The value for p will be equal to 3 / 4.
We have the function as:
f(x) = (x - 1)³ + 6(p x + 4) 2
f(x) = x³ - 3 x² + 3 x - 1 + 12 p x + 48
f(x) = x³ - 3 x² + 3 x ( 1 + 4 p) + 47
Now, it is divided by x + 2 and leaves a remainder -3.
This means that if we will subtract 3 from f(x), it will be perfectly divisible by x + 2.
g(x) = x³ - 3 x² + 3 x ( 1 + 4 p) + 47 - 3
g(x) = x³ - 3 x² + 3 x ( 1 + 4 p) + 44
Now put x = -2:
(-2)³ - 3 (-2)² + 3 (-2) ( 1 + 4 p) + 44 = 0
-8 - 12 - 6 ( 1 + 4 p) + 44 = 0
- 20 - 6 - 24 p + 44 = 0
24 p = 18
p = 3 / 4.
Therefore, the value for p will be equal to 3 / 4.
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Answer:
x=50
Step-by-step explanation:
-0.2(x-20)=44-x
Distribute
-0.2x+4=44-x
Add x to each side
-.2x +4+x = 44-x+x
.8x+4 = 44
Subtract 4 from each side
.8x+4-4 = 44-4
.8x = 40
Divide each side by .8
.8x/.8 = 40/.8
x=50
Answer:
Axis of symmetry are lines x=-6 and y=-4, center (-6,-4)
Step-by-step explanation:
Consideer the equation 
First, complete perfect squares:

This equation represents a circle with center at point (-6,-4) and radius r=10.
Axis of symmetry are lines x=-6 and y=-4 (vertical and horizontal lines passing through the center).
Answer
x=-5
and
x=1
Explanation
The equation y = 2(x+2)^2 - 18 corresponds to a translation 2 units left and 18 units down, and a and a shrinkage about the x-axis with factor 2.
Making these transformations to y=x^2, we have:




Factoring:


The x-intercept are found when y=0, that is:

and
Answer:
yes it does not curve at any point