25%
If you are buying 2 shirts for the same price, you have to calculate the cost of the shirt at half price first (1 piece of the pie) and then add it the original price (2 equal pieces of the pie since you just divided that to the price of the second shirt). That would be considered 3 out of 4 pieces off the pie or 75%. Your savings would be 25%.
Answer:
(y2 -y1) / (x2 - x1)
Step-by-step explanation:
use that formula. The answer should be -3/0 which doesn't make sense. Are you sure you have your x values correct? Since in that case it would be a straight line and the equation for that would be x = 6 since it is a straight line up with no y intercept.
Hope that helped
Answer: 0.963
explanaontion :Step-by-step
divide value by 1000
Answer:
The answer is "5051".
Step-by-step explanation:
Given equation:
![\bold{E(x)= 2(x+3)^2-3(x-1)(x+3)+(x-2)^2-31}\\\\](https://tex.z-dn.net/?f=%5Cbold%7BE%28x%29%3D%202%28x%2B3%29%5E2-3%28x-1%29%28x%2B3%29%2B%28x-2%29%5E2-31%7D%5C%5C%5C%5C)
put the 1, 2, 3, ........2019, 20202:
When E(1),
![E(1) =2(1+3)^2-3(1-1)(1+3)+(1-2)^2-31\\\\](https://tex.z-dn.net/?f=E%281%29%20%3D2%281%2B3%29%5E2-3%281-1%29%281%2B3%29%2B%281-2%29%5E2-31%5C%5C%5C%5C)
![=2(4)^2-3(0)(4)+(-1)^2-31\\\\=2(16)-0+1-31\\\\=32+1-31\\\\=2](https://tex.z-dn.net/?f=%3D2%284%29%5E2-3%280%29%284%29%2B%28-1%29%5E2-31%5C%5C%5C%5C%3D2%2816%29-0%2B1-31%5C%5C%5C%5C%3D32%2B1-31%5C%5C%5C%5C%3D2)
When E(2),
![E(2) =2(2+3)^2-3(2-1)(2+3)+(2-2)^2-31\\\\](https://tex.z-dn.net/?f=E%282%29%20%3D2%282%2B3%29%5E2-3%282-1%29%282%2B3%29%2B%282-2%29%5E2-31%5C%5C%5C%5C)
![=2(5)^2-3(1)(5)+(0)^2-31\\\\=2(25)-15+0-31\\\\=50-15-31\\\\=4](https://tex.z-dn.net/?f=%3D2%285%29%5E2-3%281%29%285%29%2B%280%29%5E2-31%5C%5C%5C%5C%3D2%2825%29-15%2B0-31%5C%5C%5C%5C%3D50-15-31%5C%5C%5C%5C%3D4)
When E(3),
![E(3) =2(3+3)^2-3(3-1)(3+3)+(3-2)^2-31\\](https://tex.z-dn.net/?f=E%283%29%20%3D2%283%2B3%29%5E2-3%283-1%29%283%2B3%29%2B%283-2%29%5E2-31%5C%5C)
![=2(6)^2-3(2)(6)+(1)^2-31\\\\=2(36)-36+1-31\\\\=72-66\\\\=6](https://tex.z-dn.net/?f=%3D2%286%29%5E2-3%282%29%286%29%2B%281%29%5E2-31%5C%5C%5C%5C%3D2%2836%29-36%2B1-31%5C%5C%5C%5C%3D72-66%5C%5C%5C%5C%3D6)
When E(2019),
![E(2019) =2(2019+3)^2-3(2019-1)(2019+3)+(2019-2)^2-31\\](https://tex.z-dn.net/?f=E%282019%29%20%3D2%282019%2B3%29%5E2-3%282019-1%29%282019%2B3%29%2B%282019-2%29%5E2-31%5C%5C)
![=2(2022)^2-3(2018)(2022)+(2017)^2-31\\\\=8,176,968-12,241,188+4,068,289-31 \\\\= 4038](https://tex.z-dn.net/?f=%3D2%282022%29%5E2-3%282018%29%282022%29%2B%282017%29%5E2-31%5C%5C%5C%5C%3D8%2C176%2C968-12%2C241%2C188%2B4%2C068%2C289-31%20%5C%5C%5C%5C%3D%204038)
When E(2020),
![E(2020) =2(2020+3)^2-3(2020-1)(2020+3)+(2020-2)^2-31\\\\](https://tex.z-dn.net/?f=E%282020%29%20%3D2%282020%2B3%29%5E2-3%282020-1%29%282020%2B3%29%2B%282020-2%29%5E2-31%5C%5C%5C%5C)
![=2(2023)^2-3(2019)(2023)+(2018)^2-31\\\\=8,185,058-12,253,311+4,072,324-31\\\\=4040\\](https://tex.z-dn.net/?f=%3D2%282023%29%5E2-3%282019%29%282023%29%2B%282018%29%5E2-31%5C%5C%5C%5C%3D8%2C185%2C058-12%2C253%2C311%2B4%2C072%2C324-31%5C%5C%5C%5C%3D4040%5C%5C)
![\ Calculate: \\\\ \bold{A= E(1)-E(2)+E(3)-E(4).....+E(2019)-E(2020)}\\\\A= 2-4+6-8.....+4038-4040](https://tex.z-dn.net/?f=%5C%20Calculate%3A%20%5C%5C%5C%5C%20%5Cbold%7BA%3D%20E%281%29-E%282%29%2BE%283%29-E%284%29.....%2BE%282019%29-E%282020%29%7D%5C%5C%5C%5CA%3D%202-4%2B6-8.....%2B4038-4040)
![A= (2+6....+4038)-(4+ 8+12...4040)\\](https://tex.z-dn.net/?f=A%3D%20%282%2B6....%2B4038%29-%284%2B%208%2B12...4040%29%5C%5C)
Formula:
![t_n= a+(n-1)d\\\\\ When \\ \\ T_n =4040 \\ a= 4 \\ d= 4\\4040= 4+(n-1)4\\4040=4+4n-4\\4n=4040\\n= \frac{4040}{4}\\n= 1010\\\\When \\\\T_n =4038 \\ a= 2 \\ d= 4\\4038= 2+(n-1)4\\4038=2+4n-4\\4038=-2+4n\\4036=4n \\ n= \frac{4036}{4}\\n= 1009\\\\](https://tex.z-dn.net/?f=t_n%3D%20a%2B%28n-1%29d%5C%5C%5C%5C%5C%20When%20%5C%5C%20%5C%5C%20%20T_n%20%3D4040%20%5C%5C%20a%3D%204%20%5C%5C%20d%3D%204%5C%5C4040%3D%204%2B%28n-1%294%5C%5C4040%3D4%2B4n-4%5C%5C4n%3D4040%5C%5Cn%3D%20%5Cfrac%7B4040%7D%7B4%7D%5C%5Cn%3D%201010%5C%5C%5C%5CWhen%20%5C%5C%5C%5CT_n%20%3D4038%20%5C%5C%20a%3D%202%20%5C%5C%20d%3D%204%5C%5C4038%3D%202%2B%28n-1%294%5C%5C4038%3D2%2B4n-4%5C%5C4038%3D-2%2B4n%5C%5C4036%3D4n%20%5C%5C%20n%3D%20%5Cfrac%7B4036%7D%7B4%7D%5C%5Cn%3D%201009%5C%5C%5C%5C)
Formula for sum:
![When, n= 1010\\ a=4 \\ l=4040\\ \\ S= \frac{n}{2}(2a+l)\\\\S= \frac{1010}{2} (2\times 4+4040)\\\\S= 505(8+4040)\\\\S_1= 2044240 \\\\\\](https://tex.z-dn.net/?f=When%2C%20n%3D%201010%5C%5C%20a%3D4%20%5C%5C%20l%3D4040%5C%5C%20%5C%5C%20S%3D%20%5Cfrac%7Bn%7D%7B2%7D%282a%2Bl%29%5C%5C%5C%5CS%3D%20%5Cfrac%7B1010%7D%7B2%7D%20%282%5Ctimes%204%2B4040%29%5C%5C%5C%5CS%3D%20505%288%2B4040%29%5C%5C%5C%5CS_1%3D%202044240%20%5C%5C%5C%5C%5C%5C)
![When, n= 1009\\ a=2 \\ l=4038\\ \\ S= \frac{n}{2}(2a+l)\\\\S= \frac{1009}{2} (2\times 2+4038)\\\\S= 504.5(4+4038)\\\\S_2= 2039189 \\\\\\](https://tex.z-dn.net/?f=When%2C%20n%3D%201009%5C%5C%20a%3D2%20%5C%5C%20l%3D4038%5C%5C%20%5C%5C%20S%3D%20%5Cfrac%7Bn%7D%7B2%7D%282a%2Bl%29%5C%5C%5C%5CS%3D%20%5Cfrac%7B1009%7D%7B2%7D%20%282%5Ctimes%202%2B4038%29%5C%5C%5C%5CS%3D%20504.5%284%2B4038%29%5C%5C%5C%5CS_2%3D%202039189%20%5C%5C%5C%5C%5C%5C)
![S= S_1-S_2\\\\S= 2044240 -2039189\\\\S= 5051](https://tex.z-dn.net/?f=S%3D%20S_1-S_2%5C%5C%5C%5CS%3D%202044240%20-2039189%5C%5C%5C%5CS%3D%205051)
The absolute value is = 5051
We can do anything to an equation as long as we do it to both sides
given:
![\sqrt{3+\frac{(4+\sqrt{x+3})^2}{6}}=3](https://tex.z-dn.net/?f=%5Csqrt%7B3%2B%5Cfrac%7B%284%2B%5Csqrt%7Bx%2B3%7D%29%5E2%7D%7B6%7D%7D%3D3)
square both sides
![3+\frac{(4+\sqrt{x+3})^2}{6}=9](https://tex.z-dn.net/?f=3%2B%5Cfrac%7B%284%2B%5Csqrt%7Bx%2B3%7D%29%5E2%7D%7B6%7D%3D9)
minus 3 from both sides
![\frac{(4+\sqrt{x+3})^2}{6}=6](https://tex.z-dn.net/?f=%5Cfrac%7B%284%2B%5Csqrt%7Bx%2B3%7D%29%5E2%7D%7B6%7D%3D6)
multiply both sides by 6
![(4+\sqrt{x+3})^2=36 square root both sides, remember to take the positive and negative roots [tex]4+\sqrt{x+3}=+/-6](https://tex.z-dn.net/?f=%284%2B%5Csqrt%7Bx%2B3%7D%29%5E2%3D36%20square%20root%20both%20sides%2C%20remember%20to%20take%20the%20positive%20and%20negative%20roots%20%5Btex%5D4%2B%5Csqrt%7Bx%2B3%7D%3D%2B%2F-6)
minus 4
![\sqrt{x+3}=-4+/-6](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B3%7D%3D-4%2B%2F-6)
square both sides
do for -4+6 and -4-6 (2 and -10)
![x+3=4](https://tex.z-dn.net/?f=x%2B3%3D4)
and
![x+3=100](https://tex.z-dn.net/?f=x%2B3%3D100)
minus 3
![x=1](https://tex.z-dn.net/?f=x%3D1)
and
![x=97](https://tex.z-dn.net/?f=x%3D97)
test for extraneous roots
x=97 doesn't work
the answer is x=1