Answer=A
To find the gcf, we need to factor each number.
154=2*7*11
196=2*2*7*7
The number have a factor of 2 and a factor of 7 in common, so...
GCF=2*7
Answer:
![5(x^2+4x)=7](https://tex.z-dn.net/?f=5%28x%5E2%2B4x%29%3D7)
![5(x^2+4x+4)=7+20](https://tex.z-dn.net/?f=5%28x%5E2%2B4x%2B4%29%3D7%2B20)
![(x+2)=\pm\sqrt{\frac{27}{5}}](https://tex.z-dn.net/?f=%28x%2B2%29%3D%5Cpm%5Csqrt%7B%5Cfrac%7B27%7D%7B5%7D%7D)
Step-by-step explanation:
we have
step 1
Group terms that contain the same variable, and move the constant to the opposite side of the equation
![5x^2+20x=7](https://tex.z-dn.net/?f=5x%5E2%2B20x%3D7)
step 2
Factor 5 left side
![5(x^2+4x)=7](https://tex.z-dn.net/?f=5%28x%5E2%2B4x%29%3D7)
step 3
Complete the square
![5(x^2+4x+2^2)=7+2^2(5)](https://tex.z-dn.net/?f=5%28x%5E2%2B4x%2B2%5E2%29%3D7%2B2%5E2%285%29)
![5(x^2+4x+4)=7+20](https://tex.z-dn.net/?f=5%28x%5E2%2B4x%2B4%29%3D7%2B20)
![5(x^2+4x+4)=27](https://tex.z-dn.net/?f=5%28x%5E2%2B4x%2B4%29%3D27)
step 4
Rewrite as perfect squares
![5(x+2)^2=27](https://tex.z-dn.net/?f=5%28x%2B2%29%5E2%3D27)
step 5
![(x+2)^2=\frac{27}{5}](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%3D%5Cfrac%7B27%7D%7B5%7D)
![(x+2)=\pm\sqrt{\frac{27}{5}}](https://tex.z-dn.net/?f=%28x%2B2%29%3D%5Cpm%5Csqrt%7B%5Cfrac%7B27%7D%7B5%7D%7D)
![(x+2)=\pm\frac{3\sqrt{15}}{5}](https://tex.z-dn.net/?f=%28x%2B2%29%3D%5Cpm%5Cfrac%7B3%5Csqrt%7B15%7D%7D%7B5%7D)
step 6
![x=-2\pm\frac{3\sqrt{15}}{5}](https://tex.z-dn.net/?f=x%3D-2%5Cpm%5Cfrac%7B3%5Csqrt%7B15%7D%7D%7B5%7D)
Composite is a number that is NOT prime. So we want to find an odd perfect square that IS prime to be a counterexample.
√36 = Not odd
√49 = 7 Factors only 1 * 7 so it is prime
√81 = 9 Factors 1, 3, 9 composite
√225 = 15 Factors 1,3, 5,9,15, 25, 45, 75, 225 composite
Counterexample for 2∧n - 1 Is prime
2^6 - 1 = 64 - 1 = 63 NOT PRIME Factors are: 1, 3, 7, 9,21, 63
2^5 - 1 = 32 - 1 = 31 Prime
2^3 - 1 = 8 - 1 = 7 Prime
2^2 - 1 = 4 - 1 = 3 Prime
Answer:
1:+35
2:-270
3:-12
4+19
5:-15
6:-25
Step-by-step explanation: