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Solve:

Step 1. Multiply by (a-7)(a+4) to both sides of the equation to get rid of denominators.







Step 2. Add 4a-40 to both sides of the equation to get numbers on one side and variables on the other side.





Step 3. Divide by 14 to both sides of the equation to get a.








Step 4. Check solution with original equation to see if it leads to a true statement.










which is a true statement.

Step 5. ANSWER is


I hope the above steps were helpful.

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Find the inverse of the given function:
f(x)= 3x + 13

Step 1. Let f(x)=y, then y=3x+13. Now solve for x.

Step 2. Subtract 13 from both sides of the equation





Step 3. Divide by 3 to both sides of the equation



where g(y) is the inverse function

Step 4. ANSWER the inverse is

So check answer with following where we substitute f(x) into g(y). Then, which is true that .

I hope the above steps were helpful.

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Step 1. Add 8y to both sides of the equation to get numbers on one side and variables on the right.





Step 2. Subtract 3 from both sides of the equation to isolate y-term.




Step 3. Divide by 6 to both sides of the equation





Step 4. Check solution with original equation to see if it leads to a true statement.





which is a true statement

Step 5. ANSWER: Solution is .


I hope the above steps were helpful.

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Step 1. Add 2x to both sides of the equation to get numbers on one side and variables on the right.





Step 2. Subtract 6 from both sides of the equation to isolate x-terms.





Step 3. Divide by 6 to both sides of the equation





Step 4. Check solution with original equation to see it leads to true statement.





which is a true statement

Step 5. ANSWER: Solution is .


I hope the above steps were helpful.

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, what is the answer if and

Step 1. Substitute values B and y into given equation .





Step 2. Divide by 2 to both sides of the equation





Step 3. Check solution with original equation to see if it leads to a true statement.





which is a true statement.

Step 4. ANSWER: The solution is

I hope the above steps were helpful.

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Step 1. Subtract 3m from both sides of the equation to get numbers on one side and variables on the right.





Step 2. Add 3 to both sides of the equation to isolate m-terms.





Step 3. Divide by 5 to both sides of the equation





Step 4. Check solution with original equation to see it leads to true statement.





which is a true statement

Step 5. ANSWER: Solution is .


I hope the above steps were helpful.

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If I were traveling at 253 mph, how many feet will I travel in 1 second?

Step 1. Convert 253 mph to feet/sec.

Step 2. 5280 feet = 1 mile

Step 3. 1 hour = 60 minutes = 60 minutes*60 seconds/minute = 3600 seconds

Step 4.

Note the units of miles and hours cancel they these units appear both in the numerator and denominator.

Step 5. ANSWER: Since , then in 1 second you travel 371.1 feet.


I hope the above steps were helpful.

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Step 1. Use quadratic formula given below to solve problem.



where a=25, b=20 and c=4.

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=0 is zero! That means that there is only one solution: . Expression can be factored: Again, the answer is: -0.4, -0.4. Here's your graph:

Step 2. ANSWER: Solutions are -0.4 and -0.4

I hope the above steps were helpful.

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Step 1. Subtract 3x from both sides of the equation to isolate numbers on one side and variables on the other side





Step 2. Subtract 5 from both of the equation to isolate the x-terms.





Step 3. Divide by 5 to both side of the equation to get x





Step 4. Check with original equation for a true statement.





which is a true statement

Step 5. ANSWER: Solution is .


I hope the above steps were helpful.

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One number exceeds another number by 32. The sum of the numbers is 82. What are the numbers?

Step 1. Let n be one number

Step 2. Let n+32 be the other number since it exceeds the number n by 32.

Step 3. Then n+n+32=82 since the sum of the numbers is 82.

Step 4. Solving will yield the following steps


Subtract 32 from both sides of the equation





Divide by 2 to both sides of the equation



Then

Step 5. ANSWER: The numbers are 25 and 57.

I hope the above steps were helpful.

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A car depreciates by 30% the first year and 12% per year afterward. How much will a $25000 car be worth after 5 years?

Step 1. 30% means 0.30 and 12% means 0.12.

Step 2. Let the initial price of car.

Step 3. Let be dollar value of car after first year.

Step 4. Let be dollar value of car after second year. Also, after third year

Step 5. Then be the dollar value of car after 5 years.



Step 6. ANSWER: The dollar value of the car after 5 years is $10,494.67.

I hope the above steps were helpful.

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Find 2 consecutive integers such that three times the square of the first is equal to seven more than five times the second.
What is the answer?

Step 1. Let be the first integer.

Step 2. Let be the next consecutive integer

Step 3. Let be three times the square of the first.

Step 4. Let be seven more than five times the second.

Step 5. Then since three times the square of the first is equal to seven more than five times the second.

Step 6. Solving the equation in Step 5 yields the following steps.





Subtract 5n+12 from both sides of the equation





Step 7. To solve use the quadratic equation given as



where a=3, b=-5, and c=-12

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=16 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3, -1. Here's your graph:

With n=3 then n+1=4. Check if true so or which is a true statement.

With n=-1 then n+1=0 Check if true so or which is not a true statement.

Step 8. ANSWER: The numbers are 3 and 4

I hope the above steps were helpful.

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Find three consecutive even integers such that the sum of the first integer and three times the third integer is 64 more than the second integer.

Step 1. Let n be the first even integer.

Step 2. Let n+2 and n+4 be the next two consecutive even integers.

Step 3. Let 3(n+4) be three times the third integer.

Step 4. Let n+3(n+4) be the sum of the first integer and 3 times the third integer

Step 5. Let n+2+64=n+66 be 64 more than the second integer.

Step 6. Then, n+3(n+4)=n+66 since the sum of the first integer and three times the third integer is 64 more than the second integer

Step 7. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: n=18. Graphical form: Equation was fully solved. Text form: n+3*(n+4)=n+66 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( n+3*(n+4)=n+66 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Moved these terms to the left , It becomes . Look at . Eliminated similar terms , replacing them with It becomes . Look at . Since has zero as a factor, it should be replaced with a zero Look at . Added fractions or integers together It becomes . Look at . Remove extraneous zero It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Solved linear equation equivalent to 3*n-54 =0 It becomes . Result: This is an equation! Solutions: n=18. Universal Simplifier and Solver Done!

With n=18, then n+2=20 and n+4=22

Check equation in Step 6: n+3(n+4)=n+66...18+3*22=18+66 or 84=84...which is a true statement.

Step 8 The three consecutive even integers are 18, 20, and 22.

I hope the above steps were helpful.

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Please help me identify the system as consistent or inconsistent, and dependent or independent.

3x=y+3 Equation 1
6x-2y=3 Equation 2

Step 1. Equation 1 in slope-intercept form is y=3x-3. It has a slope m=3.

Step 2. We can put Equation 2 in slope-intercept form as follows:

Subtract 6x from both sides of the equation





Divide by -2 to both sides of the equation





So this equation has a slope m=3. Since the equations of lines have the same slope they are in parallel and cannot intersect.

Step 3. The equations are inconsistent since they have the same slope and they are also independent (one equation is not a multiple of another).

I hope the above steps and explanation were helpful.

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Find The Equation Of The Line That Passes Through (4,6) And Is Parallel To The Line That Passes Through (6,-6) And (10,-4)?

Step 1. We'll put the equation of the line in slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). Also we know that parallel lines have the same slope. So let's find the slope of the line passing through the point (6,-6) and (10,-4)

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



Step 2. Now we have to find the line with slope going through point (4,6).

Step 3. As mentioned earlier, given two points (x1,y1) and (x2,y2), then the slope m is given as



Step 4. Let (x1,y1)=(4,6) or x1=4 and y1=6. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given . Substituting above values and variables in the slope equation m yields the following steps:





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





Step 7. Add 6 to both sides of the equation





Step 7. ANSWER: The equation in slope-intercept form is where the slope and the y-intercept b=4.

Note: the above equation can be rewritten in standard form as



And the graph is shown below which is consistent with the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/-1 = -8. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4. Slope is --1/2 = 0.5. Equation in slope-intercept form: y=0.5*x+4.

I hope the above steps and explanation were helpful.

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Step 1. Add the x-terms





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





Step 3. ANSWER: The solution is

I hope the above steps and explanation were helpful.

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Please help me determine the slope and the y-intercept; y= -18x-772

Step 1. The slope-intercept form of a linear equation is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). The given equation y=-18x-772 is in slope-intercept form.

Step 2. ANSWER: Comparing y=-18x-772 with y=mx+b, then the slope m=-18 and b=-772.
I hope the above steps and explanation were helpful.

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What is the perimeter of a square whose one side is 3/4

Step 1. Perimeter P means adding 4 sides of the square where we define s as the length of the square's side.

Step 2.

Step 3. ANSWER:

I hope the above steps and explanation were helpful.

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can you help me please. 6=3+5(d-2)
this is what i tried. 6=3+5(d-2)
6=3+5d-10 good
6=-7+5d good

Step 1. Now add 7 to both sides of the equation and to isolate d on the right side.





Step 2. Divide by 5 to both sides of the equation to get d





Step 3. Check solution with original equation

or which is a true statement.

Step 4. ANSWER:

I hope the above steps and explanation were helpful.

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Please help me tell whether the lines are "parallel,perpendicular,or neither". f(x)=y

f(x)=2x-4 or y=2x-4 where y=f(x)
8x+4f(x)=8 or 4y=-8x-8 where y=f(x)

Step 1. Line are parallel when they have the same slope and lines are perpendicular when the product of the slopes between the two lines is -1 or m1*m2=-1 where m1 is the slope of the first line and m2 is the slope of the perpendicular line.

Step 2. Let's put the equations in slope intercept form where y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b)

Step 3. Here, y=2x-4 is in slope intercept form so it has a slope of 2.

Step 4. Now 4y=8x-8 can be put in slope intercept form where we can divide by 4 to both sides of the equation giving y=-2x-2. So the slope is -2.

Step 5. The slopes in Step 3 and 4 are not equal so it's not parallel and their product is not -1 so they are not perpendicular.

Step 6. ANSWER: Based on the Steps 3-5, the lines are neither parallel nor perpendicular.

I hope the above steps were helpful.

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Step 1. Subtract 24 from both sides of the equation.





Step 2. ANSWER:

I hope the above steps were helpful.

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Please help me factor this Trinomial.



Step 2. Find the common factor for x-terms with the highest exponent and in this case it is x.



Step 3. Find the common factor for y-terms with the highest exponent and in this case it is y.



Step 4. ANSWER:

I hope the above steps were helpful.

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Find the equation of the line that has a slope of -8 and passes through the point (-1,-5) write the equation in standard form.

Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). From the slope intercept form we can derive the standard form given as Ax+By=C where A, B, and C are constants. Now, let's find the equation of the line in slope-intercept form

Step 2. Here, we have to find the line with slope m=-8 going through point (-1,-5).

Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as



Step 4. Let (x1,y1)=(-1,-5) or x1=-1 and y1=-5. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given . Substituting above values and variables in the slope equation m yields the following steps:





Step 6. Multiply x+1 to both sides to get rid of denominator on right side of equation.





Step 7. Add -5 to both sides of the equation





Step 7. The equation in slope-intercept form is where the slope m=-8 and the y-intercept b=-13.

Note: the above equation can be rewritten in standard form by adding 8x to both sides of the equation.





Step 8. ANSWER: The equation of the line in standard form is .


And the graph is shown below which is consistent with the above steps.



I hope the above steps and explanation were helpful.

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Translate but do not solve. The sum of negative 6 and twice a number is equal to negative 43.

Step 1. Let x be a number.

Step 2. Let 2x be twice a number.

Step 3. Let -6+2x be the sum of negative 6 and twice a number

Step 4. ANSWER: Then, -6+2x=-43 since the sum of negative 6 and twice a number is equal to negative 43.

I hope the above steps were helpful.

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Please help me find the center (h,k) and radius of the given equation;



Step 1. The general equation of the circle is



where the center is at point (a,b) and r is the radius

Step 2. Factor the first three terms and the last three terms as follows:





Step 3. Comparing the equations with Step 1 and the last one in Step 2 yields a center at (-9,-6) with radius 2.

Step 4. ANSWER: Center is at (-9,-6) with radius 2.

I hope the above steps were helpful.

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Combine the like terms



ANSWER:

I hope the above steps were helpful.

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How do I solve and graph for x intercept and y intercept the following equation: y = -x ? Thanks!!

Step 1. The slope-intercept form is 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 with we have the slope m=-1 and b=0.

Step 3. To graph to get the y-intercept we set x=0 and in this case y=b=0.

Step 4. To get the x-intercept we set y=0 and again in this case x=0. So we have (0,0) as a point. Since the x-intercept and y-intercept are the same then we need another point. Say at x=1 then y=-1 so (1,-1) is a point on the line. We can use these two points (0,0) and (1,-1) to plot the line.

Step 5. Another way to graph: With the slope m=-1 then for every unit you go to the right you go one unit down. You get the same result (1,-1) or from (1,-1) you get (2,-2) as another point on the line.

Step 6. Here's the graph,



I hope the above steps were helpful.

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Factor by grouping:



Step 1. Factor out x in the first two terms and factor out 3 in the last two terms:



Step 2. The factor is common to both groups in parenthesis, so factor that out.



Step 3. ANSWER:

I hope the above steps were helpful.

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The perimeter of rectangular poster is 80 inch. The length is 10 inches greater than the width. Find the length.

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+10 be the length since the length is 10 inches greater than the width

Step 4. Then, P=w+w+w+10+w+10=80.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: w=15. Graphical form: Equation was fully solved. Text form: w+w+w+10+w+10=80 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( w+w+w+10+w+10=80 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Added fractions or integers together It becomes . Look at . Moved to the right of expression 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 . Removed extra sign in front of It becomes . Look at . Solved linear equation equivalent to 4*w-60 =0 It becomes . Result: This is an equation! Solutions: w=15. Universal Simplifier and Solver Done!

For w=15 , then w+10=25 and P=2(15+25)=80 which is a true statement.

Step 6. ANSWER: The length is 25 inches.

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

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If two events A and B are independent and you know that P(A) = 0.75, what is the value of P(A | B)?

Step 1. P(A|B)=P(A) since A and B are independent. It doesn't matter what the event B is the probability of P(A|B) will equal P(A).

Step 2. ANSWER: P(A|B)=P(A)=0.75

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

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 . Moved to the right of expression It becomes . Look at . Moved to the right of expression It becomes . Look at . Moved these terms to the left , It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together 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 . Solved linear equation equivalent to 5*A-722 =0 It becomes . Result: 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