the answers b. hope this helps!! :)
They are ratios of two sides of a right triangle and a related angle. Trigonometric functions are typically used to calculate unknown lengths or angles in a right triangle.
Answer:
(4,2)
Step-by-step explanation:
Just by looking at the graph, you can see that they intersect at (4,2). But just to check:
x - 2 = -0.5x + 4
1.5x = 6
x = 4
y = 4 - 2 = 2
(4,2)
Answer:
Divide both sides by 6 :)
Answer:
![4x^2+xy-18y^2=(4x+9y)\,(x-2y)](https://tex.z-dn.net/?f=4x%5E2%2Bxy-18y%5E2%3D%284x%2B9y%29%5C%2C%28x-2y%29)
Step-by-step explanation:
Let's examine the following general product of two binomials with variables x and y in different terms:
![(ax+by)\,(cx+dy)= ac\,x^2+adxy+bcxy+bdy^2](https://tex.z-dn.net/?f=%28ax%2Bby%29%5C%2C%28cx%2Bdy%29%3D%20ac%5C%2Cx%5E2%2Badxy%2Bbcxy%2Bbdy%5E2)
so we want the following to happen:
![a\,c = 4\\ad+bc=1\\bd--18](https://tex.z-dn.net/?f=a%5C%2Cc%20%3D%204%5C%5Cad%2Bbc%3D1%5C%5Cbd--18)
Notice as well that
means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product
, then we can consider the case in which one of this (b or d) is the negative factor. So let's then assume that
are positive.
We can then try combinations for
such as:
![a = 4;\,\,c=1\\a=2;\,\,c=2\\a=1;\,\,c=4](https://tex.z-dn.net/?f=a%20%3D%204%3B%5C%2C%5C%2Cc%3D1%5C%5Ca%3D2%3B%5C%2C%5C%2Cc%3D2%5C%5Ca%3D1%3B%5C%2C%5C%2Cc%3D4)
Just by selecting the first one ![(a=4;\,\,c=1)](https://tex.z-dn.net/?f=%28a%3D4%3B%5C%2C%5C%2Cc%3D1%29)
we get that ![4d_b=1\\b=-4d-1](https://tex.z-dn.net/?f=4d_b%3D1%5C%5Cb%3D-4d-1)
and since
![bd=-18\\(-4d-1)\,d=-18\\-4d^2-d=-18\\4d^2+d-18=0](https://tex.z-dn.net/?f=bd%3D-18%5C%5C%28-4d-1%29%5C%2Cd%3D-18%5C%5C-4d%5E2-d%3D-18%5C%5C4d%5E2%2Bd-18%3D0)
This quadratic equation give as one of its solutions the integer: d = -2, and consequently,
![d=-18/(-2)\\d=9](https://tex.z-dn.net/?f=d%3D-18%2F%28-2%29%5C%5Cd%3D9)
Now we have a good combination of parameters to render the factoring form of the original trinomial:
![a=4; \,\,b=9;\,\,c=1;\,\,d=-2](https://tex.z-dn.net/?f=a%3D4%3B%20%5C%2C%5C%2Cb%3D9%3B%5C%2C%5C%2Cc%3D1%3B%5C%2C%5C%2Cd%3D-2)
which makes our factorization:
![(4x+9y)\,(x-2y)=4x^2+xy-18y^2](https://tex.z-dn.net/?f=%284x%2B9y%29%5C%2C%28x-2y%29%3D4x%5E2%2Bxy-18y%5E2)