Answer:
f(x) has a minimum value of -10.
Step-by-step explanation:
It will have a minimum value because the coefficient of x^2 is positive.
To find its value we convert to vertex form:
f(x) = 4x^2 - 16x + 6
= 4(x^2 - 4x) + 6
= 4[(x - 2)^2 - 4] + 6
= 4(x - 2)^2 - 16 + 6
= 4(x - 2)^2 - 10.
So the minimum value is -10.
Y > 5x + 5 . . . (1)y > -1/2x + 1 . . . (2)
Part A: The graph of the system are two straight dotted lines with the first line passing through points (-1, 0) and (0, 5) with the region above the line shaded and the second line passing through (0, 1) and (2, 0) with the region above the line shaded. The two lines intersect at point (-8/11, 15/11).
Part B: The point (-2, 5) is included in the solution area.5 > 5(-2) + 5 and 5 > -1/2(2) + 15 > -10 + 5 and 5 > -1 + 15 > -5 and 5 > 0
hope i helped
Using the concept of probability and the arrangements formula, there is a
0.002 = 0.2% probability that the first 8 people in line are teachers.
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- A probability is the <u>number of desired outcomes divided by the number of total outcomes.</u>
- The order in which they are positioned is important, and all people will be positioned, and thus, the arrangements formula is used to find the number of outcomes.
The number of possible arrangements from a set of n elements is given by:
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The desired outcomes are:
- First 8 people are teachers, in <u>8! possible ways.</u>
- Last 4 are students, in <u>4! possible ways.</u>
Thus, 
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For the total outcomes, <u>number of arrangements of 12 people</u>, thus:
The probability is:
0.002 = 0.2% probability that the first 8 people in line are teachers.
A similar problem is given at brainly.com/question/24650047
The lines are more then you think they are
Answer:
Step-by-step explanation:
sin(2x) = 2 sin(x) cos(x) cos(2x) = cos2(x) – sin2(x) = 1 – 2 sin2(x) = 2 cos2(x) – 1. Now I am not sure if this is right but I remember another similar formula. Here is the correct formula cot x = cos x / sin x
2 ) ( sin² x + cos² x ) / cos x = sec x
1/cos x = sec x
sec x = sec x
cos² x + sin² x = 1
