I think it's C all real numbers
The distance between Durham to Birmingham is 240 miles
Answer: x = 7
Explanation:
6(x - 4) + x = 5(x - 2)
6x - 24 + x = 5x - 10
7x - 24 = 5x - 10
2x = 14
x = 7
:)
Answer:
- Shannon's expression in scientific notation is ![3.0 * 10^5](https://tex.z-dn.net/?f=3.0%20%2A%2010%5E5)
- Kristoph's expression in scientific notation is ![3.0 * 10^5](https://tex.z-dn.net/?f=3.0%20%2A%2010%5E5)
Step-by-step explanation:
Given
Shannon’s expression: ![4.2 * 10^9 /1.4 * 10^4](https://tex.z-dn.net/?f=4.2%20%2A%2010%5E9%20%2F1.4%20%2A%2010%5E4)
Kristoph’s expression: ![4.2 * 10^2 /1.4 * 10^{-3}](https://tex.z-dn.net/?f=4.2%20%2A%2010%5E2%20%2F1.4%20%2A%2010%5E%7B-3%7D)
Required
What is the value of their expressions written in standard form
First, we solve Shannon's expression:
![4.2 * 10^9 /1.4 * 10^4](https://tex.z-dn.net/?f=4.2%20%2A%2010%5E9%20%2F1.4%20%2A%2010%5E4)
Writing the expression properly
![\frac{4.2 * 10^9}{1.4 * 10^4}](https://tex.z-dn.net/?f=%5Cfrac%7B4.2%20%2A%2010%5E9%7D%7B1.4%20%2A%2010%5E4%7D)
Split into two
![\frac{4.2}{1.4} * \frac{10^9}{10^4}](https://tex.z-dn.net/?f=%5Cfrac%7B4.2%7D%7B1.4%7D%20%2A%20%5Cfrac%7B10%5E9%7D%7B10%5E4%7D)
![3.0 * \frac{10^9}{10^4}](https://tex.z-dn.net/?f=3.0%20%2A%20%5Cfrac%7B10%5E9%7D%7B10%5E4%7D)
From laws of indices ![\frac{a^m}{a^n} = a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%20%3D%20a%5E%7Bm-n%7D)
Applying the above law, we have
![3.0 * 10^{9-4}](https://tex.z-dn.net/?f=3.0%20%2A%2010%5E%7B9-4%7D)
![3.0 * 10^5](https://tex.z-dn.net/?f=3.0%20%2A%2010%5E5)
Hence, Shannon's expression in scientific notation is ![3.0 * 10^5](https://tex.z-dn.net/?f=3.0%20%2A%2010%5E5)
Applying the same steps on Kristoph's expression; we have
![4.2 * 10^2 /1.4 * 10^{-3}](https://tex.z-dn.net/?f=4.2%20%2A%2010%5E2%20%2F1.4%20%2A%2010%5E%7B-3%7D)
Writing the expression properly
![\frac{4.2 * 10^2}{1.4 * 10^{-3}}](https://tex.z-dn.net/?f=%5Cfrac%7B4.2%20%2A%2010%5E2%7D%7B1.4%20%2A%2010%5E%7B-3%7D%7D)
Split into two
![\frac{4.2}{1.4} * \frac{10^2}{10^{-3}}](https://tex.z-dn.net/?f=%5Cfrac%7B4.2%7D%7B1.4%7D%20%2A%20%5Cfrac%7B10%5E2%7D%7B10%5E%7B-3%7D%7D)
![3.0 * \frac{10^2}{10^{-3}}](https://tex.z-dn.net/?f=3.0%20%2A%20%5Cfrac%7B10%5E2%7D%7B10%5E%7B-3%7D%7D)
From laws of indices ![\frac{a^m}{a^n} = a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%20%3D%20a%5E%7Bm-n%7D)
Applying the above law, we have
![3.0 * 10^{2-(-3)}](https://tex.z-dn.net/?f=3.0%20%2A%2010%5E%7B2-%28-3%29%7D)
![3.0 * 10^{2+3}](https://tex.z-dn.net/?f=3.0%20%2A%2010%5E%7B2%2B3%7D)
![3.0 * 10^5](https://tex.z-dn.net/?f=3.0%20%2A%2010%5E5)
Hence, Kristoph's expression in scientific notation is ![3.0 * 10^5](https://tex.z-dn.net/?f=3.0%20%2A%2010%5E5)
Answer:
x^2+2xy+y^2
Step-by-step explanation:
(x + y)(x + y)
FOIL
first x*x = x^2
Outer x*y = xy
inner: y*x = xy
last y*y = y^2
add together
x^2+xy+xy+y^2
Combine like terms
x^2+2xy+y^2