So a absolute value is just the opposite of the value given, (unless it is a positive number) so you start on -12 and count 24 units to the right so it would make positive 12
Answer:
is there any sign between -14 and 4t2?
Step-by-step explanation:
The first thing to is factor the denominator of the rational function:

to do this we'll need to find two number whose product is -3 and its sum is -2; those numbers are 1 and -3, so:

Now we can rewrite our rational function as follows:

Notice that we have a common factor (x-3) in both numerator and denominator; therefore we can cancel them:

Taking all the above into consideration we realize that x=3 is a removable discontinuity; the correct answer is the first one: there is a hole in x=3 and asymptote at x=-1.
You could simplify this work by factoring "3" out of all four terms, as follows:
3(x^2 + 2x - 3) =3(0) = 0
Hold the 3 for later re-insertion. Focus on "completing the square" of x^2 + 2x - 3.
1. Take the coefficient (2) of x and halve it: 2 divided by 2 is 1
2. Square this result: 1^2 = 1
3. Add this result (1) to x^2 + 2x, holding the "-3" for later:
x^2 +2x
4 Subtract (1) from x^2 + 2x + 1: x^2 + 2x + 1 -3 -1 = 0,
or x^2 + 2x + 1 - 4 = 0
5. Simplify, remembering that x^2 + 2x + 1 is a perfect square:
(x+1)^2 - 4 = 0
We have "completed the square." We can stop here. or, we could solve for x: one way would be to factor the left side:
[(x+1)-2][(x+1)+2]=0 The solutions would then be:
x+1-2=0=> x-1=0, or x=1, and
x+1 +2 = 0 => x+3=0, or x=-3. (you were not asked to do this).
5:7 (pencils to pens)
7/12 chance that a pen from the first box will be selected.
4:4 (colour pencils to crayons)
4/8 = 1/2 chance that a crayon from the second box will be selected.
The probability of picking both:
7/12 * 1/2 = 8/24 = 1/3