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2 years ago

One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?

Mathematics

1 answer:

pychu [463]2 years ago

6 0

Answer:

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.

Dividing by the leading coefficient gives ...

x^2 -18x -81 . . . . . a negative constant

Dividing by the leading coefficient gives ...

x^2 -2x +3 . . . . . . constant is not a perfect square

Dividing by the leading coefficient gives ...

x^2 -4x +4 = (x -2)^2 . . . . . has a repeated root of x=2

Dividing by the leading coefficient gives ...

x^2 -1.2x -0.36 . . . . . . a negative constant

The x-coefficient is not 2 times the root of the constant.

14 = √196 ≠ 2√196

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One carton of eggs contains 12 eggs.

noname [10]

Answer:

yes

Step-by-step explanation:

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3 years ago

An automated egg carton loader has a 1% probability of cracking an egg, and a customer will complain if more than one egg per do

vaieri [72.5K]

Answer:

a) Binomial distribution B(n=12,p=0.01)

b) P=0.007

c) P=0.999924

d) P=0.366

Step-by-step explanation:

a) The distribution of cracked eggs per dozen should be a binomial distribution B(12,0.01), as it can model 12 independent events.

b) To calculate the probability of having a carton of dozen eggs with more than one cracked egg, we will first calculate the probabilities of having zero or one cracked egg.

$P(k=0)=\binom{12}{0}p^0(1-p)^{12}=1*1*0.99^{12}=1*0.886=0.886\\\\P(k=1)=\binom{12}{1}p^1(1-p)^{11}=12*0.01*0.99^{11}=12*0.01*0.895=0.107$

Then,

$P(k>1)=1-(P(k=0)+P(k=1))=1-(0.886+0.107)=1-0.993=0.007$

c) In this case, the distribution is B(1200,0.01)

$P(k=0)=\binom{1200}{0}p^0(1-p)^{12}=1*1*0.99^{1200}=1* 0.000006 = 0.000006 \\\\ P(k=1)=\binom{1200}{1}p^1(1-p)^{1199}=1200*0.01*0.99^{1199}=1200*0.01* 0.000006 \\\\P(k=1)= 0.00007\\\\\\P(k\leq1)=0.000006+0.000070=0.000076\\\\\\P(k>1)=1-P(k\leq 1)=1-0.000076=0.999924$

d) In this case, the distribution is B(100,0.01)

We can calculate this probability as the probability of having 0 cracked eggs in a batch of 100 eggs.

$P(k=0)=\binom{100}{0}p^0(1-p)^{100}=0.99^{100}=0.366$

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3 years ago

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3 years ago

AN AIRCRAFT FLYING WITH THE WIND FLIES TO

maxonik [38]

Answer:

643

Step-by-step explanation:

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3 years ago

A regular polygon has sides all the same length, and angles all the same measure. Find the pelmeter of the regular polygon below

Ede4ka [16]

The perimeter of the regular polygon is 70 inches

<h3>How to determine the perimeter of the regular polygon?</h3>

The sides of the regular polygon is given as:

Side = 10 in

The regular polygon has 7 sides

So, the perimeter of the polygon is calculated as:

P = Side lengths * Number of sides

This gives

P = 10 inches * 7

Evaluate

P = 70 inches

Hence, the perimeter of the regular polygon is 70 inches