Answer:
Domain:
-∞<x<∞, or (-∞,∞) in interval notation
Range:
-∞<f(x)<∞, or (-∞,∞) in interval notation
Step-by-step explanation:
It’s infinite both ways, so:
Domain:
-∞<x<∞, or (-∞,∞) in interval notation
Range:
-∞<f(x)<∞, or (-∞,∞) in interval notation
Answer:
5 full sandwich
Step-by-step explanation:
Total roasted beef kelly has = 4 3/8 ounces
lets convert it into improper fraction for ease of calculation
Total roasted beef kelly has = ( 4*8+ 3)/8 ounces = 35/8 ounces.
weight of beef in 1 sandwich = 3/4 ounce
let the no. of sanwich be x
Total weight of beef in x sandwich = 3/4 *x ounce
given that total weight of roasted beef is 35/8 ounces. so
3/4 *x = 35/8
=> 3x = 35*4/8 = 35/2
=> x = 35/2*3 = 35/6
=> x = 5 5/6
Thus, kelly can make 5 full sandwich and 5/6 part of full sandwich.
If answer should be for full sandwich , then kelly can make 5 sandwich.
Answer:
10.5 hours.
Step-by-step explanation:
Please consider the complete question.
Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 14 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?
Let t represent time taken by newer pump in hours to drain the pool on its own.
So part of pool drained by newer pump in one hour would be
.
We have been given that it takes the older pump 14 hours to drain the pool by itself, so part of pool drained by older pump in one hour would be
.
Part of pool drained by both pumps working together in one hour would be
.
Now, we will equate the sum of part of pool emptied by both pumps with
and solve for t as:
![\frac{1}{14}+\frac{1}{t}=\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B14%7D%2B%5Cfrac%7B1%7D%7Bt%7D%3D%5Cfrac%7B1%7D%7B6%7D)
![\frac{1}{14}\times 42t+\frac{1}{t}\times 42t=\frac{1}{6}\times 42t](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B14%7D%5Ctimes%2042t%2B%5Cfrac%7B1%7D%7Bt%7D%5Ctimes%2042t%3D%5Cfrac%7B1%7D%7B6%7D%5Ctimes%2042t)
![3t+42=7t](https://tex.z-dn.net/?f=3t%2B42%3D7t)
![7t=3t+42](https://tex.z-dn.net/?f=7t%3D3t%2B42)
![7t-3t=3t-3t+42](https://tex.z-dn.net/?f=7t-3t%3D3t-3t%2B42)
![4t=42](https://tex.z-dn.net/?f=4t%3D42)
![\frac{4t}{4}=\frac{42}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4t%7D%7B4%7D%3D%5Cfrac%7B42%7D%7B4%7D)
![t=10.5](https://tex.z-dn.net/?f=t%3D10.5)
Therefore, it will take 10.5 hours for the newer pump to drain the pool on its own.
The polynomial 9x^5+36x^4+189x^3 in factored form is ![-9 x \times x \times x \times(x-7) \times(x+3)](https://tex.z-dn.net/?f=-9%20x%20%5Ctimes%20x%20%5Ctimes%20x%20%5Ctimes%28x-7%29%20%5Ctimes%28x%2B3%29)
<u>Solution:</u>
Given, polynomial equation is ![-9 x^{5}+36 x^{4}+189 x^{3}](https://tex.z-dn.net/?f=-9%20x%5E%7B5%7D%2B36%20x%5E%7B4%7D%2B189%20x%5E%7B3%7D)
We have to find the factored form of the above given polynomial equation.
Let us solve it by grouping.
Now, take the polynomial ⇒ ![-9 x^{5}+36 x^{4}+189 x^{3}](https://tex.z-dn.net/?f=-9%20x%5E%7B5%7D%2B36%20x%5E%7B4%7D%2B189%20x%5E%7B3%7D)
By taking common term out, we get
![\rightarrow-9 x^{3}\left(x^{2}-4 x-21\right)](https://tex.z-dn.net/?f=%5Crightarrow-9%20x%5E%7B3%7D%5Cleft%28x%5E%7B2%7D-4%20x-21%5Cright%29)
![\rightarrow-9 x^{3}\left(x^{2}-(7-3) x-7 \times 3\right)](https://tex.z-dn.net/?f=%5Crightarrow-9%20x%5E%7B3%7D%5Cleft%28x%5E%7B2%7D-%287-3%29%20x-7%20%5Ctimes%203%5Cright%29)
Grouping the terms we get,
![\rightarrow-9 x^{3}\left(\left(x^{2}-7 x\right)+(3 x-7 x^3)\right)](https://tex.z-dn.net/?f=%5Crightarrow-9%20x%5E%7B3%7D%5Cleft%28%5Cleft%28x%5E%7B2%7D-7%20x%5Cright%29%2B%283%20x-7%20x%5E3%29%5Cright%29)
Taking common terms out from each group,
![\rightarrow-9 x^{3}(x(x-7)+3(x-7))](https://tex.z-dn.net/?f=%5Crightarrow-9%20x%5E%7B3%7D%28x%28x-7%29%2B3%28x-7%29%29)
![\Rightarrow-9 x^{3}((x-7)(x+3))](https://tex.z-dn.net/?f=%5CRightarrow-9%20x%5E%7B3%7D%28%28x-7%29%28x%2B3%29%29)
![\rightarrow-9 x \times x \times x \times(x-7) \times(x+3)](https://tex.z-dn.net/?f=%5Crightarrow-9%20x%20%5Ctimes%20x%20%5Ctimes%20x%20%5Ctimes%28x-7%29%20%5Ctimes%28x%2B3%29)
Thus the factored form of polynomial is found out