Answer:
The sum of the coefficients of the terms in (-1.5·x² + 0.5·x + 4)¹⁶ that have even degree is -4273411167.501
Step-by-step explanation:
The parameters given are;
f(-4) = -22
f(-1) = 2
f(2) = -1
g(x) = f(x)¹⁶
The function f(x) is presented as follows;
f(x) = a·x² + b·x +c
We have;
-22 = a·(-4)² + b·(-4) +c
-22 = a·16 - 4·b +c ..............(1)
2 = a·(-1)² + b·(-1) +c
2 = a - b +c...........................(2)
-1 = a·(2)² + b·(2) +c
-1 = 4·a + 2·b +c...................(3)
Solving the equations (1), (2), and (3) by using an online linear systems solver, we get;
a = -1.5, b = 0.5, c = 4
Therefore, f(x) = -1.5·x² + 0.5·x + 4
f(x)¹⁶ = (-1.5·x² + 0.5·x + 4)¹⁶ which gives the coefficients of the even terms as follows;
656.841 - 19267.331 + 248302.054 - 1772904.419 + 6735603.932 - 2868054.635 - 119602865.901 + 750783340.827 + -2542435585.611 + 5338903756.992 - 6048065910.25 -1031335136 + 17223697920 - 32238338048 + 32107397120 - 17716740096 = -4273411167.501.
It is C. The first part is raised to the 2nd power. so it goes first since that is the highest. then the -20x because variables are understood to the power of 1, while normal numbers are understood to the power of 0. so the order is highest to lowest (2,1,0)
24 divided by 6 equals 4. Each sweet is worth 4p. If you multiply 5 by 4 you get 20, so the answer is 5 sweets cost 20p.
Step-by-step explanation:
option C is the answer
hope it helps
