Answer:
3
1
4
-2
Step-by-step explanation:
imma math mannnnn
Answer:
Option: D is correct.
Step-by-step explanation:
since we are given a inequality as:
![y](https://tex.z-dn.net/?f=y%3C%5Cdfrac%7B2%7D%7B3%7D%5Ctimes%20x%2B2)
Clearly from the graph of the following inequality we could see that the origin is included in the shaded region and the shaded area is below the line.
Also it could be seen that if we put the origin points i.e. (0,0) in the inequality than 0<2 and the condition is true and hence origin is included in the shaded area.
Hence, option D is true.
To find the function that has the following end behavior:
![\begin{gathered} f(x)\rightarrow-\infty\text{ as }x\rightarrow\infty \\ f(x)\rightarrow\infty\text{ as }x\rightarrow-\infty \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%28x%29%5Crightarrow-%5Cinfty%5Ctext%7B%20as%20%7Dx%5Crightarrow%5Cinfty%20%5C%5C%20f%28x%29%5Crightarrow%5Cinfty%5Ctext%7B%20as%20%7Dx%5Crightarrow-%5Cinfty%20%5Cend%7Bgathered%7D)
Considering the function which is given in option C.
When x tends to infinity,
![\begin{gathered} f\mleft(x\mright)=-x^3-4x^2+x \\ \lim _{x\to\infty}(-x^3-4x^2+x)=-\infty \\ \lim _{x\to-\infty}(-x^3-4x^2+x)=\infty \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%5Cmleft%28x%5Cmright%29%3D-x%5E3-4x%5E2%2Bx%20%5C%5C%20%5Clim%20_%7Bx%5Cto%5Cinfty%7D%28-x%5E3-4x%5E2%2Bx%29%3D-%5Cinfty%20%5C%5C%20%5Clim%20_%7Bx%5Cto-%5Cinfty%7D%28-x%5E3-4x%5E2%2Bx%29%3D%5Cinfty%20%5Cend%7Bgathered%7D)
In other words, the degree of the given function is 3.
That is, odd.
The leading coefficient is -1.
That is, negative.
Hence, the end behavior is,
![\begin{gathered} f(x)\rightarrow-\infty\text{ as }x\rightarrow\infty \\ f(x)\rightarrow\infty\text{ as }x\rightarrow-\infty \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%28x%29%5Crightarrow-%5Cinfty%5Ctext%7B%20as%20%7Dx%5Crightarrow%5Cinfty%20%5C%5C%20f%28x%29%5Crightarrow%5Cinfty%5Ctext%7B%20as%20%7Dx%5Crightarrow-%5Cinfty%20%5Cend%7Bgathered%7D)
Hence, the correct option is C.
2/5 = 8/20
3/4= 15/20
Therefore, 3/4 is larger than 2/5~
Answer:
II quadrant.
Step-by-step explanation:
Consider given function:
![h(x)=-6+\dfrac{2}{3}x](https://tex.z-dn.net/?f=h%28x%29%3D-6%2B%5Cdfrac%7B2%7D%7B3%7Dx)
Here, we have to find the quadrant from which the graph of function is not passing.
For x=0,
![h(0)=-6+\dfrac{2}{3}(0)=-6](https://tex.z-dn.net/?f=h%280%29%3D-6%2B%5Cdfrac%7B2%7D%7B3%7D%280%29%3D-6)
Thus, y-intercept is (0,-6).
For h(x)=0,
![0=-6+\dfrac{2}{3}x](https://tex.z-dn.net/?f=0%3D-6%2B%5Cdfrac%7B2%7D%7B3%7Dx)
![6=\dfrac{2}{3}x](https://tex.z-dn.net/?f=6%3D%5Cdfrac%7B2%7D%7B3%7Dx)
![18=2x](https://tex.z-dn.net/?f=18%3D2x)
![9=x](https://tex.z-dn.net/?f=9%3Dx)
Thus, x-intercept is (9,0).
Plot (0,-6) and (9,0) on a coordinate plane and join them by a straight line as shown below.
From the graph it is clear that the graph is not passing through the II quadrant.
Therefore, the graph is not passing through the II quadrant.