I'll start 18 and 22 for you, and you should then be able to do the rest on your own!
For 18, what we literally do is apply the distance formula for all the points and add them up. For B to C, we get the distance between them to be
sqrt((x1-x2)^2+(y1-y2)^2)=sqrt((0-4)^2+(3-(-1))^2)=sqrt((-4)^2+4^2)=sqrt(16+16)=sqrt(32). Repeat the process for C to E, E and F, and F to B then add the results up to get your answer!
For 22, since the area of a rectangle is length*width (we know given the right angles and that the opposite sides are equal in how long they are), we can multiply 2 perpendicular lines, for example, BC and CE to get sqrt(32)*sqrt(8)=16 as the area
Let's make a system of equations.
1 large bottle = l
1 regular bottle = r
l + r = 113
221 = 2.5l + r
Isolate r in the first equation and substitute it into the second equation:
l + r = 113
r = 113 - l
---
221 = 2.5l + 113 - l
221 = 1.5l + 113
108 = 1.5l
72 = l
Now, substitute that back into the first equation:
l + r = 113
72 + r = 113
r = 41
Finally, check your work by substituting back into both equations:
72 + 41 = 113 --> 113 = 113 <-- True
221 = 2.5(72) + 41 --> 221 = 180 + 41 <--True
Answer:
Franklin sold 72 large bottle of water and 41 regular-sized bottles of water.
3 to the power of 4 is 81
Answer is 31.5% vegetarian. Here is the my work. Hope this helps!
For the answer to this, we turn to the all-important Fundamental Theorem of Algebra<em /><em>, </em>which states that every degree-<em>n</em> polynomial has exactly <em>n </em>imaginary roots. It's important to keep in mind that this theorem doesn't tell you how to <em>find </em>these roots - it just tells you that they <em>exist</em>.
