Answer:
k = –10
Step-by-step explanation:
From the question given above, the following data were obtained:
f(x) = x³ – 6x² – 11x + k
Factor => x + 2
Value of K =?
Next, we shall obtained the value of x from x + 2. This is illustrated below:
x + 2 = 0
Collect like terms
x = 0 – 2
x = –2
Finally, we shall determine the value of k as illustrated below:
f(x) = x³ – 6x² – 11x + k
x = –2
Thus,
f(–2) = 0
x³ – 6x² – 11x + k = 0
(–2)³ – (–2)² – 11(–2) + k = 0
–8 – (4) + 22 + K = 0
–8 – 4 + 22 + K = 0
10 + k = 0
Collect like terms
k = 0 – 10
k = –10
Thus, the value of k is –10
I'm going to use the slope formula which is
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are the two points the line goes through
Slope of line PQ
m = (y2 - y1)/(x2 - x1)
m = (-6 - 8)/(-5 - (-7))
m = (-6 - 8)/(-5 + 7)
m = (-14)/(2)
m = -7
The slope of line PQ is -7
Slope of RS
m = (y2 - y1)/(x2 - x1)
m = (0 - (-5))/(-2 - 3)
m = (0 + 5)/(-2 - 3)
m = (5)/(-5)
m = -1
The slope of line RS is -1
Because the slopes are NOT equal (one is -7 and the other is -1), this means the lines are NOT parallel.
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Answer: Choice B) No, the lines have unequal slopes
Answer:
14.13 in³
Step-by-step explanation:
Volume of a ball (sphere) is:
V = ⁴/₃ π r³
Circumference of a ball (circle) is:
C = 2π r
Use the circumference to find the radius.
9.42 in = 2π r
r = 1.50 in
Use the radius to find the volume:
V = ⁴/₃ π (1.50 in)³
V = 14.13 in³
Answer:
Step-by-step explanation:
Note that this function resembles the absolute value function y = |x|.
The graph of y = |x| has its vertex at (0, 0) and opens up in a v-shape.
The graph of y = |x - 2| looks the same as that of y = |x|, but the entire graph has been translated 2 units to the right.
The graph of y = |x - 2| + 4 is that of y = |x - 2|, translated 4 units up.
