Answer:
Step-by-step explanation:
It could be 42 pencils
I think it would be A. Sorry if I'm wrong.
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:
![1,715\ in^{2}](https://tex.z-dn.net/?f=1%2C715%5C%20in%5E%7B2%7D)
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z-----> the scale factor
x-----> surface area of the enlarged figure
y----> surface area of the original figure
![z^{2}=\frac{x}{y}](https://tex.z-dn.net/?f=z%5E%7B2%7D%3D%5Cfrac%7Bx%7D%7By%7D)
we have
![z=7](https://tex.z-dn.net/?f=z%3D7)
![y=35\ in^{2}](https://tex.z-dn.net/?f=y%3D35%5C%20in%5E%7B2%7D)
substitute
![7^{2}=\frac{x}{35}](https://tex.z-dn.net/?f=7%5E%7B2%7D%3D%5Cfrac%7Bx%7D%7B35%7D)
![x=7^{2}(35)=1,715\ in^{2}](https://tex.z-dn.net/?f=x%3D7%5E%7B2%7D%2835%29%3D1%2C715%5C%20in%5E%7B2%7D)
Answer:
y = 4
x = 104°
Step-by-step explanation:
3y = y + 8
-y -y
2y÷2 = 8÷2
2y÷2 cancels out so
8 ÷ 2 = 4
y = 4
all sides are congruent so all angles are congruent so that means that all the angles are 104°