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Geometry_Word_Problems/225160: 10. Angles A and B are supplementary angles and angle A is 2⁰ more than 4 times angle B. Find the measures of angle A and angle B.
1 solutions

Answer 168078 by drj(1380) on 2009-10-11 21:57:10 (Show Source):

You can put this solution on YOUR website!
Angles A and B are supplementary angles and angle A is 2⁰ more than 4 times angle B. Find the measures of angle A and angle B.

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

Step 2. Let A be one angle.

Step 3. Let B=180-A be its supplementary angle.

Step 4. Let A=2+4(180-A) since angle A is 2 degrees more than 4 times angle B=180-A.

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

YOUR ANSWER

Here's what you tried:
This is an equation! Solutions: A=144.4.
Graphical form: Equation was fully solved.
Text form: A=2+4*(180-A) simplifies to 0=0
Cartoon (animation) form:
For tutors: simplify_cartoon( A=2+4*(180-A) )
If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at

A=2%2B4%2A%28highlight_red%28+180+%29-A%29

.
Moved

to the right of expression
It becomes A=2%2B4%2A%28-A%2Bhighlight_green%28+180+%29%29

Look at

A=highlight_red%28+2+%29%2B4%2A%28-A%2B180%29

.
Moved

to the right of expression
It becomes A=4%2A%28-A%2B180%29%2Bhighlight_green%28+2+%29

Look at

A=highlight_red%28+4%2A%28-A%2B180%29%2B2+%29

.
Moved these terms to the left highlight_green%28+-4%2A%28-A%2B180%29+%29

It becomes A-highlight_green%28+4%2A%28-A%2B180%29+%29-highlight_green%28+2+%29=0

Look at

A-highlight_red%28+4%2A%28-A%2B180%29+%29-2=0

.
Expanded term

by using associative property on %28-A%2B180%29

It becomes A%2Bhighlight_green%28+4%2AA+%29-highlight_green%28+4%2A180+%29-2=0

Look at

A%2B4%2AA-highlight_red%28+4+%29%2Ahighlight_red%28+180+%29-2=0

.
Multiplied numerator integers
It becomes A%2B4%2AA-highlight_green%28+720+%29-2=0

Look at

A%2B4%2AA-highlight_red%28+720+%29-highlight_red%28+2+%29=0

.
Added fractions or integers together
It becomes A%2B4%2AA%2Bhighlight_green%28+-722+%29=0

Look at

.
Removed extra sign in front of

It becomes A%2B4%2AA-highlight_green%28+722+%29=0

Look at

highlight_red%28+A+%29%2Bhighlight_red%28+4%2AA+%29-722=0

.
Eliminated similar terms highlight_red%28+A+%29

replacing them with highlight_green%28+%281%2B4%29%2AA+%29

It becomes highlight_green%28+%281%2B4%29%2AA+%29-722=0

Look at

%28highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%29%2AA-722=0

.
Added fractions or integers together
It becomes %28highlight_green%28+5+%29%29%2AA-722=0

Look at

highlight_red%28+%28highlight_red%28+5+%29%29%2AA+%29-722=0

.
Remove unneeded parentheses around factor highlight_red%28+5+%29

It becomes highlight_green%28+5+%29%2AA-722=0

Look at

.
Solved linear equation highlight_red%28+5%2AA-722=0+%29

equivalent to 5*A-722 =0
It becomes highlight_green%28+0+%29=0

.
Result: 0=0

This is an equation! Solutions: A=144.4.

Universal Simplifier and Solver

Done!

With A=144.4 then B=180-144.4=35.6 so check if equation in Step 4 is true... 144.4=2+4(35.6)...which it is.

Step 5. ANSWER: Angle A is 144.4 degrees and angle B is 35.6 degrees.

I hope the above steps and explanation were helpful.

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

And good luck in your studies!

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

Miscellaneous_Word_Problems/225137: Recall that the sum of the measures of the angles of a triangle is 180 degrees. In the triangle below, angle c has the same measure as angle b, and a measures 42 degrees less than angle b. Find the measure of each angle.
1 solutions

Answer 168075 by drj(1380) on 2009-10-11 21:49:31 (Show Source):

You can put this solution on YOUR website!
Recall that the sum of the measures of the angles of a triangle is 180 degrees. In the triangle below, angle c has the same measure as angle b, and a measures 42 degrees less than angle b. Find the measure of each angle.

Step 1. Given c=b

Step 2. a=b-42 since angle a measures 42 less than angle b.

Step 3. Then, b-42+b+b=180 since c=b and the three angles add to 180 degrees.

3b=222%7D%7D%0D%0A%0D%0A%0D%0A%7B%7B%7B3b%2F3=222%2F3

3b=222%7D%7D%0D%0A%0D%0A%0D%0A%7B%7B%7B3b%2F3=222%2F3

and

and

Step 4. Check if the angles equal to 180...74+74+32=180 which it does.

Step 6. ANSWER: Angle a is 32 degrees and angles b and c is each 74 degrees.

I hope the above steps and explanation were helpful.

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

And good luck in your studies!

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

Numbers_Word_Problems/225116: One number is 2 more than 5 times another. Their product is 3. Find the numbers.
1 solutions

Answer 168072 by drj(1380) on 2009-10-11 21:23:45 (Show Source):

You can put this solution on YOUR website!
One number is 2 more than 5 times another. Their product is 3. Find the numbers.

Step 1. Let x be one number

Step 2. Let 2+5x be the other number since its 2 more than 5 times the first number.

Step 3. Then, x%282%2B5x%29=3

since their product is 3.

Step 4. Turn this equation into a quadratic one in standard form as follows:

x%282%2B5x%29=3

Subtract 3 from both sides

2x%2B5x%5E2-3=3-3

Simplify and arrange in descending order to get our quadratic equation

5x%5E2%2B2x-3=0

Step 4. To solve, 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=5, b=2, and c=-3

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 5x%5E2%2B2x%2B-3+=+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

.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+64+%29%29%2F2%5Ca

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+64+%29%29%2F2%5C5+=+0.6

x%5B2%5D+=+%28-%282%29-sqrt%28+64+%29%29%2F2%5C5+=+-1

Quadratic expression 5x%5E2%2B2x%2B-3

can be factored:
5x%5E2%2B2x%2B-3+=+5%28x-0.6%29%2A%28x--1%29

Again, the answer is: 0.6, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B2%2Ax%2B-3+%29

With x=0.6 then 2+5x=2+5*0.6=5

With x=-1 then 2+5*(-1)=-3.

Step 5. ANSWER: The numbers are 0.6 and 5 as one pair and -1 and -3 as the other pair of numbers.

I hope the above steps and explanation were helpful.

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

And good luck in your studies!

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

test/225054: graph y=3x+1
1 solutions

Answer 168068 by drj(1380) on 2009-10-11 21:05:12 (Show Source):

You can put this solution on YOUR website!
Graph y=3x+1

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

Step 2. Comparing the given equation with y=mx+b shows that the slope m=3 and y-intercept is 1 when x=0 or at point (0,1).

Step 3. To graph, start with the point (0,1) and the slope means for every one unit to the right we go three units up since the slope is 3. This means that one point is (0+1,1+3) or (1,4) is a point on the line.

Step 4. Using the two points (0,1) and (1,4) we have the following graph of the line since it takes two points to make a line.

graph%28400%2C400%2C+-5%2C+5%2C+-5%2C+5%2C+3x%2B1%29

graph%28400%2C400%2C+-5%2C+5%2C+-5%2C+5%2C+3x%2B1%29

I hope the above steps and explanation were helpful.

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

And good luck in your studies!

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

test/225051: Find the equation of the line containing the point (4, 25) and perpendicular to the line 11x+55y=-12 .

1 solutions

Answer 168066 by drj(1380) on 2009-10-11 20:56:57 (Show Source):

You can put this solution on YOUR website!
Find the equation of the line containing the point (4, 25) and perpendicular to the line 11x+55y=-12.

Step 1. Two lines are perpendicular if their product of the slopes is -1. In equation form m1*m2=-1 where m1 is the slope given by the first equation. And m2 is the slope of the line perpendicular to the first line.

Step 2. We need to put the above given line in slope intercept form so we can find the slope of the given line. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept b when x=0 or at point (0,b).

Step 3. The following steps puts the above equation in slope-intercept form

11x%2B55y=-12

Subtract 11 from both sides of the equation

11x%2B55y-11x=-12-11x

Divide by 5 to both sides of the equation

55y%2F55=-11x%2F55-12%2F55

Step 4. Comparing the last equation with y=mx+b, the slope m1=-1/5.

Step 5. Therefore, the slope of the perpendicular line is m2=-1%2F%28-1%2F5%29=5

since the product of the slopes between the two lines is -1 (or m1*m2=-1)

Step 6. So now we have a perpendicular line with slope m2=5 that must pass through the point (4,25)

Step 7. Given two points (x1,y1) and (x2,y2), then the slope m is given as

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

Step 4. Let (x1,y1)=(4,25) or x1=4 and y1=25. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given m=5

. Substituting above values and variables in the slope equation m yields the following steps:

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

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

5%28x-4%29=%28x-4%29%28y-25%29%2F%28x-4%29

Add 25 to both sides of the equation

5x-20%2B25=y-25%2B25

Step 7. ANSWER: The equation of the perpendicular line in slope-intercept form is y=5x%2B5

And the graph of the two lines are shown below.

graph%28600%2C600%2C+-10%2C+10%2C+-10%2C+10%2C+5x%2B5%2C-x%2F5-12%2F55%29

Graphs/225024: solve the system of equations by graphing. then classify
6x + y = 46
7x + 8y = 40
1 solutions

Answer 168059 by drj(1380) on 2009-10-11 20:34:33 (Show Source):

You can put this solution on YOUR website!
Solve the system of equations by graphing. Then classify

6x + y = 46
7x + 8y = 40

Step 1. Graph the two lines from above as shown below

graph%28400%2C400%2C+-10%2C10%2C-10%2C10%2C+-6x%2B46%2C+-7x%2F8%2B5%29

graph%28400%2C400%2C+-10%2C10%2C-10%2C10%2C+-6x%2B46%2C+-7x%2F8%2B5%29

Step 2. Based on the graph the intersection point is (8,-2) or x=8 and y=-2.

Step 3. Check if the solution (8,2) satisfies the above linear system of equations

6x + y = 46 or 6*8+-2=46 or 46=46 which is a true statement
7x + 8y = 40 or 7*8+8*(-2)=40 or 40=40 which is another true statement

Step 4. ANSWER: The solution is (8,2). The equations are independent and consistent providing a unique solution.

I hope the above explanation was useful.

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

test/225057: Graph y=x/2-3 by using the slope and y-intercept.
1 solutions

Answer 168054 by drj(1380) on 2009-10-11 20:28:10 (Show Source):

You can put this solution on YOUR website!
Graph y=x/2-3 by using the slope and y-intercept.

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

Step 2. Comparing y=x%2F2-3

with

, the slope m=1%2F2

and the y-intercept b=-3

Step 3. Now the slope of 1%2F2

for every two units you go the right, you go one unit up.
To plot the line take the y-intercept at point (0,-3). So starting at point (0,-3) or x1=0 and y1=-3 we go two units to the right means x2=0+2=2 and 1 unit up means y2=-3+1=-2. So we have two points (0,-3) and (2,-2) used to plot the line.

graph%28400%2C400%2C+-10%2C+10%2C+-10%2C+10%2C+x%2F2-3%29

graph%28400%2C400%2C+-10%2C+10%2C+-10%2C+10%2C+x%2F2-3%29

I hope the above explanation was useful.

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

Expressions-with-variables/225065: x+8y=76
-x+9y=77
1 solutions

Answer 168049 by drj(1380) on 2009-10-11 20:19:27 (Show Source):

You can put this solution on YOUR website!
x+8y=76
-x+9y=77

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:

+system%28+%0D%0A++++1%5Cx+%2B+8%5Cy+=+76%2C%0D%0A++++-1%5Cx+%2B+9%5Cy+=+77+%29%0D%0A++

We'll use substitution. After moving 8*y to the right, we get:
1%2Ax+=+76+-+8%2Ay

, or

. Substitute that
into another equation:
-1%2A%2876%2F1+-+8%2Ay%2F1%29+%2B+9%5Cy+=+77

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

drjctu@gmail.com

http://www.FreedomUniversity.TV
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Miscellaneous_Word_Problems/225094: The perimeter of a standard high school basketball court is 268ft. The length is 34ft longer than the width. Find the dimensions of the court.
1 solutions

Answer 168048 by drj(1380) on 2009-10-11 20:17:38 (Show Source):

You can put this solution on YOUR website!
The perimeter of a standard high school basketball court is 268ft. The length is 34ft longer than the width. Find the dimensions of the court.

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

Step 2. Let w be the width.

Step 3. Let w+34 be the length since the length is 34 ft longer than the width.

Step 4. Then, P=w+w+w+34+w+34=268.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: