Answer:
0=0
Step-by-step explanation:
![2(x+1)=3x-x+2\\\\\mathrm{Add\:similar\:elements:}\:3x-x=2x\\2\left(x+1\right)=2x+2\\\\\mathrm{Expand\:}2\left(x+1\right):\quad 2x+2\\2x+2=2x+2\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\2x+2-2=2x+2-2\\\\Simplify\\2x=2x\\\\\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}\\2x-2x=2x-2x\\\\Simplify\\0=0\\\\\mathrm{True\:for\:all}\:x](https://tex.z-dn.net/?f=2%28x%2B1%29%3D3x-x%2B2%5C%5C%5C%5C%5Cmathrm%7BAdd%5C%3Asimilar%5C%3Aelements%3A%7D%5C%3A3x-x%3D2x%5C%5C2%5Cleft%28x%2B1%5Cright%29%3D2x%2B2%5C%5C%5C%5C%5Cmathrm%7BExpand%5C%3A%7D2%5Cleft%28x%2B1%5Cright%29%3A%5Cquad%202x%2B2%5C%5C2x%2B2%3D2x%2B2%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D2%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C2x%2B2-2%3D2x%2B2-2%5C%5C%5C%5CSimplify%5C%5C2x%3D2x%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D2x%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C2x-2x%3D2x-2x%5C%5C%5C%5CSimplify%5C%5C0%3D0%5C%5C%5C%5C%5Cmathrm%7BTrue%5C%3Afor%5C%3Aall%7D%5C%3Ax)
Answer:
268.25
Step-by-step explanation:
by using the fact that one year is 365.25 days, we can subtract our 365.25 by our 97 to get 268.25, written in the equation of 365.25-97=268.25
*edit, messed up how long a year was, corrected my issue, answer & equation.
False
6(p + q) = 6p + 6q ( distribute 6 to both p and q) (distribute to everything in the parenthesis)
6p + q = 6p + q
They are not equivalent
hope this helps
Answer:
5/8
Step-by-step explanation:
There are two numbers from one to eight that are less than three (1 and 2). So 2/8 of the numbered sections are less than three.
There are three numbers from one to eight that are greater than five (6, 7, and 8). So 3/8 of the numbered sections are greater than five
Probability of getting a number less than three: 2/8
Probability of getting a number greater than five: 3/8
Probability of getting either in a single spin = 2/8 + 3/8 = 5/8
Answer:
Prat 9) ![SF=2, x=16\ in](https://tex.z-dn.net/?f=SF%3D2%2C%20x%3D16%5C%20in)
Part 10) ![SF=0.5, x=14\ ft](https://tex.z-dn.net/?f=SF%3D0.5%2C%20x%3D14%5C%20ft)
Part 11) ![SF=0.5, x=3.5\ ft](https://tex.z-dn.net/?f=SF%3D0.5%2C%20x%3D3.5%5C%20ft)
Part 12) ![SF=3, x=7\ m](https://tex.z-dn.net/?f=SF%3D3%2C%20x%3D7%5C%20m)
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
SF-----> the scale factor
a----> area of the shaded figure
b----> area of the unshaded figure
![SF^{2} =\frac{x}{y}](https://tex.z-dn.net/?f=SF%5E%7B2%7D%20%3D%5Cfrac%7Bx%7D%7By%7D)
Problem 9) we have
![a=216\ in^{2}](https://tex.z-dn.net/?f=a%3D216%5C%20in%5E%7B2%7D)
![b=54\ in^{2}](https://tex.z-dn.net/?f=b%3D54%5C%20in%5E%7B2%7D)
substitute in the formula
![SF^{2}=\frac{216}{54}](https://tex.z-dn.net/?f=SF%5E%7B2%7D%3D%5Cfrac%7B216%7D%7B54%7D)
![SF^{2}=4](https://tex.z-dn.net/?f=SF%5E%7B2%7D%3D4)
------> the scale factor
To find the value of x, multiply the length of the unshaded figure by the scale factor
![x=(2)(8)=16\ in](https://tex.z-dn.net/?f=x%3D%282%29%288%29%3D16%5C%20in)
Problem 10) we have
![a=161\ ft^{2}](https://tex.z-dn.net/?f=a%3D161%5C%20ft%5E%7B2%7D)
![b=644\ ft^{2}](https://tex.z-dn.net/?f=b%3D644%5C%20ft%5E%7B2%7D)
substitute in the formula
![SF^{2}=\frac{161}{644}](https://tex.z-dn.net/?f=SF%5E%7B2%7D%3D%5Cfrac%7B161%7D%7B644%7D)
![SF^{2}=0.25](https://tex.z-dn.net/?f=SF%5E%7B2%7D%3D0.25)
------> the scale factor
To find the value of x, multiply the length of the unshaded figure by the scale factor
![x=(0.5)(28)=14\ ft](https://tex.z-dn.net/?f=x%3D%280.5%29%2828%29%3D14%5C%20ft)
Problem 11) we have
![a=10.5\ ft^{2}](https://tex.z-dn.net/?f=a%3D10.5%5C%20ft%5E%7B2%7D)
![b=42\ ft^{2}](https://tex.z-dn.net/?f=b%3D42%5C%20ft%5E%7B2%7D)
substitute in the formula
![SF^{2}=\frac{10.5}{42}](https://tex.z-dn.net/?f=SF%5E%7B2%7D%3D%5Cfrac%7B10.5%7D%7B42%7D)
![SF^{2}=0.25](https://tex.z-dn.net/?f=SF%5E%7B2%7D%3D0.25)
------> the scale factor
To find the value of x, multiply the length of the unshaded figure by the scale factor
![x=(0.5)(7)=3.5\ ft](https://tex.z-dn.net/?f=x%3D%280.5%29%287%29%3D3.5%5C%20ft)
Problem 12) we have
![a=4,590\ m^{2}](https://tex.z-dn.net/?f=a%3D4%2C590%5C%20m%5E%7B2%7D)
![b=510\ m^{2}](https://tex.z-dn.net/?f=b%3D510%5C%20m%5E%7B2%7D)
substitute in the formula
![SF^{2}=\frac{4,590}{510}](https://tex.z-dn.net/?f=SF%5E%7B2%7D%3D%5Cfrac%7B4%2C590%7D%7B510%7D)
![SF^{2}=9](https://tex.z-dn.net/?f=SF%5E%7B2%7D%3D9)
------> the scale factor
To find the value of x, divide the length of the shaded figure by the scale factor
![x=(21)/(3)=7\ m](https://tex.z-dn.net/?f=x%3D%2821%29%2F%283%29%3D7%5C%20m)