2F2%29%5E2%2A5

V=pi%2A5 in%5E3

Step 4. 1 inch cube = (2.54)^3 centimeters cube or 16.387 cm^3. So

V=pi%2A5%2A16.387

V=+pi%2A81.935=257.41 cubic centimeters ANSWER

I hope the above steps were helpful.

And good luck in your studies!

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

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Dr J






Length-and-distance/213430: A box measures 1 metre X 1 metre X 1 metre. What would a box need to measure to hold twice the volume of this box?
1 solutions
Answer 161248 by drj(1380) About Me  on 2009-09-14 10:22:29 (Show Source):
You can put this solution on YOUR website!
A box measures 1 metre X 1 metre X 1 metre. What would a box need to measure to hold twice the volume of this box?

Volume of the box is V=s^3 where s is the edge of the box and they are equal in this case.

Given V=2 means that

V=2=s%5E3

s=2%5E%281%2F3%29=1.26

Therefore, to get twice the volume the dimensions of the box would be 1.26 metre x 1.26 metre x 1.26 metre


I hope the above steps were helpful.

And good luck in your studies!

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

Respectfully,
Dr J

Quadratic_Equations/213428: f(x)=-3x^2 make a table and a graph

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

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

Here's the graph:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B0x%2B0+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A-3%2A0=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%280%29%29%2F2%5C-3.
Expression can be factored: -3x%5E2%2B0x%2B0+=+-3%28x--0%29%2A%28x--0%29

Again, the answer is: -0, -0. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B0%2Ax%2B0+%29



Note: The vertex is (0,0)

I hope the above steps were helpful.

And good luck in your studies!

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

Respectfully,
Dr J

Inequalities/213454: please help me solve y=-x%2B3
1 solutions
Answer 161242 by drj(1380) About Me  on 2009-09-14 10:11:42 (Show Source):
You can put this solution on YOUR website!
Please help me solve y=-x%2B3

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

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

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 1+x+%2B+1+y+=+3 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 3/1 = 3.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 3/1 = 3.
  • Slope is -1/1 = -1.
  • Equation in slope-intercept form: y=-1*x+3.
graph%28+500%2C+500%2C+3-8%2C+3%2B8%2C+3-8%2C+3%2B8%2C+-1%2Ax%2B3+%29+



I hope the above steps were helpful.

And good luck in your studies!

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

Respectfully,
Dr J

Angles/213452: An angle is equal to 5 times its complement,determine its measure ?
1 solutions
Answer 161233 by drj(1380) About Me  on 2009-09-14 09:33:16 (Show Source):
You can put this solution on YOUR website!
An angle is equal to 5 times its complement,determine its measure ?

Step 1. Complementary angles are those angles when they add up to 90 degrees.

Step 2. Let x be the angle and let 5x be its complement.

Step 3. Then

x%2B5x=90

6x=90

Divide by 6 to both sides of equation to get x

6x%2F6=90%2F6

x=15

Step 4. The angle is 15 degrees and its complement is 75 degrees.


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Respectfully,
Dr J

Bodies-in-space/213431: This question is from textbook
Find the ratio, reduced to lowest terms, of the volume of a sphere with a radius of 3 inches to the volume of a sphere with a radius of 6 inches
1 solutions
Answer 161230 by drj(1380) About Me  on 2009-09-14 09:28:39 (Show Source):
You can put this solution on YOUR website!
Find the ratio, reduced to lowest terms, of the volume of a sphere with a radius of 3 inches to the volume of a sphere with a radius of 6 inches

Step 1. Let V1=4pi%2Ar1%5E3%2F3 and V2=4pi%2Ar2%5E3%2F3 where V1 volume of Sphere 1 with radius r1=3 and V2 volume of Sphere 2 with radius r2=6. And pi=3.14159

Step 2. Now find V1/V2

V1%2FV2=%284pi%28r1%29%5E3%2F3%29%2F%284pi%28r2%29%5E3%2F3%29

V1%2FV2=r1%5E3%2Fr2%5E3=%28r1%2Fr2%29%5E3

V1%2FV2=%283%2F6%29%5E3=%281%2F2%29%5E3

V1%2FV2=1%2F8


I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J

Quadratic_Equations/213435: Divide: (4 + 2i)/ (4 – 2i)
I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. Thankyou for you time. Your are appreshated.
1 solutions
Answer 161226 by drj(1380) About Me  on 2009-09-14 09:20:28 (Show Source):
You can put this solution on YOUR website!
Divide: %284%2B2i%29%2F+%284-2i%29

Step 1. Multiply by 1 where %284%2B2i%29%2F%284%2B2i%29=1 so that the denominator is not complex.

Step 2. This will result in the following steps

%284%2B2i%29%2F%284-2i%29=%28%284%2B2i%29%2F%284-2i%29%29%2A%284%2B2i%29%2F%284%2B2i%29

Now the denominator will be

%284-2i%29%284%2B2i%29=%284%29%284%29-%284%29%282i%29%2B%282i%29%284%29-%282i%29%282i%29

%284-2i%29%284%2B2i%29=16-%284%29i%5E2=16-4%2A%28-1%29%29=20 where i=sqrt%28-1%29

%284%2B2i%29%2F%284-2i%29=%284%2B2i%29%2A%284%2B2i%29%2F20

Now the numerator will be

%284+%2B+2i%29%5E2=16%2B2i%2B2i%2B4i%5E2=16-4%2B4i=12%2B4i

%284%2B2i%29%2F%284-2i%29=%2812%2B4i%29%2F20=%283%2Bi%29%2F5


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Quadratic_Equations/213438: (x^2⁄2)- 4 – 6x = - 4
I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. Thankyou for you time. Your are appreshated.
1 solutions
Answer 161220 by drj(1380) About Me  on 2009-09-14 09:02:53 (Show Source):
You can put this solution on YOUR website!
%28x%5E2%29%2F2-4%966x=-4+

The following steps will simplify and solve the equation.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=12,x=0.
  • Graphical form: Equation %28x%5E2%29%2F2-4-6x=-4 was fully solved.
  • Text form: (x^2)/2-4-6x=-4 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%28x%5E2%29%2F2-4-6x=-4+%29
    For tutors: simplify_cartoon( (x^2)/2-4-6x=-4 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28highlight_red%28+x%5E2+%29%29%2F2+%29-4-6%2Ax=-4.
Remove unneeded parentheses around factor highlight_red%28+x%5E2+%29
It becomes highlight_green%28+x%5E2+%29%2F2-4-6%2Ax=-4.
Look at x%5E2%2F2-highlight_red%28+4+%29-6%2Ax=-4.
Moved -4 to the right of expression
It becomes x%5E2%2F2-6%2Ax-highlight_green%28+4+%29=-4.
Look at x%5E2%2F2-6%2Ax-4=highlight_red%28+-4+%29.
Moved these terms to the left highlight_green%28+4+%29
It becomes x%5E2%2F2-6%2Ax-4%2Bhighlight_green%28+4+%29=0.
Look at x%5E2%2F2-6%2Ax-highlight_red%28+4+%29%2Bhighlight_red%28+4+%29=0.
Added fractions or integers together
It becomes x%5E2%2F2-6%2Ax%2Bhighlight_green%28+0+%29=0.
Look at x%5E2%2F2-6%2Ax%2Bhighlight_red%28+0+%29=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes x%5E2%2F2-6%2Ax=0.
Look at highlight_red%28+x%5E2%2F2-6%2Ax+%29=0.
Equation highlight_red%28+x%5E2%2F2-6%2Ax=0+%29 is a quadratic equation: 0.5*x^2-6*x =0, and has solutions 12,0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=12,x=0.

Universal Simplifier and Solver


Done!



You can also use the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1/2, b=-6, and c=0

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.5x%5E2%2B-6x%2B0+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A0.5%2A0=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+36+%29%29%2F2%5C0.5+=+12
x%5B2%5D+=+%28-%28-6%29-sqrt%28+36+%29%29%2F2%5C0.5+=+0

Quadratic expression 0.5x%5E2%2B-6x%2B0 can be factored:
0.5x%5E2%2B-6x%2B0+=+0.5%28x-12%29%2A%28x-0%29
Again, the answer is: 12, 0. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.5%2Ax%5E2%2B-6%2Ax%2B0+%29



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