Answer:
No. We can conclude that (x-4) is <u>not</u> a factor of the polynomial.
Step-by-step explanation:
The <em>polynomial remainder theorem</em> tells you (x-4) will be a factor of the polynomial f(x) if and only if f(4) = 0. When we evaluate ...
f(x) = 4x³ -20x² +18x -12
at x=4, we find that f(4) = -4. This is not zero, so (x-4) is not a factor of f(x).
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The evaluation is perhaps easiest done by hand when the function is written in Horner form:
f(x) = ((4x -20)x +18)x -12
f(4) = ((4·4 -10)4 +18)4 -12 = ((-4)4 +18)4 -12 = 2·4 -12
f(4) = -4
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The one real factor of this polynomial is irrational, and the remaining factors are complex and irrational.
Answer:
about 5.3
Step-by-step explanation:
Answer: 4/5 or 80%
Step-by-step explanation:
10 total
2 are white (2/10)
8/10 of the marbles are not white
8/10 can be reduced to 4/5
as a percent, it is 80%
Answer:
Length of arc AC = 10.6 ft
Length of arc ADC = 73.4 ft
Step-by-step explanation:
θ = 45°
Circumference = 85 ft
✔️First, find the radius:
Circumference of a circle = 2πr
Thus:
85 = 2πr
Solve for r
Use 3.14 as π
Divide both sides by 2π
85/2π = r
85/2*3.14 = r
85/6.28 = r
r = 13.5350318 ≈ 13.5 ft (nearest tenth)
✔️Find length of arc ADC:
Length of arc = θ/360 × Circumference of the circle
θ = 360 - 45° = 315°
Circumference = 85 ft
Plug in the values
Length of arc ADC = 315/360 × 85
= 74.375 ≈ 73.4 ft (nearest tenth)
✔️Find length of arc AD:
Length of arc = θ/360 × Circumference of the circle
θ = 45°
Circumference = 85 ft
Plug in the values
Length of arc AC = 45/360 × 85
= 10.625 ≈ 10.6 ft (nearest tenth)
The change in elevation is 14 meters.
The diver started at 10 meters above water but ended up 4 meters below water. This means you must add the 4 meters after passing the water line for a total elevation change of 14 meters.