My guess is that you're doing the Law of Cosines? You have everything you need for that except the angle theta, which is the thing you need to find. It's set up like this: (8)^2 = (10)^2 + (5)^2 -[2(10)(5)cos A] I used A instead of theta. Doing that math, you have: 64 = 100 + 25 -[ 100 cos A]; 64 = 125 - 100 cos A;
-61 = - 100 cos A; -61 / -100 = cos A; .61 = cos A. Now use your inverse function on your calculator to find cos^-1(.61) and that equals 52.4
5x^2-4x+1 + -3x^2+x-3= 2x^2-3x-2
Given:
The piecewise function is
To find:
The range of given piecewise function.
Solution:
Range is the set of output values.
Both functions 
and 
as linear functions.
Starting value of is at x=-4 and end value is at x=3.
Starting value: 
End value: 
Starting value of is at x=3 and end value is at x=6.
Starting value: 
End value: 
Least range value is 0 at x=-4 and 0 is included in the range because -4 is included in the domain.
Largest range value is 11 at x=6 and 11 is not included in the range because 6 is not included in the domain.
So, the range of the given piecewise function is [0,11).
Therefore, the correct option is A.
Hello!
On the graph, when the X values are between 4 and 8, they are being constant. The X values between 4 and 8 are constant because the line shown between 4 and 8 on the graph show the line as a straight line. It is not going up nor is it going down, so you can conclude that the X values are not increasing or decreasing.
I hope this helps!
The correct answer is C: 1/(x + 4)(x - 5)
Why? Well, let's first simplify x^2 - 3x - 10 and x^2 + x - 12; the two denominators. Each of these should become an (x +/- number), and to figure out the number, as well as whether it is positive or negative, we can do a simple trick
Look at the factors of the right number (In this case, -10 and -12)
-10 -12
1 * -10 1 * -12
-1 * 10 -1 * 12
-2 * 5 -2 * 6
2 * -5 2 * -6
-3 * 4
4 * -3
Now for part 2
Which of these pairs add up to the middle number? One of the pairs of -10 should make -3, and likewise, one of the pairs of -12 should make 1 (when x has no number in front of it you may safely assume it is 1).
2 - 5 = -3 and 4 - 3 = 1, so we now know that the 2 fraction equations simplified is
x + 2 / (x + 2)(x - 5) * x - 3/(x -3)(x + 4)
Notice anything repeating? As long as they are apart of the same fraction, we can cross out anything that has the same x - number. Crossing out both x + 2 and x - 3, we now simply have x - 5 * x + 4. Because we crossed out both numerators, the top numbers both become 1, thus giving our answer, C.
