What is the side length of a cube with a volume of 64 mm3? Cube V = s3
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Answer:
Γ = 15
Step-by-step explanation:
Given
f(x) = x² - 8x + Γ
with a = 1, b = - 8 and c = Γ , then
sum of zeros α + β = - = -
= 8
product of zeros = αβ = = Γ
Given α - β = 2 , then
(α - β)² = 2²
α² - 2αβ + β² = 4 → (1)
and
(α + β)² = 8²
α² + 2αβ + β² = 64 → (2)
Add (1) and (2) term by term
2α² + 2β² = 68 ( divide through by 2 )
α² +β² = 34
Substitute α² + β² = 34 into (1)
34 - 2αβ = 4 ( subtract 34 from both sides )
- 2αβ = - 30 ( divide both sides by - 2 )
αβ = 15
Now
αβ = Γ = 15
Thus
f(x) = x² - 8x + 15
First, plot the points. Point R would be somewhere in the second Quadrant, point M would be in the first quadrant 1, point B would be in the fourth quadrant, and point S would be on the negative y-axis. A property of rhombi is that their diagonals are perpendicular. One would need to calculate the slopes of the diagonals and determine whether or not they are perpendicular. Lines are perpendicular if and only if their slopes are opposite reciprocals. Example: 2 and -0.5
Formulas needed:
Slope formula:
The figure would look kinda like this:
R
M
S
B
Diagonals are segment RB and segment SM
So, your slope equations would look like this:
and
Slope of RB= -1
Slope of SM=7
Not a rhombus, slopes aren't perpendicular. But this figure may very well be a parallelogram
Formulas needed:
Slope formula:
The figure would look kinda like this:
R
M
S
B
Diagonals are segment RB and segment SM
So, your slope equations would look like this:
and
Slope of RB= -1
Slope of SM=7
Not a rhombus, slopes aren't perpendicular. But this figure may very well be a parallelogram
Answer:
Step-by-step explanation:
The average is 7.5 hours of sleep each night.
There are 365 nights in 1 year.