<em>Complete Question:</em>
<em>Alicia is writing the program for a video game. For one part of the game she uses the rule (x,y)->(x-3,y+4) to move points on the screen. </em>
<em>A) what output does the rule give when the input is (-6,0)? </em>
<em>B)What output does the rule give when the input is (3,-4)? </em>
<em>C) Is the rule a function? Explain why it is or why it is not
</em>
Answer:
a. The output is (-9,4)
b. The output is (0,0)
c. See Explanation
Step-by-step explanation:
Given
Rule: (x,y)->(x - 3, y + 4)
Solving (a):
Inputs:
The outputs is as follows;
Hence:
The output is (-9,4)
Solving (b):
Inputs:
The outputs is as follows;
Hence:
The output is (0,0)
Solving (c):
The function is a rule and the rule is that:
It shifts the graph left by 3 units and up by 4 units
Taylor series of a function g(x) that can be differentiated indefinitely at "a" (a=complex or real number) is given by:
pn(a) = g(a)+g'(a)(x-a)/1! +g''(a)(x-a)^2/2! + g'''(a)(x-a)^3/3! + g''''(a)(x-a)^4/4! + ...
Where n= 0,1,2,3,4, ... respectively = degrees of the polynomial series
In the current task,
n=2, a=7
Substituting;
p2(x) = g(7)+g'(7)(x-7)+g''(7)(x-7)^2/2! = 4+(-1)(x-7)+(1)(x-7)^2/2!
= 4-(x-7)+1/2(x-7)^2
The answer would be that she could make 4.
20 over 100 percent is 20%
hope it helps
Find the possible rational roots and use synthetic division to find the first zero.
I chose x=1 (which represents the factor "x-1")
1║2 -7 -13 63 -45
║ 2 -5 -18 45
2 -5 -18 45 0
(x-1) is a factor, (2x³ - 5x² - 18x + 45) is the other factor.
Use synthetic division on the decomposed polynomial to find the next zero.
I chose x = 3 (which represents the factor "x-3")
3║2 -5 -18 45
║ 6 3 -45
2 1 -15 0
Using synthetic division, we discovered that (x-1), (x-3), & (2x² + x -15) are factors. Take the new decomposed polynomial (2x² + x -15) and find the last two factors using any method.
Final Answer: (x-1)(x-3)(x+3)(2x-5)