Hello! So, we could set up a proportion to solve this, because the price and CPI increased at the same rate. Let's set it up like this: 34.6/82.4 = 0.75/x. This is because we know the prices from the 1960's, but we don't know the gallon of milk price in 1980, and we line them up like that to make sure we get the proper answer. Cross multiply the values in order to get 34.6x = 61.8. Now, divide each side by 34.6 to isolate the variable. x ≈ 1.7861 and other numbers behind it or 1.79 when rounded to the nearest hundredth. The price for a gallon of milk in 1980 was about $1.79.
![\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.
Answer:
a) identity property of multiplication
b) commutative property in addition
Answer:
B. 9
Step-by-step explanation:
We know that a full circle should equal 360°, that'll help!
Since the 140°+3x+13 should equal to 180, because that makes the half of the circle it covers, we know how to set up our equation!
It should look like this:
3x+13=40
ISOLATE YOUR VARIABLE:
- Subtract 13 from both sides
NEXT, CONTINUE ISOLATING:
3x=27
- Divide by 3 from both sides.
FINALLY:
You will get X=9!
Answer:
48 ounces
Step-by-step explanation:
(48+32)/10=800/10=8<9
(48*2)/10=96/10=9.6>9
