Frankie's Responses in WyzAnt Answers

Hello Alli,

   I will have to disagree with the first two comments. The answer to this problem is non-existant. It is an unsolvable problem. Which is why it probably gave you so much trouble.

   Reisa's Steps are right, but her Math was wrong.

    Step One:   Before moving terms across the equation, it is easier to complete the Math on each side. According to PEMDAS, we do parenthesis first.------>>>

3(x-2)+2x=5(x-2)-1-------> 3x-6+2x=5x-10-1

     Combine like terms via addition and subtraction, since there is no exponents, multiplication or division that can be completed at this time.

3x-6+2x=5x-10-1-----> 5x-6=5x-11

      Step Two: Group like terms on different sides of the = sign. (terms with x = numbers). In order to move terms from one side of the equation to the other, you must perform the opposite operation (If a term is being added, you would subtract it and vice versa. If a term is Multiplied, you would Divide and vice versa. A little beyond the scope, but if you are squaring a term (^2), you would take the square root, and vice versa)------->

5x-6=5x-11----> 5x-5x=-11+6.

     From here it is simple math.

5x-5x=-11+6--------> 5x-5x=0 and -11+6= -5 ------> 0=-5  This is simply untrue Zero doesn't equal negative five. Therefore this is False or Unsolvable.

     Please feel free to give me feedback and let me know if this helped.

     For me it is hard to write out words for Math. Haha. Therefore if there is ANYTHING I can or should explain better let me know!

       Thanks for taking the time to read and consider : )

Hello Cool, : )

The important thing to understand is what an asymptote is. An asymptote is a line on a graph that a curved line or curved lines will approach but NEVER touch or cross.

Next question should be why? The reason why is that zero CANNOT be in the denominator of an equation. Therefore if we substitute a value in for x or y that gives us a zero in the denominator we will have undefined solution.

Therefore, for all values of x or y where a denominator will end up equaling zero we place an asymptote. This will say that we can get close to the asymptote, but our line will never cross. In Calculus you will learn that this is called your limit. Just a heads up ; )

Ok, so here is how you find the vertical asymptote(s):

f(x) =     3x^2

         x^2 - 7x + 12

First let’s factor the denominator (bottom of the fraction)

* A way to avoid the quadratic is to ask yourself if you can come up with two numbers that multiply together to give 12(term c in ax^2+bx +c) and that can be added to give you -7(term b).

The good thing about the quadratic though is that it works FOR ANY TRINOMIAL.

Quadratic Formula: x= -b+or- sqrt of b^2-4ac

                                             2a

After factoring we have:

f(x)=    3x^2

        (x-3)(x-4)

(A great way to check your factoring multiply them out (foil first outer inner last). This should yield your original denominator.)

Now that we have our two factors we can set them independently equal to zero. Remember that anything multiplied by zero is zero. Therefore if one of our factors equals zero, we have a zero in a denominator; which yes YIELDS AN ASYMPTOTE.

X-3=0 and x-4=0--------> x=3 and x=4-----> Asymptotes at x=3 and x=4 (these will be vertical dotted lines as a solid line represents the line your equation graphed.)

(To determine the behavior of your graph between these two asymptotes I recommend picking three points and plugging into your equation. These should be spaced out to give you an accurate signature. So x=3.1, x=3.5, and x=3.9 should give you a great idea of what this section of the graph looks like.)

Now for the horizontal asymptote:

If there is an exponent of x in the numerator that is greater than the largest exponent of x in the denominator there will not be a horizontal asymptote. (Largest Numerator exponent of x > Largest Denominator exponent of x ---> NO HORIZANTAL ASYMPTOTE)

If the largest exponent of x in the numerator is smaller or equal to that of the largest exponent of x in the denominator -----> Horizontal Asymptote

f(x) =       3x^2

          x^2 - 7x + 12

For this we will leave it in this form (standard form) as it is easier to identify exponents.

Notice we have 3x^2 in the numerator and x^2 in the denominator. 2 and 2 for exponents---> Horizontal Asymptote.

In order to find the asymptote we must do away with all other terms except the one in the numerator with the largest exponent and the one in the denominator with the largest exponent.

This yields:    3x^2

                     x^2

Next only consider the number adjacent to x(coefficient) :

3

1

3/1 can be reduced to 3

Therefore we will have a horizontal asymptote at y=3 (a dotted line at y=3)

I hope this has helped you out ; )

Have a Good Day!

Hello Kelly,

   I will take a shot at helping you. ;)

An example of two adjacent angles would be bisecting a 90 degree angle. Picture or draw a 90 degree angle. Then starting at the point of the angle(Vertex) draw a line outward dividing the angle into two angles. Now you have two adjacent angles. Adjacent meaning they are side by side. 

If you were to bisect the 90 degree angle evenly, you would have two angles equal to 45 degrees. ;)

Vertical Angles:

    The easiest way to envision vertical angles would be to think of a pair of scissors.  When you open up the scissors you form two sets of vertical angles. 

    The two finger holes form an angle that is equal to the angle of the two blades. These two angles are vertical angles.

   Consequently on each side, the handle and blade would form an angle that can be paired with the other handle and blade making another set of vertical angles.

   Another way to describe this would be the letter "X".

    The top and bottom are vertical angles and the left and right side form vertical angles.

   VERTICAL ANGLES WILL ALWAYS HAVE THE SAME NUMBER OF DEGREES

 I hope this helps you :)