Answer:
Step-by-step explanation:
<h3>To prove quadrilateral is a square:</h3>
a) Slope of CB
C(-3,-1) ; B = (0,3)
![\sf = \dfrac{3-[-1]}{0-[-3]}\\\\ =\dfrac{3+1}{0+3}\\\\ = \dfrac{4}{3}](https://tex.z-dn.net/?f=%5Csf%20%3D%20%5Cdfrac%7B3-%5B-1%5D%7D%7B0-%5B-3%5D%7D%5C%5C%5C%5C%20%3D%5Cdfrac%7B3%2B1%7D%7B0%2B3%7D%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B4%7D%7B3%7D)
b) D(1,-4) ; A(4,0)
![Slope \ of \ DA = \dfrac{0-[-4]}{4-1}\\](https://tex.z-dn.net/?f=Slope%20%5C%20of%20%5C%20DA%20%3D%20%5Cdfrac%7B0-%5B-4%5D%7D%7B4-1%7D%5C%5C)
Slope of CB = slope of DA
c) C(-3,-1) ; D(1 , -4)
![\sf Slope \ of \ CD =\dfrac{-4-[-1]}{1-[-3]}](https://tex.z-dn.net/?f=%5Csf%20Slope%20%5C%20of%20%5C%20CD%20%3D%5Cdfrac%7B-4-%5B-1%5D%7D%7B1-%5B-3%5D%7D)
So, CD is perpendicular to CB
d) B(0,3) ; D(1,-4)
e) C(-3,-1) ; A(4,0)
![\sf Slope \ of \ CA = \dfrac{0-[-1]}{4-[-3]}\\](https://tex.z-dn.net/?f=%5Csf%20Slope%20%5C%20of%20%5C%20CA%20%3D%20%5Cdfrac%7B0-%5B-1%5D%7D%7B4-%5B-3%5D%7D%5C%5C)
So, CA is perpendicular to BD
Answer:
17
Step-by-step explanation:
So, this is a percentage problem.
Start off by finding how many students 0.28% is:
If 100% = 5780
0.01% = 0.578
Now:
0.01% = 0.578
0.28% = 16.184
The exercise tells you to round for a whole person, so 16.184 turns 17
And that's the answer!
Answer:
215g for 40p is best value for money.
Step-by-step explanation:
215g/40p = 5.38 g/p
395g/74p = 5.33 g/p
It's a question of decimal division.
Answer:
40 more paintings in order to maximize sales making a total of 60 paintings
Step-by-step explanation:
Let x= no.of copies above 20
Total Sales(x) = (number of copies)(price per copy)
Sales (x)= (20 +x)(100 –x)
Open bracket
=1200-20x+100x-x^2
=1200+80x-x^2
Derivative of the sales
80-2x=0
80=2x
Divide both sides by 2
40=x
Because Sales(x)= –2, this is maximal by the second derivative test
The artist should make 40 more paintings in order to maximize sales making a total of 60 paintings.
