Answer:
4 out of 52 or simplified 2 out of 26
Step-by-step explanation:
There are 4 suites of cards, spades, hearts, clubs, diamonds and there is one card for two in each suite, so we therefore know that the probability of picking a two out of a 52 card deck will be four out of 52 or the simplified answer would be 2 out of 26. Hope this helps, have a great day!
Answer:
![\textsf{A)} \quad 5u^3-2u^2+5u+8](https://tex.z-dn.net/?f=%5Ctextsf%7BA%29%7D%20%5Cquad%205u%5E3-2u%5E2%2B5u%2B8)
Step-by-step explanation:
Given expression:
![(-2u^3+5u-1)+(7u^3-2u^2+9)](https://tex.z-dn.net/?f=%28-2u%5E3%2B5u-1%29%2B%287u%5E3-2u%5E2%2B9%29)
Remove parentheses:
![\implies -2u^3+5u-1+7u^3-2u^2+9](https://tex.z-dn.net/?f=%5Cimplies%20-2u%5E3%2B5u-1%2B7u%5E3-2u%5E2%2B9)
Collect like terms:
![\implies -2u^3+7u^3-2u^2+5u-1+9](https://tex.z-dn.net/?f=%5Cimplies%20-2u%5E3%2B7u%5E3-2u%5E2%2B5u-1%2B9)
Combine like terms:
![\implies 5u^3-2u^2+5u+8](https://tex.z-dn.net/?f=%5Cimplies%205u%5E3-2u%5E2%2B5u%2B8)
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Answer:
A) y^3+27
Step-by-step explanation:
There are two ways of solving this problem:
1. Recognizing this as the factored form of the sum of perfect cubes
2. Distribute and add the like terms.
1. In order to distribute we must multiply y by y^2-3y+9, and then 3 by y^2-3y+9:
![(y+3)(y^2-3y+9)=y(y^2-3y+9)+3(y^2-3y+9)](https://tex.z-dn.net/?f=%28y%2B3%29%28y%5E2-3y%2B9%29%3Dy%28y%5E2-3y%2B9%29%2B3%28y%5E2-3y%2B9%29)
![y(y^2-3y+9)+3(y^2-3y+9)=y^3-3y^2+9y+3y^2-9y+27](https://tex.z-dn.net/?f=y%28y%5E2-3y%2B9%29%2B3%28y%5E2-3y%2B9%29%3Dy%5E3-3y%5E2%2B9y%2B3y%5E2-9y%2B27)
After we add the positive and negative 3y^2 and 9y, they will cancel out and be gone entirely:
![y^3-3y^2+9y+3y^2-9y+27=y^3+27](https://tex.z-dn.net/?f=y%5E3-3y%5E2%2B9y%2B3y%5E2-9y%2B27%3Dy%5E3%2B27)
2. You know how you can factor the difference of perfect squares?
As an example:
![a^2-b^2=(a+b)(a-b)](https://tex.z-dn.net/?f=a%5E2-b%5E2%3D%28a%2Bb%29%28a-b%29)
Well, not many people know this but you can actually factor both the sum and difference of perfect cubes:
![a^3+b^3=(a+b)(a^2-ab+b^2)](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%3D%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29)
![a^3-b^3=(a-b)(a^2+ab+b^2)](https://tex.z-dn.net/?f=a%5E3-b%5E3%3D%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29)
Because we have these identities, we can easily establish here that we have the sum of perfect cubes, and that (y+3)(y^2-3y+9)= y^3+3^3 = y^3+27
Answer:
4.243
Step-by-step explanation:
To calculate the diagonal of a square, multiply the length of the side by the square root of 2:
d = a√2
d = 3√2=4.24264068