Answer: OPTION C
Step-by-step explanation:
To solve the exercise shown in the image attached, you need to subtract the functions f(x) and g(x).
Keeping the above on mind, you have:
![(f-g)(x)=2x^{2}+2-(x^{2}-1)](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3D2x%5E%7B2%7D%2B2-%28x%5E%7B2%7D-1%29)
You must distribute the negative sign and then you must add the like terms, therefore, you obtain:
![(f-g)(x)=2x^{2}+2-x^{2}+1\\(f-g)(x)=x^{2} +3](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3D2x%5E%7B2%7D%2B2-x%5E%7B2%7D%2B1%5C%5C%28f-g%29%28x%29%3Dx%5E%7B2%7D%20%2B3)
The answer should be 14.
You just have to substitute x with the given number and finish the equation.
Answer: ![90cm^3](https://tex.z-dn.net/?f=90cm%5E3)
Step-by-step explanation:
A rectangular prism is a three-dimensional solid.
A rectangular prism has six faces (each one of these faces are rectangles), eight vertices and twelve edges.
You know that this rectangular prism has 5 layers and the volume of one of these layers is 18 cubic centimeters (
).
Assuming that all these layers are equal, the volume of this rectangular prism can be calculated with:
![V_{prism}=5*V_1](https://tex.z-dn.net/?f=V_%7Bprism%7D%3D5%2AV_1)
Where
is the volume of one layer.
Substituting, you get:
![V_{prism}=(5)(18cm^3)\\\\V_{prism}=90cm^3](https://tex.z-dn.net/?f=V_%7Bprism%7D%3D%285%29%2818cm%5E3%29%5C%5C%5C%5CV_%7Bprism%7D%3D90cm%5E3)
Answer:
The closed linear form of the given sequence is ![a_{n}=0.75n-0.45](https://tex.z-dn.net/?f=a_%7Bn%7D%3D0.75n-0.45)
Step-by-step explanation:
Given that the first term
and ![a_{n+1}=a_{n}+0.75](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%3Da_%7Bn%7D%2B0.75)
To find the closed linear form for the given sequence
The formula for arithmetic sequence is
(where d is the common difference)
The above equation is of the given form ![a_{n+1}=a_{n}+0.75](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%3Da_%7Bn%7D%2B0.75)
Comparing this we get d=0.75
With
and d=0.75
We can substitute these values in
![=0.3+(n-1)(0.75)](https://tex.z-dn.net/?f=%3D0.3%2B%28n-1%29%280.75%29)
![=0.3+0.75n-0.75](https://tex.z-dn.net/?f=%3D0.3%2B0.75n-0.75)
![=-0.45+0.75n](https://tex.z-dn.net/?f=%3D-0.45%2B0.75n)
Rewritting as below
![=0.75n-0.45](https://tex.z-dn.net/?f=%3D0.75n-0.45)
Therefore ![a_{n}=0.75n-0.45](https://tex.z-dn.net/?f=a_%7Bn%7D%3D0.75n-0.45)
Therefore the closed linear form of the given sequence is ![a_{n}=0.75n-0.45](https://tex.z-dn.net/?f=a_%7Bn%7D%3D0.75n-0.45)