Answer:
The answer is C f(x)=(x – 5(x + 1)
Step-by-step explanation:
Hi there!
α, β, γ are the zeroes of the polynomial x³ + px² + qx + 2
Then,
• α + β + γ = - p ---(i)
• αβ + βγ + γα = q. ---(ii)
• αβγ = - 2. ---(iii)
We're Given :-
αβ + 1 = 0 Or αβ = - 1
Substitute " αβ = - 1 " in eqn. (iii) :-
(- 1) γ = - 2
γ =
![\dfrac {- 2}{- 1}](https://tex.z-dn.net/?f=%5Cdfrac%20%7B-%202%7D%7B-%201%7D)
γ = 2
Now. Accr'ding to the question :-
2p + q + 5 = - 2 (α + β + γ) + (αβ + βγ + γα) + 5
= - 2 (α + β + γ) + (αβ + [ γ (β + α) ] + 5
= - 2 (α + β + 2) + [ - 1 + 2 ( α + β ) ] + 5
= - 2α - 2β - 4 - 1 + 2α + 2β + 5
= 5 - 5
= 0
∴ 2p + q + 5 = 0
~ Hope it helps!
Answer:
2.26 in
Step-by-step explanation:
Given: the area of the slice is 4 in^2.
The formula for the area of a circle is A = (pi)(r)^2, where r is the radius.
Therefore,
A = 4 in^2 = (pi)(r^2), or
4 in^2
r^2 = ------------ = 1.273
pi
Since the area of the slice is A = (pi)(r^2), and since (d/2)^2 = r^2 = d^2/4
A = (4 in^2) = (pi)(d^2 / 4)
Solving for d^2, we divide both sides by pi/4, obtaining:
4 in^2
---------- = d^2 = 5.093 in^2
pi/4
and so d = √5.093 = 2.26 in (to the nearest 100th)
Answer:
b=14
Step-by-step explanation:
![-8b+56=-56\\-8b+56(-56)=-56-56\\-8b=-112\\\frac{-8b}{-8} =\frac{-112}{-8} \\b=14](https://tex.z-dn.net/?f=-8b%2B56%3D-56%5C%5C-8b%2B56%28-56%29%3D-56-56%5C%5C-8b%3D-112%5C%5C%5Cfrac%7B-8b%7D%7B-8%7D%20%3D%5Cfrac%7B-112%7D%7B-8%7D%20%5C%5Cb%3D14)
<em>The value of b is 14.</em>
If Origami paper is always in the shape of a square. The dimensions of the paper square that can be used is 8.5" x 8.5". the length of the diagonal is 12 inches.
<h3>
Hypotenuse</h3>
Square piece of paper=8.5" x 8.5"
Using the Pythagorean theorem
Diagonal or hypotenuse of a square with sides = 8.5" will be:
Hypotenuse = √[(8.5)×+ (8.5)²]
Hypotenuse=√72.25+72.25
Hypotenuse=√144.5
Hypotenuse=12 inches
Therefore the dimensions of the paper square that can be used is 8.5" x 8.5". the length of the diagonal is 12 inches.
The complete question is:
Origami paper is always in the shape of a square. If you take the top corner of either side of an 8.5 x 11-inch piece of paper and fold it to the lower opposite side and trim off the excess paper, this creates the square that we need. Then fold the top corner to the opposite corner to create a diagonal, which is a typical first step to most origami designs. What are the dimensions of your square? What is the length of the diagonal?
Learn more about Hypotenuse here:
brainly.com/question/27301528
brainly.com/question/2217700
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