Answer:
729
Step-by-step explanation:
hope this helps!
Answer:
Because the price did not stay the same when they discounted it by 10% percent before.
Step-by-step explanation:
10% percent of 450 is 45 so Subtracting that from 450 would give you,405.
They deducted another 10% percent a week later 10 percent of 405 would be 40.5 so you would subtract that from 405 which would make it 364.5
If you took 20% off originally then 20% of 450 is 90 so subtracting that would make 450 into 360 which is different from 364.5
Answer:
See Below.
Step-by-step explanation:
We want to verify the equation:
![\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B1%2B%5Csin%5Ctheta%7D%20%3D%20%5Csec%5E2%5Ctheta%20-%20%5Csec%5Ctheta%20%5Ctan%5Ctheta)
To start, we can multiply the fraction by (1 - sin(θ)). This yields:
![\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B1%2B%5Csin%5Ctheta%7D%5Cleft%28%5Cfrac%7B1-%5Csin%5Ctheta%7D%7B1-%5Csin%5Ctheta%7D%5Cright%29%20%3D%20%5Csec%5E2%5Ctheta%20-%20%5Csec%5Ctheta%20%5Ctan%5Ctheta)
Simplify. The denominator uses the difference of two squares pattern:
![\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1-%5Csin%5Ctheta%7D%7B%5Cunderbrace%7B1-%5Csin%5E2%5Ctheta%7D_%7B%28a%2Bb%29%28a-b%29%3Da%5E2-b%5E2%7D%7D%20%3D%20%5Csec%5E2%5Ctheta%20-%20%5Csec%5Ctheta%20%5Ctan%5Ctheta)
Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:
![\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cdisplaystyle%20%5Cfrac%7B1-%5Csin%5Ctheta%7D%7B%5Ccos%5E2%5Ctheta%7D%20%3D%20%5Csec%5E2%5Ctheta%20-%20%5Csec%5Ctheta%20%5Ctan%5Ctheta)
Split into two separate fractions:
![\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B%5Ccos%5E2%5Ctheta%7D%20-%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5E2%5Ctheta%7D%20%3D%20%5Csec%5E2%5Ctheta%20-%20%5Csec%5Ctheta%5Ctan%5Ctheta)
Rewrite the two fractions:
![\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28%5Cfrac%7B1%7D%7B%5Ccos%5Ctheta%7D%5Cright%29%5E2-%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D%5Ccdot%20%5Cfrac%7B1%7D%7B%5Ccos%5Ctheta%7D%3D%5Csec%5E2%5Ctheta%20-%20%5Csec%5Ctheta%20%5Ctan%5Ctheta)
By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:
![\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csec%5E2%5Ctheta%20-%20%5Csec%5Ctheta%5Ctan%5Ctheta%20%5Cstackrel%7B%5Ccheckmark%7D%7B%3D%7D%20%20%5Csec%5E2%5Ctheta%20-%20%5Csec%5Ctheta%5Ctan%5Ctheta)
Hence verified.
Answer is <span>16y + 7z
</span><span><span><span><span>9y</span>+<span>11z</span></span>+<span>7y</span></span>−<span>4z
</span></span><span>=<span><span><span><span><span>9y</span>+<span>11z</span></span>+<span>7y</span></span>+</span>−<span>4z
</span></span></span>Combine Like Terms:
<span>=<span><span><span><span>9y</span>+<span>11z</span></span>+<span>7y</span></span>+<span>−<span>4z
</span></span></span></span><span>=<span><span>(<span><span>9y</span>+<span>7y</span></span>)</span>+<span>(<span><span>11z</span>+<span>−<span>4z</span></span></span>)
</span></span></span><span>=<span><span>16y</span>+<span>7z</span></span></span><span>
</span>