Answer:
4,548 liters per hour. 20 x 3.79 = 75.8. 75.8 x 60 = 4,548. hope this helps
Step-by-step explanation:
#6 is -10.7
Explanation: 3.5-14.2= -10.7
#7 -18 1/4
Explanation: -12 3/4 + -5 1/2= -18 1/4
Complete Question:
Construct a table of values of the following functions using the interval of -5 to 5.
![g(x) = \frac{x^3 + 3x - 5}{x^2}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7Bx%5E3%20%2B%203x%20-%205%7D%7Bx%5E2%7D)
Answer:
See Explanation
Step-by-step explanation:
Required
Construct a table with the given interval
When ![x = -5](https://tex.z-dn.net/?f=x%20%3D%20-5)
becomes
![g(-5) = \frac{-5^3 + 3(-5) - 5}{-5^2}](https://tex.z-dn.net/?f=g%28-5%29%20%3D%20%5Cfrac%7B-5%5E3%20%2B%203%28-5%29%20-%205%7D%7B-5%5E2%7D)
![g(-5) = \frac{-125 -15 - 5}{25}](https://tex.z-dn.net/?f=g%28-5%29%20%3D%20%5Cfrac%7B-125%20-15%20-%205%7D%7B25%7D)
![g(-5) = \frac{-145}{25}](https://tex.z-dn.net/?f=g%28-5%29%20%3D%20%5Cfrac%7B-145%7D%7B25%7D)
![g(-5) = -5.8](https://tex.z-dn.net/?f=g%28-5%29%20%3D%20-5.8)
When ![x = -4](https://tex.z-dn.net/?f=x%20%3D%20-4)
becomes
![g(-4) = \frac{-4^3 + 3(-4) - 5}{-4^2}](https://tex.z-dn.net/?f=g%28-4%29%20%3D%20%5Cfrac%7B-4%5E3%20%2B%203%28-4%29%20-%205%7D%7B-4%5E2%7D)
![g(-4) = \frac{-64 -12 - 5}{16}](https://tex.z-dn.net/?f=g%28-4%29%20%3D%20%5Cfrac%7B-64%20-12%20-%205%7D%7B16%7D)
![g(-4) = \frac{-81}{16}](https://tex.z-dn.net/?f=g%28-4%29%20%3D%20%5Cfrac%7B-81%7D%7B16%7D)
![g(-4) = -5.0625](https://tex.z-dn.net/?f=g%28-4%29%20%3D%20-5.0625)
When ![x = -3](https://tex.z-dn.net/?f=x%20%3D%20-3)
becomes
![g(-3) = \frac{-3^3 + 3(-3) - 5}{-3^2}](https://tex.z-dn.net/?f=g%28-3%29%20%3D%20%5Cfrac%7B-3%5E3%20%2B%203%28-3%29%20-%205%7D%7B-3%5E2%7D)
![g(-3) = \frac{-27 -9 - 5}{9}](https://tex.z-dn.net/?f=g%28-3%29%20%3D%20%5Cfrac%7B-27%20-9%20-%205%7D%7B9%7D)
![g(-3) = \frac{-41}{9}](https://tex.z-dn.net/?f=g%28-3%29%20%3D%20%5Cfrac%7B-41%7D%7B9%7D)
![g(-3) = -4.56](https://tex.z-dn.net/?f=g%28-3%29%20%3D%20-4.56)
When ![x = -2](https://tex.z-dn.net/?f=x%20%3D%20-2)
becomes
![g(-2) = \frac{-2^3 + 3(-2) - 5}{-2^2}](https://tex.z-dn.net/?f=g%28-2%29%20%3D%20%5Cfrac%7B-2%5E3%20%2B%203%28-2%29%20-%205%7D%7B-2%5E2%7D)
![g(-2) = \frac{-8 -6 - 5}{4}](https://tex.z-dn.net/?f=g%28-2%29%20%3D%20%5Cfrac%7B-8%20-6%20-%205%7D%7B4%7D)
![g(-2) = \frac{-19}{4}](https://tex.z-dn.net/?f=g%28-2%29%20%3D%20%5Cfrac%7B-19%7D%7B4%7D)
![g(-2) = -4.75](https://tex.z-dn.net/?f=g%28-2%29%20%3D%20-4.75)
When ![x = -1](https://tex.z-dn.net/?f=x%20%3D%20-1)
becomes
![g(-1) = \frac{-1^3 + 3(-1) - 5}{-1^2}](https://tex.z-dn.net/?f=g%28-1%29%20%3D%20%5Cfrac%7B-1%5E3%20%2B%203%28-1%29%20-%205%7D%7B-1%5E2%7D)
![g(-1) = \frac{-1 + 3 - 5}{1}](https://tex.z-dn.net/?f=g%28-1%29%20%3D%20%5Cfrac%7B-1%20%2B%203%20-%205%7D%7B1%7D)
![g(-1) = \frac{-3}{1}](https://tex.z-dn.net/?f=g%28-1%29%20%3D%20%5Cfrac%7B-3%7D%7B1%7D)
![g(-1) = -3](https://tex.z-dn.net/?f=g%28-1%29%20%3D%20-3)
When ![x = 0](https://tex.z-dn.net/?f=x%20%3D%200)
becomes
![g(0) = \frac{0^3 + 3(0) - 5}{0^2}](https://tex.z-dn.net/?f=g%280%29%20%3D%20%5Cfrac%7B0%5E3%20%2B%203%280%29%20-%205%7D%7B0%5E2%7D)
![g(0) = \frac{0 + 0 - 5}{0}](https://tex.z-dn.net/?f=g%280%29%20%3D%20%5Cfrac%7B0%20%2B%200%20-%205%7D%7B0%7D)
![g(0) = \frac{- 5}{0}](https://tex.z-dn.net/?f=g%280%29%20%3D%20%5Cfrac%7B-%205%7D%7B0%7D)
<em>g(0) = undefined</em>
When ![x = 1](https://tex.z-dn.net/?f=x%20%3D%201)
becomes
![g(1) = \frac{1^3 + 3(1) - 5}{1^2}](https://tex.z-dn.net/?f=g%281%29%20%3D%20%5Cfrac%7B1%5E3%20%2B%203%281%29%20-%205%7D%7B1%5E2%7D)
![g(1) = \frac{1 + 3 - 5}{1}](https://tex.z-dn.net/?f=g%281%29%20%3D%20%5Cfrac%7B1%20%2B%203%20-%205%7D%7B1%7D)
![g(1) = \frac{-1}{1}](https://tex.z-dn.net/?f=g%281%29%20%3D%20%5Cfrac%7B-1%7D%7B1%7D)
![g(1) = 1](https://tex.z-dn.net/?f=g%281%29%20%3D%201)
When ![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
becomes
![g(2) = \frac{2^3 + 3(2) - 5}{2^2}](https://tex.z-dn.net/?f=g%282%29%20%3D%20%5Cfrac%7B2%5E3%20%2B%203%282%29%20-%205%7D%7B2%5E2%7D)
![g(2) = \frac{8 + 6 - 5}{4}](https://tex.z-dn.net/?f=g%282%29%20%3D%20%5Cfrac%7B8%20%2B%206%20-%205%7D%7B4%7D)
![g(2) = \frac{9}{4}](https://tex.z-dn.net/?f=g%282%29%20%3D%20%5Cfrac%7B9%7D%7B4%7D)
![g(2) = 2.25](https://tex.z-dn.net/?f=g%282%29%20%3D%202.25)
When ![x = 3](https://tex.z-dn.net/?f=x%20%3D%203)
becomes
![g(3) = \frac{3^3 + 3(3) - 5}{3^2}](https://tex.z-dn.net/?f=g%283%29%20%3D%20%5Cfrac%7B3%5E3%20%2B%203%283%29%20-%205%7D%7B3%5E2%7D)
![g(3) = \frac{27 + 9 - 5}{9}](https://tex.z-dn.net/?f=g%283%29%20%3D%20%5Cfrac%7B27%20%2B%209%20-%205%7D%7B9%7D)
![g(3) = \frac{31}{9}](https://tex.z-dn.net/?f=g%283%29%20%3D%20%5Cfrac%7B31%7D%7B9%7D)
![g(3) = 3.44](https://tex.z-dn.net/?f=g%283%29%20%3D%203.44)
When ![x = 4](https://tex.z-dn.net/?f=x%20%3D%204)
becomes
![g(4) = \frac{4^3 + 3(4) - 5}{4^2}](https://tex.z-dn.net/?f=g%284%29%20%3D%20%5Cfrac%7B4%5E3%20%2B%203%284%29%20-%205%7D%7B4%5E2%7D)
![g(4) = \frac{64 + 12 - 5}{16}](https://tex.z-dn.net/?f=g%284%29%20%3D%20%5Cfrac%7B64%20%2B%2012%20-%205%7D%7B16%7D)
![g(4) = \frac{71}{16}](https://tex.z-dn.net/?f=g%284%29%20%3D%20%5Cfrac%7B71%7D%7B16%7D)
![g(4) = 4.4375](https://tex.z-dn.net/?f=g%284%29%20%3D%204.4375)
When ![x = 5](https://tex.z-dn.net/?f=x%20%3D%205)
becomes
![g(5) = \frac{5^3 + 3(5) - 5}{5^2}](https://tex.z-dn.net/?f=g%285%29%20%3D%20%5Cfrac%7B5%5E3%20%2B%203%285%29%20-%205%7D%7B5%5E2%7D)
![g(5) = \frac{125 + 15 - 5}{25}](https://tex.z-dn.net/?f=g%285%29%20%3D%20%5Cfrac%7B125%20%2B%2015%20-%205%7D%7B25%7D)
![g(5) = \frac{135}{25}](https://tex.z-dn.net/?f=g%285%29%20%3D%20%5Cfrac%7B135%7D%7B25%7D)
![g(5) = 5.4](https://tex.z-dn.net/?f=g%285%29%20%3D%205.4)
<em>Hence, the complete table is:</em>
x ---- g(x)
-5 --- -5.8
-4 --- -5.0625
-3 --- -4.56
-2 --- -4.75
-1 --- -3
0 -- Undefined
1 --- 1
2 -- 2.25
3 --- 3.44
4 --- 4.4375
5 --- 5.4
Using translation concepts, it is found that the transformed image of (5,-4) after the composition will be given by:
D.) (-6, 6)
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, first the image is rotated 180º around the origin, hence:
(x,y) -> (-x, -y), then:
(5,-4) -> (-5, 4).
Then, T(-1,2) means that:
(x,y) -> (x - 1, y + 2).
Then:
(-5,4) -> (-5 -1, 4 + 2) -> (-6,6)
Hence option D is correct.
More can be learned about translation concepts at brainly.com/question/4521517
#SPJ1
Answer:
The answer to your question is: BC = 9
Step-by-step explanation:
Data
BC = 8x + 1
AB = 11
AC = 20x
AB + BC = AC
11 + 8x + 1 = 20x
12 + 8x = 20x
12 = 20x - 8x
12 = 12x
x = 12/12 = 1
BC = 8(1) + 1
BC = 8 + 1 = 9
AC = 20(1) = 20
11 + 9 = 20