Answer:
$30
Step-by-step explanation:
2 bags = 3
1 bag = 3/2
1 bag = 1.5
20 bags = 1.5x20
20 bags = $30
Answer:
![\bold{\dfrac{11}{2 }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cdfrac%7B11%7D%7B2%20%7D%7D)
Step-by-step explanation:
Given the geometric series:
![\{\dfrac{1}2, -1, 2, -4, ..... \}](https://tex.z-dn.net/?f=%5C%7B%5Cdfrac%7B1%7D2%2C%20-1%2C%202%2C%20-4%2C%20%20.....%20%5C%7D)
To find:
Sum of series upto 5 terms using the geometric series formula = ?
Solution:
Formula for sum of a n terms of a geometric series is given as:
![S_n=\dfrac{a(1-r^n)}{1-r} \ \{r](https://tex.z-dn.net/?f=S_n%3D%5Cdfrac%7Ba%281-r%5En%29%7D%7B1-r%7D%20%5C%20%5C%7Br%3C1%20%5C%7D)
is the first term of the geometric series
is the common ratio between each term (2nd term divided by 1st term or 3rd term divided by 2nd term ..... ).
Here:
![a = \dfrac{1}{2}](https://tex.z-dn.net/?f=a%20%3D%20%5Cdfrac%7B1%7D%7B2%7D)
![r = \dfrac{-1}{\dfrac{1}{2}} = -2](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7B-1%7D%7B%5Cdfrac%7B1%7D%7B2%7D%7D%20%3D%20-2)
![n=5](https://tex.z-dn.net/?f=n%3D5)
So, applying the formula for given values:
![S_5=\dfrac{\dfrac{1}2(1-(-2)^5)}{1-(-2)} \\\Rightarrow S_5=\dfrac{1-(-32)}{2 \times 3} \\\Rightarrow S_5=\dfrac{1+32}{6} \\\Rightarrow S_5=\dfrac{33}{6} \\\Rightarrow \bold{S_5=\dfrac{11}{2}}](https://tex.z-dn.net/?f=S_5%3D%5Cdfrac%7B%5Cdfrac%7B1%7D2%281-%28-2%29%5E5%29%7D%7B1-%28-2%29%7D%20%5C%5C%5CRightarrow%20S_5%3D%5Cdfrac%7B1-%28-32%29%7D%7B2%20%5Ctimes%203%7D%20%5C%5C%5CRightarrow%20S_5%3D%5Cdfrac%7B1%2B32%7D%7B6%7D%20%5C%5C%5CRightarrow%20S_5%3D%5Cdfrac%7B33%7D%7B6%7D%20%5C%5C%5CRightarrow%20%5Cbold%7BS_5%3D%5Cdfrac%7B11%7D%7B2%7D%7D)
So, the answer is
![\bold{\dfrac{11}{2 }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cdfrac%7B11%7D%7B2%20%7D%7D)
Answer:
C
Step-by-step explanation:
substitute f(x) into g(x)
g(x) = f(x) + 9 = -3x - 5 + 9 = - 3x + 4
To find the y-intercept solve g(0)
g(0) = 0 + 4 = 4 ← y- intercept → (0, 4 ) → C
All you have to do is to make (6’0) x=6. And y=-8 (0’8) on the graph