Perform the indicated operation. (5 - 2122
1 answer:
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The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
What is the intermediate value theorem?
Intermediate value theorem is theorem about all possible y-value in between two known y-value.
x-intercepts
-x^2 + x + 2 = 0
x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1, x = 2
y intercepts
f(0) = -x^2 + x + 2
f(0) = -0^2 + 0 + 2
f(0) = 2
(Graph attached)
From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3
For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.
<em>Your question is not complete, but most probably your full questions was</em>
<em>Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?</em>
Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
Learn more about intermediate value theorem here:
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Answer:
See below
Step-by-step explanation:
is the average
is the variance
is the standard deviation
Answer:
The equation of the line containing (4,2) and (3,5) in the slope-intercept form will be:
- y=-3x+14
Step-by-step explanation:
Given the points
- (4, 2)
- (3, 5)
We know that the slope-intercept form of the line equation is
where m is the slope and b is the y-intercept
substituting m=-3 and the point (4, 2) to get the y-intercept i.e. b
2=(-3)4 + b
2 = -12 + b
b = 2+12
b = 14
Now, substituting b=14 and m=-3 in the slope-intercept form to determine the equation of a line in the slope-intercept.
y=(-3)x+(14)
y=-3x+14
Thus, the equation of the line containing (4,2) and (3,5) in the slope-intercept form will be:
- y=-3x+14