<span>Triangles exist:
</span>3 acute angles<span>
2 acute angles, 1 right angle
</span><span>2 acute angles, 1 obtuse angle
</span>
Triangles DON'T exist for:
<span>1 acute angle, 1 right angle, 1 obtuse angle
</span><span>1 acute angle, 2 obtuse angles</span>
Answer:
true
Step-by-step explanation:
one tree has 13 apples
Answer:
Step-by-step explanation:
4 is coefficient
x is variable
12 is constant
<h2><u><em>
If you rather have the link to get this info lmk!!</em></u></h2>
Example: f(x) = 2x+3 and g(x) = x2
"x" is just a placeholder. To avoid confusion let's just call it "input":
f(input) = 2(input)+3
g(input) = (input)2
Let's start:
(g º f)(x) = g(f(x))
First we apply f, then apply g to that result:
Function Composition
- (g º f)(x) = (2x+3)2
What if we reverse the order of f and g?
(f º g)(x) = f(g(x))
First we apply g, then apply f to that result:
Function Composition
- (f º g)(x) = 2x2+3
We get a different result! When we reverse the order the result is rarely the same. So be careful which function comes first.
<h2 />
Answer:
![\[3x+\frac{2}{3}\]](https://tex.z-dn.net/?f=%5C%5B3x%2B%5Cfrac%7B2%7D%7B3%7D%5C%5D)
Step-by-step explanation:
![\[f(x)=x-\frac{1}{3}\]](https://tex.z-dn.net/?f=%5C%5Bf%28x%29%3Dx-%5Cfrac%7B1%7D%7B3%7D%5C%5D)
![\[g(x)=3x+1\]](https://tex.z-dn.net/?f=%5C%5Bg%28x%29%3D3x%2B1%5C%5D)
Hence, ![\[(f o g)(x)=f(3x+1)\]](https://tex.z-dn.net/?f=%5C%5B%28f%20o%20g%29%28x%29%3Df%283x%2B1%29%5C%5D)
But, ![\[f(3x+1)=(3x+1)-\frac{1}{3}\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D%283x%2B1%29-%5Cfrac%7B1%7D%7B3%7D%5C%5D)
Simplifying,
![\[f(3x+1)=3x+(1-\frac{1}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%281-%5Cfrac%7B1%7D%7B3%7D%29%5C%5D)
= ![\[f(3x+1)=3x+(\frac{3-1}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%28%5Cfrac%7B3-1%7D%7B3%7D%29%5C%5D)
= ![\[f(3x+1)=3x+(\frac{2}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5C%5D)
Hence, ![\[(f o g)(x)=3x+(\frac{2}{3})\]](https://tex.z-dn.net/?f=%5C%5B%28f%20o%20g%29%28x%29%3D3x%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5C%5D)
