Answer:
the vertex is (-4,2)
Step-by-step explanation:
Given:
LCM(a,b) = 90 and GCD(a,b) = 3.
b is three more than a.
To find:
The values of a and b.
Solution:
We have,
LCM(a,b) = 90
GCD(a,b) = HCF(a,b) = 3
According to the question,
![b=a+3](https://tex.z-dn.net/?f=b%3Da%2B3)
If a and b are two positive integers, then
![a\times b=HCF(a,b)\times LCM(a,b)](https://tex.z-dn.net/?f=a%5Ctimes%20b%3DHCF%28a%2Cb%29%5Ctimes%20LCM%28a%2Cb%29)
![a\times (a+3)=3\times 90](https://tex.z-dn.net/?f=a%5Ctimes%20%28a%2B3%29%3D3%5Ctimes%2090)
![a^2+3a=270](https://tex.z-dn.net/?f=a%5E2%2B3a%3D270)
![a^2+3a-270=0](https://tex.z-dn.net/?f=a%5E2%2B3a-270%3D0)
Splitting the middle terms, we get
![a^2+18a-15a-270=0](https://tex.z-dn.net/?f=a%5E2%2B18a-15a-270%3D0)
![a(a+18)-15(a+18)=0](https://tex.z-dn.net/?f=a%28a%2B18%29-15%28a%2B18%29%3D0)
![(a+18)(a-15)=0](https://tex.z-dn.net/?f=%28a%2B18%29%28a-15%29%3D0)
Using zero product property, we get
and ![a-15=0](https://tex.z-dn.net/?f=a-15%3D0)
and ![a=15](https://tex.z-dn.net/?f=a%3D15)
a is a positive integer so it cannot be negative. So, a=15.
Now,
![b=a+3](https://tex.z-dn.net/?f=b%3Da%2B3)
![b=15+3](https://tex.z-dn.net/?f=b%3D15%2B3)
![b=18](https://tex.z-dn.net/?f=b%3D18)
Therefore, the value of a is 15 and the value of b is 18.
Answer: the answer is B
Step-by-step explanation:
Answer:
The answer is X=21
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Simplify 1/3 and 1/2
It would look like ![\frac{(x+6)}{3} -\frac{(x-3)}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B6%29%7D%7B3%7D%20-%5Cfrac%7B%28x-3%29%7D%7B2%7D)
then![\frac{21-x}{6}=0](https://tex.z-dn.net/?f=%5Cfrac%7B21-x%7D%7B6%7D%3D0)
then mutiply 6 to each side and it will look like 21-x = 0
Last, subtract 21 from each side and it will be
21=x