The answer is C and brainliest answer please.
By using trigonometric relations, we will see that x = 9.97°.
<h3>
How to find the missing angle?</h3>
First, we need to find the bottom cathetus of the smaller triangle, we will use the relation:
Tan(θ) = (opposite cathetus)/(adjacent cathetus).
Where:
- θ = 26°
- Adjacent cathetus = k
- Opposite cathetus = 55ft.
Replacing that we get:
Tan(26°) = 50ft/k
Solving this for k, we get:
k = 55ft/tan(26°) = 112.8 ft
Now, we can see that the longer triangle adds 200ft to this cathetus, so now we will have:
- angle = x
- opposite cathetus = 55ft
- adjacent cathetus = 112.8ft + 200ft = 312.8ft.
Then we have:
Tan(x) = (55ft/312.8ft)
Using the inverse tangent function in both sides, we get:
x = Atan(55ft/312.8ft) = 9.97°
If you want to learn more about right triangles, you can read:
brainly.com/question/2217700
Answer: ![P(A\cap B)=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3D%5Cfrac%7B1%7D%7B3%7D)
![P(A)=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7B1%7D%7B3%7D)
![P(B)=1](https://tex.z-dn.net/?f=P%28B%29%3D1)
![P(A|B)=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%5Cfrac%7B1%7D%7B3%7D)
Step-by-step explanation:
From the given figure it can be seen that
Total number on cube= n(S)=6
Intersection of A and B = n(A ∩ B)= 2
Therefore,
![P(A\cap B)=\frac{n(A\cap B)}{n(s)}=\frac{2}{6}=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3D%5Cfrac%7Bn%28A%5Ccap%20B%29%7D%7Bn%28s%29%7D%3D%5Cfrac%7B2%7D%7B6%7D%3D%5Cfrac%7B1%7D%7B3%7D)
Also, The number of elements in A = 2
Therefore,
![P(A)=\frac{n(A)}{n(s)}=\frac{2}{6}=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7Bn%28A%29%7D%7Bn%28s%29%7D%3D%5Cfrac%7B2%7D%7B6%7D%3D%5Cfrac%7B1%7D%7B3%7D)
Similarly, The number of elements in B= 6
Therefore,
![P(B)=\frac{n(B)}{n(s)}=\frac{6}{6}=1](https://tex.z-dn.net/?f=P%28B%29%3D%5Cfrac%7Bn%28B%29%7D%7Bn%28s%29%7D%3D%5Cfrac%7B6%7D%7B6%7D%3D1)
The formula to find the conditional probability is given by :-
![P(A|B)=\frac{P(A\cap B)}{P(B)}\\\\\Rightarrow P(A|B)=\frac{\frac{1}{3}}{1}=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%5Cfrac%7BP%28A%5Ccap%20B%29%7D%7BP%28B%29%7D%5C%5C%5C%5C%5CRightarrow%20P%28A%7CB%29%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7D%7D%7B1%7D%3D%5Cfrac%7B1%7D%7B3%7D)
Answer:
x is less than -3
Step-by-step explanation:
3x^2+9x<0
x^2+3x<0
x(x+3)<0
x+3<0
x<-3