Sure, that's what solving triangles is. Trigonometry has a short menu. Basically we choose between three formulas: Law of Sines, Law of Cosines, Sum of Triangle Angles
The Law of Sines has two sides and two opposite angles; given any three we can solve for the fourth.
The Law of Cosines has three sides and one angle; again given any three we solve for the remaining one.
The Sum of Triangle Angles says all three angles add to 180 degrees, so given two we can find the third.
Here we have all the angles and one side, that's Law of Sines to get the remaining sides.
Answer x=5, y= 3.5
Find y by plugging the x value into the 2nd equation
4(2y-2) -9=11
8y - 8 - 9 =11 combine like terms
8y = 28 divide both sides by 8
y = 3.5
Now find x
Plug your y value into first equation
X = 2(3.5) -2
X= 7-2
X=5
You can check your work by putting your x or y values into the equations
For the first equation
5=2(3.5) -2
5=5
For the second equation
4(5) -9 = 11
20 - 9 = 11
11 =11
9514 1404 393
Answer:
- f(x) = x
- g(x) = -2x+1
- f(x) -(-g(x)) = -x+1
- f(x) +g(x) = -x+1
- f(x)-(-g(x)) = (f+g)(x) is true for all functions f and g, linear or not
Step-by-step explanation:
We can define a couple of linear functions as ...
f(x) = x
g(x) = -2x+1
Then the reflected function -g(x) is ...
-g(x) = -(-2x +1) = 2x -1
And the difference from f(x) is ...
f(x) -(-g(x)) = x -(2x -1) = -x +1 . . . . f(x) -(-g(x))
We want to compare that to the sum of the functions:
f(x) +g(x) = x +(-2x +1) = -x +1 . . . . f(x) +g(x)
The two versions of the function expression have the same value.
These results are <em>a property of addition</em>, so do not depend on the nature of f(x) or g(x). They will hold for every function.