SOLUTIONS
Solve a given equations or algebraic symbols?
![\begin{gathered} f(x)=x^2+2x \\ g(x)=1-x^2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%28x%29%3Dx%5E2%2B2x%20%5C%5C%20g%28x%29%3D1-x%5E2%20%5Cend%7Bgathered%7D)
(A)
![\begin{gathered} (f+g)(x)=(x^2+2x)+(1-x^2) \\ collect\text{ like terms} \\ x^2-x^2+2x+1 \\ (f+g)(x^)=2x+1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%28f%2Bg%29%28x%29%3D%28x%5E2%2B2x%29%2B%281-x%5E2%29%20%5C%5C%20collect%5Ctext%7B%20like%20terms%7D%20%5C%5C%20x%5E2-x%5E2%2B2x%2B1%20%5C%5C%20%28f%2Bg%29%28x%5E%29%3D2x%2B1%20%5Cend%7Bgathered%7D)
(B)
![\begin{gathered} (f-g)(x)=(x^2+2x)-(1-x^2) \\ =x^2+2x-1+x^2 \\ =x^2+x^2+2x-1 \\ (f-g)(x)=2x^2+2x-1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%28f-g%29%28x%29%3D%28x%5E2%2B2x%29-%281-x%5E2%29%20%5C%5C%20%3Dx%5E2%2B2x-1%2Bx%5E2%20%5C%5C%20%3Dx%5E2%2Bx%5E2%2B2x-1%20%5C%5C%20%28f-g%29%28x%29%3D2x%5E2%2B2x-1%20%5Cend%7Bgathered%7D)
(C)
![\begin{gathered} fg(x)=(x^2+2x)(1-x^2) \\ =x^2-x^4+2x-2x^3 \\ fg(x)=-x^4-2x^3+x^2+2x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20fg%28x%29%3D%28x%5E2%2B2x%29%281-x%5E2%29%20%5C%5C%20%3Dx%5E2-x%5E4%2B2x-2x%5E3%20%5C%5C%20fg%28x%29%3D-x%5E4-2x%5E3%2Bx%5E2%2B2x%20%5Cend%7Bgathered%7D)
(D)
The logarithm of 10 to base 10 is 1
<h3>How to determine the logarithm?</h3>
The given parameters are:
Base = 10
Number = 10
So, the expression is:
![\log_{10}10](https://tex.z-dn.net/?f=%5Clog_%7B10%7D10)
As a general rule;
![\log_{a}a = 1](https://tex.z-dn.net/?f=%5Clog_%7Ba%7Da%20%3D%201)
The above means that;
When the base and the number are the same, the logarithm is 1
So, we have:
![\log_{10}10 = 1](https://tex.z-dn.net/?f=%5Clog_%7B10%7D10%20%3D%201)
Hence, the logarithmic value is 1
Read more about logarithm at:
brainly.com/question/20785664
#SPJ1
Answer:
3
Step-by-step explanation:
Slope = y2- y1/ x2- x1
= 4 - (-2) / 3 -1
= 4+2/ 2
=6/2 = 3
Answer:
6.67408 × 10^-11 m^3 kg^-1 s^-2
Step-by-step explanation:
F = G M 1 M 2 d 2 , where F is the gravitational force between two point masses, M1 and M2; d is the distance between M1 and M2; G is the universal gravitational constant, usually taken as 6.670 × 1011 m3/(kg)(s2) or 6.670 × 10−8 in centimeter–gram–second units. a = F M 1 = G M 2 r 2 .