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Graph the equation and show your slope: -4x-2y=-6

Step 1. Let's put the equation 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. Putting in slope-intercept form yields the following steps.

Add 2y+6 to both sides of the equation





Divide 2y to both sides of the equation







Step 3. ANSWER: The equation is where the slope m=-2 and y-intercept b=3.

Need one more point to graph the line since we have (0,3) as one point. A slope m=-2 means every move to one unit to the right yields two step downward.

So starting at (0,3) then one unit to the right means x2=0+1=1 and then two units down means y2=3-2=1. Then, the other point we can use to plot the line is (1,1). We can check if it satisfies the equation or

which it does.

Here's the graph:




I hope the above steps and explanation were helpful.

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Find the x and y intercepts of the graph of -2x-4y=-20

Step 1. The intercepts occur when the one of the coordinates is zero. The y-intercept is when x=0 or at point (0,b) where b is the y-intercept. The x-intercept is when y=0 or at point (a,0) where a is the x-intercept.

Step 2. So let x=0, then -2*0-4y-20 or 4y=20 or y=5 after dividing by 4 to both sides. Therefore, the y-intercept is 5.

Step 3. So let y=0, then -2x-4*0-20 or 2x=20 or x=10 after dividing by 10 to both sides. Therefore, the x-intercept is 10.

Step 4. ANSWER: The x-intercept is 10 and the y-intercept is 5.

I hope the above steps and explanation were helpful.

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Four consecutive integers whose sum is 58.

Step 1. Let n be an integer

Step 2. Let n+1, n+2, and n+3 be the next three consecutive integers.

Step 3. Then, n+n+1+n+2+n+3=58 since the sum of four consecutive integers is 58.

Step 4. Solving, 4n+6=58, yields the following steps:

Subtract 6 from both sides of the equation.





Divide 4 to both sides of the equation.



Then , and

Check if sum is 58....13+14+15+16=29+29=58....which is a true statement.

Step 5. ANSWER: Numbers are 13, 14, 15, and 16.


I hope the above steps and explanation were helpful.

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The supplement of an angle exceeds five times the complement of an angle by 10 degrees. Find the angle.

Step 1. Complementary angles is when two angles add up to 90 degrees.

Step 2. Supplementary angles is when two angles add up to 180 degrees.

Step 3. Let x be the angle.

Step 4. Let 90-x its complementary angle.

Step 5. Let 180-x be its supplementary angle.

Step 6. Let 5(90-x) be five times the complement

Step 7. 180-x=5(90-x)+10 since the supplement of an angle exceeds five times the complement of an angle by 10 degrees. Find the angle.

Step 8. 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: x=70. Graphical form: Equation was fully solved. Text form: 180-x=5*(90-x)+10 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( 180-x=5*(90-x)+10 ) 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 . Added fractions or integers together It becomes . Look at . Moved to the right of expression 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 4*x-280 =0 It becomes . Result: This is an equation! Solutions: x=70. Universal Simplifier and Solver Done!

With x=70, then 90-x=20 and 180-x=110.

Check...180-x=5(90-x)+10 or 110=5*20+10=110...which is a true statement.

Step 9. ANSWER: The angle is 70 degrees.

I hope the above steps and explanation were helpful.

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Graph using the slope and the y-intercept
x+5y=10

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. Put the given equation in slope intercept form.



Subtract x from both sides of the equation





Divide 5 to both sides of equation





Step 3. The equation has a slope m=-1/5 and y-intercept b=2.

Now the slope of for every five unit you go the right, you go one unit down.
To plot the line take the y-intercept at point (0,2). So starting at point (0,2) or x1=0 and y1=2 we go five unit to the right means x2=0+5=5 and 1 unit down means y2=2-1=1. So we have two points (0,2) and (5,1).



I hope the above explanation was useful.

And good luck in your studies!

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3. Use the intercepts to graph the equation:


Step 1. We can put this in standard form given as

where we added 2-y to both sides of the equation

Step 2. Now the intercepts occur when one of the coordinates is equal to zero, that is, x=0 or y=0.

Step 3. Let x=0, then we have the y-intercept given as







So for x=0, we have y=-2 and therefore point (0,-2) can be used to plot the line.

Step 4. Let y=0, the we have the x-intercept given as






So for y=0 we have x=2 and therefore another point (2,0) can be used to plot the line.

Step 5. It takes two points to draw a line and these point from Steps 3 and 4 is (0,-2) and (2,0)

Step 6. Graph the line as shown below using the intercepts point in Step 5.



And good luck in your studies!

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Find the slope if it exists of the line containing the pair of points:
(4,5) and (8,-3)

However, here are the steps showing you how you can check your work with one of the points.

Step 1. The slope of the line m is given as



where for our example is x1=4, y1=5, x2=8 and y2=-3 (think of ). 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 2. Substituting the above values in the slope equation gives







Step 3. The slope is calculated as -2 or m=-2

Step 4. Now use the slope equation of step 1 and choose one of the given points. I'll choose point (4,5). Letting y=y2 and x=x2 and substituting m=-2 in the slope equation given as,








Step 5. Multiply both sides of equation by x-4 to get rid of denomination found on the right side of the equation








Step 6. Now simplify and put the above equation into slope-intercept form.



Add 5 to both sides of the equation





ANSWER in slope-intercept form. m=-2 and y-intercept=13

Step 7. See if the other point (8,-3) or x=8 and y=-3 satisfies this equation



which is a true statement

So the point (8,-3) 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



See graph below to check the above steps and note the slope and the y-intercept at x=0



I hope the above steps were helpful.

And good luck in your studies!

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Is -2/3 a solution of 3x + 6 =4?

To find out if this is a solution substitute the value in the equation and see if it leads a true statement.







which is a true statement.

I hope the above steps were helpful.

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What is the greatest common factor of the terms and ?

Step 1. Look at the numbers 14 and 42. The common factor is 14 since 3*2*7=42 and 2*7=14.

Step 2. Look at the c terms and . The common factor is since and .

Step 3. Look at the d terms and the common factor is d.

Step 4. Based on Steps 1, 2, and 3, the greatest common factor is .

Step 5. ANSWER is

I hope the above steps were helpful.

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A right triangle has one leg three times as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg.

Step 1. Let x be the shorter leg.

Step 2. Let 3x be the longer leg and since it is three times longer than the shorter leg.

Step 3. Perimeter P means we add up all three sides of a triangle.

Step 4. Use Pythagorean Theorem to find the hypotenuse which states that the sum of the squares of the legs (x and 3x) is equal to the sum of the squares of the hypotenuse.

where c is the hypotenuse



Step 5. So

Step 6. ANSWER is

I hope the above steps were helpful.

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If a, b are elements of the REAL numbers and a+b=0, then a= -b.
I am having trouble with the steps, I kinda of know what types of axioms I need to use. Inverse and DEF. of Subtraction are some of those.

Step 1. Given

Step 2. Add -b to both sides of the equation:

Step 3. Simplify to both sides of the equation to get: ANSWER

I hope the above steps were helpful.

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The sum of two consecutive integers is 237. Find the two integers.

Step 1. Let n be an integer.

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

Step 3. Then n+n+1=237 since the sum of two consecutive integers is 237.

Step 4. Solving yields the following steps



Subtract 1 from both sides of the equation.



Divide by 2 to both sides of the equation.



and

Step 4. ANSWER: The integers are 118 and 119.

I hope the above steps were helpful.

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Use the intercept method to graph x-y=3.

Step 1. Intercepts occur when one of the coordinates is equal to 0. So the y-intercept occurs at x=0 and the x-intercept occurs at y=0.

Step 2. It takes two points to make a line. So use these intercepts points

Step 3. When x=0, then 0-y=3 or y=-3. So we have point (0,-3).

Step 4. When y=0, then x-0=3 or x=3. So we have another point (3,0).

Step 5. Graph the line as shown below using these two points found in Steps 3 and 4.



Note x-y=3 can be written as y=x-3 in slope-intercept form where slope m=1 and y-intercept b=-3.

I hope the above steps were helpful.

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Find the maximum area of a rectangle with a perimeter of 54 centimeters.

Step 1. Perimeter P means adding up all 4 sides of a rectangle or P=w+w+L+L=2(w+L) where w is the width and L is the Length.

Step 2. Maximum Area A=w*L is when the rectangle is a square or where s=w=L.

Step 3. So P=2(w+L)=2(s+s)=4s.

Step 4. P=54=4s or s=54/4=13.5.

Step 5. .

Step 6. ANSWER: Maximum area is 182.25 square centimeters.

I hope the above steps were helpful.

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Find the maximum area of a rectangle with a perimeter of 54 centimeters.

Step 1. Perimeter P means adding up all 4 sides of a rectangle or P=w+w+L+L=2(w+L) where w is the width and L is the Length.

Step 2. Maximum Area A=w*L is when the rectangle is a square or where s=w=L.

Step 3. So P=2(w+L)=2(s+s)=4s.

Step 4. P=54=4s or s=54/4=13.5.

Step 5. .

Step 6. ANSWER: Maximum area is 182.25 square centimeters.

I hope the above steps were helpful.

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2n+3n+7=-41

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: n=-9.6. Graphical form: Equation was fully solved. Text form: 2n+3n+7=-41 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( 2n+3n+7=-41 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION 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 5*n+48 =0 It becomes . Result: This is an equation! Solutions: n=-9.6. Universal Simplifier and Solver Done!

I hope the above steps were helpful.

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How do I solve problems like this 5x+6=2x+15?

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: x=3. Graphical form: Equation was fully solved. Text form: 5x+6=2x+15 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( 5x+6=2x+15 ) 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 . 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 . Solved linear equation equivalent to 3*x-9 =0 It becomes . Result: This is an equation! Solutions: x=3. Universal Simplifier and Solver Done!

I hope the above steps were helpful.

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This is an equation of a circle centered at point (0,0) with radius 1.

This is an equation of a line with slope m=-1 and y-intercept at b=-1 or at point (0,-1).

Step 1. Let's solve for x in

Subtract -y to both sides of the equation

}



Step 2. Substitute into

but and





Step 3. Subtract 1 to both sides of the equation







Then and

Step 4. Find x-coordinates when and

At , then . One intersection point is (-1,0).

At then . One intersection point is (0,-1).

Step 5. Then intersection points are (-1,0) and (0,-1)

Here are the graphs of the circle and line and note they have two common points.






I hope the above steps were helpful.

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Write an equation for the line described as slope=-3/5 and passes through (7,6). Write in slope intercept form.

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 x=0 or point (0,b). Here, the slope m=-3/5.

Step 2. The slope m is given as



Step 3. Let (x1,y1)=(6,7) or x1=7 and y1=6. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 4. Now we're given . Substituting above values and variables in the slope equation m yields the following steps:





Step 5. Multiply (x-7) to both sides to get rid of denominators on both sides of equation.





Step 6. Now add +6 to both sides of equation to solve for y.






Step 7. ANSWER: The equation is

Here's a graph below and note the slope and y-intercept at x=0 or point (0, 51/5) and the x-intercept at y=0 or at point (17, 0)and note it is consistent with the equation when substituting these



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



I hope the above steps were helpful.

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1. In how many ways can 5 questions be selected out of 8 questions?

Step 1. This is a combination problem where we have the following formula for this problem.



where n! means n factorial or n*(n-1)*....1 and n=8 and x=5 for this example.

Step 2. Then,



Step 3. ANSWER: There are 6720 ways to select 5 out of 8 questions.

I hope the above steps were helpful.

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How to convert 25/49 to exponential form?



I hope the above steps were helpful.

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Can you tell me what 6 ordered pairs are for this problem ?

Step 1. Let's define .

Step 2. Form two columns one for x and the for y. Try different values of x and substitute into equation in Step 1. We'll try points -4, -3, -2, -1, 0, 1, 2, 3, 4 to get 9 ordered pairs...extra credit :)

so ordered pair is (x,y)

so ordered pair is (-4,4)

so ordered pair is (-3,1)

so ordered pair is (-2,0)

so ordered pair is (-1,1)

so ordered pair is (0,4)

so ordered pair is (1,9)

so ordered pair is (2,16)

so ordered pair is (3,25)

so ordered pair is (4,36)

Step 3. ANSWER: Ordered pairs for this example are: (-4,4), (-3,1), (-2,0), (-1,1), (0,4), (1,9), (2,16), (3,25), (4,36)

Here's a graph of the equation and see note there are ordered pairs as given above.



I hope the above steps were helpful.

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Can you please help me solve this equation:

I tried to work it out on my own and this is what I worked out:

-3x-3y+14x+7
-3y+11x+7

That's all I got so far. If you could help me I would greatly appreciate it! Thank you very much! Morgan

Hi Morgan,

My guess of the problem is that you want to solve for y as a function of x.

What you have so far is correct. So let's set the equation = 0 in order to get y.




Now add 3y to both sides to get y-terms on the right side.





Now divide by 3 to both sides of the equation



ANSWER if the problem is to solve for y.

We now have y as a function of x which is a line.

I hope the above steps were helpful.

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The supplement of an angle is 4 more than twice its complement. Find the measure of the angle.

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

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

Step 3. Let x be the angle.

Step 4. Let 180-x be its supplementary angle.

Step 5. Let 90-x be its complementary angle.

Step 6. Let 2(90-x) be twice its complement

Step 7. Then, 180-x=4+2(90-x) since the supplement of an angle is 4 more than twice its complement.

Step 8. The following steps will solve the equatio in Step 7.





Add 2x-180 to both sides of the equation.



then and

Check if in Step 7 is true......which is a true statement.

Step 9. ANSWER: The angle is 4 degrees, its supplement is 176 degrees, and its complement is 86 degrees.

I hope the above steps and explanation were helpful.

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Solve the system of equations using the addition method. If the answer is a unique solution, present it as an ordered pair: (x,y). If not specify whether the answer is no solution or infinitely many solutions.]

3x-11y = 9 Equation A
-9x+ 33y = -27 Equation B

Step 1. Multiply Equation A by 3: to get Equation A1 below:

9x-33y=27 Equation A1
-9x+33y=-27 Equation B

Step 2. Add Equations A1 and B to get




which means that there are many solutions and these equations are not independent.

Step 3. ANSWER: There are an infinite number of solutions that satisfies the above linear system of equations.

I hope the above steps were helpful.

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What is the length of a rectangle that is 6.5 cm wide and has a perimeter of 32 cm?

Step 1. Perimeter P means adding up all four sides of a rectangle.

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

Step 3. Then

Step 4. But w=6.5 and P=32, then



Subtract 12 from both sides of the equation to get only L terms on the right side.





Divide by 2 to both sides of the equation





Check P=2*(6.5+9.5)=2*16=32 which is a true statement.

Step 5. ANSWER: The length is 9.5 cm.

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!
Please help me simplify this equation: 2x(2x-4)

2x(2x-4)=4x^2-8x=4x(x-2)

ANSWER is or depending how you want to express the simplified expression.

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!
Please help me simplify this equation: 2x(2x-4)

2x(2x-4)=4x^2-8x=4x(x-2)

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

You can put this solution on YOUR website!


Step 1. Use the FOIL (multiply the First, Outer, Inner, and Last terms)





Step 2. Simplify by combining like terms and in this case -30x-30x=-60x



Step 3. 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, please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your future studies.

Respectfully,
Dr J