You can put this solution on YOUR website!
Graph the inequality

Step 1. Let's put the inequality as a 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. Add 2y-9 to both sides of the inequality to yield





Step 3. Divide 2 to both sides of the inequality

or

Solved by pluggable solver: Plot Any Inequality

Graphing function :

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonmetry please visit http://www.FreedomUniversity.TV/courses/Trignometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

You can put this solution on YOUR website!
The area of rectangle is 45 square inches. One dimension is 5 inches. What is the perimeter.

Step 1. Let where is the width and is the length.

Step 2. Given inches, then inches.

Step 3. Perimeter P means adding up all four sides or inches

Step 4. ANSWER: The perimeter is 28 inches.

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonmetry please visit http://www.FreedomUniversity.TV/courses/Trignometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

You can put this solution on YOUR website!
Find the dimensions of a rectangle , if the area equals 144 square in. and the length and the width are in the ratio of 2 to 1/2. (hint : in order to eliminate the fraction , the ratio may be changed to 4 to 1.

Step 1. Let A=Area = width * length = 144 square inches

Step 2. Let w be the width and 4w be the length.

Step 3. Then

Step 4. Divide 4 to both sides of equation.

Step 5. Take the square root yields or

Step 6. Then ...Check the area ...which is a true statement.

Step 7. ANSWER: The dimensions are 6 feet as the width and 24 feet as the length.

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonmetry please visit http://www.FreedomUniversity.TV/courses/Trignometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

You can put this solution on YOUR website!
Hi. I'm really struggling on the the process required to solve the following absolute value inequality:
absolute value of x squared minus 2 is less than 1



Step 1. Yep, absolute value is a tricky concept. Think of absolute value as a distance measurement. Say you walk five steps forward the distance is 5 steps. Say you walk five steps backward the distance is still 5 steps. That is .
The absolute value will lead to two inequalities.

Also, when taking the will always be positive even if x is negative. So when you take the . Please try to understand this concept.

Step 2. The absolute value leads to two equations given as follows

Equation A where is positive

Equation B where is negative. To make it positive we reverse the positions in to .

Step 3. Let's start with Equation A

Add 2 to both sides of inequality





Taking the square root to both sides yields



which also leads to two more equations as

for positive x and

for negative x or
where we mulitplied -1 to both sides of the equation and reversed the inequality.

We can combine the two inequalities as

ANSWER:

Step 4. For equation B, let's add to both sides of the inequality





Take the square root to both sides of the equation.

or

This also leads to two more equations

where x is for positive number and

where x is for negative numbers or
where we multiplied by -1 and reversed the inequality.

ANSWER: and

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

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Graph

Step 1. Form two columns: one for x and one for y. Try different values of x say -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Substitute x into the equation for y. For example when x=0, then y=0^2+4=4. So one point on the graph is (0,4) and see graph in Step 2. Try the other values of x.
Step 2. Here's the graph:



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

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Find two consecutive odd integers in which the sum is equal to one or more than three times the smallest.

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

Step 2. Let 3n be three times the smallest.

Step 3. Then n+n+2=1+3n or 2n+2=1+3n. Then n=1 and n+2=3.

Step 4. ANSWER: The numbers are 1 and 3.

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

You can put this solution on YOUR website!
Two angles are supplementary. One angle measures 12 degrees more than the other. What is the measure of the angles.

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

Step 2. Let x be one angle and let x+12 be its supplementary angle and one angle measures 12 degrees more than the other

Step 3. Then x+x+12=180 or 2x+12=180. Subtracting 12 from both sides of the equation yields 2x=168. Dividing by 2 to both sides yields x=84 degrees. Then x+12=96. Also, note that 84+96 add up to 180 degrees.

Step 4. ANSWER: The supplementary angles are 84 and 96 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
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Respectfully,
Dr J

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What you would do to simplify each one.
1. Since square root has an exponent of 1/2 and 4*4=16
2. Since 10*10=100.

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

You can put this solution on YOUR website!
The length of a rectangle is 6 feet more than three times the width. The area of the rectangle is 240 square feet. What are the dimensions?

Step 1. Let w be the width and 3w+6 is the length since rectangle is 6 feet more than three times the width.

Step 2. Area = width * length = w(3w+6) = 240 square feet

Step 3. Then we can put the equation in Step 2 in quadratic form



Subtract 240 to both sides of the equation



Step 4. We can use the quadratic formula given as



where a=3, b=6, and c=-240

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=2916 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 8, -10. Here's your graph:

So select the positive solution for positive dimensions:

and

Verify area.... ...which is a true statement.

Step 5. Dimensions of the rectangle are a width of 8 feet and a length of 30 feet.

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

You can put this solution on YOUR website!
find the intersection of these two lines...

Equation A
Equation B

Step 1. Let's put the variable terms x and y on the left side and numbers on the right side of equation as given by Step 2.

Step 2. For Equation A, subtract 4y to both sides of the equation and; for equation B add 5x to both sides of the equation.

Equation A-1
Equation B-1

Step 3. Multiply 2 to both sides of Equation B-1 to get


Equation A-1
Equation B-2

Step 4. Add Equations A-1 and B-2 and note the y-terms cancel each other out leaving the x-terms on the left side.



or

Step 5. Substitute this value of x into either Equations A-1 or B-2. Let's choose Equation A-1.
Equation A-1



Multiply by 13 to both sides of equation to get rid of denominator





Add 52y-26 to both sides of equation





Divide 52 to both sides of the equation





Step 6. ANSWER: So x=14/13 and y=4/13 or the intersection point is (14/13,4/13).

We can verify the above result by substituting these values into both equations to see if it leads to a true statement.

Here's another approach to solving the linear system equations by substitution:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve: We'll use substitution. After moving -4*y to the right, we get: , or . Substitute that into another equation: and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. error_location: 101 Same result as before. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J

Finance/216147: what is 18=5p+3? 1 solutions Answer 163238 by drj(1380)   on 2009-09-23 17:00:40 (Show Source): You can put this solution on YOUR website! what is 18=5p+3? Step 1. Subtract 3 from both sides of equation to get p-terms on right side and numbers only on left side. Step 2. Divide 5 from both sides of the equation Check if or which is a true statement. Step 3. 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

Linear-equations/216116: Solve for x/2 + y/5=1 for y. answer : y= -5/2x + 5 anyone knows why the answer is y= -5/2 + 5 1 solutions Answer 163234 by drj(1380)   on 2009-09-23 16:55:18 (Show Source): You can put this solution on YOUR website! Solve for x/2 + y/5=1 for y. Answer : y= -5/2x +5 Step 1. The answer is in slope-intercept form where m is the slope and b is the y-intercept when x=0 at point (0,b). In this example, the answer reveals that m=-5/2 and b=5. Step 2. To get this equation from , use the following steps: Multiply by 10 to both sides of the equation to get rid of the denominators. Subtract 5x from both sides of the equation Divide 2 to both sides of the equation ANSWER Now here's a plot and note the slope m=-5/2 and y-intercept b=5 at point (0,5) 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

Systems-of-equations/216118: How do you solve this(7a+3)+(-a-5)=-16? 1 solutions Answer 163229 by drj(1380)   on 2009-09-23 16:46:51 (Show Source): You can put this solution on YOUR website! How do you solve this(7a+3)+(-a-5)=-16? 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: a=-2.33333333333333. Graphical form: Equation was fully solved. Text form: (7a+3)+(-a-5)=-16 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( (7a+3)+(-a-5)=-16 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Remove unneeded parentheses around terms , It becomes . Look at . Remove unneeded parentheses around terms , It becomes . Look at . Added fractions or integers together It becomes . Look at . Moved to the right of expression It becomes . Look at . Removed extra sign in front of It becomes . Look at . Eliminated similar terms , replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Moved these terms to the left It becomes . Look at . Added fractions or integers together It becomes . Look at . Solved linear equation equivalent to 6*a+14 =0 It becomes . Result: This is an equation! Solutions: a=-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

Linear-equations/216122: Find the equation of each line in y=mx+b form (-3,5) slope 1/5 1 solutions Answer 163225 by drj(1380)   on 2009-09-23 16:45:06 (Show Source): You can put this solution on YOUR website! Find the equation of each line in y=mx+b form (-3,5) slope 1/5 Step 1. The equation of the line given as y=mx+b is the slope-intercept form where m is the slope at b is the y-intercept when x=0 or at point (0,b). Step 2. Since the slope is , we have . To get the y-intercept b, substitute x=-3 and y=5 since this line passes through the point (-3,5). Multiply 5 to both sides to get rid of denominator. Add 3 to both sides of the equation Divide 5 to both sides of the equation Step 3. ANSWER: The equation is The graph is shown below. Note the y-intercept at x=0 and the slope of 1/5 which means five units to the left, then one unit up. 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/216107: answer this problem step by step:wright an equation for eac line. then graph the line. through (-2,1) and parallel to y = -3 + 1 1 solutions Answer 163218 by drj(1380)   on 2009-09-23 16:34:09 (Show Source): You can put this solution on YOUR website! answer this problem step by step:wright an equation for eac line. then graph the line. through (-2,1) and parallel to y = -3x + 1 Step 1. The line is in slope-intercept form given as y=mx+b where m is the slope and y-intercept is b at point (0,b). For this example, m=-3 and b=1. Step 2. Parallel lines have the same slope. So m=-3. Now we need to pass this line through (-2,1) or x=-2 and y=1. Then, to find b the y-intercept for this line substitute x and y values into the equation y=-3x+b (this is the line parallel to y=-3x+1. Subtract 6 from both sides of the equation Step 3. Now that we have slope and the y-intercept , then the equation becomes Step 4. ANSWER The graph of the two parallel lines is shown below and note the y-intercepts to determine which line is which. You should observe that the red line is described as and the green line is described as . 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/216079: (x-6x+9)/(x-3) 1 solutions Answer 163206 by drj(1380)   on 2009-09-23 15:49:55 (Show Source): You can put this solution on YOUR website! Step 1. Look at the numerator . Step 2. Need to integers m and n whose sum is -6 and product is 9. Step 3. The two integers are -3 and -3. We can factor through grouping where -6x=-3x-3x. We can also recognize that the trinomial is a perfect square, that is . Nevertheless the following steps, will show the technique of grouping. Factor (x-3) from both groups Step 4. Now substitute the expression in Step 3 with Note we can cancel the factor (x-3) in the numerator and denominator. Step 4. ANSWER: I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J

Equations/216081: Please help to solve this problem: the larger of 2 numbers is 20 more than the smaller. 4 times the larger is 70 more than 5 times the smaller, find the number. thank you Rick 1 solutions Answer 163202 by drj(1380)   on 2009-09-23 15:36:32 (Show Source): You can put this solution on YOUR website! Please help to solve this problem: The larger of 2 numbers is 20 more than the smaller. 4 times the larger is 70 more than 5 times the smaller, find the number. thank you Rick Step 1. Let x be the smaller number and let x+20 be the larger number. Step 2. Let 4(x+20) be four times the larger. Step 3. Let 5x be five times the smaller. Step 4. Then since 4 times the larger is 70 more than 5 times the smaller. Step 5. The following steps will solve the equation in Step 4. Subtract 4x+70 from both sides of the equation to get x-terms on the right side and numbers on the left side of the equation. and Check if or which is a true statement. Step 6. ANSWER. The numbers are 10 and 32. I hope the above steps were helpful. For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J

Numbers_Word_Problems/215773: What are three consecutive integers such that the sum of twice the smallest and three times the largest is 126? 1 solutions Answer 163199 by drj(1380)   on 2009-09-23 15:26:30 (Show Source): You can put this solution on YOUR website! What are three consecutive integers such that the sum of twice the smallest and three times the largest is 126? Step 1. Let n be an integer (smallest integer), n+1 and n+2 (largest integer) be the next two consecutive integers. Step 2. Let 2n be twice the smallest integer. Step 3. Let 3(n+2) be three times the largest integer. Step 4. Then since the sum of twice the smallest and three times the largest is 126. Step 5. The following steps will solve the equation in Step 4. Subtract 6 from both sides of the equation Divide 5 to both sides of the equation With , then and Check sum... which is a true statement. Step 6. ANSWER: The numbers are 24, 25, and 26. 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

Age_Word_Problems/215999: Tom is half as old as Ellen was three years ago. In 10 years, Ellen will be one-and-one-half times as old as Tom. Would you please show me the formula to use? And the answer? Thank you. 1 solutions Answer 163158 by drj(1380)   on 2009-09-23 12:24:04 (Show Source): You can put this solution on YOUR website! Tom is half as old as Ellen was three years ago. In 10 years, Ellen will be one-and-one-half times as old as Tom. Would you please show me the formula to use? And the answer? I probably need more info but here is the problem set-up. Step 1. Let be Tom's current age and let be Ellen's age Step 2. Let be Tom's age three years ago and be Ellen's age three years ago Step 3. Let be Ellen's age three years ago since Tom is half of Ellen's age three years ago. Simply this equation as follows Add 6-y to both sides of the equation to isolate x and y terms on one side and numbers on the right side Step 4. Let be Ellen's age in ten years since Ellen will be one and one half times as old as Tom where , x+10 is Tom's age in ten years, and y+10 is Ellen's age in ten years. Multiply by 2 to both sides of the equation to get rid of denominator Subtract 3x-20 to both sides of the equation Step 5. Now we have a linear system of equations from Steps 3 and 4 and is shown below: Step 6. Now solve the linear system of equations in Step 5 using substitution. Solved by pluggable solver: SOLVE linear system by SUBSTITUTION Solve: We'll use substitution. After moving -1*y to the right, we get: , or . Substitute that into another equation: and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. error_location: 101 So x=16 and y=29. Check the ages three ago and where Ellen is twice the age of Tom three years ago...so this is a true statement. Check the ages ten years from now. and or which is another true statement. Step 7. So Tom is 16 years old and Ellen is 29 years old. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J expressions/216002: This question is from textbook PREALGEBRA -20=-4X-6X 1 solutions Answer 163150 by drj(1380)   on 2009-09-23 11:26:39 (Show Source): You can put this solution on YOUR website! Step 1. Combine the x-terms on the right side of the equation Step 2. Divide by -10 to both sides of the equation Step 3. 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 Linear-systems/215986: Could you help me solve this inequality 5w+2 < 8w+23 1 solutions Answer 163147 by drj(1380)   on 2009-09-23 11:22:30 (Show Source): You can put this solution on YOUR website! Could you help me solve this inequality Step 1. Subtract 5w to both sides of the inequality Step 2. Subtract 23 from both sides of the inequality Step 3. Divide 3 to both sides of the inequality. Step 4. The answer is or 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/215978: This question is from textbook Intermediate Algebra Write an equivalent expression using exponential notation and simplify (125x)^2/3 1 solutions Answer 163145 by drj(1380)   on 2009-09-23 11:15:35 (Show Source): You can put this solution on YOUR website! Write an equivalent expression using exponential notation and simplify where 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/215993: graph the line y-4= -2(x+1) Please help I don't know where to begin 1 solutions Answer 163138 by drj(1380)   on 2009-09-23 10:07:10 (Show Source): You can put this solution on YOUR website! Graph the line y-4= -2(x+1) Please help I don't know where to begin. Step 1. Put the 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) or x=0 and y=b. Step 2. Add 4 to both sides of the equation to get the equation in slope-intercept form. Note the slope m=-2 and the y-intercept b=2. (see graph on last step) Step 3. Now, it takes two points to draw a line. Say we pick one point is at x=0 then evaluate y and the other point is y=0 and find x. These points are relatively easy to find when compared to other points on the line. Step 4. Find y when x=0 So at x=0, then y=2 or we have point (0,2) as one point. Step 5. Find x when y=0 Add 2x to both sides of the equation. Divide 2 to both sides of the equation to get x Now we have the other point at (1,0) Step 6. Use the two points (0,2) and (1,0), to plot the graph below Note the slope m=-2 and the y-intercept b=2=y at x=0 and it passes through the points (0,2) and (1,0). 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/215988: This question is from textbook mathematical excursions Graph the orderer-pair solutions of y=x+1 when x= -5,-3,0,-3, and 5. 1 solutions Answer 163137 by drj(1380)   on 2009-09-23 09:47:22 (Show Source): You can put this solution on YOUR website! Graph the ordered-pair solutions of y=x+1 when x= -5,-3,0,3, and 5. Step 1. The given equation y=x+1 where it is in slope-intercept form where m is the slope and the y-intercept b at (0,b). Here m=1 and b=1. Step 2. Form a two-columns: one for x and the other for y point to evaluate slope see Step 3 where x1=0, y1=1 point to evaluate slope see Step 3 where x2=5, y2=6 Step 3. To verify given equation, y=mx+b=x+1, we have the slope is given as Step 4. As mentioned before, the slope-intercept point is given as where m is the slope and b is the y-intercept at point (0,1) or x=0 and y=b. In our case x=0 implies b=1. Then our equation is as given by the problem The graph is shown below and note that the line passes through all the points in Step 2. 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/215984: This question is from textbook derive the slope intercept form of a linear equation from the slope formula using (0,b) as the coordinates of the point where the line crosses the y axis and an arbitary point (x,y) 1 solutions Answer 163136 by drj(1380)   on 2009-09-23 09:32:22 (Show Source): You can put this solution on YOUR website! Derive the slope intercept form of a linear equation from the slope formula using (0,b) as the coordinates of the point where the line crosses the y axis and an arbitary point (x,y) Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept b at point (0,b). Step 2. The slope formula is given for two points P(x1,y1) and Q(x2,y2) as Step 3. Now let x2=x, y2=y, x1=0, and y1=b and substitute in the slope formula in Step 2. Multiply x to both sides of the equation to get rid of denominator Now add b to both sides of the equation. 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 Linear-equations/215957: Your gym membership costs $33 per month after an initial membership fee. You paid a total of $225 after 5 months. Write an equation that gives the total cost as a function of the length of your gym membership (in months). Find the total cost after 10 months. 1 solutions Answer 163135 by drj(1380)   on 2009-09-23 09:22:03 (Show Source): You can put this solution on YOUR website! Your gym membership costs $33 per month after an initial membership fee. You paid a total of $225 after 5 months. Write an equation that gives the total cost as a function of the length of your gym membership (in months). Find the total cost after 10 months. Step 1. Let x be the number of months paid. Step 2. Let 33x be the dollar value of the cost paid after x months (no initial fee yet) Step 3. Let 33*5=165 be the cost paid on a monthly basis for 5 months. But the total cost is 225 dollars after 5 months. This implies that the membership fee is 225-165=60 dollars. Step 4. Let TC be the total cost. Step 5. ANSWER: Then the equation of the total cost . Step 6. ANSWER: After 10 months, total cost dollars. 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/215983: The second angle of a triangle is fifty less than four times the first angle. The third angle is forty less than the first. Find the measures of the three angles. 1 solutions Answer 163134 by drj(1380)   on 2009-09-23 09:15:02 (Show Source): You can put this solution on YOUR website! The second angle of a triangle is fifty less than four times the first angle. The third angle is forty less than the first. Find the measures of the three angles. Step 1. Let x be the first angle and 4x means 4 times the first angle. Step 2. Let 4x-50 be the second angle Step 3. Let x-40 be the third angle. Step 4. Sum of the angles in a triangle is 180 degrees. Step 5. Adding up the three angles is . Solving yields the following steps. Add 90 to both sides of the equation Divide 6 to both sides of the equation Then and . Step 6. ANSWER. The angles of the triangle are 45, 130, and 5. Note=45+130+5=180 which is a true statement. 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/215964: what is the measure of an angle if the measure of its complement is 47 degrees 1 solutions Answer 163131 by drj(1380)   on 2009-09-23 09:00:17 (Show Source): You can put this solution on YOUR website! What is the measure of an angle if the measure of its complement is 47 degrees Step 1. Complementary angles means two angles add up to 90 degrees. Step 2. Let x be the angle and 90-x be the complementary angles. Step 3. As given, 90-x=47 or x=90-47=43 Step 4. ANSWER. Angle is 43 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 Trigonometry-basics/215934: evaluate the six trigonometric functions of the real number t= 5pi/6 1 solutions Answer 163129 by drj(1380)   on 2009-09-23 08:55:42 (Show Source): You can put this solution on YOUR website! Evaluate the six trigonometric functions of the real number t= 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/215920: The length of the rectangular tennis court at wimbledon is 6 feet longer than twice the width. If the courts perimeter is 228 feet,what are the courts dimensions 1 solutions Answer 163101 by drj(1380)   on 2009-09-23 00:29:32 (Show Source): You can put this solution on YOUR website! The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the courts perimeter is 228 feet,what are the courts dimensions Step 1. Let w be the width and let w+6 be the length. Step 2. Perimeter P is when you add up all four sides of the rectangle. That is, Step 3. Solving yields the following steps. Subtract 12 from both sides of the equation. Divide 4 to both sides of the equation With w=54 then w+6=60 and P=54+54+60+60=228...which is a true statement. Step 4. ANSWER. The width is 54 feet and the length is 60 feet. 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/215918: 7y=6y+1 1 solutions Answer 163100 by drj(1380)   on 2009-09-23 00:24:03 (Show Source): You can put this solution on YOUR website! Subtract 6y to both sides of the equation. Check. 7*1=6*1+1 or 7=7 which is a true statement. 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