Given:
The quadratic equation is
![y=6x^2-15x+6](https://tex.z-dn.net/?f=y%3D6x%5E2-15x%2B6)
To find:
The x-intercepts of the given equation.
Solution:
We have,
![y=6x^2-15x+6](https://tex.z-dn.net/?f=y%3D6x%5E2-15x%2B6)
Splitting the middle term, we get
![y=6x^2-12x-3x+6](https://tex.z-dn.net/?f=y%3D6x%5E2-12x-3x%2B6)
![y=6x(x-2)-3(x-2)](https://tex.z-dn.net/?f=y%3D6x%28x-2%29-3%28x-2%29)
![y=(x-2)(6x-3)](https://tex.z-dn.net/?f=y%3D%28x-2%29%286x-3%29)
For x-intercepts, y=0.
![(x-2)(6x-3)=0](https://tex.z-dn.net/?f=%28x-2%29%286x-3%29%3D0)
Using zero product property, we get
![x-2=0\text{ and }6x-3=0](https://tex.z-dn.net/?f=x-2%3D0%5Ctext%7B%20and%20%7D6x-3%3D0)
![x=2\text{ and }6x=3](https://tex.z-dn.net/?f=x%3D2%5Ctext%7B%20and%20%7D6x%3D3)
![x=2\text{ and }x=\dfrac{3}{6}](https://tex.z-dn.net/?f=x%3D2%5Ctext%7B%20and%20%7Dx%3D%5Cdfrac%7B3%7D%7B6%7D)
![x=2\text{ and }x=0.5](https://tex.z-dn.net/?f=x%3D2%5Ctext%7B%20and%20%7Dx%3D0.5)
So, the x-intercepts are (0.5,0) and (2,0).
Therefore, the correct option is a.
Answer:
12m
Step-by-step explanation:
Answer:
8% is equivalent to the fraction 8/100
Step-by-step explanation:
Answer:
The correct answer is option D: ![y = 10^{3.994}](https://tex.z-dn.net/?f=y%20%3D%2010%5E%7B3.994%7D)
Step-by-step explanation:
Given:
log(y)= 3.994
Solution:
A logarithm base b of a positive number x satisfies the following definition:
![y =log_b(x) => b^y =x](https://tex.z-dn.net/?f=y%20%3Dlog_b%28x%29%20%3D%3E%20b%5Ey%20%3Dx)
For ![x > 0, b >0, b \neq 1](https://tex.z-dn.net/?f=x%20%3E%200%2C%20b%20%3E0%2C%20b%20%5Cneq%201)
Also if no base b is indicated, the base of the logarithm is assumed to be 10
.
Thus, in log(y)= 3.994 base b is not indicated. so its base is assumed to be 10
now
![log_{10}(y)= 3.994](https://tex.z-dn.net/?f=log_%7B10%7D%28y%29%3D%203.994)
Then
![y = 10^{3.994}](https://tex.z-dn.net/?f=y%20%3D%2010%5E%7B3.994%7D)