Answer:
(c) 8x^2 -32x +32, repeated root is x=2.
Step-by-step explanation:
A quadratic with repeated roots will be a multiple of a perfect square trinomial. The form of it will be ...
a(x -b)² = ax² -2abx +ab² = a(x² -2bx +b²)
Dividing by the leading coefficient will leave a monic quadratic whose constant is a (positive) perfect square, and whose linear term has a coefficient that is double the root of the constant.
__
<h3>-x^2 + 18x + 81</h3>
Dividing by the leading coefficient gives ...
x^2 -18x -81 . . . . . a negative constant
__
<h3>3x^2 - 6x + 9</h3>
Dividing by the leading coefficient gives ...
x^2 -2x +3 . . . . . . constant is not a perfect square
__
<h3>8x^2 - 32x + 32</h3>
Dividing by the leading coefficient gives ...
x^2 -4x +4 = (x -2)^2 . . . . . has a repeated root of x=2
__
<h3>25x^2 - 30x - 9</h3>
Dividing by the leading coefficient gives ...
x^2 -1.2x -0.36 . . . . . . a negative constant
__
<h3>x^2 - 14x + 196</h3>
The x-coefficient is not 2 times the root of the constant.
14 = √196 ≠ 2√196
Using the slope-intercept form, the slope is −7 .
Answer:
57.926%
Step-by-step explanation:
Calculation for the probability that it is less than
16.4 inches long
Using this formula
z = (X - μ) / σ
Where,
X represent Date=16.4
μ represent Mean=16.2
σ represent Standard deviation=0.9 inches
Let plug in the formula
z = (16.4 - 16.2) /0.9 inches
z=0.2/0.9 inches
z = 0.2
Using Z-score table to find the area of 0.2
z=0.57926*100
z=57.926%
Therefore the probability that it is less than
16.4 inches long is 57.926%