Answer:
Step-by-step explanation:
If you want to determine the domain and range of this analytically, you first need to factor the numerator and denominator to see if there is a common factor that can be reduced away. If there is, this affects the domain. The domain are the values in the denominator that the function covers as far as the x-values go. If we factor both the numerator and denominator, we get this:

Since there is a common factor in the numerator and the denominator, (x + 3), we can reduce those away. That type of discontinuity is called a removeable discontinuity and creates a hole in the graph at that value of x. The other factor, (x - 4), does not cancel out. This is called a vertical asymptote and affects the domain of the function. Since the denominator of a rational function (or any fraction, for that matter!) can't EVER equal 0, we see that the denominator of this function goes to 0 where x = 4. That means that the function has to split at that x-value. It comes in from the left, from negative infinity and goes down to negative infinity at x = 4. Then the graph picks up again to the right of x = 4 and comes from positive infinity and goes to positive infinity. The domain is:
(-∞, 4) U (4, ∞)
The range is (-∞, ∞)
If you're having trouble following the wording, refer to the graph of the function on your calculator and it should become apparent.
Answer:
m∠ABC = 74
Step-by-step explanation:
The sum of the measures of three angles of any triangle is invariably equal to the straight angle, also expressed as 180 °
So you subtract the given measurements of ∠BAC (76°) and ∠ ACB (19°) from 180. 180-76-19 = 74
The measurement of angle ABC is 74°
Answer:
4
Step-by-step explanation:
Those two added together are equal to
14 and
Answer:
Option 2: 
Step-by-step explanation:
Given:
From the triangle shown below;
A triangle QRS with angle QRS = 90°, ∠QSR = 30°.
Side QR = 5, SQ = 10 and RS = 5√3
Now, we know from trigonometric ratio that,

Here, opposite side of angle QSR is QR and Hypotenuse is the side opposite angle QRS which is SQ. Therefore,

Therefore, the value of sine of 30° is one-half. So, second option is correct.