I believe it would be the third option
Answer:
-8.228 and -13.416
Step-by-step explanation:
math
Angela is saving $8.00 on the dress bc 20% of 40 is 8.
well, another way to word it will be, we know "x" and "y" are directly proportional, we also know that x = 6 when y = 42, what is "y" when x = 1?
![\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} x = 6\\ y =42 \end{cases}\implies 42 = k(6)\implies \cfrac{42}{6}=k\implies 7=k \\\\\\ \textit{therefore}\qquad \qquad \boxed{y = 7x} \\\\\\ \textit{when x = 1, what is \underline{y}?}\qquad y = 7(1)\implies y = 7](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bdirect%20proportional%20variation%7D%20%5C%5C%5C%5C%20%5Ctextit%7B%5Cunderline%7By%7D%20varies%20directly%20with%20%5Cunderline%7Bx%7D%7D%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bconstant%20of%20variation%7D%7D%7By%3D%5Cstackrel%7B%5Cdownarrow%20%7D%7Bk%7Dx~%5Chfill%20%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ctextit%7Bwe%20know%20that%20%7D%20%5Cbegin%7Bcases%7D%20x%20%3D%206%5C%5C%20y%20%3D42%20%5Cend%7Bcases%7D%5Cimplies%2042%20%3D%20k%286%29%5Cimplies%20%5Ccfrac%7B42%7D%7B6%7D%3Dk%5Cimplies%207%3Dk%20%5C%5C%5C%5C%5C%5C%20%5Ctextit%7Btherefore%7D%5Cqquad%20%5Cqquad%20%5Cboxed%7By%20%3D%207x%7D%20%5C%5C%5C%5C%5C%5C%20%5Ctextit%7Bwhen%20x%20%3D%201%2C%20what%20is%20%5Cunderline%7By%7D%3F%7D%5Cqquad%20y%20%3D%207%281%29%5Cimplies%20y%20%3D%207)
The given triangle is a right-angled triangle. This means that special trig identities can be applies
<u>These identities are as follows:</u>
sin (theta) = opposite / hypotenuse
cos (theta) = adjacent / hypotenuse
tan (theta) = opposite / adjacent
<u>Now, for the unknown theta in the triangle:</u>
The opposite side is 16 and the hypotenuse is 20
This means that we will use the <u>sin</u> not the cos as Bob did
<u>The solution will be as follows:</u>
sin (theta) = opposite / hypotenuse
sin (theta) = 16 / 20
theta = sin^-1(16/20)
theta = 53.13°
Hope this helps :)
