If I understood the task, then here are the answers: 1/2=2/4 or 0.5=1/2
3k=7Q+6p
Solve for P which means we have to make 'p' alone
![3k=7Q+6p\\\\ Add 7Q on both sides \\\\ 3k - 7Q = 7Q - 7Q + 6p\\\\ \left ( 3k - 7Q \right ) = 6p\\\\ Divide both side by 6 to make p alone \\\\ \frac{\left ( 3k - 7Q \right )}{6} = \frac{6p}{6}\\\\ p = \frac{\left ( 3k - 7Q \right )}{6}](https://tex.z-dn.net/?f=%203k%3D7Q%2B6p%5C%5C%5C%5C%20Add%20%207Q%20on%20both%20sides%20%5C%5C%5C%5C%203k%20-%207Q%20%3D%207Q%20-%207Q%20%2B%206p%5C%5C%5C%5C%20%5Cleft%20%28%203k%20-%207Q%20%5Cright%20%29%20%3D%206p%5C%5C%5C%5C%20Divide%20both%20side%20by%206%20to%20make%20p%20alone%20%5C%5C%5C%5C%20%5Cfrac%7B%5Cleft%20%28%203k%20-%207Q%20%20%5Cright%20%29%7D%7B6%7D%20%3D%20%5Cfrac%7B6p%7D%7B6%7D%5C%5C%5C%5C%20p%20%3D%20%5Cfrac%7B%5Cleft%20%28%203k%20-%207Q%20%20%5Cright%20%29%7D%7B6%7D%20%20)
Answer:
a. Graph A: Cost vs Volume
Graph B: Calories vs Volume
b. Graph B (Calories vs Volume)
c. k = 15
Step-by-step explanation:
a. It is not possible for a volume of 10 oz of drink to be sold for $150. It doesn't make common sense. Also, calorie level of 150 in 10 oz of drink seem plausible.
It makes more sense if 10 oz of the drink cost $3.75. Therefore, the graphs should be titled as follows:
Graph A: Cost vs Volume
Graph B: Calories vs Volume
b. The quantities in Graph B (Calories vs Volume) appear to be in a proportional relationship. We know this because if we try drawing a line to connect the points on the graph, it will give us a straight line. A straight line connotes proportionality.
Also the ratio of the quantities of the two known points given are the same. I.e. ![\frac{150}{10} = \frac{360}{24} = 15](https://tex.z-dn.net/?f=%20%5Cfrac%7B150%7D%7B10%7D%20%3D%20%5Cfrac%7B360%7D%7B24%7D%20%3D%2015%20)
Therefore the quantities compared in Graph B shows a proportional relationship.
c. Constant of proportionality = ![\frac{150}{10} = \frac{360}{24} = 15](https://tex.z-dn.net/?f=%20%5Cfrac%7B150%7D%7B10%7D%20%3D%20%5Cfrac%7B360%7D%7B24%7D%20%3D%2015%20)
<em>The right answer for:</em>
<em>cos(-170°) = _____</em>
<em>is:</em>
<em>-cos10°</em>
<h2>
Explanation:</h2>
The cosine function is an even function, which means that for every point
on the graph of
then the point
also lies on the graph of the function. In other words, we can write:
![cos(-170^{\circ})=cos(170^{\circ})](https://tex.z-dn.net/?f=cos%28-170%5E%7B%5Ccirc%7D%29%3Dcos%28170%5E%7B%5Ccirc%7D%29)
But:
![170^{\circ}=180^{\circ}-10^{\circ}](https://tex.z-dn.net/?f=170%5E%7B%5Ccirc%7D%3D180%5E%7B%5Ccirc%7D-10%5E%7B%5Ccirc%7D)
So:
![cos(170^{\circ})=cos(180^{\circ}-10^{\circ})](https://tex.z-dn.net/?f=cos%28170%5E%7B%5Ccirc%7D%29%3Dcos%28180%5E%7B%5Ccirc%7D-10%5E%7B%5Ccirc%7D%29)
By property:
![cos(a-b)=cosacosb+sinasinb \\ \\ a=180^{\circ} \\ \\ b=10^{\circ} \\ \\ cos(170^{\circ} )=cos(180^{\circ} -10^{\circ})=cos180^{\circ} cos10^{\circ} +sin180^{\circ} sin10^{\circ} \\ \\ cos(170^{\circ})=-cos(10^{\circ})+0 \\ \\ \boxed{cos(170^{\circ})=-cos(10^{\circ})}](https://tex.z-dn.net/?f=cos%28a-b%29%3Dcosacosb%2Bsinasinb%20%5C%5C%20%5C%5C%20a%3D180%5E%7B%5Ccirc%7D%20%5C%5C%20%5C%5C%20b%3D10%5E%7B%5Ccirc%7D%20%5C%5C%20%5C%5C%20cos%28170%5E%7B%5Ccirc%7D%20%29%3Dcos%28180%5E%7B%5Ccirc%7D%20-10%5E%7B%5Ccirc%7D%29%3Dcos180%5E%7B%5Ccirc%7D%20cos10%5E%7B%5Ccirc%7D%20%2Bsin180%5E%7B%5Ccirc%7D%20sin10%5E%7B%5Ccirc%7D%20%5C%5C%20%5C%5C%20%20cos%28170%5E%7B%5Ccirc%7D%29%3D-cos%2810%5E%7B%5Ccirc%7D%29%2B0%20%5C%5C%20%5C%5C%20%5Cboxed%7Bcos%28170%5E%7B%5Ccirc%7D%29%3D-cos%2810%5E%7B%5Ccirc%7D%29%7D)
<h2>Learn more:</h2>
Trigonometric functions: brainly.com/question/2680050
#LearnWithBrainly