![\bf 2cos^2(x)+3cos(x)-2=0\impliedby \textit{so, notice is just a quadratic} \\\\\\\ [2cos(x)~~-~~1][cos(x)~~+~~2]=0\\\\ -------------------------------\\\\ 2cos(x)-1=0\implies 2cos(x)=1\implies cos(x)=\cfrac{1}{2} \\\\\\ \measuredangle x=cos^{-1}\left( \frac{1}{2} \right)\implies \measuredangle x= \begin{cases} \frac{\pi }{3}\\\\ \frac{5\pi }{3} \end{cases}\\\\ -------------------------------\\\\ cos(x)+2=0\implies cos(x)=-2](https://tex.z-dn.net/?f=%5Cbf%202cos%5E2%28x%29%2B3cos%28x%29-2%3D0%5Cimpliedby%20%5Ctextit%7Bso%2C%20notice%20is%20just%20a%20quadratic%7D%0A%5C%5C%5C%5C%5C%5C%5C%0A%5B2cos%28x%29~~-~~1%5D%5Bcos%28x%29~~%2B~~2%5D%3D0%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A2cos%28x%29-1%3D0%5Cimplies%202cos%28x%29%3D1%5Cimplies%20cos%28x%29%3D%5Ccfrac%7B1%7D%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cmeasuredangle%20x%3Dcos%5E%7B-1%7D%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%5Cimplies%20%5Cmeasuredangle%20x%3D%0A%5Cbegin%7Bcases%7D%0A%5Cfrac%7B%5Cpi%20%7D%7B3%7D%5C%5C%5C%5C%0A%5Cfrac%7B5%5Cpi%20%7D%7B3%7D%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0Acos%28x%29%2B2%3D0%5Cimplies%20cos%28x%29%3D-2)
now, for the second case, recall that the cosine is always a value between -1 and 1, so a -2 is just a way to say, such angle doesn't exist.
(x-1)(5x-6)
Factor
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out of
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Rewrite
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plus
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Apply the distributive property.
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Don't know if I answered it right...but trying to help!...
<span><span>$782.7 billion: Restaurant industry sales.</span><span>1 million+: Restaurant locations in the United States.</span><span>14.4 million: Restaurant industry employees.</span><span>1.7 million: New restaurant jobs created by the year 2026.</span><span>10%: Restaurant workforce as part of the overall U.S. workforce.</span><span>9 in 10: Restaurant managers who started at entry level. </span><span>8 in 10: Restaurant owners who started their industry careers in entry-level positions.</span><span>9 in 10: Restaurants with fewer than 50 employees.</span><span>7 in 10: Restaurants that are single-unit operations.</span></span>
Answer:
The correct answer is not shown in your picture. You must get a = 60.
Step-by-step explanation:
(1/2)a + (2/3)b = 50
b = 30
(1/2)a + (2/3)(30) = 50
(1/2)a + 20 = 50
(1/2)a + 20 - 20 = 50 - 20
(1/2)a = 30
2 * (1/2)a = 2 * 30
a = 60
The correct answer is not shown in your picture. You must get a = 60.
