S=350 your starting amount + 30w which is 30× the number of weeks (19) which comes out to give you s=920 if I did it correctly
Answer: -3 ≤ -2c
Step-by-step explanation:
First multiply C by -2, and make sure it's not less than -3. It can be -3, but it can't be less than.
well, we know that θ is in the III Quadrant, where the sine is negative and the cosine is negative as well, or if you wish, where "x" as well as "y" are both negative, now, the hypotenuse or radius of the circle is just a distance amount, so is never negative, so in the equation of cos(θ) = - (2/5), the negative must be the adjacent side, thus
![cos(\theta)=\cfrac{\stackrel{adjacent}{-2}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2 - (-2)^2}=b\implies \pm\sqrt{25-4}\implies \pm\sqrt{21}=b\implies \stackrel{III~Quadrant}{-\sqrt{21}=b}](https://tex.z-dn.net/?f=cos%28%5Ctheta%29%3D%5Ccfrac%7B%5Cstackrel%7Badjacent%7D%7B-2%7D%7D%7B%5Cunderset%7Bhypotenuse%7D%7B5%7D%7D%5Cqquad%20%5Ctextit%7Blet%27s%20find%20the%20%5Cunderline%7Bopposite%20side%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%20%5C%5C%5C%5C%20c%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20%5Csqrt%7Bc%5E2-a%5E2%7D%3Db%20%5Cqquad%20%5Cbegin%7Bcases%7D%20c%3Dhypotenuse%5C%5C%20a%3Dadjacent%5C%5C%20b%3Dopposite%5C%5C%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20%5Cpm%5Csqrt%7B5%5E2%20-%20%28-2%29%5E2%7D%3Db%5Cimplies%20%5Cpm%5Csqrt%7B25-4%7D%5Cimplies%20%5Cpm%5Csqrt%7B21%7D%3Db%5Cimplies%20%5Cstackrel%7BIII~Quadrant%7D%7B-%5Csqrt%7B21%7D%3Db%7D)
![\dotfill\\\\ csc(\theta)\implies \cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{-\sqrt{21}}}\implies \stackrel{\textit{rationalizing the denominator}}{-\cfrac{5}{\sqrt{21}}\cdot \cfrac{\sqrt{21}}{\sqrt{21}}\implies -\cfrac{5\sqrt{21}}{21}} \\\\\\ tan(\theta)=\cfrac{\stackrel{opposite}{-\sqrt{21}}}{\underset{adjacent}{-2}}\implies tan(\theta)=\cfrac{\sqrt{21}}{2}](https://tex.z-dn.net/?f=%5Cdotfill%5C%5C%5C%5C%20csc%28%5Ctheta%29%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Bhypotenuse%7D%7B5%7D%7D%7B%5Cunderset%7Bopposite%7D%7B-%5Csqrt%7B21%7D%7D%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Brationalizing%20the%20denominator%7D%7D%7B-%5Ccfrac%7B5%7D%7B%5Csqrt%7B21%7D%7D%5Ccdot%20%5Ccfrac%7B%5Csqrt%7B21%7D%7D%7B%5Csqrt%7B21%7D%7D%5Cimplies%20-%5Ccfrac%7B5%5Csqrt%7B21%7D%7D%7B21%7D%7D%20%5C%5C%5C%5C%5C%5C%20tan%28%5Ctheta%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B-%5Csqrt%7B21%7D%7D%7D%7B%5Cunderset%7Badjacent%7D%7B-2%7D%7D%5Cimplies%20tan%28%5Ctheta%29%3D%5Ccfrac%7B%5Csqrt%7B21%7D%7D%7B2%7D)
The correct answer is -163
Explanation:
First you calculate within the parentheses; (8+4)= 12: 5-7*12*2
Next you multiply and divide; 7*12 is 84*2 is 168
Then you add and subtract; 5-168 is -163
Hope This Helps!!!