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Put a DOT in the middle of this:

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y = 5x
(0,0) and (-1.-5) only.

y = 5x
If x = -2, then y does NOT equal 10.

y = 5x
If x = -3, then y does NOT equal 9.

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y=mx+b
y=4x-5


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Solve for y:




The y intercept is -4 and the slope is 2/1. See my lesson plan on graphing by slope intercept method:


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write 7/16 as a percent:
The tutor did NOT write this as a percent. The final answer should be

write the ratio of 4/13 to 6 in simplest form. Again I disagree with the answer posted by the other tutor!!

The ratio of a to b means a/b. Therefore the ratio of 4/13 to 6 means to divide 4/13 by 6. This means to take . I get the answer of .

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OOPS!! The other tutor missed this one!! It should be




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From first base to third base on a baseball diamond is actually the hyptenuse of a right triangle with right angle at second base! Therefore, the legs of the right triangle are each 90 feet, and the hypotenuse is the direct distance (over the pitcher's mound) from first to third base. By the Theorem of Pythagoras, this would be





feet
feet approximately!

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Just substitute the values for x and y: (5,3) means that x=5 and y =3.
3x+2y=21
3(5) + 2(3) = 21
15 + 6= 21 True

x+y=8
5+3 = 8 True

Yes, it is a solution.

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Just add the two equations together, and the y terms subtract out:
x+y=7
2x-y=5
--------------
3x=12
x=4

Substitute back into the first equation:
x+y=7
4+y=7
y=3

Check by substituting both values in the second equation:
2x-y=5
2*(4)-3=5
It checks.

The solution is the point (4,3).

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3x + y = –1
9x + 3y = –3


Multiply both sides of the first equation by -3 to eliminate the y terms.
-3*(3x + y) = (-3)*–1
9x + 3y = –3

-9x -3 y = 3
9x + 3y = –3

When you add the equations together you get 0=0, which is ALWAYS TRUE. Any time you get 0=0, it means that the equations actually represent the SAME LINE. The entire line is the solution.

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5x – 4y = –5
x – 2y = –7

Multiply the second equation by -2 to eliminate the y terms:
5x – 4y = –5
-2x +4y = 14

Add the equations:
3x=9
x=3

Substitute x=3 into the first equation:
5x – 4y = –5
5(3) -4y =-5
15-4y = -5
15-15-4y = -5-15
-4y = -20
y=5

Check by substituting both numbers into the second equation:
x – 2y = –7
3-2(5) = -7
It checks

Solution: (3,5)

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You seem to have TWO errors in your second step!
0.14x+0.13(20,000-x)=2,720
0.14x+2,800-.013x=2,720

Should be
0.14x+0.13(20,000-x)=2,720
0.14x+2,600-0.13x=2,720

Continuing:
0.01x = 120
x= $12000
20000-x = $8000

Check: .14(12000)+.13(8000)=2720

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The equilibrium price is where supply = demand.

D=-5p+40
S=-p^2+30p-8





Use either the quadratic formula or a graphing calculator:
p=1.43 or p = 33.57

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If angles A and C are supplementary, and angle C is 40 degrees, then angle A is 180-40 = 140 degrees.

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The greatest common factor for is 6a. Take out the common factor, and this is left:


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I may be misunderstanding your question, but when you are solving an EQUATION, you usually have a single variable, like . You can find roots or solutions of the equation (in this case, it would be x=2 or x=-2) by equation solving methods.

However, to have x and y intercepts, you must have TWO variables (TWO dimensions!). This would be like . In order to find the x intercepts, you let y = 0, and find x--in this case it would be (0,2) and (0,-2). You can find the y-intercepts by letting x=0, and find y--in this case, it would be (0,-4). I'm not sure how completing the square fits into this question.

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This is a difference of two squares:
First times First must give you x^2:
(x____)(x____)

Last times Last must give you -25. Try -5*+5= -25!!
(x-5)(x+5)

The middle term is +5x -5x, which subtract out.

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Yes! It is a perfect square trinomial essentially because the x^2 coefficient is 1, and if you take HALF of the middle term and SQUARE the result, you get the last term which is 81. In other words, if you take half of -18, you get -9, then if you square the (-9) you get 81, which is the last term of the trinomial. Therefore, it IS a perfect square trinomial!!

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You are correct so far. What you have is a quadratic equation. You must set it equal to zero, and solve for y. It's probably best to subtract 2y and 7 from each side:





y= 9 or y = 1

Now, check the answers to make sure you don't have any extraneous roots (that is, extra solutions that don't really work in the original equation!).


If y=9

This one checks!


If y=1

This one does NOT check! Reject this answer.

The only solution is y=9.

I have a page for this on my website, if you want to click on my tutor name "Rapaljer" anywhere in algebra.com, go to my MATH IN LIVING COLOR page, and in Intermediate Algebra, look for Radical Equations in Chapter 3. In College Algebra, look for Radical Equations in Chapter 1. I hope this is helpful.

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I think the tutor may have been saying the answer was x=2, but since it did not work it was rejected. Therefore, the tutor may have been saying NO SOLUTION, which in math is sometimes represented by the Greek letter "PHI". It looks like a zero that has a slash through it, and it is frequently confused with zero. The answer is NOT 0. The answer is NO SOLUTION.

The reason you have a situation like this is because you squared both sides. This is not a "kosher" thing to do, and sometimes it leads to answers that don't really work. This is why when you square both sides, you MUST go back and check the answers to see if they really work. If they don't work in the original equation, they are called "extraneous roots" and they must be rejected.

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You are correct so far. What you have is a quadratic equation. You must set it equal to zero, and solve for y. It's probably best to subtract 2y and 7 from each side:




IT ALWAYS FACTORS!!

y= 9 or y = 1

Now, check the answers to make sure you don't have any extraneous roots (that is, extra solutions that don't really work in the original equation!).


If y=9

This one checks!


If y=1

This one does NOT check! Reject this answer.

The only solution is y=9.

I have a page for this on my website, if you want to click on my tutor name "Rapaljer" anywhere in algebra.com, go to my MATH IN LIVING COLOR page, and in Intermediate Algebra, look for Radical Equations in Chapter 3. In College Algebra, look for Radical Equations in Chapter 1. I hope this is helpful.

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--Another "Advanced Trinomial Factoring". See my own website, or send me an Email, as I have mentioned on several of my last postings!!

Try this:
(2x____)(2x____)

Last times last has to be 3*1 or 1*3, and in this case, it doesn't really matter what order you use.
(2x+3)(2x+1)

Notice that the outer times outer and inner times inner give you 2x + 6x = 8x, which is the correct middle term.

Final answer: (2x+3)(x+1)

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See my Lesson Plans on Factoring on algebra.com, or see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for "Basic Algebra", then "Samples from Basic Algebra: One Step at a Time", "Chapter 2." There are several sections on Factoring, especially "Factoring Trinomials." See also my page called "MATH IN LIVING COLOR", then Basic Algebra, Chapter 2. It's all FREE and in COLOR.

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This is what I call Advanced Trinomial Factoring again.
5x2+13x+6

First times First MUST be:
(5x____)(x____)

The Last times Last has several possibilities. It could be 1*6 or 6*1. It could be 2*3 or 3*2. You need to get a combination of numbers such that the OUTER times OUTER plus the INNER times INNER will add up to the middle term which is 13x. The combination that works is 3*2. See below:
(5x+3)(x+2)

Notice that the OUTER times OUTER would be 5x*2 = 10x, and the INNER times INNER would be 3*x = 3x. This adds up to 13x, so this is the answer:

(5x+3)(x+2)

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-5x+7y
-1(5x-7y}

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The GCF is the largest factor that divides into both terms in this expression. If variables are involved, it will be the LOWEST power of each variable. This would be .

When you take out the NEGATIVE of this common factor, it changes all the signs. What is left is this:


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Here is another problem from the section that I call Advanced Trinomial Factoring.


First times First has to come out to . This would have to be 2x*x


The Last times Last has to come out to +1. This would have to be 1*1, with the SAME signs--that is either a (-1)*(-1) or a (+1)*(+1).


Now, the middle term must come out to a -3x, so the signs must both be negative.


The Lesson on Advanced Trinomial Factoring can be found in algebra.com or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Next, click on "Basic Algebra", then "Samples from Basic Algebra: One Step at a Time", then in Chapter 2, look for the section about "Advanced Trinomial Factoring." While you are there, check out ALL the sections on Factoring. There are several sections devoted to this important skill.

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The first problem is to FACTOR the numerator and denominator. It's like in the last solution that I posted, but this time the factoring is a LOT harder. You may need some help with what I call "Advanced Trinomial Factoring" and I have a lesson on this if you are interested.




Now, the (3x-2) factors divide out:


The Lesson on Advanced Trinomial Factoring can be found in algebra.com or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Next, click on "Basic Algebra", then "Samples from Basic Algebra: One Step at a Time", then in Chapter 2, look for the section about "Advanced Trinomial Factoring." While you are there, check out ALL the sections on Factoring. There are several sections devoted to this important skill.

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