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Fantom [35]
3 years ago
15

Find the zeros of y = x2 - 6x - 4 by completing the square.

Mathematics
2 answers:
Anuta_ua [19.1K]3 years ago
7 0

Answer:

i got x = -1

Step-by-step explanation:

all i did is find the x intercep nor zero

motikmotik3 years ago
3 0
Uh I don’t think the question or answer choices are typed in correctly, I’ll help once it is
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An urn contains n white balls andm black balls. (m and n are both positive numbers.) (a) If two balls are drawn without replacem
Genrish500 [490]

DISCLAIMER: Please let me rename b and w the number of black and white balls, for the sake of readability. You can switch the variable names at any time and the ideas won't change a bit!

<h2>(a)</h2>

Case 1: both balls are white.

At the beginning we have b+w balls. We want to pick a white one, so we have a probability of \frac{w}{b+w} of picking a white one.

If this happens, we're left with w-1 white balls and still b black balls, for a total of b+w-1 balls. So, now, the probability of picking a white ball is

\dfrac{w-1}{b+w-1}

The probability of the two events happening one after the other is the product of the probabilities, so you pick two whites with probability

\dfrac{w}{b+w}\cdot \dfrac{w-1}{b+w-1}=\dfrac{w(w-1)}{(b+w)(b+w-1)}

Case 2: both balls are black

The exact same logic leads to a probability of

\dfrac{b}{b+w}\cdot \dfrac{b-1}{b+w-1}=\dfrac{b(b-1)}{(b+w)(b+w-1)}

These two events are mutually exclusive (we either pick two whites or two blacks!), so the total probability of picking two balls of the same colour is

\dfrac{w(w-1)}{(b+w)(b+w-1)}+\dfrac{b(b-1)}{(b+w)(b+w-1)}=\dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

<h2>(b)</h2>

Case 1: both balls are white.

In this case, nothing changes between the two picks. So, you have a probability of \frac{w}{b+w} of picking a white ball with the first pick, and the same probability of picking a white ball with the second pick. Similarly, you have a probability \frac{b}{b+w} of picking a black ball with both picks.

This leads to an overall probability of

\left(\dfrac{w}{b+w}\right)^2+\left(\dfrac{b}{b+w}\right)^2 = \dfrac{w^2+b^2}{(b+w)^2}

Of picking two balls of the same colour.

<h2>(c)</h2>

We want to prove that

\dfrac{w^2+b^2}{(b+w)^2}\geq \dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

Expading all squares and products, this translates to

\dfrac{w^2+b^2}{b^2+2bw+w^2}\geq \dfrac{w^2+b^2-b-w}{b^2+2bw+w^2-b-w}

As you can see, this inequality comes in the form

\dfrac{x}{y}\geq \dfrac{x-k}{y-k}

With x and y greater than k. This inequality is true whenever the numerator is smaller than the denominator:

\dfrac{x}{y}\geq \dfrac{x-k}{y-k} \iff xy-kx \geq xy-ky \iff -kx\geq -ky \iff x\leq y

And this is our case, because in our case we have

  1. x=b^2+w^2
  2. y=b^2+w^2+2bw so, y has an extra piece and it is larger
  3. k=b+w which ensures that k<x (and thus k<y), because b and w are integers, and so b<b^2 and w<w^2

4 0
3 years ago
You buy a package of 12 pencils for $2.64 write this rate as a unit rate?
iogann1982 [59]
Unit rate means how much does it cost for 1 unit

2.64 for 12 pencils
find 1 pencil
divide both sides by 12
0.22 for 1 pencil

0.22 per pencil
3 0
2 years ago
Please really need help on this thanks
VARVARA [1.3K]
5X-20=4X+7

5X-4x=20+7

X=27°
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Convert 300 g to kg.<br>​
padilas [110]

Answer:

0.3 kg

Step-by-step explanation:

I hope it helps, have a good day

5 0
2 years ago
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Please answer this question hahahahh
KengaRu [80]

The 5 in the hundredths place represents 5/100, whereas the 5 in the tens place represents 50, Figure out how 5/100 and 50 are related to each other: (5/100)x = 50. Mult. both sides by 100, we get 5x = 5000. Thus, the 5 in the tens place is 1000 times the 5 in the hundreths place.

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2 years ago
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