Answer:
y=-2x+5
Step-by-step explanation:
y=mx+b
m=-2
b=5
Answer:
29
Step-by-step explanation:
because you add 19 and 9
Answer:
Linearly independent, x = 0
Step-by-step explanation:
- We are given three functions as follows:
![f ( x ) = e^4^x\\\\g ( x ) = xe^4^x\\\\h( x ) = x^2e^4^x](https://tex.z-dn.net/?f=f%20%28%20x%20%29%20%3D%20e%5E4%5Ex%5C%5C%5C%5Cg%20%28%20x%20%29%20%3D%20xe%5E4%5Ex%5C%5C%5C%5Ch%28%20x%20%29%20%3D%20x%5E2e%5E4%5Ex)
- We are to determine the linear - independence of the given functions. We will use the theorem of linear independence which states that:
![c_1*f(x) + c_2*g(x) + c_3*h(x) = 0](https://tex.z-dn.net/?f=c_1%2Af%28x%29%20%2B%20c_2%2Ag%28x%29%20%2B%20c_3%2Ah%28x%29%20%3D%200)
Where,
c1 , c2 , c3 are all zeroes then for all values of (x),
- The system of function is said to be linearly independent
- We will express are system of equations as such:
- To express our system of linear equations we will choose three arbitrary values of ( x ). We will choose, x = 0. then we have:
![c_1*( 1 ) + c_2*(0) + c_3*(0 ) = 0\\\\c_1 = 0](https://tex.z-dn.net/?f=c_1%2A%28%201%20%29%20%2B%20c_2%2A%280%29%20%2B%20c_3%2A%280%20%29%20%3D%200%5C%5C%5C%5Cc_1%20%3D%200)
- Next choose x = 1:
![c_2*e^4 + c_3*e^4 = 0\\\\c_2 + c_3 = 0](https://tex.z-dn.net/?f=c_2%2Ae%5E4%20%2B%20c_3%2Ae%5E4%20%3D%200%5C%5C%5C%5Cc_2%20%2B%20c_3%20%3D%200)
- Next choose x = 2:
![2*c_2*e^8 + 4*c_3*e^8 = 0\\\\c_2 + 2c_3 = 0](https://tex.z-dn.net/?f=2%2Ac_2%2Ae%5E8%20%2B%204%2Ac_3%2Ae%5E8%20%3D%200%5C%5C%5C%5Cc_2%20%2B%202c_3%20%3D%200)
- Solve the last two equations simultaneously we have:
.... ( Only trivial solution exist )
Answer: The functions are linearly independent
- The only zero exist is x = 0.
x= 522-7+10+14
×=539
Pete had 539 points after the three games
Answer:
10
Step-by-step explanation: