1) [x=0; y=-6] [x=1;y=-4]
2) [x=0; y=6] [x=1; y=7]
Answer:
Bruce collected 60 other stamps.
Explanation:
76% of 250 =76/100 × 250/1 = 19,000/100 = 190/1 = 190
Bruce collected 190 foreign stamps.
250 - 190 = 60 stamps
0.262 turned into a fraction is 262/1000
Answer:
A
Step-by-step explanation:
7 - (-7/5) x 5 =
7 - (-7) =
7 + 7 = 14
Hope that helps!
Answer:
![x = 0 \: or \:x = \pi](https://tex.z-dn.net/?f=x%20%3D%200%20%5C%3A%20or%20%5C%3Ax%20%3D%20%20%20%5Cpi%20)
Step-by-step explanation:
The given equation is
![\tan^{2} (x) \sec^{2} (x) + \sec^{2} (x) - \tan^{2} (x) = 2](https://tex.z-dn.net/?f=%20%5Ctan%5E%7B2%7D%20%28x%29%20%5Csec%5E%7B2%7D%20%28x%29%20%20%2B%20%5Csec%5E%7B2%7D%20%28x%29%20%20-%20%5Ctan%5E%7B2%7D%20%28x%29%20%3D%20%202)
Subtract 2 from both sides and factor by grouping to get:
![\sec^{2} (x)(\tan^{2} (x) + 2) -1( \tan^{2} (x) + 2)](https://tex.z-dn.net/?f=%20%5Csec%5E%7B2%7D%20%28x%29%28%5Ctan%5E%7B2%7D%20%28x%29%20%2B%202%29%20%20-1%28%20%5Ctan%5E%7B2%7D%20%28x%29%20%20%2B%20%202%29)
![(\tan^{2} (x) + 2) (\sec^{2} (x) - 1) = 0](https://tex.z-dn.net/?f=%20%28%5Ctan%5E%7B2%7D%20%28x%29%20%2B%202%29%20%28%5Csec%5E%7B2%7D%20%28x%29%20-%201%29%20%3D%200)
By the zero product principle:
![(\tan^{2} (x) + 2) = 0 \: or \: (\sec^{2} (x) - 1) = 0](https://tex.z-dn.net/?f=%28%5Ctan%5E%7B2%7D%20%28x%29%20%2B%202%29%20%3D%200%20%5C%3A%20or%20%5C%3A%20%20%28%5Csec%5E%7B2%7D%20%28x%29%20-%201%29%20%3D%200)
![(\tan^{2} (x) = - 2 \: or \: \sec^{2} (x) = 1](https://tex.z-dn.net/?f=%28%5Ctan%5E%7B2%7D%20%28x%29%20%20%3D%20%20-%202%20%5C%3A%20or%20%5C%3A%20%20%5Csec%5E%7B2%7D%20%28x%29%20%20%3D%20%201)
When
![\sec^{2} (x) = 1 \implies\cos^{2} (x) = 1](https://tex.z-dn.net/?f=%5Csec%5E%7B2%7D%20%28x%29%20%20%3D%20%201%20%5Cimplies%5Ccos%5E%7B2%7D%20%28x%29%20%20%3D%20%201)
![\implies \: \cos(x) = \pm1](https://tex.z-dn.net/?f=%20%5Cimplies%20%5C%3A%20%20%5Ccos%28x%29%20%20%3D%20%20%5Cpm1)
This implies
![x = 0 \: or \:x = \pi](https://tex.z-dn.net/?f=x%20%3D%200%20%5C%3A%20or%20%5C%3Ax%20%3D%20%20%20%5Cpi%20)
When
![{ \tan }^{2} (x) = - 2](https://tex.z-dn.net/?f=%20%7B%20%5Ctan%20%7D%5E%7B2%7D%20%28x%29%20%3D%20%20-%202)
We have
![\tan(x) = \pm \sqrt{ - 2}](https://tex.z-dn.net/?f=%20%5Ctan%28x%29%20%20%3D%20%20%5Cpm%20%5Csqrt%7B%20-%202%7D%20)
hence x is not defined for all real numbers