Answer:
The second: ![\bold{f (x) =4(x+\frac34)^2-\frac{21}4}](https://tex.z-dn.net/?f=%5Cbold%7Bf%20%28x%29%20%3D4%28x%2B%5Cfrac34%29%5E2-%5Cfrac%7B21%7D4%7D)
Step-by-step explanation:
![f (x) =4x^2+6x-3\\\\f (x) =4(x^2+\frac64x]-3\\\\f (x) =4[x^2+2\cdot x\cdot\frac34+(\frac34)^2-(\frac34)^2]-3\\\\f (x) =4[(x+\frac34)^2-(\frac34)^2]-3\\\\f (x) =4(x+\frac34)^2-4(\frac34)^2-3\\\\f (x) =4(x+\frac34)^2-\frac94-\frac{12}4\\\\\underline{f (x) =4(x+\frac34)^2-\frac{21}4}](https://tex.z-dn.net/?f=f%20%28x%29%20%3D4x%5E2%2B6x-3%5C%5C%5C%5Cf%20%28x%29%20%3D4%28x%5E2%2B%5Cfrac64x%5D-3%5C%5C%5C%5Cf%20%28x%29%20%3D4%5Bx%5E2%2B2%5Ccdot%20x%5Ccdot%5Cfrac34%2B%28%5Cfrac34%29%5E2-%28%5Cfrac34%29%5E2%5D-3%5C%5C%5C%5Cf%20%28x%29%20%3D4%5B%28x%2B%5Cfrac34%29%5E2-%28%5Cfrac34%29%5E2%5D-3%5C%5C%5C%5Cf%20%28x%29%20%3D4%28x%2B%5Cfrac34%29%5E2-4%28%5Cfrac34%29%5E2-3%5C%5C%5C%5Cf%20%28x%29%20%3D4%28x%2B%5Cfrac34%29%5E2-%5Cfrac94-%5Cfrac%7B12%7D4%5C%5C%5C%5C%5Cunderline%7Bf%20%28x%29%20%3D4%28x%2B%5Cfrac34%29%5E2-%5Cfrac%7B21%7D4%7D)
Answer:2.5
Step-by-step explanation:
The answer is 2/6 or if it is reduced 1/3
Answer:
All numbers less than 2 or
or ![(-\infty, 2)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%202%29)
Step-by-step explanation:
Given that:
Number is added to itself is less than the number subtracted from 6.
To find:
All such numbers.
Solution:
Let the number be
.
Here, an inequality will be made.
When solved, it might give more than one answers.
As per the question statement, let us write the inequality.
Number added to itself ![\Rightarrow x +x =2x](https://tex.z-dn.net/?f=%5CRightarrow%20x%20%2Bx%20%3D2x)
Number subtracted from six = ![6-x](https://tex.z-dn.net/?f=6-x)
As per question:
![2x](https://tex.z-dn.net/?f=2x%3C6-x%5C%5C%5CRightarrow%203x%3C6%5C%5C%5CRightarrow%20x%3C2)
So, the answer is:
All numbers less than 2 or
or
.