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3 years ago

Complete the square for the following quadratic function:

2 answers:

8 0

Y = -6x^2 + 36x - 12

y = -6(x^2 - 6x) - 12

y = -6[ (x - 3)^2 - 9] - 12

y = -6(x - 3)^2 + 54 - 12

y = -6(x - 3)^2 + 42

the vertex is at x = 3 so line of symmetry is x = 3

it will have a maximum value of 42 (as the vertex is at (3,42)

juin [17]3 years ago

4 0

Answer:

Line of symmetry x = 3

Maximum of the parabola is 42.

Step-by-step explanation:

The given equation is of a quadratic function y = -6x² + 36 x - 12

Now we will convert this equation in the vertex form to get the the maximum value.

y = -6(x²- 6x + 2 + 9 - 9)

y = -6[(x² - 6x + 9) -7]

y = -6[(x - 3)² - 7]

y = -6(x - 3)² + 42

Vertex of the given parabola will be (3, 42) and the maximum value is 42.

Since coefficient is negative so opening of the parabola is downwards.

Line of symmetry is x = 3.

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Lyrx [107]

Answer:

Sister = 15 years old

Brother = 12 years old

Step-by-step explanation:

Right now, if the brother is B years old and the sister is S years old, B = (4/5)S because the ratio from brother to sister is 4:5, so if one unit is X, B = 4X and S = 5X

Three years ago, the brother was B-3 years old and the sister was S-3 years old. Keeping one unit as X, we have

B = 3X

S = 4X

B-3 = (3/4)(S-3)

Therefore, we have a system of equations

B = (4/5)S

B-3 = (3/4)(S-3)

Substitute (4/5)S for B into the second equation to only have one variable

(4/5)S - 3 = (3/4)(S-3)

(4/5)S - 3 = (3/4)S - 9/4

add 3 to both sides and subtract (3/4)S from both sides to isolate the variable and its coefficient

(1/20)S = 3/4

multiply both sides by 20 to isolate the S

S = 15

B = (4/5)S = 12

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3 years ago

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Citrus2011 [14]

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Step-by-step explanation:

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3 years ago

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pshichka [43]

Answer:

See the proof below.

Step-by-step explanation:

Assuming this complete question: "For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed with parameters q and M. Formulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M."

Solution to the problem

For this case we can assume that we have N independent variables $X_i$ with the following distribution:

$X_i Bin (1,p) = Be(p)$ bernoulli on this case with probability of success p, and all the N variables are independent distributed. We can define the random variable Z like this:

$Z = \sum_{i=1}^N X_i$

From the info given we know that $N \sim Bin (M,q)$

We need to proof that $Z \sim Bin (M, pq)$ by the definition of binomial random variable then we need to show that:

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The deduction is based on the definition of independent random variables, we can do this:

$E(Z) = E(N) E(X) = Mq (p)= Mpq$

And for the variance of Z we can do this:

$Var(Z)_ = E(N) Var(X) + Var (N) [E(X)]^2$

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And if we take common factor $Mpq$ we got:

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4 years ago

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laila [671]

Answer:

Step-by-step explanation:

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artcher [175]

Hello there,

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The closest we can get to 1000 undefined without exceeding it is 0 which is 0 × 3062.These values have been added to the division, highlighted in red.

In this case the target of 1000 is less than 3062 so a division is not possible. Put a 0 in the answer to show this and 0s below the 1000.

Leaving out the 0 from the answer line when this occurs is one of the easiest mistakes to make with long division.

Hope this helps.

~Jurgen

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