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attashe74 [19]
3 years ago
13

Princess Poly has found most of the matches after spending a few hours working on the map of the garden and the labeled fences.

She has one piece of fencing left and three rectangular plots it might belong to.
The polynomial label for the final section of fencing is r(x)=2x3+x2−41x+20.

One of the rectangular plots has a side labeled as c(x)=x+1.

Which method shows the correct way to test whether c(x) is a factor of r(x)?
Mathematics
1 answer:
vovangra [49]3 years ago
7 0

Answer:

46

Step-by-step explanation:

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A system of the equation to be Dependent Consistent System the system must have multiple solutions. The correct option is C.

<h3>What is a System of equation?</h3>

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

For the system of equations to have infinite number of solutions, the lines of the equations must coincide, therefore, the line must overlap on each other.

For the lines to overlap the equations must be in a ratio. Therefore, the ratio of the left sides of the equations must be equal to the right side,

\dfrac{35x+14y}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac{7(5x+2y)}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac71 = \dfrac{119}{k}\\\\k = 17

Hence, the value of k must be 17, therefore, the correct option is C.

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5 0
2 years ago
Customer arrivals at a bank are random and independent; the probability of an arrival in any one-minute period is the same as th
IgorLugansk [536]

Answer:

0.2240418 ; 0.57681

Step-by-step explanation:

Given the information above :

A) What is the probability of exactly three arrivals in a one-minute period?

Using poisson probability function :

p(x ; m) = [(m^x) * (e^-m)] / x!

Here, m = mean = 3, x = 3

P(3 ; 3) = [(3^3) * (e^-3)] / 3!

P(3;3) = [27 * 0.0497870] / 6

= 1.3442508 / 6

= 0.2240418

B) What is the probability of at least three arrivals in a one-minute period?

Atleast 3 arrivals

X >= 3 = 1 - [p(0) + p(1) + p(2)]

P(0 ; 3) = [(3^0) * (e^-3)] / 0! = (1 * 0.0497870) / 1 = 0.0497870

P(1 ; 3) = [(3^1) * (e^-3)] / 1! = (3 * 0.0497870) / 1 = 0.1493612

P(2 ; 3) = [(3^2) * (e^-3)] / 2! = (9 * 0.0497870) / 2 = 0.2240418

1 - [0.0497870 + 0.1493612 + 0.2240418]

1 - 0.42319 = 0.57681

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Answer:

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Step-by-step explanation:

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