Answer:
The slope is -1/5 and the y intercept is 12
Step-by-step explanation:
Y=-1/5x+12
This is in the form
y=mx+b where m is the slope and b is the y intercept
The slope is -1/5 and the y intercept is 12
Answer:
(a)![S_6=1092](https://tex.z-dn.net/?f=S_6%3D1092)
(b)![S_5=363](https://tex.z-dn.net/?f=S_5%3D363)
Step-by-step explanation:
<u>Question 1</u>
Given the geometric series
3+15+75+375+...
![a_1=3, r=15/3=75/15=5\\$Therefore using:\\S_n=\dfrac{a_1(1-r^n)}{1-r} \\S_6=\dfrac{3(1-3^6)}{1-3}=\dfrac{3(-728)}{-2}=\dfrac{-2184}{-2}\\\\S_6=1092](https://tex.z-dn.net/?f=a_1%3D3%2C%20r%3D15%2F3%3D75%2F15%3D5%5C%5C%24Therefore%20using%3A%5C%5CS_n%3D%5Cdfrac%7Ba_1%281-r%5En%29%7D%7B1-r%7D%20%5C%5CS_6%3D%5Cdfrac%7B3%281-3%5E6%29%7D%7B1-3%7D%3D%5Cdfrac%7B3%28-728%29%7D%7B-2%7D%3D%5Cdfrac%7B-2184%7D%7B-2%7D%5C%5C%5C%5CS_6%3D1092)
<u>Question 2</u>
Given the series: ![\sum_{n=1}^5 3^n](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D1%7D%5E5%203%5En)
![3^1=3;3^2=9;3^3=27\\$The series is 3+9+27+\cdots\\$Therefore: r=9/3=27/9=3](https://tex.z-dn.net/?f=3%5E1%3D3%3B3%5E2%3D9%3B3%5E3%3D27%5C%5C%24The%20series%20is%203%2B9%2B27%2B%5Ccdots%5C%5C%24Therefore%3A%20r%3D9%2F3%3D27%2F9%3D3)
![a_1=3, r=3\\$Therefore using:\\S_n=\dfrac{a_1(1-r^n)}{1-r} \\S_5=\dfrac{3(1-3^5)}{1-3}=\dfrac{3(-242)}{-2}=\dfrac{-726}{-2}\\\\S_5=363](https://tex.z-dn.net/?f=a_1%3D3%2C%20r%3D3%5C%5C%24Therefore%20using%3A%5C%5CS_n%3D%5Cdfrac%7Ba_1%281-r%5En%29%7D%7B1-r%7D%20%5C%5CS_5%3D%5Cdfrac%7B3%281-3%5E5%29%7D%7B1-3%7D%3D%5Cdfrac%7B3%28-242%29%7D%7B-2%7D%3D%5Cdfrac%7B-726%7D%7B-2%7D%5C%5C%5C%5CS_5%3D363)
Answer:
<h2>The range: {0, 10, 42}</h2>
Step-by-step explanation:
Put the values of x from the domain to the equation of the function
f(x) = 2x² - 8
for x = -2
f(-2) = 2(-2)² - 8 = 2(4) - 8 = 8 - 8 = 0
for x = 3
f(3) = 2(3)² - 8 = 2(9) - 8 = 18 - 8 = 10
for x = 5
f(5) = 2(5)² - 8 = 2(25) - 8 = 50 - 8 = 42
The answer would be: 18 9/10
First notice that f(x) is negative, so entire graph will be below x-axis.
Next find domain by setting what is inside sqrt greater than 0.
You can't take sqrt of neg number.
![1-x \geq 0 \\ x \leq 1](https://tex.z-dn.net/?f=1-x%20%20%5Cgeq%200%20%20%20%5C%5C%20%20x%20%20%5Cleq%201)
Finally plot some points, start at x = 1, y=0.
Then try x = 0, y = -1.
x = -3, y = -2.
Connect the points, done.