<span>It means that the point lies directly on the regression line.
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Answer: Choice B
Range = {-3, 1, 5}
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Explanation:
The domain is the set of all possible input x values. The range is the set of all possible y outputs.
Plug in each x value from the domain, one at a time, to get its corresponding range y value.
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Start with x = -3
f(x) = 2x+3
f(-3) = 2(-3)+3
f(-3) = -6+3
f(-3) = -3
So -3 is in the range.
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Move onto x = -1
f(x) = 2x+3
f(-1) = 2(-1)+3
f(-1) = -2+3
f(-1) = 1
1 is also in the range
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Finally plug in x = 1
f(x) = 2x+3
f(1) = 2(1)+3
f(1) = 2+3
f(1) = 5
The value 5 is the final value in the range.
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All of those values form the set {-3, 1, 5} which is the complete range.
Option A. All the real values of x where x < -1
Procedure
Solve the inequality:
(x -3)(x+1)>0
That happens in two cases.
1) When both factors >0
x-3>0 and x+1>0
x>3 and x >-1
The intersection is x >3
2) When both factors <0
x-3<0 and x+1<0
x<3 and x<-1
the intersection is x<-1.
We have obtained that the function is positive for the intervals x < -1 and x > 3. But in one of those intervals the function is decresing and in the other is increasing.
You can recognize that the function given is a parabola and, because the coefficient of the quadratic term is positive, the parabola opens upward. Then the function is decreasing in the first interval and increasing in the second interval.
Answer:
1^sqrt(2) = 1 is always true
Step-by-step explanation:
A gray kangaroo jumped and it's path through the air is given by
y =
where x is the kangaroo's horizontal distance traveled (in feet) wand y is the corresponding height (in feet).
For maximum distance we have to differentiate this expression.
For maxima or minima
=0
-0.0267×2 x + 0.8=0
⇒-0.0534 x + 0.8=0
⇒0.8=0.0534 x
⇒x=0.8/0.0534
x =14.98 (approx)
Now differentiating the expression again
=-0.0534
Since double derivative is negative , so
x=14.98 will be the point of Maxima.
The Kangaroo can go the maximum distance of 14.98 feet (approx)
and the height that can kangaroo go through=-0.0267×14.98×14.98+0.8×14.98
= -5.9914 +11.984
= 5.9925 feet
= 6 feet (approx)
So, X=Horizontal distance covered=14.98×2=29.96 feet,[∵ at x=14.98 it attains maximum height, So total distance Travelled by kangaroo will be two times of the distance covered that it has gone through to achieve maximum height.]⇒ The path is parabolic. = 30 feet (approx)
Y= Vertical distance covered= 5.9925=6 feet(approx)
