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Linear-equations/215918: 7y=6y+1
1 solutions
Answer 163100 by drj(1380) About Me  on 2009-09-23 00:24:03 (Show Source):
You can put this solution on YOUR website!
7y=6y%2B1

Subtract 6y to both sides of the equation.

7y-6y=6y%2B1-6y

y=1

Check. 7*1=6*1+1 or 7=7 which is a true statement.

y=1 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

Angles/215898: Five times the complement of an angle less twice the angle's supplement is 40 degrees. Find the measure of the supplement.
1 solutions
Answer 163099 by drj(1380) About Me  on 2009-09-23 00:18:39 (Show Source):
You can put this solution on YOUR website!
Five times the complement of an angle less twice the angle's supplement is 40 degrees. Find the measure of the supplement.

Step 1. Complementary angles means two angles add up to 90 degrees.

Step 2. Supplementary angles means two angles add up to 180 degrees.

Step 3. Let x be the angle, let 90-x be its complement, let 180-x be its supplement.

Step 4. Let 5(90-x) be five times the complement and 2(180-x) be twice the supplement.

Step 5. Five times the complement of an angle less twice the angle's supplement is 40 degrees is translated as

5%2890-x%29-2%28180-x%29=40

The following will solve this 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=16.6666666666667.
  • Graphical form: Equation 5%2A%2890-x%29-2%2A%28180-x%29=40 was fully solved.
  • Text form: 5*(90-x)-2*(180-x)=40 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5%2A%2890-x%29-2%2A%28180-x%29=40+%29
    For tutors: simplify_cartoon( 5*(90-x)-2*(180-x)=40 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2A%28highlight_red%28+90+%29-x%29-2%2A%28180-x%29=40.
Moved 90 to the right of expression
It becomes 5%2A%28-x%2Bhighlight_green%28+90+%29%29-2%2A%28180-x%29=40.
Look at 5%2A%28-x%2B90%29-2%2A%28highlight_red%28+180+%29-x%29=40.
Moved 180 to the right of expression
It becomes 5%2A%28-x%2B90%29-2%2A%28-x%2Bhighlight_green%28+180+%29%29=40.
Look at 5%2A%28-x%2B90%29-2%2A%28-x%2B180%29=highlight_red%28+40+%29.
Moved these terms to the left highlight_green%28+-40+%29
It becomes 5%2A%28-x%2B90%29-2%2A%28-x%2B180%29-highlight_green%28+40+%29=0.
Look at highlight_red%28+5%2A%28-x%2B90%29+%29-2%2A%28-x%2B180%29-40=0.
Expanded term 5 by using associative property on %28-x%2B90%29
It becomes -highlight_green%28+5%2Ax+%29%2Bhighlight_green%28+5%2A90+%29-2%2A%28-x%2B180%29-40=0.
Look at -5%2Ax%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+90+%29-2%2A%28-x%2B180%29-40=0.
Multiplied numerator integers
It becomes -5%2Ax%2Bhighlight_green%28+450+%29-2%2A%28-x%2B180%29-40=0.
Look at -5%2Ax%2Bhighlight_red%28+450+%29-2%2A%28-x%2B180%29-highlight_red%28+40+%29=0.
Added fractions or integers together
It becomes -5%2Ax%2Bhighlight_green%28+410+%29-2%2A%28-x%2B180%29=0.
Look at -5%2Ax%2Bhighlight_red%28+410+%29-2%2A%28-x%2B180%29=0.
Moved 410 to the right of expression
It becomes -5%2Ax-2%2A%28-x%2B180%29%2Bhighlight_green%28+410+%29=0.
Look at -5%2Ax-highlight_red%28+2%2A%28-x%2B180%29+%29%2B410=0.
Expanded term -2 by using associative property on %28-x%2B180%29
It becomes -5%2Ax%2Bhighlight_green%28+2%2Ax+%29-highlight_green%28+2%2A180+%29%2B410=0.
Look at -5%2Ax%2B2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+180+%29%2B410=0.
Multiplied numerator integers
It becomes -5%2Ax%2B2%2Ax-highlight_green%28+360+%29%2B410=0.
Look at -5%2Ax%2B2%2Ax-highlight_red%28+360+%29%2Bhighlight_red%28+410+%29=0.
Added fractions or integers together
It becomes -5%2Ax%2B2%2Ax%2Bhighlight_green%28+50+%29=0.
Look at -highlight_red%28+5%2Ax+%29%2Bhighlight_red%28+2%2Ax+%29%2B50=0.
Eliminated similar terms highlight_red%28+-5%2Ax+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%28-5%2B2%29%2Ax+%29
It becomes highlight_green%28+%28-5%2B2%29%2Ax+%29%2B50=0.
Look at %28-highlight_red%28+5+%29%2Bhighlight_red%28+2+%29%29%2Ax%2B50=0.
Added fractions or integers together
It becomes %28highlight_green%28+-3+%29%29%2Ax%2B50=0.
Look at %28highlight_red%28+-3+%29%29%2Ax%2B50=0.
Removed extra sign in front of -3
It becomes %28-highlight_green%28+3+%29%29%2Ax%2B50=0.
Look at highlight_red%28+%28-highlight_red%28+3+%29%29%2Ax+%29%2B50=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes -highlight_green%28+3+%29%2Ax%2B50=0.
Look at highlight_red%28+-3%2Ax%2B50+%29=0.
Solved linear equation highlight_red%28+-3%2Ax%2B50=0+%29 equivalent to -3*x+50 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=16.6666666666667.

Universal Simplifier and Solver


Done!



With x=16.67, then 180-x=163.33 and 90-x=73.33

Step 6. ANSWER. The supplement is 163.33 degrees

I hope the above steps were helpful.

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

Good luck in your studies!

Respectfully,
Dr J

Inequalities/215829: solve and graph 3-6n-4 < 17
1 solutions
Answer 163097 by drj(1380) About Me  on 2009-09-23 00:10:34 (Show Source):
You can put this solution on YOUR website!
3-6n-4+%3C+17

Step 1. Add to both sides of the inequality.

-6n-1%3C17

-6n%3C18

Step 2. Divide by 6 to both sides of the inequality.

-n%3C3

Step 3. Multiply by -1 to both sides of inequality and reverse the inequality from "<" to ">"

n%3E-3 ANSWER

Graph follows below:

number_line%28+600%2C+-10%2C+10%2C+-3%2C+10%29

where the solution goes from the red dot starting at -3 to 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/215864: Delmas flew to Detroit in 90 minutes and drove his car back home in 6 hours. If he drove 150mph slower than he flew, then how fast did he fly?
1 solutions
Answer 163096 by drj(1380) About Me  on 2009-09-23 00:00:41 (Show Source):
You can put this solution on YOUR website!
Delmas flew to Detroit in 90 minutes and drove his car back home in 6 hours. If he drove 150mph slower than he flew, then how fast did he fly?

Step 1. Let x be the speed of the plane.

Step 2. Let x-150 be the speed of the car.

Step 3. Let 1.5x be the distance flew by plane where 90 minutes=1.5 hours and 60 minutes = 1 hour.

Step 4. Let 6(x-150) be the distance drove by car.

Step 5. Distances traveled by plane and car means setting equations in Steps 3 and 4 to be equal.

1.5x=6%28x-150%29

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


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=200.
  • Graphical form: Equation 1.5x=6%2A%28x-150%29 was fully solved.
  • Text form: 1.5x=6*(x-150) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+1.5x=6%2A%28x-150%29+%29
    For tutors: simplify_cartoon( 1.5x=6*(x-150) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 1.5%2Ax=highlight_red%28+6%2A%28x-150%29+%29.
Moved these terms to the left highlight_green%28+-6%2A%28x-150%29+%29
It becomes 1.5%2Ax-highlight_green%28+6%2A%28x-150%29+%29=0.
Look at 1.5%2Ax-highlight_red%28+6%2A%28x-150%29+%29=0.
Expanded term -6 by using associative property on %28x-150%29
It becomes 1.5%2Ax-highlight_green%28+6%2Ax+%29%2Bhighlight_green%28+6%2A150+%29=0.
Look at 1.5%2Ax-6%2Ax%2Bhighlight_red%28+6+%29%2Ahighlight_red%28+150+%29=0.
Multiplied numerator integers
It becomes 1.5%2Ax-6%2Ax%2Bhighlight_green%28+900+%29=0.
Look at highlight_red%28+1.5%2Ax+%29-highlight_red%28+6%2Ax+%29%2B900=0.
Eliminated similar terms highlight_red%28+1.5%2Ax+%29,highlight_red%28+-6%2Ax+%29 replacing them with highlight_green%28+%281.5-6%29%2Ax+%29
It becomes highlight_green%28+%281.5-6%29%2Ax+%29%2B900=0.
Look at %28highlight_red%28+1.5+%29-highlight_red%28+6+%29%29%2Ax%2B900=0.
Added fractions or integers together
It becomes %28-highlight_green%28+45%2F10+%29%29%2Ax%2B900=0.
Look at highlight_red%28+%28-highlight_red%28+45%2F10+%29%29%2Ax+%29%2B900=0.
Remove unneeded parentheses around factor highlight_red%28+45+%29,highlight_red%28+1%2F10+%29
It becomes -highlight_green%28+45+%29%2Fhighlight_green%28+10+%29%2Ax%2B900=0.
Look at -highlight_red%28+45+%29%2Fhighlight_red%28+10+%29%2Ax%2B900=0.
Factors 45 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes -highlight_green%28+9+%29%2Fhighlight_green%28+2+%29%2Ax%2B900=0.
Look at highlight_red%28+-9%2F2%2Ax%2B900+%29=0.
Solved linear equation highlight_red%28+-9%2F2%2Ax%2B900=0+%29 equivalent to -4.5*x+900 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=200.

Universal Simplifier and Solver


Done!


With x=200, then x-150=50.

Check if distances are equal... 1.5*200=6*50 or 300=300 a true statement

Step 6. The speed of the plane is 200 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

Equations/215856: Thirty students bought pennants for the football game. Plain pennants cost $4 each and fancy ones cost $8 each. If the total bill was $168, how many students bought the fancy pennants?
1 solutions
Answer 163092 by drj(1380) About Me  on 2009-09-22 23:40:36 (Show Source):
You can put this solution on YOUR website!
Thirty students bought pennants for the football game. Plain pennants cost $4 each and fancy ones cost $8 each. If the total bill was $168, how many students bought the fancy pennants?

Step 1. Let x be the number of fancy pennants bought by students.

Step 2. Let 30-x be the number of plain pennants bought by students.

Step 3. Let 8x be the dollar value of the fancy pennants bought by students.

Step 4. Let 4(30-x) be the dollar value of the fancy pennants bought by students.

Step 5. Total cost is then 8x%2B4%2830-x%29=168 as given by the problem statement. The following steps will solve this 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.
  • Graphical form: Equation 8x%2B4%2A%2830-x%29=168 was fully solved.
  • Text form: 8x+4*(30-x)=168 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+8x%2B4%2A%2830-x%29=168+%29
    For tutors: simplify_cartoon( 8x+4*(30-x)=168 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 8%2Ax%2B4%2A%28highlight_red%28+30+%29-x%29=168.
Moved 30 to the right of expression
It becomes 8%2Ax%2B4%2A%28-x%2Bhighlight_green%28+30+%29%29=168.
Look at 8%2Ax%2B4%2A%28-x%2B30%29=highlight_red%28+168+%29.
Moved these terms to the left highlight_green%28+-168+%29
It becomes 8%2Ax%2B4%2A%28-x%2B30%29-highlight_green%28+168+%29=0.
Look at 8%2Ax%2Bhighlight_red%28+4%2A%28-x%2B30%29+%29-168=0.
Expanded term 4 by using associative property on %28-x%2B30%29
It becomes 8%2Ax-highlight_green%28+4%2Ax+%29%2Bhighlight_green%28+4%2A30+%29-168=0.
Look at 8%2Ax-4%2Ax%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+30+%29-168=0.
Multiplied numerator integers
It becomes 8%2Ax-4%2Ax%2Bhighlight_green%28+120+%29-168=0.
Look at 8%2Ax-4%2Ax%2Bhighlight_red%28+120+%29-highlight_red%28+168+%29=0.
Added fractions or integers together
It becomes 8%2Ax-4%2Ax%2Bhighlight_green%28+-48+%29=0.
Look at 8%2Ax-4%2Ax%2Bhighlight_red%28+-48+%29=0.
Removed extra sign in front of -48
It becomes 8%2Ax-4%2Ax-highlight_green%28+48+%29=0.
Look at highlight_red%28+8%2Ax+%29-highlight_red%28+4%2Ax+%29-48=0.
Eliminated similar terms highlight_red%28+8%2Ax+%29,highlight_red%28+-4%2Ax+%29 replacing them with highlight_green%28+%288-4%29%2Ax+%29
It becomes highlight_green%28+%288-4%29%2Ax+%29-48=0.
Look at %28highlight_red%28+8+%29-highlight_red%28+4+%29%29%2Ax-48=0.
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2Ax-48=0.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2Ax+%29-48=0.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2Ax-48=0.
Look at highlight_red%28+4%2Ax-48+%29=0.
Solved linear equation highlight_red%28+4%2Ax-48=0+%29 equivalent to 4*x-48 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=12.

Universal Simplifier and Solver


Done!



With x=12, then 30-x=18

Check total cost if true...8*12+4*18=96+72=168...which is a true statement

Step 6. ANSWER: 12 students bought the fancy pennants.

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/215896: the area of a rectangle is three times more than twice its width. if the area is 35. Find the dimensions of the rectangle.

1 solutions
Answer 163090 by drj(1380) About Me  on 2009-09-22 23:30:35 (Show Source):
You can put this solution on YOUR website!
The area of a rectangle is three times more than twice its width. If the area is 35. Find the dimensions of the rectangle.

Step 1. Let w be the width and l be the length.

Step 2. Area A = length * width = l*w = 35.

Step 3. A = 3*2w =35 or 6w=35 or w=35/6 and l=35/(35/6)=6

Step 4. ANSWER. The length is 6 and the width is 35/6.

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_And_Systems_Word_Problems/215907: A technician measures the current in a circuit to be -6.1 ampers and the resistance is 7 ohms. find the voltage.
1 solutions
Answer 163087 by drj(1380) About Me  on 2009-09-22 23:24:21 (Show Source):
You can put this solution on YOUR website!
A technician measures the current in a circuit to be -6.1 amperes and the resistance is 7 ohms. find the voltage.

Based on Ohm's Law which basically state that the voltage is proportional to current or V=I*R where the current I=-6.1 amperes and the resistance R=7 ohm's

V=(-6.1)*(7)=-42.7 volts (ANSWER)

I hope the above steps were helpful.

For Step-By-Step videos in Circuit Analysis and Design, please visit http://www.FreedomUniversity.TV

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

Angles/215826: One third of the supplement of an angle added to the complement of an angle is 86. Find the measure of the angle, its complement, and its supplement.
Any help provided, preferably with steps, would be immensely appreciated. Much thanks in advance!
1 solutions
Answer 163086 by drj(1380) About Me  on 2009-09-22 23:19:22 (Show Source):
You can put this solution on YOUR website!
One third of the supplement of an angle added to the complement of an angle is 86. Find the measure of the angle, its complement, and its supplement.

Step 1. Supplementary angles means two angles add up to 180 degrees.

Step 2. Complementary angles means two angles add up to 90 degrees.

Step 3. Let x be the angle, let 180-x be its supplementary angle, and let 90-x be its complementary angle.

Step 4. Let %28180-x%29%2F3 be one third of the supplementary angle.

Step 5. Then the statement one third of the supplement of an angle added to the complement of an angle is 86 and translated as

%28180-x%29%2F3%2B90-x=86

Multiplying 3 to both sides of the equations to get rid of the denominator

3%2A%28%28180-x%29%2F3%2B90-x%29=3%2A86

180-x%2B270-3x=258

450-4x=258

Add 4x-258 to both sides of the equation to prepare in solving for x

450-4x%2B4x-258=258%2B4x-258

192=4x

Divide by 4 to both sides of the equatiion

192%2F4=4x%2F4

x=48

Then 180-x=132 and 90-x=42

Check...%28180-x%29%2F3%2B90-x=86 if true. Then 132%2F3%2B42=86...which is a true statement.

Step 6. ANSWER. The angle is 42, its supplement is 132, and its complement is 42.

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/215883: w/2+7=w/3+9
1 solutions
Answer 163081 by drj(1380) About Me  on 2009-09-22 23:04:53 (Show Source):
You can put this solution on YOUR website!
w%2F2%2B7=w%2F3%2B9

Step 1. Multiply 6 to both sides of the equation to get rid of denominators.

6%2A%28w%2F2%2B7%29=6%2A%28w%2F3%2B9%29

3w%2B42=2w%2B54

Step 2. Subtract 42 to both sides of the equation

3w%2B42-42=2w%2B54-42

3w=2w%2B12

Step 3. Subtract 2w to both sides of the equation

3w-2w=2w%2B8-2w

w=12

Check with original equation...w%2F2%2B7=w%2F3%2B9 then

12%2F2%2B7=12%2F3%2B9

6%2B7=4%2B9

13=13 which is a true statement

Step 4. ANSWER is w=12.

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

Probability-and-statistics/215725: What is the sum of the probabilities of all the outcomes in a sample space?
1 solutions
Answer 162992 by drj(1380) About Me  on 2009-09-22 18:32:36 (Show Source):
You can put this solution on YOUR website!
What is the sum of the probabilities of all the outcomes in a sample space?

The answer is 1.

For example, a coin has two possible outcomes: heads or tails.

Probability of heads is 1/2 and probability of tails is 1/2 for one toss. 1/2+1/2=1.

Another example: consider six-headed die where each face has a probability of 1/6 for a single toss. But all the outcomes is added to 1 since its sum is 6*(1/6)=1.

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-equations/215765: Is 7x-6(y+x)=4 a Linear Equation? If so, put it in standard form.
1 solutions
Answer 162990 by drj(1380) About Me  on 2009-09-22 18:27:20 (Show Source):
You can put this solution on YOUR website!
Is 7x-6(y+x)=4 a Linear Equation? If so, put it in standard form.

The above equation is linear.

Step 1. To put in standard form given as Ax+By=C where A, B, and C are constants.

Step 2. Multiply to get rid of parenthesis: 7x-6%28y%2Bx%29=4 or 7x-6y-6x=4

Step 3. Collect like terms 7x-6x=x: x-6y=4

Step 4. ANSWER The equation in standard form is x-6y=4 where A=1, B=-6 and C=4.

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

Graphs/215735: Solve the sytem of equation.
9x-8y=-16
8y-9x=16
Is the system consistent or inconsistent?
Are the equations independent or dependent?
1 solutions
Answer 162982 by drj(1380) About Me  on 2009-09-22 17:52:51 (Show Source):
You can put this solution on YOUR website!
Solve the sytem of equation.
9x-8y=-16
8y-9x=16

Is the system consistent or inconsistent? Consistent since both equations will give the same answer which is many solutions in this example. No contradictiion takes place since both equations are really the same as described below.
Are the equations independent or dependent? The second equation is just the negative of the first equation because adding those equations leads to 0=0. So they are dependent.

I hope the above explanations 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

Graphs/215731: The perimeter of a rectangle is 98m. The length is 10m more than twice the width. Find the dimensions?
What is the length?
What is the width?
1 solutions
Answer 162979 by drj(1380) About Me  on 2009-09-22 17:42:06 (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 98m. The length is 10m more than twice the width. Find the dimensions?
What is the length?
What is the width?

Step 1. Let w be the width and 2w be twice the width

Step 2. Let 2w+10 be the length since it's 10m more than twice the width

Step 3. Perimeter P is when you add up all 4 sides or P=w%2Bw%2B2w%2B10%2B2w%2B10=6w%2B20=98. Now 6w=78 or w=13 m. Then the length is 2w+10=36 and P=13+13+36+36=98 m...which is a true statement.

Step 4. ANSWER. The width is 13 m and the length is 36 m.

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_And_Systems_Word_Problems/215677: An auto averaged 40 mph for part of a trip and 50 mph for the remainder.
If the 5-hour trip covered 210 miles, for how long did the car average 40mph?
1 solutions
Answer 162977 by drj(1380) About Me  on 2009-09-22 17:34:56 (Show Source):
You can put this solution on YOUR website!
An auto averaged 40 mph for part of a trip and 50 mph for the remainder.
If the 5-hour trip covered 210 miles, for how long did the car average 40mph?

Step 1. Let x be the length of time when traveling 40 mph.

Step 2. Let 5-x be the length of time traveling 50 mph.

Step 3. Let 40x be the distance traveled at 40 mph.

Step 4. Let 50(5-x) be the distance traveled at 50 mph.

Step 5. Then 40x+ 50(5-x)=210 as given by the problem statement.

The following steps will solve this 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=4.
  • Graphical form: Equation 40x%2B50%2A%285-x%29=210 was fully solved.
  • Text form: 40x+50*(5-x)=210 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+40x%2B50%2A%285-x%29=210+%29
    For tutors: simplify_cartoon( 40x+50*(5-x)=210 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 40%2Ax%2B50%2A%28highlight_red%28+5+%29-x%29=210.
Moved 5 to the right of expression
It becomes 40%2Ax%2B50%2A%28-x%2Bhighlight_green%28+5+%29%29=210.
Look at 40%2Ax%2B50%2A%28-x%2B5%29=highlight_red%28+210+%29.
Moved these terms to the left highlight_green%28+-210+%29
It becomes 40%2Ax%2B50%2A%28-x%2B5%29-highlight_green%28+210+%29=0.
Look at 40%2Ax%2Bhighlight_red%28+50%2A%28-x%2B5%29+%29-210=0.
Expanded term 50 by using associative property on %28-x%2B5%29
It becomes 40%2Ax-highlight_green%28+50%2Ax+%29%2Bhighlight_green%28+50%2A5+%29-210=0.
Look at 40%2Ax-50%2Ax%2Bhighlight_red%28+50+%29%2Ahighlight_red%28+5+%29-210=0.
Multiplied numerator integers
It becomes 40%2Ax-50%2Ax%2Bhighlight_green%28+250+%29-210=0.
Look at 40%2Ax-50%2Ax%2Bhighlight_red%28+250+%29-highlight_red%28+210+%29=0.
Added fractions or integers together
It becomes 40%2Ax-50%2Ax%2Bhighlight_green%28+40+%29=0.
Look at highlight_red%28+40%2Ax+%29-highlight_red%28+50%2Ax+%29%2B40=0.
Eliminated similar terms highlight_red%28+40%2Ax+%29,highlight_red%28+-50%2Ax+%29 replacing them with highlight_green%28+%2840-50%29%2Ax+%29
It becomes highlight_green%28+%2840-50%29%2Ax+%29%2B40=0.
Look at %28highlight_red%28+40+%29-highlight_red%28+50+%29%29%2Ax%2B40=0.
Added fractions or integers together
It becomes %28highlight_green%28+-10+%29%29%2Ax%2B40=0.
Look at %28highlight_red%28+-10+%29%29%2Ax%2B40=0.
Removed extra sign in front of -10
It becomes %28-highlight_green%28+10+%29%29%2Ax%2B40=0.
Look at highlight_red%28+%28-highlight_red%28+10+%29%29%2Ax+%29%2B40=0.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes -highlight_green%28+10+%29%2Ax%2B40=0.
Look at highlight_red%28+-10%2Ax%2B40+%29=0.
Solved linear equation highlight_red%28+-10%2Ax%2B40=0+%29 equivalent to -10*x+40 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=4.

Universal Simplifier and Solver


Done!



With x=4, then 5-x=1.

Check distance...4*40+1*50=210...which is a true statement

Step 6. ANSWER. The car traveled for 4 hours at 40 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

Numbers_Word_Problems/215647: finding three consecutive integers such that the sum of the first, twice the second, and three times the third is 62
1 solutions
Answer 162973 by drj(1380) About Me  on 2009-09-22 17:18:24 (Show Source):
You can put this solution on YOUR website!
Finding three consecutive integers such that the sum of the first, twice the second, and three times the third is 62


Step 1. Let n be one integer,

Step 2. Let n+1 be the second consecutive number and 2(n+1) is twice the second number

Step 3. Let n+2 is the third consecutive number and 3(n+2) is three times the third

Step 4. Then the sum is n+2(n+1)+3(n+2)=62 as given by the problem statement. The following steps will solve this equation.

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


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: n=9.
  • Graphical form: Equation n%2B2%2A%28n%2B1%29%2B3%2A%28n%2B2%29=62 was fully solved.
  • Text form: n+2*(n+1)+3*(n+2)=62 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2B2%2A%28n%2B1%29%2B3%2A%28n%2B2%29=62+%29
    For tutors: simplify_cartoon( n+2*(n+1)+3*(n+2)=62 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at n%2B2%2A%28n%2B1%29%2B3%2A%28n%2B2%29=highlight_red%28+62+%29.
Moved these terms to the left highlight_green%28+-62+%29
It becomes n%2B2%2A%28n%2B1%29%2B3%2A%28n%2B2%29-highlight_green%28+62+%29=0.
Look at n%2Bhighlight_red%28+2%2A%28n%2B1%29+%29%2B3%2A%28n%2B2%29-62=0.
Expanded term 2 by using associative property on %28n%2B1%29
It becomes n%2Bhighlight_green%28+2%2An+%29%2Bhighlight_green%28+2%2A1+%29%2B3%2A%28n%2B2%29-62=0.
Look at n%2B2%2An%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2B3%2A%28n%2B2%29-62=0.
Multiplied numerator integers
It becomes n%2B2%2An%2Bhighlight_green%28+2+%29%2B3%2A%28n%2B2%29-62=0.
Look at n%2B2%2An%2Bhighlight_red%28+2+%29%2B3%2A%28n%2B2%29-highlight_red%28+62+%29=0.
Added fractions or integers together
It becomes n%2B2%2An%2Bhighlight_green%28+-60+%29%2B3%2A%28n%2B2%29=0.
Look at n%2B2%2An%2Bhighlight_red%28+-60+%29%2B3%2A%28n%2B2%29=0.
Moved -60 to the right of expression
It becomes n%2B2%2An%2B3%2A%28n%2B2%29%2Bhighlight_green%28+-60+%29=0.
Look at n%2B2%2An%2B3%2A%28n%2B2%29%2Bhighlight_red%28+-60+%29=0.
Removed extra sign in front of -60
It becomes n%2B2%2An%2B3%2A%28n%2B2%29-highlight_green%28+60+%29=0.
Look at highlight_red%28+n+%29%2Bhighlight_red%28+2%2An+%29%2B3%2A%28n%2B2%29-60=0.
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+2%2An+%29 replacing them with highlight_green%28+%281%2B2%29%2An+%29
It becomes highlight_green%28+%281%2B2%29%2An+%29%2B3%2A%28n%2B2%29-60=0.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2An%2B3%2A%28n%2B2%29-60=0.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2An%2B3%2A%28n%2B2%29-60=0.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2An+%29%2B3%2A%28n%2B2%29-60=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2An%2B3%2A%28n%2B2%29-60=0.
Look at 3%2An%2Bhighlight_red%28+3%2A%28n%2B2%29+%29-60=0.
Expanded term 3 by using associative property on %28n%2B2%29
It becomes 3%2An%2Bhighlight_green%28+3%2An+%29%2Bhighlight_green%28+3%2A2+%29-60=0.
Look at 3%2An%2B3%2An%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+2+%29-60=0.
Multiplied numerator integers
It becomes 3%2An%2B3%2An%2Bhighlight_green%28+6+%29-60=0.
Look at 3%2An%2B3%2An%2Bhighlight_red%28+6+%29-highlight_red%28+60+%29=0.
Added fractions or integers together
It becomes 3%2An%2B3%2An%2Bhighlight_green%28+-54+%29=0.
Look at 3%2An%2B3%2An%2Bhighlight_red%28+-54+%29=0.
Removed extra sign in front of -54
It becomes 3%2An%2B3%2An-highlight_green%28+54+%29=0.
Look at highlight_red%28+3%2An+%29%2Bhighlight_red%28+3%2An+%29-54=0.
Eliminated similar terms highlight_red%28+3%2An+%29,highlight_red%28+3%2An+%29 replacing them with highlight_green%28+%283%2B3%29%2An+%29
It becomes highlight_green%28+%283%2B3%29%2An+%29-54=0.
Look at %28highlight_red%28+3+%29%2Bhighlight_red%28+3+%29%29%2An-54=0.
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2An-54=0.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2An+%29-54=0.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2An-54=0.
Look at highlight_red%28+6%2An-54+%29=0.
Solved linear equation highlight_red%28+6%2An-54=0+%29 equivalent to 6*n-54 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=9.

Universal Simplifier and Solver


Done!


With n= 9, then n+1= 10 , and n+2=11

Check sum..9+2*10+3*11=9+20+33=622...which is a true statement.

Step 5. ANSWER: The numbers are 9, 10, and 11.

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/215655: x+y=57
.25x+50y=925
1 solutions
Answer 162970 by drj(1380) About Me  on 2009-09-22 17:10:41 (Show Source):
You can put this solution on YOUR website!
x+y=57
25x+50y=925

The following will solve the linear system of equation with Substitution.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+57%2C%0D%0A++++25%5Cx+%2B+50%5Cy+=+925+%29%0D%0A++We'll use substitution. After moving 1*y to the right, we get:
1%2Ax+=+57+-+1%2Ay, or x+=+57%2F1+-+1%2Ay%2F1. Substitute that
into another equation:
25%2A%2857%2F1+-+1%2Ay%2F1%29+%2B+50%5Cy+=+925 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.

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
Geometry_Word_Problems/215723: Can you please explain how I can solve this problem?
The legnth of a rectangle is 5ft more than its width. If the perimeter is 70ft, find the dimension.
1 solutions
Answer 162968 by drj(1380) About Me  on 2009-09-22 17:07:53 (Show Source):
You can put this solution on YOUR website!

The length of a rectangle is 5ft more than its width. If the perimeter is 70ft, find the dimension.

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

Step 2. Perimeter P means that we add up all the lengths of the four sides.

Step 3. Then we have

P=w%2Bw%2Bw%2B5%2Bw%2B5=70

4w%2B10=70

Subtract 10 from both sides of the equation

4w%2B10-10=70-10=60

Divide 4 to both sides of the equation

4w%2F4=60%2F4

w=15

With w=15, then w+5=20. Check perimeter...P=15+15+20+20=70 which is a true statement.

Step 4. ANSWER. The width is 15 ft and the length is 20 ft.

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

Average/215682: if the average of six numbers is 18 and the average of three of the numbers is 15 then what is the sum of the remaining three numbers

1 solutions
Answer 162962 by drj(1380) About Me  on 2009-09-22 17:02:26 (Show Source):
You can put this solution on YOUR website!
If the average of six numbers is 18 and the average of three of the numbers is 15 then what is the sum of the remaining three numbers.

Step 1. Let y=3x be the sum of the remaining numbers where x is the average of the three numbers.

Step 2. Let 3*15 be the sum of the other three numbers or 45.

Step 3. 18=(45+y)/6 since the average of six numbers is 18 and the average of three of the numbers is 15. Solving for y yields the following steps:

18=%2845%2By%29%2F6

Multiply by 6 to both sides of the equation to get rid of denominator.

18%2A6=45%2By

108=45%2By

Subtract 45 from both sides of the equation

108-45=45%2By-45

y=63

Step 4. ANSWER: The average of the remaining three numbers is 63.

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/215717: How long will it take to drive 47 miles at 25 miles per hour
1 solutions
Answer 162959 by drj(1380) About Me  on 2009-09-22 16:53:42 (Show Source):
You can put this solution on YOUR website!
How long will it take to drive 47 miles at 25 miles per hour?

Step 1. distance = speed * time OR time =distance/speed.

Step 2. time =47 miles/25 miles per hour = 1.88 hours.

Step 3. Convert 1.88 hours into hours and minutes. 1 hour = 60 minutes. Then, 1.88 hours = 1 hour + 0.88 hour*60 minutes/hour = 1 hour and 53 minutes.

Step 4. ANSWER. It will take 1.88 hours or approximately 1 hour and 53 minutes.

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



Graphs/215713: Ok, I'm going to try this one more time...
I need help solving AND factoring the following equation (taken from Bittinger's College Algebra: Graphs and Models 4th Edition, page 76, problem number 39.)
+y+=+-x%5E2+%2B+2x+%2B+3
A point to remember: The x^2 is NEGATIVE, and the 2x and 3 are both POSITIVE.
Thank you in advance!
1 solutions
Answer 162954 by drj(1380) About Me  on 2009-09-22 16:45:25 (Show Source):
You can put this solution on YOUR website!
y+=+-x%5E2+%2B+2x+%2B+3

Step 1. Let's factor out negative 1 so now we have y=-1%28x%5E2-2x-3%29

Step 2. We need two integers m and n such that their sum is -2=m+n and their product mn=-3.

Step 3. The integers are -3 and 1. Then, x%5E2-3x-3=%28x-3%29%28x%2B1%29

Step 4. ANSWER: y = -x^2 + 2x + 3=-1*(x-3)(x+1) when y=0 we are finding x as solutions where it intersects the x-axis or in our case (x-3)=0 and (x+1)=0 or x=3 and x=-1.

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, b=2 and c=3.

The graph is shown below:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B2x%2B3+=+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=%282%29%5E2-4%2A-1%2A3=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+16+%29%29%2F2%5C-1+=+-1
x%5B2%5D+=+%28-%282%29-sqrt%28+16+%29%29%2F2%5C-1+=+3

Quadratic expression -1x%5E2%2B2x%2B3 can be factored:
-1x%5E2%2B2x%2B3+=+-1%28x--1%29%2A%28x-3%29
Again, the answer is: -1, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B2%2Ax%2B3+%29



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/215709: What is the greatest possible area of a rectangle if its perimeter is 30 centimeters?
1 solutions
Answer 162952 by drj(1380) About Me  on 2009-09-22 16:37:44 (Show Source):
You can put this solution on YOUR website!
What is the greatest possible area of a rectangle if its perimeter is 30 centimeters?

Step 1. The greatest possible area A occurs with the rectangle is a square or the sides of the rectangle are equal or A=s^2 where s is the length of the side of a square.

Step 2. Perimeter P is when you add up all the lengths of the sides of a rectangle or square in our case or P=s+s+s+s=4s
P=4s=30

s=30%2F4=7.5

Step 3. Area is 7.5%5E2=56.25

Step 4. ANSWER: The maximum area is 56.25 square centimeters.

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

Angles/215691: Five times the measure of an angle less the complement of that angle equals 9. Find the measure of the angle.
1 solutions
Answer 162948 by drj(1380) About Me  on 2009-09-22 16:32:55 (Show Source):
You can put this solution on YOUR website!
Five times the measure of an angle less the complement of that angle equals 9. Find the measure of the angle.

Step 1. Angles are complementary when the two angles add to 90 degrees.

Step 2. Let x be the angle and 90-x be the complementary angle.

Step 3. Let 5x be five times the angle.

Step 4. Then 5x-(90-x)=9 since five times the measure of an angle less the complement of that angle equals 9

Step 5. The following will solve the equation in Step 4:

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


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=16.5.
  • Graphical form: Equation 5x-%2890-x%29=9 was fully solved.
  • Text form: 5x-(90-x)=9 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5x-%2890-x%29=9+%29
    For tutors: simplify_cartoon( 5x-(90-x)=9 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2Ax-highlight_red%28+%2890-x%29+%29=9.
Remove unneeded parentheses around terms highlight_red%28+-90+%29,highlight_red%28+x+%29
It becomes 5%2Ax-highlight_green%28+90+%29%2Bhighlight_green%28+x+%29=9.
Look at 5%2Ax-highlight_red%28+90+%29%2Bx=9.
Moved -90 to the right of expression
It becomes 5%2Ax%2Bx-highlight_green%28+90+%29=9.
Look at highlight_red%28+5%2Ax+%29%2Bhighlight_red%28+x+%29-90=9.
Eliminated similar terms highlight_red%28+5%2Ax+%29,highlight_red%28+x+%29 replacing them with highlight_green%28+%285%2B1%29%2Ax+%29
It becomes highlight_green%28+%285%2B1%29%2Ax+%29-90=9.
Look at %28highlight_red%28+5+%29%2Bhighlight_red%28+1+%29%29%2Ax-90=9.
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Ax-90=9.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Ax+%29-90=9.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Ax-90=9.
Look at 6%2Ax-90=highlight_red%28+9+%29.
Moved these terms to the left highlight_green%28+-9+%29
It becomes 6%2Ax-90-highlight_green%28+9+%29=0.
Look at 6%2Ax-highlight_red%28+90+%29-highlight_red%28+9+%29=0.
Added fractions or integers together
It becomes 6%2Ax%2Bhighlight_green%28+-99+%29=0.
Look at 6%2Ax%2Bhighlight_red%28+-99+%29=0.
Removed extra sign in front of -99
It becomes 6%2Ax-highlight_green%28+99+%29=0.
Look at highlight_red%28+6%2Ax-99+%29=0.
Solved linear equation highlight_red%28+6%2Ax-99=0+%29 equivalent to 6*x-99 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=16.5.

Universal Simplifier and Solver


Done!




With x=16.5 , then 90-x=73.5

Check 5x-90-x=5*16.5-73.5=9 which is a true statement.

Step 6. The angle is 16.5 degrees and its complement is 73.5 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

Linear-systems/215585: what is the y intercept of the points (1, 202) and (4, 382)?
1 solutions
Answer 162893 by drj(1380) About Me  on 2009-09-22 11:17:32 (Show Source):
You can put this solution on YOUR website!
What is the y intercept of the points (1, 202) and (4, 382)?

Step 1. We need to find an equation in slope intercept form given as y=mx+b where m is the slope and b is the y-intercept at point (0,b).

Step 2. The slope of the line m is given as

+m=%28y2-y1%29%2F%28x2-x1%29

where for our example is x1=1, y1=202, x2=4 and y2=382 (think of slope=rise%2Frun). You can choose the points the other way around but be consistent with the x and y coordinates. You will get the same result.

Step 3. Substituting the above values in the slope equation gives

m=%28382-202%29%2F%284-1%29

m=180%2F3

m=60

Step 4. The slope is calculated as 60 or m=60.

Step 5. Now use the slope equation of step 1 and choose one of the given points. I'll choose point (1,202). Letting y=y2 and x=x2 and substituting m=60 in the slope equation given as,

+m=%28y2-y1%29%2F%28x2-x1%29


+60=%28y-202%29%2F%28x-1%29

+60=%28y-202%29%2F%28x-1%29

Step 6. Multiply both sides of equation by x-1 to get rid of denomination found on the right side of the equation


+60%28x-1%29=%28x-1%29%28y-202%29%2F%28x-1%29


+60x-60=y-202


Step 7. Now simplify and put the above equation into slope-intercept form.

60x-60=y-202

Add 202 to both sides of the equation

60x-60%2B202=y-202%2B202

60x%2B142=y

y=60x%2B142 ANSWER in slope-intercept form. m=60 and y-intercept=142

Step 8. See if the other point (4, 382) or x=4 and y=382 satisfies this equation

y=60x%2B142

382=60%2A4%2B142

{{382=382}}} So the point (4,382) satisfies the equation and is on the line. In other words, you can use the other point to check your work.

Note: above equation can be also be transform into standard form as

-60x%2By=142

See graph below to check the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -60+x+%2B+1+y+=+142 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--60%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 142/-60 = -2.36666666666667.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 142/1 = 142.
  • Slope is --60/1 = 60.
  • Equation in slope-intercept form: y=60*x+142.



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

Linear-systems/215581: is the ordered pair (5,2) a solution to the given equations 2x-y=8 and 3x+2y=20?
1 solutions
Answer 162890 by drj(1380) About Me  on 2009-09-22 10:47:17 (Show Source):
You can put this solution on YOUR website!
Is the ordered pair (5,2) a solution to the given equations 2x-y=8 and 3x+2y=20?

Step 1. To determine if (5,2) is a solution substitute x=5 and y=2 into the linear system of equations.

Step 2. For 2x-y=8, then 2%2A5-2=8 which is a true statement.

Step 3. For 3x%2B2y=20 then 3%2A5%2B2%2A2=19=20 which is a FALSE statement.

Step 4. ANSWER: Therefore, (5,2) is not a solution to the linear system of equations.

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_Equations_And_Systems_Word_Problems/215565: Marc sold 563 tickets for the school play. Student tickets cost $4 and adult tickets cost $6. Marc’s sales totaled $2840. How many adult tickets and how many student tickets did Marc sell?
1 solutions
Answer 162880 by drj(1380) About Me  on 2009-09-22 10:13:31 (Show Source):
You can put this solution on YOUR website!
Marc sold 563 tickets for the school play. Student tickets cost $4 and adult tickets cost $6. Marc’s sales totaled $2840. How many adult tickets and how many student tickets did Marc sell?

Step 1. Let x be the number of students tickets sold and let 4x be the dollar value of student tickets sold.

Step 2. Let 563-x be the number of adult tickets sold and let 6(563-x) be the dollar value of adult tickets sold.

Step 3. Given total sales is $2840, then 4x%2B6%28563-x%29=2840. The following steps will solve this 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=269.
  • Graphical form: Equation 4x%2B6%2A%28563-x%29=2840 was fully solved.
  • Text form: 4x+6*(563-x)=2840 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4x%2B6%2A%28563-x%29=2840+%29
    For tutors: simplify_cartoon( 4x+6*(563-x)=2840 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2Ax%2B6%2A%28highlight_red%28+563+%29-x%29=2840.
Moved 563 to the right of expression
It becomes 4%2Ax%2B6%2A%28-x%2Bhighlight_green%28+563+%29%29=2840.
Look at 4%2Ax%2B6%2A%28-x%2B563%29=highlight_red%28+2840+%29.
Moved these terms to the left highlight_green%28+-2840+%29
It becomes 4%2Ax%2B6%2A%28-x%2B563%29-highlight_green%28+2840+%29=0.
Look at 4%2Ax%2Bhighlight_red%28+6%2A%28-x%2B563%29+%29-2840=0.
Expanded term 6 by using associative property on %28-x%2B563%29
It becomes 4%2Ax-highlight_green%28+6%2Ax+%29%2Bhighlight_green%28+6%2A563+%29-2840=0.
Look at 4%2Ax-6%2Ax%2Bhighlight_red%28+6+%29%2Ahighlight_red%28+563+%29-2840=0.
Multiplied numerator integers
It becomes 4%2Ax-6%2Ax%2Bhighlight_green%28+3378+%29-2840=0.
Look at 4%2Ax-6%2Ax%2Bhighlight_red%28+3378+%29-highlight_red%28+2840+%29=0.
Added fractions or integers together
It becomes 4%2Ax-6%2Ax%2Bhighlight_green%28+538+%29=0.
Look at highlight_red%28+4%2Ax+%29-highlight_red%28+6%2Ax+%29%2B538=0.
Eliminated similar terms highlight_red%28+4%2Ax+%29,highlight_red%28+-6%2Ax+%29 replacing them with highlight_green%28+%284-6%29%2Ax+%29
It becomes highlight_green%28+%284-6%29%2Ax+%29%2B538=0.
Look at %28highlight_red%28+4+%29-highlight_red%28+6+%29%29%2Ax%2B538=0.
Added fractions or integers together
It becomes %28highlight_green%28+-2+%29%29%2Ax%2B538=0.
Look at %28highlight_red%28+-2+%29%29%2Ax%2B538=0.
Removed extra sign in front of -2
It becomes %28-highlight_green%28+2+%29%29%2Ax%2B538=0.
Look at highlight_red%28+%28-highlight_red%28+2+%29%29%2Ax+%29%2B538=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes -highlight_green%28+2+%29%2Ax%2B538=0.
Look at highlight_red%28+-2%2Ax%2B538+%29=0.
Solved linear equation highlight_red%28+-2%2Ax%2B538=0+%29 equivalent to -2*x+538 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=269.

Universal Simplifier and Solver


Done!



With x=269 , the 563-x= 563-269=294.

Check dollar value...4*269+6*294=2840...which is a true statement

Step 4. ANSWER. The number of student tickets sold is 269 and the number of adult tickets sold is 294.

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

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

Angles/215573: The measure of an angle is 36 degrees less than the measue of its supplement. What is the measure of the angle and its supplement.

1 solutions
Answer 162879 by drj(1380) About Me  on 2009-09-22 09:58:09 (Show Source):
You can put this solution on YOUR website!
The measure of an angle is 36 degrees less than the measure of its supplement. What is the measure of the angle and its supplement.

Step 1. Supplementary angles means that two angles add up to 180 degrees.

Step 2. Let x be the angle and 180-x be the supplement.

Step 3. Then x=180-x-36 since the measure of an angle is 36 degrees less than the measure of its supplement. Solving yields the following steps

Add x to both sides of the equation to get

x%2Bx=180-x-36%2Bx

2x=144

Divide 2 to both sides of the equation

2x%2F2=144%2F2

x=72 and 180-x=108 where x is 36 degrees less than its supplement of 108 degrees.

Step 4. ANSWER: The angle is 72 degrees and its supplement is 108 degrees.

I hope the above steps were helpful.

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

Good luck in your studies!

Respectfully,
Dr J

Proportions/215571: The ratio of men to women at a certain company is 3:5 . How many male employees does the company have if there are 112 employees?

1 solutions
Answer 162876 by drj(1380) About Me  on 2009-09-22 09:48:37 (Show Source):
You can put this solution on YOUR website!
The ratio of men to women at a certain company is 3:5 . How many male employees does the company have if there are 112 employees?

Step 1. Let 3%2F5=males%2Ffemales=x%2Fy+where x is the number of males and y is the number of females.

Step 2. If 3%2F5=x%2Fy, then this leads to 3y=5x or y=5x%2F3

Step 3. Given, x%2By=112, then x%2B5x%2F3=112. Solving for x yields the following steps:

Multiply 3 to both sides of equation to get rid of denominator

3%2A%28x%2B5x%29%2F3=3%2A112

3%2A%28x%2B5x%2F3%29=3%2A112

3x%2B5x=336

8x=336

Divide by 8 to both sides of the equation

8x%2F8=336%2F8

x=42

Step 4. There are 42 males and 70 females as employees.

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

Average/215557: After taking 4 quizzes, your average is 76 out of 100. What must your average score be on the next five quizzes to increase your average to 81?
1 solutions
Answer 162875 by drj(1380) About Me  on 2009-09-22 09:38:56 (Show Source):
You can put this solution on YOUR website!
After taking 4 quizzes, your average is 76 out of 100. What must your average score be on the next five quizzes to increase your average to 81?

Step 1. Let x be the average of the next five quizzes.

Step 2. Let 4*76 be the 4 quizzes with each quiz having a score of 76 so the average of the four quizzes is 76.

Step 3. There will be a total of 9 quizzes.

Step 4. The average of nine quizzes is 81=%284%2A76%2B5x%29%2F9. Solve for x as follow

Multiply 9 to both sides of equation to get rid of denominator

81=%284%2A76%2B5x%29%2F9

9%2A81=9%2A%28304%2B5x%29%2F9

729=304%2B5x

Subtract 304 to both sides of equation to get 5x on the right side

729-304=304%2B5x-304

425=5x

Divide by 5 to both sides of equation to solve for x

425%2F5=5x%2F5

x=85

Step 5. ANSWER: To get an overall average of 81, the next five quizzes must average 85.

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

Functions/215548: a 2 w of power per square inch.150 km W of pwer to function. to the nearest square meter, how many square meters are required?
1 solutions
Answer 162874 by drj(1380) About Me  on 2009-09-22 09:19:50 (Show Source):
You can put this solution on YOUR website!
A 2 w of power per square inch. 150 kW of power to function. To the nearest square meter, how many square meters are required?

Step 1. Let I+=+P%2FA=2+W%2Finch%5E2 and P+=150+%2A10%5E3 W where P is the power and A is the area.

Step 2. Then A=P%2FI

Step 3. Convert units of A in square inch to square meters where 2.54 cm = 1 inch = 0.0254 m. Then, 1 inch * 1 inch = 0.0254+%2A+0.0254+=+6.451%2A10%5E%28-4%29

Step 4. Then A=P%2FI=150%2A10%5E3%2F%282%2A6.451%2A10%5E%28-4%29%29=1.163%2A10%5E8 square meters.

Step 5. ANSWER is 1.163%2A10%5E8 square meters.

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/215553: What are the steps to convert this problem into a polynomial equation?
f(x)=-3x3(x-2)2(x+5)
1 solutions
Answer 162872 by drj(1380) About Me  on 2009-09-22 09:03:03 (Show Source):
You can put this solution on YOUR website!
What are the steps to convert this problem into a polynomial equation?
f%28x%29=-3x%5E3%28x-2%29%2A2%2A%28x%2B5%29

Step 1. Multiply out everything and collect like terms. Order terms in descending order in terms of its degree.

f%28x%29=-3x%5E3%28x-2%292%28x%2B5%29=-6x%5E3%28x-2%29%28x%2B5%29

Step 2. Let's multiply (x-2)(x+5) using the FOIL method:

%28x-2%29%28x%2B5%29=x%5E2%2B5x-2x-10=x%5E2%2B3x-10

Step 3. Now Take the equation in Step 2 and substitute in Step 1

f%28x%29=-6x%5E3%28x-2%29%28x%2B5%29=-6x%5E3%28x%5E2%2B3x-10%29=-6x%5E5-18x%5E4%2B60x%5E3

Step 4. Answer is f%28x%29=-6x%5E5-18x%5E4%2B60x%5E3

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/215555: i need to factorise this expression 5y squared + 7y
1 solutions
Answer 162871 by drj(1380) About Me  on 2009-09-22 08:53:10 (Show Source):
You can put this solution on YOUR website!
I need to factorise this expression 5y%5E2+%2B+7y

The common factor between 5y%5E2 and 7y is y and their are no common factors in terms of the numbers. Therefore, the expression is factored as

y%285y%2B7%29 ANSWER

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.

Good luck in your studies!

Respectfully,
Dr J