-- After dog ate 1/2 of the collection, there were 29 remaining.
-- Just before dog came along, there were (2 x 29) = 58 cards.
-- That was after Dan added 5 new ones.
-- Before he added the 5 new ones, there were (58 - 5) = 53 cards.
-- When this story began, Dan had <em>53 cards</em>.
3a3 - 5b3 + (-2)a3 + (6)b3 = a3 + b3
So -2 and 6 will be the answer.
Answer:
1.) Yes
2.) No (unless x=-3)
3.) Yes
4.) No (unless x=3)
Step-by-step explanation:
1.) 3x+9=6 is equivalent to x+3=2
![3x+9=6\\3x+9-9=6-9\\3x=-3\\\frac{3x}{3}=\frac{-3}{3}\\x=-1\\\\x+3=2\\x+3-3=2-3\\x=-1](https://tex.z-dn.net/?f=3x%2B9%3D6%5C%5C3x%2B9-9%3D6-9%5C%5C3x%3D-3%5C%5C%5Cfrac%7B3x%7D%7B3%7D%3D%5Cfrac%7B-3%7D%7B3%7D%5C%5Cx%3D-1%5C%5C%5C%5Cx%2B3%3D2%5C%5Cx%2B3-3%3D2-3%5C%5Cx%3D-1)
![3x+9=6\\3(x+3)=6\\\frac{3(x+3)}{3}=\frac{6}{3}\\x+3=2](https://tex.z-dn.net/?f=3x%2B9%3D6%5C%5C3%28x%2B3%29%3D6%5C%5C%5Cfrac%7B3%28x%2B3%29%7D%7B3%7D%3D%5Cfrac%7B6%7D%7B3%7D%5C%5Cx%2B3%3D2)
2.) 3x+9 is not equivalent to x+3 unless x=-3
![3x+9\\3(x+3)\neq x+3](https://tex.z-dn.net/?f=3x%2B9%5C%5C3%28x%2B3%29%5Cneq%20x%2B3)
3.)
is equivalent to x=4(x-2)
![\frac{x}{(x-2)}=4\\(x-2)\frac{x}{(x-2)}=4(x-2)\\x=4(x-2)\\x=4x-8\\x+8=4x-8+8\\x+8-x=4x-x\\3x=8\\x=\frac{8}{3}\\\\x=4(x-2)\\x=4x-8\\x+8=4x-8+8\\x+8-x=4x-x\\8=3x\\x=8/3](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B%28x-2%29%7D%3D4%5C%5C%28x-2%29%5Cfrac%7Bx%7D%7B%28x-2%29%7D%3D4%28x-2%29%5C%5Cx%3D4%28x-2%29%5C%5Cx%3D4x-8%5C%5Cx%2B8%3D4x-8%2B8%5C%5Cx%2B8-x%3D4x-x%5C%5C3x%3D8%5C%5Cx%3D%5Cfrac%7B8%7D%7B3%7D%5C%5C%5C%5Cx%3D4%28x-2%29%5C%5Cx%3D4x-8%5C%5Cx%2B8%3D4x-8%2B8%5C%5Cx%2B8-x%3D4x-x%5C%5C8%3D3x%5C%5Cx%3D8%2F3)
![\frac{x}{(x-2)}=4\\(x-2)\frac{x}{(x-2)}=4(x-2)\\x=4(x-2)](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B%28x-2%29%7D%3D4%5C%5C%28x-2%29%5Cfrac%7Bx%7D%7B%28x-2%29%7D%3D4%28x-2%29%5C%5Cx%3D4%28x-2%29)
4.) These two expressions could only be equivalent if x=3
Step-by-step explanation:
Area of Shaded part
= 2 * Area of Quarter-circle - Area of Square
= 0.5π(8)² - 8²
= 32(π - 2)cm².
Perimeter of Shaded part
= 0.5 * 2π(8)
= 8πcm.
By creating a common denominator, you can compare different numbers to the same ratio. For example:
Take 2/3 and 3/4
Now 3/4 is the same as 9/12
And 2/3 is the same as 8/12
Now that they have the same denominator, you can tell that 9/12 is clearly greater than 8/12, meaning 3/4 is greater than 2/3.